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Independent contrasts with non-homologous traits

Independent contrasts with non-homologous traits


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I have morphometric measurements for a trait across various animal taxa, and would like to study the relationship between the size of this trait, and the animals' body size. In theory, I can account for the non-independence of the data with phylogenetic methods, such as independent contrasts. However, I have very different groups in my tree (for example insects and lizards), and even within more closely related groups, the structures are often not homologous. Does this present a problem for independent contrasts/phylogenetic least squares? For example, the structure is not homologous between ants and flies, yet every (sensible?) tree would treat a fly as more similar to an ant than to any lizard. Is this justified if structures are analogous? If not, are there any ways to deal with this problem?


When you calculate the PICs of a trait, you are making a statement about how that trait evolved. The purpose of PICs is to account for phylogenetic non-independence. However, when you are comparing two analogous traits, those two traits are in fact phylogenetically independent of each other; they do not share a common origin. Thus, I think it would be an error to perform PICs on analogous traits because those traits do not share an evolutionary origin.

How to deal with this problem would depend on the specific question you are asking. One thing to do would be to perform PICs on each trait independently on just the portion of the tree that that trait occurs so you are not comparing analogous traits.

You've probably already read this, but I recommend that anyone who hasn't check out Felsenstein's 1985 paper describing the PIC method.


The method of phylogenetically independent contrasts is commonly used for exploring cross-taxon relationships between traits. Here we show that this phylogenetic comparative method (PCM) can fail to detect correlated evolution when the underlying relationship between traits is nonlinear. Simulations indicate that statistical power can be dramatically reduced when independent contrasts analysis is used on nonlinear relationships. We also reanalyse a published data set and demonstrate that ignoring nonlinearity can affect biological inferences. We suggest that researchers consider the shape of the relationship between traits when using independent contrasts analysis. Alternative PCMs may be more appropriate if data cannot be transformed to meet assumptions of linearity.

The use of phylogenetic comparative methods (PCMs) has become standard in studies seeking to identify evolutionary correlations across taxa. These methods address the problem of phylogenetic nonindependence: because taxa may be similar simply due to shared ancestry, comparative data often violate statistical assumptions of independence. One use of PCMs is to draw inferences about the covariation of traits across taxa while taking into account this phylogenetic nonindependence ( Felsenstein, 1985 Harvey & Pagel, 1991 Garland & Ives, 2000 Martins, 2000 ).

Perhaps the most widely used PCM is phylogenetically independent contrasts (PIC Felsenstein, 1985 Garland et al., 1992 ). This method removes the effect of shared evolutionary history by calculating differences in trait values between sister taxa (both extant and ancestral). If standardized differences, or contrasts, in one trait significantly covary with contrasts in another trait, then the two traits are evolutionarily correlated. In other words, change in one trait has been accompanied by change in the other. Simulation studies indicate that PIC performs well in a wide variety of situations and under different models of evolutionary change ( Martins et al., 2002 ). However, one important consideration, the shape of the relationship between the traits, has received less attention than it deserves.

In the original formulation of PIC, Felsenstein (1985) assumed that pairs of trait values were drawn from a bivariate normal distribution, leading to a linear relationship between expected values of the traits. If this is the case, contrasts will be linearly related as well, with the same expected slope as the true slope ( Harvey & Pagel, 1991 ). However, if the underlying relationship is nonlinear, difficulties arise in PIC analysis. Harvey & Pagel (1991, Fig. 5.19) point out that a nonlinear relationship between traits may yield a relationship between contrasts that is opposite in sign to that of the true relationship. However, arriving at such a patently false conclusion is prevented by forcing the line relating the contrasts through the origin ( Grafen, 1989, 1992 Garland et al., 1992 ). A more common consequence of nonlinearity in the underlying relationship is an increase in scatter in the relationship between the contrasts.

As an example, consider a hypothetical phylogeny of 10 species with values for two traits (Fig. 1a). The underlying relationship between the traits is nonlinear (Fig. 1b), and the relationship between the resulting contrasts is characterized by much scatter (Fig. 1c). The scatter arises because a given contrast in trait 1 is not associated with a consistent contrast in trait 2. Rather, contrasts in trait 2 are related not only to the magnitude of the contrasts in trait 1, but also to the absolute values of trait 1. An additional source of error is that nodes are assigned values away from the underlying, true line. A consequence of the increase in scatter is a reduction in the statistical power of PIC analyses to detect the true relationship between traits.

An example of the consequences of a nonlinear underlying relationship. (a) Ten species (a–j) are related as shown in the phylogeny. Each branch segment has a length of either 1 or 2 units. The internal nodes are labelled n1–n9. Values for two variables, traits 1 and 2, are given for each species. (b) Scatterplot of the relationship between the two traits, labelled by species. Note that no particular clade is responsible for the nonlinearity. (c) Plot of standardized contrasts in trait 2 against standardized contrasts in trait 1. Contrasts in trait 1 were positivized for presentation as recommended by Garland et al. (1992) . The tight underlying relationship in (B) has degenerated into a loose scatter of points, reducing our ability to detect a relationship. The points are labelled by the nodes they represent.

Empiricists and theoreticians discussing PIC rarely make explicit the assumption of linearity in the relationship between trait values. Among various descriptions of independent contrasts ( Felsenstein, 1985 Burt, 1989 Grafen, 1989 Harvey & Pagel, 1991 Garland et al., 1992, 1999 ) only Harvey & Pagel explore in any detail the consequences of nonlinearity of the underlying relationship between traits [although Garland et al. (1992) discuss nonlinear patterns between contrasts, a different issue]. This lack of emphasis from theoreticians may well be because the problem is obvious to them unfortunately, empiricists seem to overlook the issue as well. To investigate whether empiricists routinely assess linearity between traits before calculating contrasts, we searched for comparative studies published in 2002 in the journals Ecology, Evolution, Journal of Evolutional Biology and Proceedings of the Royal Society of London, Series B. Of 29 papers in which PIC analyses were carried out on continuous traits, only one states that the shape of the relationship between traits was evaluated. It would appear, then, that empiricists do not ordinarily test for linearity.

In this paper, we use computer simulations to demonstrate that when the underlying relationship between two variables is nonlinear, PIC analysis suffers from reduced statistical power. We also reanalyse a published data set to illustrate that this problem can affect inferences drawn from PIC analyses. Finally, we discuss methods of incorporating nonlinearity into phylogenetic comparative analyses.


Model Description And Analysis

Trait Evolution and Population Dynamics on Trees

We consider |$n$| species competing for the same spectrum of resources with a fixed and unimodal distribution ( Mahler et al. 2013).

We allow for stochastic evolutionary trait change due to drift by adding a noise term |$eta_$| to Eq. 3 ( Lenormand et al. 2009 Nuismer and Harmon 2015) that follows a normal distribution with mean 0 and a variance that is inversely proportional to the effective population size (which we set equal to the actual population size |$N_$|⁠ ), that is, |$eta_sim N(0,frac<1><2>frac<>><>>)$|⁠ . We incorporate demographic stochasticity by drawing species abundances from a zero-truncated Poisson distribution with a mean determined by Eq. 2. Hence, we do not allow for extinction due to demographic stochasticity, but species can become extinct if the phylogeny tells us so (see below).

Equation 7 states that the strength of competition between two species with trait means |$mu_$| and |$mu_$| increases with similarity in these trait means, and that the effect of competition on species |$i$| increases with population size of species |$j$|⁠ . The competition coefficient |$alpha$| scales the strength of the interaction and determines the effective interaction length. Finally, the parameter |$eta_<0>$| in Eq. 5 has a similar interpretation as an individual-scale carrying capacity of each species ( Abrams 2001), as it sets the scale at which competitive interactions start to strongly impact the growth of the population. Because Eq. 5 is an increasing function of |$eta_<0>$|⁠ , the ecological equilibrium |$omega(mu_)=1$| is reached at a carrying capacity set by the equilibrium condition |$eta=eta_<0>cdotln R$| where environmental stabilizing selection and competition balance each other.

The nonlinear strength of competitive repulsion of two species with identical population size that follows from our model. When the traits of two competitors are very similar, they experience intense competition but little directional repulsion. With increasing difference in traits, the repulsion force increases. Eventually, with a further increase in trait difference, repulsion decreases again because competition is avoided. Different |$alpha $| values cause different shapes of the strength of repulsion. A large |$alpha $| implies strong repulsion when competitors are very similar in traits but this competitive strength drops quickly, implying a small competitive interaction distance. In contrast, a small |$alpha $| implies a large competitive interaction distance but mild repulsion.

The nonlinear strength of competitive repulsion of two species with identical population size that follows from our model. When the traits of two competitors are very similar, they experience intense competition but little directional repulsion. With increasing difference in traits, the repulsion force increases. Eventually, with a further increase in trait difference, repulsion decreases again because competition is avoided. Different |$alpha $| values cause different shapes of the strength of repulsion. A large |$alpha $| implies strong repulsion when competitors are very similar in traits but this competitive strength drops quickly, implying a small competitive interaction distance. In contrast, a small |$alpha $| implies a large competitive interaction distance but mild repulsion.

Parameter inference using ABC-SMC

The complexity of our model precludes analytical approaches to fit the model to data. Hence, we developed an inference framework using Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC), which is a genetic algorithm that has computational advantages over Approximate Bayesian Computation with Markov Chain Monte Carlo because it allows parallellization, and it shows efficient convergence in high dimensional parameter space ( Sunnåker et al. 2013). In ABC-SMC, first introduced by Toni et al. (2009), one starts with a large number of parameter sets sampled from the prior (these are called particles in the terminology of the field), which are then used to simulate many data sets. We then evaluate the similarity of the simulated data to the empirical data (measured by one or more summary statistics). This similarity is the goodness-of-fit (GOF). The GOFs for all these data sets are used as weights to sample parameter sets in the next iteration (generation in ABC-SMC jargon), with some random noise added to it. After a few iterations, the parameter sets will form the posterior distribution. The details of the algorithm, including the computation of the GOF, can be found in the Supplementary material available on Dryad.

The choice of an efficient summary statistic is crucial to evaluate the similarity between simulated and empirical data. In the simulation study, we use the Euclidean distance between simulated and observed trait values. Because of the stochasticity of the trait change after speciation, traits of a focal species can differ substantially across replicate simulations. However, the difference in trait values between species that are adjacent in trait space regardless of species identities reflects the true strength of environmental stabilizing selection and competition. Therefore, we do not label the species in our simulation and sort both the empirical traits and the simulated traits in an increasing order before computing the Euclidean distance of these two vectors. We refer to this summary statistic as the sorted mean trait distance (SMTD). We also compute the Euclidean distance of the variance vectors corresponding to the reordered trait means. In principle, we can also add summary statistics based on abundance data and intraspecific trait variances (again using Euclidean distances between simulated and observed values), but we do not do so here because such data (for entire populations) is often unavailable empirically (as in our empirical example of baleen whales). This does not mean that abundances have no effect: according to our model they affect trait evolution and hence the species’ mean trait values.

Choosing the Euclidean distance of sorted traits may not be the best way to fit our model to empirical data, because we ignore information on the empirical order of the trait values across the phylogenetic tree. Therefore, in the empirical study (see below), we considered phylogenetic independent contrasts (PICs) ( Felsenstein 1985) as an alternative set of summary statistics. The PICs are designed to transform the original |$n$| traits of species to |$n-1$| independently and identically distributed contrasts between pairs of related species or estimated ancestral nodes ( Garland 2005). Because the PICs have one dimension less than the trait data, we combined the PICs with the unsorted mean trait distance (UMTD) to obtain a third set of summary statistics, referred to as UMTD+PICs. We compared results between the three sets of summary statistics.

Simulation Setup

To assess the behavior of our model, we first simulated data for known parameter sets and explored whether the parameter values can be correctly inferred. We considered six different values |$(0,0.001,0.01,0.1,0.5,1)$| for both the stabilizing selection coefficient |$gamma$| and the competition coefficient |$alpha$| leading to a total of 36 parameter combinations for a given phylogenetic tree. We set |$R_<0>=e$| (i.e., the mathematical constant 2.7183), |$eta_<0>=10^<9>$| and the mutation rate |$ u=10^<-11>$| for all simulations. We focused on the inference of three parameters, namely |$gamma,alpha,$| and |$ u$|⁠ .

To study how the phylogenetic information influences the evolution process, we generated several phylogenetic trees, including extinct branches, under the diversity-dependent diversification model ( Etienne et al. 2011) for various parameter settings of this macroevolutionary model (see Table 1). In addition, to mimic the fact that in practice complete trees with extinct species are often not available, we reconstructed phylogenies of only extant species by pruning the extinct species. This means that we generated the trait data under the full tree but estimated the parameters of our trait evolution model using only the reconstructed tree. Comparing this inference to inference using the complete tree informs us to what extent the loss of information of extinct species affects parameter estimation.

The scenarios of the simulated phylogenies

Scenarios . Trees . |$lambda$| . |$mu$| . |$K$| . Pruned . Time scales .
1 1 0.4 0 10 No 10,000
2 2 0.4 0 30 No 10,000
3 3 0.4 0 100 No 10,000
4 4 0.4 0.2 10 No 10,000
5 5 0.4 0.2 30 No 10,000
6 6 0.4 0.2 100 No 10,000
7 7 0.8 0 10 No 10,000
8 8 0.8 0 30 No 10,000
9 9 0.8 0 100 No 10,000
10 10 0.8 0.2 10 No 10,000
11 11 0.8 0.2 30 No 10,000
12 12 0.8 0.2 100 No 10,000
13 13 0.8 0.4 100 No 10,000
14 14 0.8 0.6 100 No 10,000
15 4 0.4 0.2 10 Yes 10,000
16 5 0.4 0.2 30 Yes 10,000
17 6 0.4 0.2 100 Yes 10,000
18 10 0.8 0.2 10 Yes 10,000
19 11 0.8 0.2 30 Yes 10,000
20 12 0.8 0.2 100 Yes 10,000
21 13 0.8 0.4 100 Yes 10,000
22 14 0.8 0.6 100 Yes 10,000
23 9 0.8 0 100 No 10,000, 20,000
24 12 0.8 0.2 100 No 10,000, 20,000
25 13 0.8 0.4 100 No 10,000, 20,000
26 14 0.8 0.6 100 No 10,000, 20,000
27 9 0.8 0 100 No 20,000
28 12 0.8 0.2 100 No 20,000
29 13 0.8 0.4 100 No 20,000
30 14 0.8 0.6 100 No 20,000
Scenarios . Trees . |$lambda$| . |$mu$| . |$K$| . Pruned . Time scales .
1 1 0.4 0 10 No 10,000
2 2 0.4 0 30 No 10,000
3 3 0.4 0 100 No 10,000
4 4 0.4 0.2 10 No 10,000
5 5 0.4 0.2 30 No 10,000
6 6 0.4 0.2 100 No 10,000
7 7 0.8 0 10 No 10,000
8 8 0.8 0 30 No 10,000
9 9 0.8 0 100 No 10,000
10 10 0.8 0.2 10 No 10,000
11 11 0.8 0.2 30 No 10,000
12 12 0.8 0.2 100 No 10,000
13 13 0.8 0.4 100 No 10,000
14 14 0.8 0.6 100 No 10,000
15 4 0.4 0.2 10 Yes 10,000
16 5 0.4 0.2 30 Yes 10,000
17 6 0.4 0.2 100 Yes 10,000
18 10 0.8 0.2 10 Yes 10,000
19 11 0.8 0.2 30 Yes 10,000
20 12 0.8 0.2 100 Yes 10,000
21 13 0.8 0.4 100 Yes 10,000
22 14 0.8 0.6 100 Yes 10,000
23 9 0.8 0 100 No 10,000, 20,000
24 12 0.8 0.2 100 No 10,000, 20,000
25 13 0.8 0.4 100 No 10,000, 20,000
26 14 0.8 0.6 100 No 10,000, 20,000
27 9 0.8 0 100 No 20,000
28 12 0.8 0.2 100 No 20,000
29 13 0.8 0.4 100 No 20,000
30 14 0.8 0.6 100 No 20,000

The experimental setup for testing the influence of phylogenetic information. The first 14 scenarios are generated under various diversification rates (speciation rate |$lambda$| and extinction rate |$mu$|⁠ ) and clade-specific carrying capacities |$K$|⁠ . Pruning these trees from extinct species results in the Scenarios 15–22 (only for nonzero extinction rates). Scenarios 23–26 are designed for studying the effect of the rate of evolution. The observations are generated under a time scaling parameter |$s$| of 10,000 (microevolutionary time steps per unit of macroevolutionary time) while the algorithm uses |$s=20,000$|⁠ . For Scenarios 27–30, |$s=20,000$| is used in both data generation and parameter inference.

The scenarios of the simulated phylogenies

Scenarios . Trees . |$lambda$| . |$mu$| . |$K$| . Pruned . Time scales .
1 1 0.4 0 10 No 10,000
2 2 0.4 0 30 No 10,000
3 3 0.4 0 100 No 10,000
4 4 0.4 0.2 10 No 10,000
5 5 0.4 0.2 30 No 10,000
6 6 0.4 0.2 100 No 10,000
7 7 0.8 0 10 No 10,000
8 8 0.8 0 30 No 10,000
9 9 0.8 0 100 No 10,000
10 10 0.8 0.2 10 No 10,000
11 11 0.8 0.2 30 No 10,000
12 12 0.8 0.2 100 No 10,000
13 13 0.8 0.4 100 No 10,000
14 14 0.8 0.6 100 No 10,000
15 4 0.4 0.2 10 Yes 10,000
16 5 0.4 0.2 30 Yes 10,000
17 6 0.4 0.2 100 Yes 10,000
18 10 0.8 0.2 10 Yes 10,000
19 11 0.8 0.2 30 Yes 10,000
20 12 0.8 0.2 100 Yes 10,000
21 13 0.8 0.4 100 Yes 10,000
22 14 0.8 0.6 100 Yes 10,000
23 9 0.8 0 100 No 10,000, 20,000
24 12 0.8 0.2 100 No 10,000, 20,000
25 13 0.8 0.4 100 No 10,000, 20,000
26 14 0.8 0.6 100 No 10,000, 20,000
27 9 0.8 0 100 No 20,000
28 12 0.8 0.2 100 No 20,000
29 13 0.8 0.4 100 No 20,000
30 14 0.8 0.6 100 No 20,000
Scenarios . Trees . |$lambda$| . |$mu$| . |$K$| . Pruned . Time scales .
1 1 0.4 0 10 No 10,000
2 2 0.4 0 30 No 10,000
3 3 0.4 0 100 No 10,000
4 4 0.4 0.2 10 No 10,000
5 5 0.4 0.2 30 No 10,000
6 6 0.4 0.2 100 No 10,000
7 7 0.8 0 10 No 10,000
8 8 0.8 0 30 No 10,000
9 9 0.8 0 100 No 10,000
10 10 0.8 0.2 10 No 10,000
11 11 0.8 0.2 30 No 10,000
12 12 0.8 0.2 100 No 10,000
13 13 0.8 0.4 100 No 10,000
14 14 0.8 0.6 100 No 10,000
15 4 0.4 0.2 10 Yes 10,000
16 5 0.4 0.2 30 Yes 10,000
17 6 0.4 0.2 100 Yes 10,000
18 10 0.8 0.2 10 Yes 10,000
19 11 0.8 0.2 30 Yes 10,000
20 12 0.8 0.2 100 Yes 10,000
21 13 0.8 0.4 100 Yes 10,000
22 14 0.8 0.6 100 Yes 10,000
23 9 0.8 0 100 No 10,000, 20,000
24 12 0.8 0.2 100 No 10,000, 20,000
25 13 0.8 0.4 100 No 10,000, 20,000
26 14 0.8 0.6 100 No 10,000, 20,000
27 9 0.8 0 100 No 20,000
28 12 0.8 0.2 100 No 20,000
29 13 0.8 0.4 100 No 20,000
30 14 0.8 0.6 100 No 20,000

The experimental setup for testing the influence of phylogenetic information. The first 14 scenarios are generated under various diversification rates (speciation rate |$lambda$| and extinction rate |$mu$|⁠ ) and clade-specific carrying capacities |$K$|⁠ . Pruning these trees from extinct species results in the Scenarios 15–22 (only for nonzero extinction rates). Scenarios 23–26 are designed for studying the effect of the rate of evolution. The observations are generated under a time scaling parameter |$s$| of 10,000 (microevolutionary time steps per unit of macroevolutionary time) while the algorithm uses |$s=20,000$|⁠ . For Scenarios 27–30, |$s=20,000$| is used in both data generation and parameter inference.

The ratio of the time scale of trait evolution and population dynamics to the time scale set by the phylogeny (i.e., the number of time-steps of trait and population size dynamics in each unit of time of the phylogeny, which can be interpreted as the number of generations per unit of time in the phylogeny, usually million years) is a crucial factor, as it determines whether trait and population dynamics can reach equilibrium before a new speciation (or extinction) event disrupts it. We denote this ratio in our model by the time scaling parameter |$s$|⁠ . For instance, given a phylogenetic tree with a crown age of 15 million years, trait and population dynamics involves |$15 imes s$| time steps. The value of |$s$| may influence our parameter estimates. So to assess how not exactly knowing the true number of time steps (i.e., the number of generations in a million years) affects parameter inference, we generated data under |$s=10,000$| and then ran our inference algorithm under |$s=10,000$| and |$s=20,000$| and compared their performance in parameter estimation (see Table S1 of the supplementary material available on Dryad).

In summary, we generated a total of 14 phylogenetic trees and pruned these trees when extinction rates were nonzero, resulting in 22 trees in total (see Table S1 of the supplementary material available on Dryad). We designed 30 scenarios to investigate the influence of tree size, speciation rate, extinction rate, removal of extinct species and number of time steps (see Table 1). We simulated our model for 36 parameter combinations for each scenario. We applied our inference algorithm on the simulated data and examined if the generating parameters could be recovered correctly. In the inference process, we set 30 iterations and 20 000 particles for each iteration. For the analysis of a single scenario, we exploited a cluster of 36 high performance computers with 32 threads running on each computer. Each parameter combination for each scenario analysis took between 2 and 80 h, depending on the number of evolutionary events and tree size of the specific scenario. All the code is available on Github (https://github.com/xl0418/The_trait_population_coevolution_model_code).

To contrast our model with a trait evolution model where abundance does not affect trait evolution, we defined a model in which the competition kernel does not depend on species abundance we call this model the unweighted competition (UWC) model (see Eqs S30–S31 of the Supplementary Material available on Dryad). The UWC model is similar to Drury et al.’s nonlinear extension ( Drury et al. 2017) of Nuismer and Harmon’s model ( Nuismer and Harmon 2015). However, it differs in the competition kernel, that is, from the population dynamics model it follows that pairwise competition is described as |$(mu_-mu_)cdot e^<-alpha(mu_-mu_)^<2>>$| instead of Drury et al.’s choice of |$ ext(mu_-mu_)cdot e^<-alpha(mu_-mu_)^<2>>$| (Eq. 1 in Drury et al. 2017 where |$ ext(a-b)=1$| when |$a>b$| while |$ ext(a-b)=-1$| when |$a&#60b$|⁠ ). We compared the simulated trait trajectories under the two models in the simulation study. We explored three values of the time scaling parameter, that is, |$s=100,1000,10,000$|⁠ , to assess whether the resulting trait patterns of the two models differ. The choice of |$s=100$| corresponding to 10,000 years per generation may be absurd. However, we used this value to examine how different values of |$s$| influence the behavior of the model. We emphasize that the choice of competition kernel in the UWC model (and in Drury et al.’s model) does not follow from a coherent fitness definition derived from population dynamics.

Applying the model to baleen whale body size evolution

Baleen whales represent the largest extant animal species and are distributed globally. They are filter-feeders on small fish and crustaceans. Body mass is an ideal trait that responds both to the abiotic factors ( Smith et al. 2010) and biotic competitors but measurements of body mass are rarely available. However, data on total length are available. It has been shown that whale total length scales with body mass raised to a power of |$frac<1><3>$| ( Lockyer 1976). So we used the total length as a proxy for body mass ( Slater et al. 2017). We log-transformed (base 10) the body length, because the log scale is a more natural scale on which evolution takes place ( Gingerich 2019). We fitted our model to mean trait data given a reconstructed phylogeny with 15 extant species ( Slater et al. 2017). We did not use abundance or trait variance data, as they were not available.

We designed eight scenarios to fully assess the effects of environmental stabilizing selection and competition: four values of the time scaling parameter |$s$| (20,000, 40,000, 60,000, and 80,000) corresponding to four reasonable generation times (50, 25, 16.7, 12.5 years/generation, respectively) and two heritability values ( ⁠|$h^<2>=0.5,1$|⁠ ). In contrast to the simulation study, we also estimated the variance due to mutation and segregation, |$V_$|⁠ , and the trait optimum, |$ heta$|⁠ . The remaining parameter settings were identical to the simulation study. In the ABC-SMC algorithm, we set 40,000 particles for each iteration and in total 40 iterations for each scenario (which are both more than in the simulation study because we are estimating more parameters).

We developed one more model for comparison with the AWC model and the UWC model. This new model, which we call the metabolism weighted competition (MWC) model, assumes that competition depends on total metabolic rate, in which abundance is multiplied by the per capita metabolic rate, which depends on body length (see Eqs S32–S33 and S35–S37 of the Supplementary Material available on Dryad). That is, the pairwise competition is |$e^<-alpha(mu_-mu_)^<2>>B_$| instead of |$e^<-alpha(mu_-mu_)^<2>>N_$| (as used in the AWC model), where |$B_$| is the total metabolic rate of species |$j$| at the |$t$| th generation. Because the logarithms of body length and body mass of whales are strongly correlated with a slope of |$frac<1><3>$| ( Lockyer 1976) and per capita metabolic rate has a scaling with body mass of |$frac<3><4>$| ( Brody and Procter 1932 Brody 1945 Kleiber 1947 Etienne et al. 2006), the total metabolic rate depends on body length and abundance as follows: |$B_=N_cdot B_<0>cdotmu_^<9/4>$| . Here, |$B_<0>$| is a basal metabolic rate per kg (BMR/kg) that is assumed to be constant across whale species, and therefore drops out of our equations because only the relative metabolic rate matters. Thus, large-bodied species have more competitive power than small-bodied species. For the two additional models (UWC and MWC models) we again estimated five parameters |$(gamma,alpha, u,V_, heta),$| but we considered only one scenario of heritability and time scaling |$(h^<2>=1s=20,000$|⁠ ), because the analyses are computationally demanding, and because we found that the scenarios were similarly supported for the AWC model (see Results section).

We used three alternative sets of summary statistics, that is, the sorted mean trait distance (SMTD), the PICs only, and the unsorted mean trait distance with the phylogenetic independent contrasts (UMTD+PICs). To compare the goodness-of-fit of the eight scenarios (for the AWC model) among each other, we took the simulations with the 5% highest GOF-values across all scenarios and computed the percentage of simulations represented by each scenario in these 5% best fitting simulations as a measure of the support of that scenario ( Toni et al. 2009). We did this for each of the three sets of summary statistics. For comparing the three models we used the exact same procedure support of a model is thus measured by its representation among the 5% best GOF-values across all three models. Lastly, because the estimates converged well, for each model we used the mean of the parameter estimates to generate 1000 data sets to compare the predicted PICs with the empirical observations.


DNA methylation and demethylation

Cells of all living organisms are continuously exposed to a plethora of harmful agents, many of which possess the ability of damaging cellular macromolecules ( Lindahl, 1993). Since DNA conveys genetic information to the next generation, and hence forms the basis of inheritance, it is of ultimate importance to ensure its integrity. Methylation of DNA can be either regulatory or erroneous. Regulatory methylations are introduced at specific sites by specific enzymes and serve various functions, e.g. regulation of transcriptional activity ( Franchini et al., 2012). In the following, the focus will be on erroneous DNA methylation.

SAM is a common co-substrate involved in the majority of intracellular methyl group transfers. However, although SAM is required for intended methylations, its promiscuous nature makes it a source of methylation damage. Indeed, methyl lesions originating from endogenous SAM sources are estimated to form in the DNA at frequencies equaling a continuous exposure to 20 nM methyl methane sulphonate (MMS), a potent alkylating substance ( Rydberg and Lindahl, 1982). This underscores the necessity of efficient repair systems. Additionally, exogenous sources, e.g. tobacco smoke and environmental toxins, also introduce damage in DNA.

Several dedicated repair pathways have evolved to counteract DNA damage. Some pathways may consist of only a single enzyme repairing a particular lesion, while others may consist of large protein complexes of 20–30 different proteins. Repair by direct reversal of the DNA damage is the simplest of the repair pathways, usually consisting of a single enzyme such as ALKBH2 or ALKBH3 (Figure 2B). Unlike base excision repair pathway ( Robertson et al., 2009) and nucleotide excision repair pathway ( Wood, 1997), no toxic or mutagenic intermediate is generated by the direct reversal pathways.

ALKBH2

A few months after the initial enzymatic characterization of E. coli AlkB, two studies confirmed similar activity of two human AlkB homologs, ALKBH2 and ALKBH3 ( Duncan et al., 2002 Aas et al., 2003). Of these, ALKBH2 seem to be the major repair enzyme for genomic DNA ( Ringvoll et al., 2006). ALKBH2 prefers double-stranded DNA structures, and has no activity on RNA substrates underscoring its role as a dedicated guardian of the genome ( Falnes et al., 2004). Yet, mice lacking the Alkbh2 gene are viable with no obvious phenotype despite accumulation of significant amounts of 1meA in the genome ( Lee et al., 2005 Ringvoll et al., 2006 Nay et al., 2012).

In contrast to other well-known DNA repair enzymes, ALKBH2 has rather broad substrate specificity. Lesions like 1mA, 3mC, and certain etheno-adducts in genomic DNA are all reversed by ALKBH2 ( Ringvoll et al., 2008). Despite the relative promiscuity of the enzyme, no damage-check step has been identified. The structure of ALKBH2 and the demethylation mechanism ensure that only a subset of substrates can be oxidized when flipped into the catalytic domain of the enzyme. Hence, a damage-check step is redundant since nothing but the ALKBH2 relevant DNA lesions can be removed ( Yang et al., 2008 Yi et al., 2012 Zhu and Yi, 2014). This contrasts to other DNA repair enzymes, which possess different damage-control mechanisms to ensure that nothing but the lesion itself or the damaged base is removed.

ALKBH2 is localized to cell nuclei where it is diffusely distributed throughout the nucleoplasm, with some accumulation in the nucleoli. During S phase ALKBH2 relocates to foci of replication where it interacts with the proliferating cell nuclear antigen (PCNA). PCNA is the processivity-promoting factor for DNA polymerase delta, a polymerase involved in both DNA replication and DNA repair. On one side, PCNA is encircling the DNA and slides along it during replication. On the other side, PCNA interacts with DNA polymerase delta, and numerous other proteins, thus preventing these proteins from disassociating from the template DNA strand. These proteins generally interact with PCNA through the so-called PCNA-interacting peptide sequence (PIP box). However, the PIP box is missing from a number of PCNA-interacting proteins, including the ALKBH2 protein. This observation initiated a search for other PCNA-interacting motifs. Indeed, Gilljam et al. (2009) identified a novel motif by studying the ALKBH2 protein. This PCNA-interacting motif was designated ALKBH2-PCNA-interacting motif (APIM). The APIM is later found in >200 proteins involved in genome maintenance, transcription and cell cycle regulation ( Muller et al., 2013a).

Alkylating compounds are widely used as anti-cancer chemotherapeutics hence, there has been much interest regarding the clinical significance of altered ALKBH2 activity in human cancers. Indeed, downregulation of ALKBH2 increases sensitivity toward chemotherapy of non-small cell lung cancer cell lines ( Wu et al., 2011). Moreover, upregulation of ALKBH2 in human glioblastoma cell lines contribute to increased resistance toward anti-cancer chemotherapeutics ( Johannessen et al., 2013). Altered expression of ALKBH2, or mutated forms of the protein, has been identified in samples from pediatric brain tumors and gastric cancers suggesting that ALKBH2 is counteracting certain types of cancers ( Cetica et al., 2009 Gao et al., 2011 Fujii et al., 2013). Mouse embryonic fibroblasts lacking the Alkbh2 gene are more sensitive to MMS induced cytotoxicity compared to wild type control cells thus illustrating the rationale for ALKBH2 downregulation as part of modern anti-cancer therapy. However, Alkbh2 −/− fibroblasts do display a statistically significant increase in mutation frequency ( Ringvoll et al., 2006 Nay et al., 2012). This increase in mutations may eventually limit the clinical use of ALKBH2 inhibitors unless a tumor specific downregulation is possible.

ALKBH3

Human ALKBH3 displays a clear enzymatic activity on methylated nucleic acids in vitro ( Duncan et al., 2002), particularly on 1mA and 3mC lesions. However, while ALKBH2 prefers double-stranded DNA and is more efficient in repairing 1meA than 3meC, the opposite is true for ALKBH3. In addition to the observed activity on DNA, ALKBH3 has activity on RNA substrates illustrated by the reactivation of a methylated single-stranded RNA phage ( Aas et al., 2003 Falnes et al., 2004). Furthermore, both E. coli AlkB and ALKBH3 are able to reactivate chemically inactivated naturally occurring RNA species such as mRNA and tRNA in vitro and in vivo ( Ougland et al., 2004). Recently it was reported that at least 10-fold more lesions are repaired in RNA than in DNA in E. coli exposed to MMS, thus underscoring the biological relevance of RNA repair ( Vagbo et al., 2013).

ALKBH3 is found both in the nucleus and in the cytoplasm, and shows no cell cycle dependant relocalization ( Aas et al., 2003). In an elegant study by Dango et al. (2011) an association between ALKBH3 and the so-called activating signal cointegrator complex (ASCC) was identified. ASCC3, the largest subunit of ASCC, is a DNA helicase, whose activity is crucial for the generation of single-stranded DNA. This suggests ALKBH3-mediated repair of transiently single-stranded DNA stretches generated during transcription and/or replication. No study yet has verified ALKBH3 catalyzed RNA repair in vivo in mammals and the study by Dango et al. (2011) confirm ALKBH3-mediated DNA repair in vivo. However, there are numerous examples of proteins with dual functions, and ALKBH3 and RNA are dispersed throughout the cytoplasm. Moreover, genomic DNA is mostly double-stranded and protected against insult at the 1-position of purines and the 3-position of pyrimidines. This makes it tempting to believe that ALKBH3 relevant substrates predominantly would be present in RNA rather than in DNA.

Although mice lacking the Alkbh2 or Alkbh3 gene are without obvious phenotype, a triple knockout of Alkbh2, Alkbh3, and the alkyl adenine DNA glycosylase (Aag) displays a massive synergistic phenotype when challenged with substances that induce inflammation of the colon and colon cancer ( Calvo et al., 2012). Etheno adducts induced by inflammation are shared substrates for these three repair enzymes, and could explain this phenotype. Several reports link ALKBH3 to human cancers. Aberrant ALKBH3 protein expression and mutations in the human ALKBH3 gene are identified in pediatric brain tumors ( Cetica et al., 2009), non-small-cell lung cancer ( Tasaki et al., 2011), rectal carcinoma ( Choi et al., 2011), papillary thyroid cancer ( Neta et al., 2011), and cells of the urogenital system ( Koike et al., 2012 Shimada et al., 2012 Yamato et al., 2012 Nakao et al., 2014). None of these reports do elucidate whether their observations are due to dysfunctional DNA or RNA repair or both. Of note is that Alkbh3-deficient mice are viable and without overt phenotypes in particular, they do not display any cancer phenotype ( Ringvoll et al., 2006).


Misleading Appearances

Some organisms may be very closely related, even though a minor genetic change caused a major morphological difference to make them look quite different. Similarly, unrelated organisms may be distantly related, but appear very much alike. This usually happens because both organisms were in common adaptations that evolved within similar environmental conditions. When similar characteristics occur because of environmental constraints and not due to a close evolutionary relationship, it is an analogy or homoplasy. For example, insects use wings to fly like bats and birds, but the wing structure and embryonic origin is completely different. These are analogous structures (Figure 2).

Similar traits can be either homologous or analogous. Homologous structures share a similar embryonic origin. Analogous organs have a similar function. For example, the bones in a whale’s front flipper are homologous to the bones in the human arm. These structures are not analogous. A butterfly or bird’s wings are analogous but not homologous. Some structures are both analogous and homologous: bird and bat wings are both homologous and analogous. Scientists must determine which type of similarity a feature exhibits to decipher the organisms’ phylogeny.

Figure 2. The (c) wing of a honeybee is similar in shape to a (b) bird wing and (a) bat wing, and it serves the same function. However, the honeybee wing is not composed of bones and has a distinctly different structure and embryonic origin. These wing types (insect versus bat and bird) illustrate an analogy—similar structures that do not share an evolutionary history. (credit a: modification of work by Steve Hillebrand, USFWS credit b: modification of work by U.S. DOI BLM credit c: modification of work by Jon Sullivan)

This website has several examples to show how appearances can be misleading in understanding organisms’ phylogenetic relationships.


Summary – Mendel’s First vs Second Law

Mendel’s first law describes the separation of the two alleles of each gene during the production of gametes and the equal chance of each gamete to get one allele. On the other hand, Mendel’s second law describes the independent transmission of alleles of one gene from the alleles of another gene into daughter cells. Second law shows that there is no interaction or influence between genes when the alleles of each gene transmit to daughter cells. However, these first and second laws are the building blocks of trait inheritance from parents to offspring. Thus, this summarizes the difference between Mendel’s first and second law.

Reference:

1. “The Law of Segregation.” Khan Academy, Khan Academy, Available here.
2. “Mendelian Inheritance.” Wikipedia, Wikimedia Foundation, 12 Mar. 2019, Available here.

Image Courtesy:

1. “Mendel 2 miguelferig” By Miguelferig – Own work (CC0) via Commons Wikimedia
2. “Independent assortment & segregation” By LadyofHats – Own work (Public Domain) via Commons Wikimedia


Summary

Inheritance means the transfer of traits from parents to the next generation. All the traits in an individual are obtained from his parents. This transfer of traits is seen in all organisms whether they reproduce sexually or asexually.

Traits are transferred to the next generation in the form of genetic material i.e. DNA.

Inheritance of sexually reproducing organisms was first studied by Gregor Mendel who published his results in 1865.

Mendel conducted several experiments on pea plants grown in his garden to study seven different traits. He formulated two universally accepted laws as a result of these experiments.

Law of Segregation states that all the traits in organisms are controlled by discrete spreadable factors that were called as genes in the subsequent years. These genes separate during gamete formation and unite again during fusion of male and female gametes to form the zygote.

Law of Independent Assortment states that the segregation and distribution of two more genes takes place independently of one another. They are linked to each other in any case.

Most of the traits follow these laws but some deviations also exist. Examples of such deviations are co-dominance and incomplete dominance.

An example of Co-dominance is the AB blood group of humans where two different alleles completely express themselves. No allele is dominant or recessive.

Examples of Incomplete dominance are pink flowers that are produced as a result of a blend of two alleles one allele for white color and one for the red color.


Comparing plants and connecting traits

The diversity of plant life histories provides a wealth of raw material for comparative studies on evolution and ecology. The two fundamental questions for any comparative study are: which traits are correlated with one another, and are these correlations the result of common descent or convergent evolution? Phylogeny should therefore be explicitly included in any comparative analysis that is concerned with the causes of correlation between traits, even when the principal research question is a purely ecological one. In illustration, the method of phylogenetically independent contrasts (PIC) is used to test two longstanding hypotheses that have not been satisfactorily tested before. In the first example we find that annuals and species of early succession have greater reproductive allocation than perennials and species of later succession. In the second example we show that the apparency hypothesis of chemical defence is supported by a positive correlation between woodiness and the frequency of tannins and by a negative correlation between tannin frequency and alkaloid frequency. Finally, we point out that PIC has a much lower type-I error than cross-species analyses and that this superiority is surprisingly robust to lack of phylogenetic resolution.


Results

NHEJ Is Sporadically Distributed across Bacteria

To identify NHEJ machinery across bacteria, we used the reference sequences of the Ku domain, and the LIG, POL, and PE domains of LigD from P. aeruginosa to search ∼6,000 complete bacterial genomes for homologs (see Materials and Methods). We defined bacteria encoding Ku and the complete, three-domain version of LigD as those harboring a conventional NHEJ system. Organisms lacking the POL and/or the PE domains of LigD, and those encoding these domains in separate proteins, were defined as those carrying nonconventional NHEJ ( fig. 1).

We found NHEJ in only ∼1,300 (22%) genomes studied here. There were various combinations of Ku and LigD domains across these organisms, but a large majority (920) carried conventional NHEJ. Seventy-five percent bacteria harboring conventional NHEJ coded for Ku and LigD in a 10-kb vicinity of each other, with 60% organisms carrying Ku and LigD on the same strand of the 10-kb vicinity. Most bacteria (84%) harboring NHEJ coded for a single copy of Ku, whereas the remaining coded for 2–8 Ku copies in their genomes. For example, as reported by McGovern et al. (2016) and Kobayashi et al. (2008), we identified four Ku-encoding genes in Sinorhizobium meliloti. About two-thirds of NHEJ positive bacteria carried multiple copies of the LIG domain, 37% carried multiple copies of the POL domain, and 8% bacteria had multiple copies of the PE domain ( supplementary table 1 , Supplementary Material online). We also noticed that 138 (2.3%) organisms encoded Ku and not LigD, and 619 (10.3%) only LigD and not Ku ( fig. 1 and supplementary table 1 , Supplementary Material online).

NHEJ was not restricted to specific bacterial classes ( fig. 2) and was found in ten classes. We found a significant enrichment of conventional NHEJ in Proteobacteria (Fisher’s Exact test, P = 3.8 × 10 −5 , odds ratio: 2.04) and Acidobacteria (Fisher’s Exact test, P = 5 × 10 −2 , odds ratio: 5.286). All Bacteroidetes with NHEJ harbor a conventional NHEJ, although we could not assign statistical significance to it (Fisher’s Exact test, P = 0.14, odds ratio: 1.38). In contrast, nonconventional NHEJ repair was significantly overrepresented in Firmicutes (Fisher’s Exact test, P = 1.23 × 10 −13 , odds ratio: 6) and Actinobacteria (Fisher’s Exact test, P = 2.12 × 10 −15 , odds ratio: 6.14). Twenty-four phyla did not include any NHEJ positive organism ( supplementary table 7 , Supplementary Material online).

NHEJ is sporadically distributed across bacteria. 16S rRNA-based species phylogenetic tree of 969 bacterial species (left) with presence/absence matrix of RecA, KU, LIG, POL, and PE domains (right). These species were included such that each genus was chosen once for each NHEJ state (see Phylogenetic Tree Reconstruction section for further details). Tip labels, representing bacteria, are colored according to the phylum names and bars (right of the phylogenetic tree) that the given tip belongs to. The phylum names arranged on either sides of the vertical bars are for representational purposes only. The first five columns of the presence/absence matrix (extreme right of the figure) depict the status if the given protein (RecA) or domain (Ku, LIG, POL, and PE) is present (black horizontal bar) or absent (white horizontal bar) in the corresponding bacteria. Each horizontal bar maps to a bacterial tip on the phylogenetic tree (left). Horizontal bars in the last column of the matrix represent the overall NHEJ status for a given species (color legend same as in fig. 1). NHEJ status—orange: NHEJ− yellow: incomplete NHEJ blue: conventional NHEJ+ pink: nonconventional NHEJ+.

NHEJ is sporadically distributed across bacteria. 16S rRNA-based species phylogenetic tree of 969 bacterial species (left) with presence/absence matrix of RecA, KU, LIG, POL, and PE domains (right). These species were included such that each genus was chosen once for each NHEJ state (see Phylogenetic Tree Reconstruction section for further details). Tip labels, representing bacteria, are colored according to the phylum names and bars (right of the phylogenetic tree) that the given tip belongs to. The phylum names arranged on either sides of the vertical bars are for representational purposes only. The first five columns of the presence/absence matrix (extreme right of the figure) depict the status if the given protein (RecA) or domain (Ku, LIG, POL, and PE) is present (black horizontal bar) or absent (white horizontal bar) in the corresponding bacteria. Each horizontal bar maps to a bacterial tip on the phylogenetic tree (left). Horizontal bars in the last column of the matrix represent the overall NHEJ status for a given species (color legend same as in fig. 1). NHEJ status—orange: NHEJ− yellow: incomplete NHEJ blue: conventional NHEJ+ pink: nonconventional NHEJ+.

NHEJ Was Gained and Lost Multiple Times through Evolution

We traced the number of NHEJ gains and losses starting from the eubacterial ancestor to the species at the tips of the 16S-based bacterial phylogenetic tree. To trace the evolutionary history of NHEJ, we defined four discrete character states: Ku only, LigD only (conventional and nonconventional), NHEJ−, and NHEJ+. Note that an NHEJ+ state is defined only when both Ku and LigD are present in a bacterium. We calculated the posterior probabilities (pp) of each character state per node on the phylogeny, the distribution of the number of times each of the 12 character state transitions occurred ( fig. 3A) and the distribution of the total time spent in each state ( supplementary fig. S1 , Supplementary Material online). We performed this analysis for a set of 969 genomes in which each genus was represented once for each state (see Materials and Methods).

Transitions to a Ku only state are rare. (A) A matrix depicting relative frequency of number of changes of a state transition type across 1,000 stochastic maps. (B) A state transition diagram depicting the number of transitions between two given states and the time spent in each state during NHEJ evolution. The node size is proportional to the amount of time spent in a particular state. The arrow size is proportional to the number of transitions from one state to another.

Transitions to a Ku only state are rare. (A) A matrix depicting relative frequency of number of changes of a state transition type across 1,000 stochastic maps. (B) A state transition diagram depicting the number of transitions between two given states and the time spent in each state during NHEJ evolution. The node size is proportional to the amount of time spent in a particular state. The arrow size is proportional to the number of transitions from one state to another.

We first asked if NHEJ was present in the common eubacterial ancestor and, given the sporadicity of NHEJ, subsequently lost in several lineages ( supplementary table 8 , Supplementary Material online). We assigned a major primary gain to an internal ancestral node if 1) all nodes leading to it from the root had NHEJ− state 2) the pp of either NHEJ+, LigD only, or Ku only at that ancestral node was ≥0.7 3) a gain of LigD only or Ku only was followed by a transition to NHEJ+ and 4) if it had at least three descendent species. We observed multiple major independent primary gains at ancestral nodes within Bacteroidetes, Actinobacteria, Firmicutes, Acidobacteria, and multiple subclades of Proteobacteria ( supplementary table 8 , Supplementary Material online). It follows that the common eubacterial ancestor likely did not have NHEJ ( fig. 4).

NHEJ was gained and lost multiple times through evolution. A trace of the evolutionary history of the two-component NHEJ system across 969 bacteria. These species were included such that each genus was chosen once for each NHEJ state (see Phylogenetic Tree Reconstruction section for further details). The phylum names arranged on either sides of the vertical bars are for representational purposes only. The tip and node labels are colored according to the NHEJ states—red: NHEJ− yellow: Ku only green: LigD only blue: NHEJ+ (conventional and nonconventional). NHEJ state for nodes is shown only when the posterior probability support is >70% interpreted as change in NHEJ state at that node as compared with shallower phylogenetic depths.

NHEJ was gained and lost multiple times through evolution. A trace of the evolutionary history of the two-component NHEJ system across 969 bacteria. These species were included such that each genus was chosen once for each NHEJ state (see Phylogenetic Tree Reconstruction section for further details). The phylum names arranged on either sides of the vertical bars are for representational purposes only. The tip and node labels are colored according to the NHEJ states—red: NHEJ− yellow: Ku only green: LigD only blue: NHEJ+ (conventional and nonconventional). NHEJ state for nodes is shown only when the posterior probability support is >70% interpreted as change in NHEJ state at that node as compared with shallower phylogenetic depths.

The gain of NHEJ can be sequential, gaining either Ku only or LigD only followed by the gain of the other component or it can be a one-step acquisition of both components ( fig. 3B). The most common transition from an NHEJ− state was to a LigD only state. Also frequent was the direct acquisition of both components to transition from an NHEJ− to an NHEJ+ state. Transition from NHEJ− to Ku only was negligible. In the reverse direction, a one-step loss of both Ku and LigD is the most likely. Again, the Ku only state is rare.

A one-step transition from NHEJ− to NHEJ+ is likely through HGT. Sixty bacterial genomes belonging to the phyla Alpha-proteobacteria (in particular the Rhizobiales)—and Beta-proteobacteria, and Streptomycetales carried their NHEJ components on plasmids ( supplementary table 1 , Supplementary Material online). However, based on abnormal word usage statistics (see Materials and Methods), we could not find NHEJ to be a part of the horizontally acquired component of the chromosomes of any bacterial genome. At least two NHEJ− to NHEJ+ transitions occurred close to the root, and it is possible that the predictions of horizontally acquired NHEJ systems made so far may be an underestimate ( fig. 4). We investigate this in greater detail below.

In summary, 1) the common eubacterial ancestor was devoid of NHEJ 2) NHEJ was gained and lost multiple times and 3) transitions to a Ku only state are rare.

NHEJ and HGT

Experimental studies in the archaea Methanocella paludicola ( Bartlett et al. 2013, 2016 Brissett et al. 2013) have confirmed the presence of a functional NHEJ repair, with crystal structures revealing close relationship with the bacterial proteins ( Bartlett et al. 2016 White and Allers 2018).

To assess the possibility of horizontal transfer of NHEJ machinery across prokaryotes, we first performed a domain wise search in 243 archaea to complement the data we had assembled for bacteria. These searches revealed the presence of both Ku and LigD-LIG domains in ten archaeal species (see Materials and Methods supplementary table 2 , Supplementary Material online). However, 230 archaeal genomes encoded LigD but no Ku. This lends support to previous reports suggesting that NHEJ is rare in archaea ( Bartlett et al. 2013, 2016 White and Allers 2018).

In order to check for horizontal transfer events between bacteria and archaea, we used phylogenetic methods based on detecting conflicts between an organismal phylogeny and a phylogeny inferred for Ku and LigD-LIG domains, respectively. This method allowed us to test for any ancient transfers across bacteria as well. We found that NHEJ proteins undergo HGT events at significantly high rate (p-AU = 0 fig. 5B and C see Materials and Methods) and these are not limited to closely related species or cospeciation events ( fig. 5D Mantel test, P < 10 −4 , rKu = 0.25 P < 10 −4 , rLIG = 0.4). We also noted incongruence with respect to the RecA phylogeny (p-AU = 0 fig. 5A) as has been reported before ( Eisen 1995 Lang et al. 2013). However, these were limited at best to transfers among closely related species ( fig. 5D Mantel test, P < 10 −4 , rRecA = 0.94).

Phylogenetic methods suggest a strong role of HGT in NHEJ evolution. (A) Unrooted RecA tree, (B) unrooted Ku tree, (C) unrooted LigD-LIG tree, and (D) Mantel test correlation coefficient (r) comparing RecA, Ku, and LigD-LIG distance matrices with 16S rRNA distance matrices, respectively, compared against a null distribution of r obtained by 10,000 matrix randomizations.

Phylogenetic methods suggest a strong role of HGT in NHEJ evolution. (A) Unrooted RecA tree, (B) unrooted Ku tree, (C) unrooted LigD-LIG tree, and (D) Mantel test correlation coefficient (r) comparing RecA, Ku, and LigD-LIG distance matrices with 16S rRNA distance matrices, respectively, compared against a null distribution of r obtained by 10,000 matrix randomizations.

An incongruence between a species and gene tree could result due to processes other than HGT, like duplications and losses. Therefore, to predict the most frequent transfer events, we used a reconciliation approach based on the DTL model. DTL employs a parsimonious framework where each evolutionary event is assigned a cost and the goal is to find a reconciliation (possible evolutionary history of gene tree inside a species tree) with minimum total cost. We observed a high rate of HGT between bacterial clades—Firmicutes, Actinobacteria, and Proteobacteria and Archaea, where each of these played the role of a donor and a recipient in Ku ( fig. 6A) and LigD-LIG transfer events ( fig. 6B). We observed that all proteobacterial species—with the exception of delta-proteobacteria, which was a donor of Ku to archaeal recipients—were recipients of both Ku and LigD from archaea or other distantly related bacteria. On one hand, we found evidence of Ku transfers from Archaea to Firmicutes and Actinobacteria and on the other hand, LigD-LIG transfers most likely occurred from Firmicutes and Actinobacteria to Archaea. Together, this raises the possibility of NHEJ transfers between bacteria and archaea.

Extensive HGT among bacterial phyla and between bacteria and archaea. 16S rRNA-based species tree depicting the most frequent donor–recipient pairs involved in (A) Ku HGT events and (B) LigD-LIG HGT events. The bacterial species included in both the species tree coded for one Ku and one LigD only. The archaeal species were included 1) in (A) if they had at least a Ku and 2) in (B) if they had at least a LigD-LIG domain (see Materials and Methods for more details). The width of the arrow corresponds to the number of reconciliations supporting a given transfer event (see supplementary files 3 and 4, Supplementary Material online, for exact number of reconciliations for each donor–recipient pair). (C) Ku domain MSA (upper panel) of prokaryotes belonging to genus Archaeoglobus and phyla Firmicutes and Actinobacteria included in (A) (transfer event marked as asterisk). LigD-LIG pairwise alignment (lower panel) of an Archaea–Actinobacteria HGT transfer event in (B) (marked as asterisk). (D) Principal component analysis of Ku domain sequences evolved from ancestors included in transfer event in (A) (marked as asterisk).

Extensive HGT among bacterial phyla and between bacteria and archaea. 16S rRNA-based species tree depicting the most frequent donor–recipient pairs involved in (A) Ku HGT events and (B) LigD-LIG HGT events. The bacterial species included in both the species tree coded for one Ku and one LigD only. The archaeal species were included 1) in (A) if they had at least a Ku and 2) in (B) if they had at least a LigD-LIG domain (see Materials and Methods for more details). The width of the arrow corresponds to the number of reconciliations supporting a given transfer event (see supplementary files 3 and 4, Supplementary Material online, for exact number of reconciliations for each donor–recipient pair). (C) Ku domain MSA (upper panel) of prokaryotes belonging to genus Archaeoglobus and phyla Firmicutes and Actinobacteria included in (A) (transfer event marked as asterisk). LigD-LIG pairwise alignment (lower panel) of an Archaea–Actinobacteria HGT transfer event in (B) (marked as asterisk). (D) Principal component analysis of Ku domain sequences evolved from ancestors included in transfer event in (A) (marked as asterisk).

An example of the former is depicted as a MSA of Ku domain sequences belonging to Archaea, Firmicutes, and Actinobacteria in figure 6C (upper panel). This transfer event corresponds to the asterisk marked in figure 6A—corresponding to that between the ancestor of the genus Archaeoglobus and that of Firmicutes and Actinobacteria. We further carried out a principal component analysis of these domain sequences that had evolved from the aforementioned ancestors ( fig. 6D). Along the first principal component, all but two Actinobacteria—Eggerthella lenta and Microlunatus phosphovorus—form a distinct cluster from Archaea and Firmicutes. Along the second principal component, we see two distinct clusters. The cluster on the bottom left consists of anaerobic prokaryotes—Archaea (genus Archaeoglobus), Firmicutes (Clostridium cellulosi and Desulfitobacterium dichloroeliminans), and Actinobacteria (Eggerthella lenta), highlighting the possibility of HGT among these prokaryotes. Another instance of a LigD-LIG transfer is depicted in figure 6C, lower panel. This transfer event corresponds to the asterisk in figure 6B, involving the Actinobacteria—Brevibacterium linens, and Archaea—Archaeoglobus veneficus (coding for both Ku and LigD-LIG domains).

In addition to the evidence supporting HGT of NHEJ components between Archaea and Bacteria, we observed transfers among different bacterial clades as well ( fig. 6A and B blue arrows). We found Ku transfers between donor–recipient pairs: 1) Alphaproteobacterium (Asticcacaulis excentricus) and common ancestor of Acidobacteria (genus Acidobacterium, Granulicella, and Terriglobus) and 2) common ancestor of Delta-proteobacteria genus Geobacter and Chlamydiae (Parachlamydia acanthamoeba). For LigD-LIG transfers, we observed the following donor–recipient pairs—1) Proteobacteria (Phenylbacterium zucineum) and Acidobacteria (Terriglobus roseus) and 2) common ancestor of Actinobacteria (genus Eggerthella) and Firmicutes (Desulfitobacterium dicholoroeliminans). A full list of donor–recipient events can be found in supplementary files 3 and 4, Supplementary Material online, for Ku and LigD-LIG domains, respectively.

Kanhere and Vingron (2009) carried out HGT detection of bacterial core genes among prokaryotes. They found that a majority of these transfers occurred from bacteria to archaea and that these genes were mostly metabolic genes. Overall, our study is consistent with their observation, with additional evidence showing a possibility of NHEJ transfers from archaea to bacteria as well. We also show evidence of NHEJ transfers between closely and distantly related bacteria. Using the approach used in our study, it remains to be tested how HGT events have shaped noncore genes like other repair pathways throughout evolution in prokaryotes.

NHEJ Occurrence Is Associated with GS, GR, and G–C Content

Recently, Ku-encoding organisms were shown to have higher genomic G + C content ( Weissman et al. 2019). Given its central role in DNA repair, we asked whether any other genome characteristics could also be associated with the presence or absence of NHEJ. First, we verified that the findings of Weissman et al. on the correlation between the presence of Ku and G + C content held true for NHEJ+ states as defined in our study ( fig. 7A and supplementary figs. S4, S5, and S7C, Supplementary Material online) ( Weissman et al. 2019). Along with this, we tested two additional characteristics: GS and GR (as measured by the copy number of rRNA operons), both of which could determine the availability or the lack of a homologous template for high fidelity recombination-based repair. We restricted these analyses to conventional NHEJ-harboring bacteria as a proxy for repair proficiency and compared them with NHEJ− genomes. Data including nonconventional NHEJ are shown in supplementary figures S2 and S3, Supplementary Material online.

NHEJ presence and absence is associated with GS, GR, and G–C content. The red asterisk indicates statistical significance (Wilcoxon rank-sum test P value < 0.01). (A) Boxplot comparing the distribution of G–C content between NHEJ– and conventional NHEJ+ bacteria. (B) Boxplot comparing the distribution of GS between NHEJ− and conventional NHEJ+ bacteria. (C) Boxplot comparing the distribution of rRNA copy number between NHEJ− and conventional NHEJ+ bacteria. (D) A density distribution plot depicting the distribution of GS (median number of protein coding sequences) expected by a random distribution (black) where the probability of having NHEJ is linearly proportional to GS and the median GS of organisms harboring NHEJ (red).

NHEJ presence and absence is associated with GS, GR, and G–C content. The red asterisk indicates statistical significance (Wilcoxon rank-sum test P value < 0.01). (A) Boxplot comparing the distribution of G–C content between NHEJ– and conventional NHEJ+ bacteria. (B) Boxplot comparing the distribution of GS between NHEJ− and conventional NHEJ+ bacteria. (C) Boxplot comparing the distribution of rRNA copy number between NHEJ− and conventional NHEJ+ bacteria. (D) A density distribution plot depicting the distribution of GS (median number of protein coding sequences) expected by a random distribution (black) where the probability of having NHEJ is linearly proportional to GS and the median GS of organisms harboring NHEJ (red).

Bacteria with NHEJ were found to have larger genomes (median = 5.4 Mb) than those without NHEJ (median= 2.9 Mb Wilcoxon rank-sum test, P < 10 −15 fig. 7B and supplementary fig. S7 A, Supplementary Material online) and significantly larger than that expected by a random distribution in which the probability of having NHEJ is linearly proportional to GS (Wilcoxon rank-sum test, P < 10 −15 , across 100 simulations fig. 7D). This relationship was found to be true within the phylum Proteobacteria, Actinobacteria, Bacteroidetes, and Firmicutes as well ( supplementary fig. S6 , Supplementary Material online).

In addition, bacteria harboring NHEJ were found to have significantly fewer rRNA copies (median = 3), and by inference slower GRs, than bacteria without NHEJ (median = 4 Wilcoxon rank-sum test P < 10 −15 fig. 7C). Although the distribution of rRNA copy numbers for genomes without NHEJ was broad, those with conventional NHEJ fell within a narrow range, representing relatively slower growth ( supplementary fig. S7 B, Supplementary Material online). At the phyla level, this relationship was found to hold true for Proteobacteria and Actinobacteria, whereas there was no significant difference for Bacteroidetes and Firmicutes, respectively ( supplementary fig. S8 , Supplementary Material online).

In order to confirm the result in a phylogenetically controlled manner, Pagel’s λ and Blomberg’s K were used to first measure whether closely related bacteria tended to have similar GSs and GRs in the data set (see Materials and Methods). These measures suggest that phylogenetic coherence is significantly greater than random expectations for both the genome characteristics ( supplementary table 9 , Supplementary Material online). Therefore, the distributions of GS between bacteria with different NHEJ status were compared while accounting for the statistical nonindependence of closely related taxa (see Materials and Methods). We found a significant difference in log10(GSs) between bacteria with conventional NHEJ and without the repair (phyloANOVA P = 6 × 10 −3 ) the characters being mapped on the phylogenetic tree of 969 bacteria with five discrete groups: NHEJ−, Ku only, LigD only, conventional NHEJ+, and nonconventional NHEJ+. However, we did not observe a significant difference in log10(rRNA copy number) between the two groups of bacteria (phyloANOVA P = 1 see Discussion).

We used ML as well as Bayesian approaches to test whether the observed associations of conventional NHEJ individually with large genomes and slow GRs are indicative of dependent or independent evolution of these traits on the phylogenetic tree (see Materials and Methods). Both suggested that the phylogenetic data fit models of evolution in which conventional NHEJ presence or absence and GS or GR are evolving in a correlated manner ( table 1). This strengthens the association between the tested variables in a phylogenetically controlled way. Phylogenetic logistic regression of the conventional NHEJ occurrence with both the continuous independent variables showed, however, that GS is the stronger correlate (see Materials and Methods table 2).

Maximum Likelihood and Bayesian RJMCMC Results for Two Character Pairs Tested for Correlated Evolution: 1) NHEJ State and Genome Size and 2) NHEJ State and Growth Rate

Method . Correlation Pair . Log-Likelihood (Independent Model) . Marginal Log-Likelihood (Independent Model) . Log-Likelihood (Dependent Model) . Marginal Log-Likelihood (Dependent Model) . Likelihood Ratio Test (LRT) Statistics . Bayes Factor (>2 = Better Fit) .
Maximum likelihood NHEJ state and genome size −1,059.97 −1,010.002 LR = 99.94 P < 0.001
Bayesian RJMCMC NHEJ state and genome size −1,110.14 −1,042.25 135.78
Maximum likelihood NHEJ state and growth rate −975.301 −950.01 LR = 25.29 P < 0.001
Bayesian RJMCMC NHEJ state and growth rate −1,051.529 −985.579 131.9
Method . Correlation Pair . Log-Likelihood (Independent Model) . Marginal Log-Likelihood (Independent Model) . Log-Likelihood (Dependent Model) . Marginal Log-Likelihood (Dependent Model) . Likelihood Ratio Test (LRT) Statistics . Bayes Factor (>2 = Better Fit) .
Maximum likelihood NHEJ state and genome size −1,059.97 −1,010.002 LR = 99.94 P < 0.001
Bayesian RJMCMC NHEJ state and genome size −1,110.14 −1,042.25 135.78
Maximum likelihood NHEJ state and growth rate −975.301 −950.01 LR = 25.29 P < 0.001
Bayesian RJMCMC NHEJ state and growth rate −1,051.529 −985.579 131.9

Note .—A chi-squared-based LRT with four degrees of freedom was used to test the better model—1) independent model where the character pair evolved independent of each other and 2) dependent model where the characters were allowed to evolve assuming a correlated evolution—based on maximum likelihood. Bayes factor was used to test the better model, based on Bayesian RJMCMC analysis.

Maximum Likelihood and Bayesian RJMCMC Results for Two Character Pairs Tested for Correlated Evolution: 1) NHEJ State and Genome Size and 2) NHEJ State and Growth Rate

Method . Correlation Pair . Log-Likelihood (Independent Model) . Marginal Log-Likelihood (Independent Model) . Log-Likelihood (Dependent Model) . Marginal Log-Likelihood (Dependent Model) . Likelihood Ratio Test (LRT) Statistics . Bayes Factor (>2 = Better Fit) .
Maximum likelihood NHEJ state and genome size −1,059.97 −1,010.002 LR = 99.94 P < 0.001
Bayesian RJMCMC NHEJ state and genome size −1,110.14 −1,042.25 135.78
Maximum likelihood NHEJ state and growth rate −975.301 −950.01 LR = 25.29 P < 0.001
Bayesian RJMCMC NHEJ state and growth rate −1,051.529 −985.579 131.9
Method . Correlation Pair . Log-Likelihood (Independent Model) . Marginal Log-Likelihood (Independent Model) . Log-Likelihood (Dependent Model) . Marginal Log-Likelihood (Dependent Model) . Likelihood Ratio Test (LRT) Statistics . Bayes Factor (>2 = Better Fit) .
Maximum likelihood NHEJ state and genome size −1,059.97 −1,010.002 LR = 99.94 P < 0.001
Bayesian RJMCMC NHEJ state and genome size −1,110.14 −1,042.25 135.78
Maximum likelihood NHEJ state and growth rate −975.301 −950.01 LR = 25.29 P < 0.001
Bayesian RJMCMC NHEJ state and growth rate −1,051.529 −985.579 131.9

Note .—A chi-squared-based LRT with four degrees of freedom was used to test the better model—1) independent model where the character pair evolved independent of each other and 2) dependent model where the characters were allowed to evolve assuming a correlated evolution—based on maximum likelihood. Bayes factor was used to test the better model, based on Bayesian RJMCMC analysis.

Phylogenetic Logistic Regression for Three Models, Based on a Phylogenetic Tree of 1,403 Species of Bacteria Harboring Either NHEJ− or Conventional NHEJ+ State

Note .—Alpha represents the phylogenetic signal of the dependent variable, that is, NHEJ state in our case. The higher the alpha, the lesser the phylogenetic signal. AIC or the Akaike Information Criterion is used to select the best model for the NHEJ state, out of the three tested against two independent variables—GS and GR. The two independent variables were tested against multicollinearity, with variance inflation factor or VIF = 0.93715 (VIF < 10 is preferred), making the analysis reliable.

Phylogenetic Logistic Regression for Three Models, Based on a Phylogenetic Tree of 1,403 Species of Bacteria Harboring Either NHEJ− or Conventional NHEJ+ State

Note .—Alpha represents the phylogenetic signal of the dependent variable, that is, NHEJ state in our case. The higher the alpha, the lesser the phylogenetic signal. AIC or the Akaike Information Criterion is used to select the best model for the NHEJ state, out of the three tested against two independent variables—GS and GR. The two independent variables were tested against multicollinearity, with variance inflation factor or VIF = 0.93715 (VIF < 10 is preferred), making the analysis reliable.

As a case study where the association of both GS and GR with NHEJ evolution was prominent, we found a gain of conventional NHEJ in the ancestor of two genera belonging to Corynebacteriales—Mycobacterium and Corynebacterium—where the former retained and the latter had a secondary loss of the machinery. Phylogenetic ancestral reconstruction analysis revealed an increase in GS in the ancestor of Corynebacteriales, followed by an NHEJ gain. Although Mycobacterium retained NHEJ, Corynebacterium lost the machinery along with a decrease in GS. Using a similar analysis, GR mapped to this subclade revealed an increase in rRNA copy number in Corynebacterium ( supplementary fig. S9 , Supplementary Material online see Materials and Methods).


Contents

Although the process of meiosis is related to the more general cell division process of mitosis, it differs in two important respects:

usually occurs between identical sister chromatids and does not result in genetic changes

Meiosis begins with a diploid cell, which contains two copies of each chromosome, termed homologs. First, the cell undergoes DNA replication, so each homolog now consists of two identical sister chromatids. Then each set of homologs pair with each other and exchange genetic information by homologous recombination often leading to physical connections (crossovers) between the homologs. In the first meiotic division, the homologs are segregated to separate daughter cells by the spindle apparatus. The cells then proceed to a second division without an intervening round of DNA replication. The sister chromatids are segregated to separate daughter cells to produce a total of four haploid cells. Female animals employ a slight variation on this pattern and produce one large ovum and two small polar bodies. Because of recombination, an individual chromatid can consist of a new combination of maternal and paternal genetic information, resulting in offspring that are genetically distinct from either parent. Furthermore, an individual gamete can include an assortment of maternal, paternal, and recombinant chromatids. This genetic diversity resulting from sexual reproduction contributes to the variation in traits upon which natural selection can act.

Meiosis uses many of the same mechanisms as mitosis, the type of cell division used by eukaryotes to divide one cell into two identical daughter cells. In some plants, fungi, and protists meiosis results in the formation of spores: haploid cells that can divide vegetatively without undergoing fertilization. Some eukaryotes, like bdelloid rotifers, do not have the ability to carry out meiosis and have acquired the ability to reproduce by parthenogenesis.

Meiosis does not occur in archaea or bacteria, which generally reproduce asexually via binary fission. However, a "sexual" process known as horizontal gene transfer involves the transfer of DNA from one bacterium or archaeon to another and recombination of these DNA molecules of different parental origin.

Meiosis was discovered and described for the first time in sea urchin eggs in 1876 by the German biologist Oscar Hertwig. It was described again in 1883, at the level of chromosomes, by the Belgian zoologist Edouard Van Beneden, in Ascaris roundworm eggs. The significance of meiosis for reproduction and inheritance, however, was described only in 1890 by German biologist August Weismann, who noted that two cell divisions were necessary to transform one diploid cell into four haploid cells if the number of chromosomes had to be maintained. In 1911, the American geneticist Thomas Hunt Morgan detected crossovers in meiosis in the fruit fly Drosophila melanogaster, which helped to establish that genetic traits are transmitted on chromosomes.

The term "meiosis" is derived from the Greek word μείωσις , meaning 'lessening'. It was introduced to biology by J.B. Farmer and J.E.S. Moore in 1905, using the idiosyncratic rendering "maiosis":

We propose to apply the terms Maiosis or Maiotic phase to cover the whole series of nuclear changes included in the two divisions that were designated as Heterotype and Homotype by Flemming. [8]

The spelling was changed to "meiosis" by Koernicke (1905) and by Pantel and De Sinety (1906) to follow the usual conventions for transliterating Greek. [9]

Meiosis is divided into meiosis I and meiosis II which are further divided into Karyokinesis I and Cytokinesis I and Karyokinesis II and Cytokinesis II respectively. The preparatory steps that lead up to meiosis are identical in pattern and name to interphase of the mitotic cell cycle. [10] Interphase is divided into three phases:

    : In this very active phase, the cell synthesizes its vast array of proteins, including the enzymes and structural proteins it will need for growth. In G1, each of the chromosomes consists of a single linear molecule of DNA. : The genetic material is replicated each of the cell's chromosomes duplicates to become two identical sister chromatids attached at a centromere. This replication does not change the ploidy of the cell since the centromere number remains the same. The identical sister chromatids have not yet condensed into the densely packaged chromosomes visible with the light microscope. This will take place during prophase I in meiosis. : G2 phase as seen before mitosis is not present in meiosis. Meiotic prophase corresponds most closely to the G2 phase of the mitotic cell cycle.

Interphase is followed by meiosis I and then meiosis II. Meiosis I separates replicated homologous chromosomes, each still made up of two sister chromatids, into two daughter cells, thus reducing the chromosome number by half. During meiosis II, sister chromatids decouple and the resultant daughter chromosomes are segregated into four daughter cells. For diploid organisms, the daughter cells resulting from meiosis are haploid and contain only one copy of each chromosome. In some species, cells enter a resting phase known as interkinesis between meiosis I and meiosis II.

Meiosis I and II are each divided into prophase, metaphase, anaphase, and telophase stages, similar in purpose to their analogous subphases in the mitotic cell cycle. Therefore, meiosis includes the stages of meiosis I (prophase I, metaphase I, anaphase I, telophase I) and meiosis II (prophase II, metaphase II, anaphase II, telophase II).

During meiosis, specific genes are more highly transcribed. [11] [12] In addition to strong meiotic stage-specific expression of mRNA, there are also pervasive translational controls (e.g. selective usage of preformed mRNA), regulating the ultimate meiotic stage-specific protein expression of genes during meiosis. [13] Thus, both transcriptional and translational controls determine the broad restructuring of meiotic cells needed to carry out meiosis.

Meiosis I Edit

Meiosis I segregates homologous chromosomes, which are joined as tetrads (2n, 4c), producing two haploid cells (n chromosomes, 23 in humans) which each contain chromatid pairs (1n, 2c). Because the ploidy is reduced from diploid to haploid, meiosis I is referred to as a reductional division. Meiosis II is an equational division analogous to mitosis, in which the sister chromatids are segregated, creating four haploid daughter cells (1n, 1c). [14]

Prophase I Edit

Prophase I is by far the longest phase of meiosis (lasting 13 out of 14 days in mice [15] ). During prophase I, homologous maternal and paternal chromosomes pair, synapse, and exchange genetic information (by homologous recombination), forming at least one crossover per chromosome. [16] These crossovers become visible as chiasmata (plural singular chiasma). [17] This process facilitates stable pairing between homologous chromosomes and hence enables accurate segregation of the chromosomes at the first meiotic division. The paired and replicated chromosomes are called bivalents (two chromosomes) or tetrads (four chromatids), with one chromosome coming from each parent. Prophase I is divided into a series of substages which are named according to the appearance of chromosomes.

Leptotene Edit

The first stage of prophase I is the leptotene stage, also known as leptonema, from Greek words meaning "thin threads". [18] : 27 In this stage of prophase I, individual chromosomes—each consisting of two replicated sister chromatids—become "individualized" to form visible strands within the nucleus. [18] : 27 [19] : 353 The chromosomes each form a linear array of loops mediated by cohesin, and the lateral elements of the synaptonemal complex assemble forming an "axial element" from which the loops emanate. [20] Recombination is initiated in this stage by the enzyme SPO11 which creates programmed double strand breaks (around 300 per meiosis in mice). [21] This process generates single stranded DNA filaments coated by RAD51 and DMC1 which invade the homologous chromosomes, forming inter-axis bridges, and resulting in the pairing/co-alignment of homologues (to a distance of

Zygotene Edit

Leptotene is followed by the zygotene stage, also known as zygonema, from Greek words meaning "paired threads", [18] : 27 which in some organisms is also called the bouquet stage because of the way the telomeres cluster at one end of the nucleus. [23] In this stage the homologous chromosomes become much more closely (

100 nm) and stably paired (a process called synapsis) mediated by the installation of the transverse and central elements of the synaptonemal complex. [20] Synapsis is thought to occur in a zipper-like fashion starting from a recombination nodule. The paired chromosomes are called bivalent or tetrad chromosomes.

Pachytene Edit

The pachytene stage ( / ˈ p æ k ɪ t iː n / PAK -i-teen), also known as pachynema, from Greek words meaning "thick threads". [18] : 27 is the stage at which all autosomal chromosomes have synapsed. In this stage homologous recombination, including chromosomal crossover (crossing over), is completed through the repair of the double strand breaks formed in leptotene. [20] Most breaks are repaired without forming crossovers resulting in gene conversion. [24] However, a subset of breaks (at least one per chromosome) form crossovers between non-sister (homologous) chromosomes resulting in the exchange of genetic information. [25] Sex chromosomes, however, are not wholly identical, and only exchange information over a small region of homology called the pseudoautosomal region. [26] The exchange of information between the homologous chromatids results in a recombination of information each chromosome has the complete set of information it had before, and there are no gaps formed as a result of the process. Because the chromosomes cannot be distinguished in the synaptonemal complex, the actual act of crossing over is not perceivable through an ordinary light microscope, and chiasmata are not visible until the next stage.

Diplotene Edit

During the diplotene stage, also known as diplonema, from Greek words meaning "two threads", [18] : 30 the synaptonemal complex disassembles and homologous chromosomes separate from one another a little. However, the homologous chromosomes of each bivalent remain tightly bound at chiasmata, the regions where crossing-over occurred. The chiasmata remain on the chromosomes until they are severed at the transition to anaphase I to allow homologous chromosomes to move to opposite poles of the cell.

In human fetal oogenesis, all developing oocytes develop to this stage and are arrested in prophase I before birth. [27] This suspended state is referred to as the dictyotene stage or dictyate. It lasts until meiosis is resumed to prepare the oocyte for ovulation, which happens at puberty or even later.

Diakinesis Edit

Chromosomes condense further during the diakinesis stage, from Greek words meaning "moving through". [18] : 30 This is the first point in meiosis where the four parts of the tetrads are actually visible. Sites of crossing over entangle together, effectively overlapping, making chiasmata clearly visible. Other than this observation, the rest of the stage closely resembles prometaphase of mitosis the nucleoli disappear, the nuclear membrane disintegrates into vesicles, and the meiotic spindle begins to form.

Meiotic spindle formation Edit

Unlike mitotic cells, human and mouse oocytes do not have centrosomes to produce the meiotic spindle. In mice, approximately 80 MicroTubule Organizing Centers (MTOCs) form a sphere in the ooplasm and begin to nucleate microtubules that reach out towards chromosomes, attaching to the chromosomes at the kinetochore. Over time the MTOCs merge until two poles have formed, generating a barrel shaped spindle. [28] In human oocytes spindle microtubule nucleation begins on the chromosomes, forming an aster that eventually expands to surround the chromosomes. [29] Chromosomes then slide along the microtubules towards the equator of the spindle, at which point the chromosome kinetochores form end-on attachments to microtubules. [30]

Metaphase I Edit

Homologous pairs move together along the metaphase plate: As kinetochore microtubules from both spindle poles attach to their respective kinetochores, the paired homologous chromosomes align along an equatorial plane that bisects the spindle, due to continuous counterbalancing forces exerted on the bivalents by the microtubules emanating from the two kinetochores of homologous chromosomes. This attachment is referred to as a bipolar attachment. The physical basis of the independent assortment of chromosomes is the random orientation of each bivalent along the metaphase plate, with respect to the orientation of the other bivalents along the same equatorial line. [17] The protein complex cohesin holds sister chromatids together from the time of their replication until anaphase. In mitosis, the force of kinetochore microtubules pulling in opposite directions creates tension. The cell senses this tension and does not progress with anaphase until all the chromosomes are properly bi-oriented. In meiosis, establishing tension ordinarily requires at least one crossover per chromosome pair in addition to cohesin between sister chromatids (see Chromosome segregation).

Anaphase I Edit

Kinetochore microtubules shorten, pulling homologous chromosomes (which each consist of a pair of sister chromatids) to opposite poles. Nonkinetochore microtubules lengthen, pushing the centrosomes farther apart. The cell elongates in preparation for division down the center. [17] Unlike in mitosis, only the cohesin from the chromosome arms is degraded while the cohesin surrounding the centromere remains protected by a protein named Shugoshin (Japanese for "guardian spirit"), what prevents the sister chromatids from separating. [31] This allows the sister chromatids to remain together while homologs are segregated.

Telophase I Edit

The first meiotic division effectively ends when the chromosomes arrive at the poles. Each daughter cell now has half the number of chromosomes but each chromosome consists of a pair of chromatids. The microtubules that make up the spindle network disappear, and a new nuclear membrane surrounds each haploid set. The chromosomes uncoil back into chromatin. Cytokinesis, the pinching of the cell membrane in animal cells or the formation of the cell wall in plant cells, occurs, completing the creation of two daughter cells. However, cytokinesis does not fully complete resulting in "cytoplasmic bridges" which enable the cytoplasm to be shared between daughter cells until the end of meiosis II. [32] Sister chromatids remain attached during telophase I.

Cells may enter a period of rest known as interkinesis or interphase II. No DNA replication occurs during this stage.

Meiosis II Edit

Meiosis II is the second meiotic division, and usually involves equational segregation, or separation of sister chromatids. Mechanically, the process is similar to mitosis, though its genetic results are fundamentally different. The end result is production of four haploid cells (n chromosomes, 23 in humans) from the two haploid cells (with n chromosomes, each consisting of two sister chromatids) produced in meiosis I. The four main steps of meiosis II are: prophase II, metaphase II, anaphase II, and telophase II.

In prophase II, we see the disappearance of the nucleoli and the nuclear envelope again as well as the shortening and thickening of the chromatids. Centrosomes move to the polar regions and arrange spindle fibers for the second meiotic division.

In metaphase II, the centromeres contain two kinetochores that attach to spindle fibers from the centrosomes at opposite poles. The new equatorial metaphase plate is rotated by 90 degrees when compared to meiosis I, perpendicular to the previous plate. [33]

This is followed by anaphase II, in which the remaining centromeric cohesin, not protected by Shugoshin anymore, is cleaved, allowing the sister chromatids to segregate. The sister chromatids by convention are now called sister chromosomes as they move toward opposing poles. [31]

The process ends with telophase II, which is similar to telophase I, and is marked by decondensation and lengthening of the chromosomes and the disassembly of the spindle. Nuclear envelopes re-form and cleavage or cell plate formation eventually produces a total of four daughter cells, each with a haploid set of chromosomes.

Meiosis is now complete and ends up with four new daughter cells.

The origin and function of meiosis are currently not well understood scientifically, and would provide fundamental insight into the evolution of sexual reproduction in eukaryotes. There is no current consensus among biologists on the questions of how sex in eukaryotes arose in evolution, what basic function sexual reproduction serves, and why it is maintained, given the basic two-fold cost of sex. It is clear that it evolved over 1.2 billion years ago, and that almost all species which are descendants of the original sexually reproducing species are still sexual reproducers, including plants, fungi, and animals.

Meiosis is a key event of the sexual cycle in eukaryotes. It is the stage of the life cycle when a cell gives rise to haploid cells (gametes) each having half as many chromosomes as the parental cell. Two such haploid gametes, ordinarily arising from different individual organisms, fuse by the process of fertilization, thus completing the sexual cycle.

Meiosis is ubiquitous among eukaryotes. It occurs in single-celled organisms such as yeast, as well as in multicellular organisms, such as humans. Eukaryotes arose from prokaryotes more than 2.2 billion years ago [34] and the earliest eukaryotes were likely single-celled organisms. To understand sex in eukaryotes, it is necessary to understand (1) how meiosis arose in single celled eukaryotes, and (2) the function of meiosis.

The new combinations of DNA created during meiosis are a significant source of genetic variation alongside mutation, resulting in new combinations of alleles, which may be beneficial. Meiosis generates gamete genetic diversity in two ways: (1) Law of Independent Assortment. The independent orientation of homologous chromosome pairs along the metaphase plate during metaphase I and orientation of sister chromatids in metaphase II, this is the subsequent separation of homologs and sister chromatids during anaphase I and II, it allows a random and independent distribution of chromosomes to each daughter cell (and ultimately to gametes) [35] and (2) Crossing Over. The physical exchange of homologous chromosomal regions by homologous recombination during prophase I results in new combinations of genetic information within chromosomes. [36]

Prophase I arrest Edit

Female mammals and birds are born possessing all the oocytes needed for future ovulations, and these oocytes are arrested at the prophase I stage of meiosis. [37] In humans, as an example, oocytes are formed between three and four months of gestation within the fetus and are therefore present at birth. During this prophase I arrested stage (dictyate), which may last for decades, four copies of the genome are present in the oocytes. The arrest of ooctyes at the four genome copy stage was proposed to provide the informational redundancy needed to repair damage in the DNA of the germline. [37] The repair process used appears to involve homologous recombinational repair [37] [38] Prophase I arrested oocytes have a high capability for efficient repair of DNA damages, particularly exogenously induced double-strand breaks. [38] DNA repair capability appears to be a key quality control mechanism in the female germ line and a critical determinant of fertility. [38]

In life cycles Edit

Meiosis occurs in eukaryotic life cycles involving sexual reproduction, consisting of the constant cyclical process of meiosis and fertilization. This takes place alongside normal mitotic cell division. In multicellular organisms, there is an intermediary step between the diploid and haploid transition where the organism grows. At certain stages of the life cycle, germ cells produce gametes. Somatic cells make up the body of the organism and are not involved in gamete production.

Cycling meiosis and fertilization events produces a series of transitions back and forth between alternating haploid and diploid states. The organism phase of the life cycle can occur either during the diploid state (diplontic life cycle), during the haploid state (haplontic life cycle), or both (haplodiplontic life cycle, in which there are two distinct organism phases, one during the haploid state and the other during the diploid state). In this sense there are three types of life cycles that utilize sexual reproduction, differentiated by the location of the organism phase(s). [ citation needed ]

In the diplontic life cycle (with pre-gametic meiosis), of which humans are a part, the organism is diploid, grown from a diploid cell called the zygote. The organism's diploid germ-line stem cells undergo meiosis to create haploid gametes (the spermatozoa for males and ova for females), which fertilize to form the zygote. The diploid zygote undergoes repeated cellular division by mitosis to grow into the organism.

In the haplontic life cycle (with post-zygotic meiosis), the organism is haploid instead, spawned by the proliferation and differentiation of a single haploid cell called the gamete. Two organisms of opposing sex contribute their haploid gametes to form a diploid zygote. The zygote undergoes meiosis immediately, creating four haploid cells. These cells undergo mitosis to create the organism. Many fungi and many protozoa utilize the haplontic life cycle. [ citation needed ]

Finally, in the haplodiplontic life cycle (with sporic or intermediate meiosis), the living organism alternates between haploid and diploid states. Consequently, this cycle is also known as the alternation of generations. The diploid organism's germ-line cells undergo meiosis to produce spores. The spores proliferate by mitosis, growing into a haploid organism. The haploid organism's gamete then combines with another haploid organism's gamete, creating the zygote. The zygote undergoes repeated mitosis and differentiation to become a diploid organism again. The haplodiplontic life cycle can be considered a fusion of the diplontic and haplontic life cycles. [39] [ citation needed ]

In plants and animals Edit

Meiosis occurs in all animals and plants. The end result, the production of gametes with half the number of chromosomes as the parent cell, is the same, but the detailed process is different. In animals, meiosis produces gametes directly. In land plants and some algae, there is an alternation of generations such that meiosis in the diploid sporophyte generation produces haploid spores. These spores multiply by mitosis, developing into the haploid gametophyte generation, which then gives rise to gametes directly (i.e. without further meiosis). In both animals and plants, the final stage is for the gametes to fuse, restoring the original number of chromosomes. [40]

In mammals Edit

In females, meiosis occurs in cells known as oocytes (singular: oocyte). Each primary oocyte divides twice in meiosis, unequally in each case. The first division produces a daughter cell, and a much smaller polar body which may or may not undergo a second division. In meiosis II, division of the daughter cell produces a second polar body, and a single haploid cell, which enlarges to become an ovum. Therefore, in females each primary oocyte that undergoes meiosis results in one mature ovum and one or two polar bodies.

Note that there are pauses during meiosis in females. Maturing oocytes are arrested in prophase I of meiosis I and lie dormant within a protective shell of somatic cells called the follicle. At the beginning of each menstrual cycle, FSH secretion from the anterior pituitary stimulates a few follicles to mature in a process known as folliculogenesis. During this process, the maturing oocytes resume meiosis and continue until metaphase II of meiosis II, where they are again arrested just before ovulation. If these oocytes are fertilized by sperm, they will resume and complete meiosis. During folliculogenesis in humans, usually one follicle becomes dominant while the others undergo atresia. The process of meiosis in females occurs during oogenesis, and differs from the typical meiosis in that it features a long period of meiotic arrest known as the dictyate stage and lacks the assistance of centrosomes. [41] [42]

In males, meiosis occurs during spermatogenesis in the seminiferous tubules of the testicles. Meiosis during spermatogenesis is specific to a type of cell called spermatocytes, which will later mature to become spermatozoa. Meiosis of primordial germ cells happens at the time of puberty, much later than in females. Tissues of the male testis suppress meiosis by degrading retinoic acid, proposed to be a stimulator of meiosis. This is overcome at puberty when cells within seminiferous tubules called Sertoli cells start making their own retinoic acid. Sensitivity to retinoic acid is also adjusted by proteins called nanos and DAZL. [43] [44] Genetic loss-of-function studies on retinoic acid-generating enzymes have shown that retinoic acid is required postnatally to stimulate spermatogonia differentiation which results several days later in spermatocytes undergoing meiosis, however retinoic acid is not required during the time when meiosis initiates. [45]

In female mammals, meiosis begins immediately after primordial germ cells migrate to the ovary in the embryo. Some studies suggest that retinoic acid derived from the primitive kidney (mesonephros) stimulates meiosis in embryonic ovarian oogonia and that tissues of the embryonic male testis suppress meiosis by degrading retinoic acid. [46] However, genetic loss-of-function studies on retinoic acid-generating enzymes have shown that retinoic acid is not required for initiation of either female meiosis which occurs during embryogenesis [47] or male meiosis which initiates postnatally. [45]

Flagellates Edit

While the majority of eukaryotes have a two-divisional meiosis (though sometimes achiasmatic), a very rare form, one-divisional meiosis, occurs in some flagellates (parabasalids and oxymonads) from the gut of the wood-feeding cockroach Cryptocercus. [48]

Recombination among the 23 pairs of human chromosomes is responsible for redistributing not just the actual chromosomes, but also pieces of each of them. There is also an estimated 1.6-fold more recombination in females relative to males. In addition, average, female recombination is higher at the centromeres and male recombination is higher at the telomeres. On average, 1 million bp (1 Mb) correspond to 1 cMorgan (cm = 1% recombination frequency). [49] The frequency of cross-overs remain uncertain. In yeast, mouse and human, it has been estimated that ≥200 double-strand breaks (DSBs) are formed per meiotic cell. However, only a subset of DSBs (

5–30% depending on the organism), go on to produce crossovers, [50] which would result in only 1-2 cross-overs per human chromosome.

Nondisjunction Edit

The normal separation of chromosomes in meiosis I or sister chromatids in meiosis II is termed disjunction. When the segregation is not normal, it is called nondisjunction. This results in the production of gametes which have either too many or too few of a particular chromosome, and is a common mechanism for trisomy or monosomy. Nondisjunction can occur in the meiosis I or meiosis II, phases of cellular reproduction, or during mitosis.

Most monosomic and trisomic human embryos are not viable, but some aneuploidies can be tolerated, such as trisomy for the smallest chromosome, chromosome 21. Phenotypes of these aneuploidies range from severe developmental disorders to asymptomatic. Medical conditions include but are not limited to:

    – trisomy of chromosome 21 – trisomy of chromosome 13 – trisomy of chromosome 18 – extra X chromosomes in males – i.e. XXY, XXXY, XXXXY, etc. – lacking of one X chromosome in females – i.e. X0 – an extra X chromosome in females – an extra Y chromosome in males.

The probability of nondisjunction in human oocytes increases with increasing maternal age, [51] presumably due to loss of cohesin over time. [52]

In order to understand meiosis, a comparison to mitosis is helpful. The table below shows the differences between meiosis and mitosis. [53]

Meiosis Mitosis
End result Normally four cells, each with half the number of chromosomes as the parent Two cells, having the same number of chromosomes as the parent
Function Production of gametes (sex cells) in sexually reproducing eukaryotes with diplont life cycle Cellular reproduction, growth, repair, asexual reproduction
Where does it happen? Almost all eukaryotes (animals, plants, fungi, and protists) [54] [48]
In gonads, before gametes (in diplontic life cycles)
After zygotes (in haplontic)
Before spores (in haplodiplontic)
All proliferating cells in all eukaryotes
Steps Prophase I, Metaphase I, Anaphase I, Telophase I,
Prophase II, Metaphase II, Anaphase II, Telophase II
Prophase, Prometaphase, Metaphase, Anaphase, Telophase
Genetically same as parent? No Yes
Crossing over happens? Yes, normally occurs between each pair of homologous chromosomes Very rarely
Pairing of homologous chromosomes? Yes No
Cytokinesis Occurs in Telophase I and Telophase II Occurs in Telophase
Centromeres split Does not occur in Anaphase I, but occurs in Anaphase II Occurs in Anaphase

How a cell proceeds to meiotic division in meiotic cell division is not well known. Maturation promoting factor (MPF) seemingly have role in frog Oocyte meiosis. In the fungus S. pombe. there is a role of MeiRNA binding protein for entry to meiotic cell division. [55]

It has been suggested that Yeast CEP1 gene product, that binds centromeric region CDE1, may play a role in chromosome pairing during meiosis-I. [56]

Meiotic recombination is mediated through double stranded break, which is catalyzed by Spo11 protein. Also Mre11, Sae2 and Exo1 play role in breakage and recombination. After the breakage happen, recombination take place which is typically homologous. The recombination may go through either a double Holliday junction (dHJ) pathway or synthesis-dependent strand annealing (SDSA). (The second one gives to noncrossover product). [57]

Seemingly there are checkpoints for meiotic cell division too. In S. pombe, Rad proteins, S. pombe Mek1 (with FHA kinase domain), Cdc25, Cdc2 and unknown factor is thought to form a checkpoint. [58]

In vertebrate oogenesis, maintained by cytostatic factor (CSF) has role in switching into meiosis-II. [56]


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