Evolvability and genetic constraint in Dalechampia blossoms: components of variance and measures of evolvability

Many evolutionary arguments are based on the assumption that quantitative characters are highly evolvable entities that can be rapidly moulded by changing selection pressures. The empirical evaluation of this assumption depends on having an operational measure of evolvability that reflects the ability of a trait to respond to a given external selection pressure. We suggest short-term evolvability be measured as expected proportional response in a trait to a unit strength of directional selection, where strength of selection is defined independently of character variation and in units of the strength of selection on fitness itself. We show that the additive genetic variance scaled by the square of the trait mean, IA, is such a measure. The heritability, h2, does not measure evolvability in this sense. Based on a diallel analysis, we use IA to assess the evolvability of floral characters in a population of the neotropical vine Dalechampia scandens (Euphorbiaceae). Although we are able to demonstrate that there is additive genetic variation in a number of floral traits, we also find that most of the traits are not expected to change by more than a fraction of a percent per generation. We provide evidence that the degree of among-population divergence of traits is related to their predicted evolvabilities, but not to their heritabilities.     

Genetic constraints predict evolutionary divergence in Dalechampia blossoms

If genetic constraints are important, then rates and direction of evolution should be related to trait evolvability. Here we use recently developed measures of evolvability to test the genetic constraint hypothesis with quantitative genetic data on floral morphology from the Neotropical vine Dalechampia scandens (Euphorbiaceae). These measures were compared against rates of evolution and patterns of divergence among 24 populations in two species in the D. scandens species complex. We found clear evidence for genetic constraints, particularly among traits that were tightly phenotypically integrated. This relationship between evolvability and evolutionary divergence is puzzling, because the estimated evolvabilities seem too large to constitute real constraints. We suggest that this paradox can be explained by a combination of weak stabilizing selection around moving adaptive optima and small realized evolvabilities relative to the observed additive genetic variance.     

Pollinators and seed predators generate conflicting selection on Dalechampia blossoms

Plant–pollinator relationships are often mediated by floral traits that advertise the presence or amount of rewards. However, herbivores may also use these traits to find their hosts. In Dalechampia scandens, we tested whether floral advertisements that attract pollinators were also used by seed predators, and whether this generated conflicting selection pressures. We studied the influence of natural variation in the size of showy bracts, amount of reward, and two shape traits on pollinator visitation, pollen arrival on stigmas, seed production and seed predation. We then built a multivariate fitness function for these traits to estimate selection generated by pollinators and seed predators. Blossoms with larger bracts were visited by bees more frequently and received more pollen on their stigmas. Seed predators laid more eggs on blossoms with larger bracts and also on blossoms later producing more seeds. Consequently, selection for larger bract size exerted by pollinators was counteracted by the selection exerted by seed predators. As a result, net selection on bract size tended to be stabilizing. Additionally, we found selection on traits that increased the rate of self‐pollination (assuming uniform seed quality). These results illustrate the importance of both mutualists and antagonists in floral evolution, as well as the value of taking an integrative approach to assessing selection on floral traits.     

Measuring and comparing evolvability and constraint in multivariate characters

The Lande equation forms the basis for our understanding of the short-term evolution of quantitative traits in a multivariate context. It predicts the response to selection as the product of an additive genetic variance matrix and a selection gradient. The selection gradient approximates the force and direction of selection, and the genetic variance matrix quantifies the role of the genetic system in evolution. Attempts to understand the evolutionary significance of the genetic variance matrix are hampered by the fact that the majority of the methods used to characterize and compare variance matrices have not been derived in an explicit theoretical context. We use the Lande equation to derive new measures of the ability of a variance matrix to allow or constrain evolution in any direction in phenotype space. Evolvability captures the ability of a population to evolve in the direction of selection when stabilizing selection is absent. Conditional evolvability captures the ability of a population to respond to directional selection in the presence of stabilizing selection on other trait combinations. We then derive measures of character autonomy and integration from these evolvabilities. We study the properties of these measures and show how they can be used to interpret and compare variance matrices. As an illustration, we show that divergence of wing shape in the dipteran family Drosophilidae has proceeded in directions that have relatively high evolvabilities.     

Robustness and evolvability in genetic regulatory networks

Living organisms are robust to a great variety of genetic changes. Gene regulation networks and metabolic pathways self-organize and reaccommodate to make the organism perform with stability and reliability under many point mutations, gene duplications and gene deletions. At the same time, living organisms are evolvable, which means that these kind of genetic perturbations can eventually make the organism acquire new functions and adapt to new environments. It is still an open problem to determine how robustness and evolvability blend together at the genetic level to produce stable organisms that yet can change and evolve. Here we address this problem by studying the robustness and evolvability of the attractor landscape of genetic regulatory network models under the process of gene duplication followed by divergence. We show that an intrinsic property of this kind of networks is that, after the divergence of the parent and duplicate genes, with a high probability the previous phenotypes, encoded in the attractor landscape of the network, are preserved and new ones might appear. The above is true in a variety of network topologies and even for the case of extreme divergence in which the duplicate gene bears almost no relation with its parent. Our results indicate that networks operating close to the so-called "critical regime" exhibit the maximum robustness and evolvability simultaneously.     

Variational and genetic properties of developmental stability in Dalechampia scandens

Because low developmental stability may compromise the precision with which adaptations can be reached, the variability and genetic basis of developmental stability are important evolutionary parameters. Developmental stability is also an important clue to understanding how traits are regulated to achieve their phenotypic target value. However, developmental stability must be studied indirectly through proxy variables, such as fluctuating asymmetry, that are suggested to have noisy and often nonlinear relationships to the underlying variable of interest. In this paper we first show that mean-standardized measures of variance and covariance in fluctuating asymmetry, unlike heritabilities, repeatabilities, and correlations, are linearly related to corresponding measures of variation in underlying developmental stability. We then examine the variational properties of developmental stability in a population of the Neotropical vine, Dalechampia scandens (Euphorbiaceae). By studying fluctuating asymmetry in a large number of floral characters in both selfed and outcrossed individuals in a diallel design, we assemble strong evidence that both additive genetic and individual variation and covariation in developmental stability are virtually absent in this population.     

The evolution of evolvability in genetic linkage patterns

A number of factors have been proposed that may affect the capacity for an evolutionary system to generate adaptation. One that has received little recent attention among biologists is linkage patterns, or the ordering of genes on chromosomes. In this study, a simple model of genetic interactions, implemented in an evolutionary simulation, demonstrates that clustering of epistatically interacting genes increases the rate of adaptation. Moreover, long-term evolution with inversion can reorganize linkage patterns from random gene ordering into this more modular organization, thereby facilitating adaptation. These results are consistent with a large body of biological observations and some mathematical theory. Although linkage patterns are neutral with respect to individual fitness in this model, they are subject to lineage level selection for evolvability. At least two candidate mechanisms may contribute to improved evolvability under epistatic clustering: clustering may reduce interference between selection on different traits, and it may allow the simultaneous optimization of different recombination rates for gene pairs with additive and epistatic fitness effects.     

Modelling biological evolvability: implicit context and variation filtering in enzyme genetic programming

This paper describes recent insights into the role of implicit context within the representations of evolving artefacts and specifically within the program representation used by enzyme genetic programming. Implicit context occurs within self-organising systems where a component's connectivity is both determined implicitly by its own definition and is specified in terms of the behavioural context of other components. This paper argues that implicit context is an important source of evolvability and presents experimental evidence that supports this assertion. In particular, it introduces the notion of variation filtering, suggesting that the use of implicit context within representations leads to meaningful variation filtering whereby inappropriate change is ignored and meaningful change is encouraged during evolution.     

The effect of genetic robustness on evolvability in digital organisms

Background  

Recent work has revealed that many biological systems keep functioning in the face of mutations and therefore can be considered genetically robust. However, several issues related to robustness remain poorly understood, such as its implications for evolvability (the ability to produce adaptive evolutionary innovations).     

Perspective: Sign epistasis and genetic constraint on evolutionary trajectories

Epistasis for fitness means that the selective effect of a mutation is conditional on the genetic background in which it appears. Although epistasis is widely observed in nature, our understanding of its consequences for evolution by natural selection remains incomplete. In particular, much attention focuses only on its influence on the instantaneous rate of changes in frequency of selected alleles via epistatic contribution to the additive genetic variance for fitness. Thus, in this framework epistasis only has evolutionary importance if the interacting loci are simultaneously segregating in the population. However, the selective accessibility of mutational trajectories to high fitness genotypes may depend on the genetic background in which novel mutations appear, and this effect is independent of population polymorphism at other loci. Here we explore this second influence of epistasis on evolution by natural selection. We show that it is the consequence of a particular form of epistasis, which we designate sign epistasis. Sign epistasis means that the sign of the fitness effect of a mutation is under epistatic control; thus, such a mutation is beneficial on some genetic backgrounds and deleterious on others. Recent experimental innovations in microbial systems now permit assessment of the fitness effects of individual mutations on multiple genetic backgrounds. We review this literature and identify many examples of sign epistasis, and we suggest that the implications of these results may generalize to other organisms. These theoretical and empirical considerations imply that strong genetic constraint on the selective accessibility of trajectories to high fitness genotypes may exist and suggest specific areas of investigation for future research.     

Estimating genetic correlations in natural populations

Information on the genetic correlation between traits provides fundamental insight into the constraints on the evolutionary process. Estimates of such correlations are conventionally obtained by raising individuals of known relatedness in artificial environments. However, many species are not readily amenable to controlled breeding programmes, and considerable uncertainty exists over the extent to which estimates derived under benign laboratory conditions reflect the properties of populations in natural settings. Here, non-invasive methods that allow the estimation of genetic correlations from phenotypic measurements derived from individuals of unknown relatedness are introduced. Like the conventional approach, these methods demand large sample sizes in order to yield reasonably precise estimates, and special precautions need to be taken to eliminate bias from shared environmental effects. Provided the sample consists of at least 20% or so relatives, informative estimates of the genetic correlation are obtainable with sample sizes of several hundred individuals, particularly if supplemental information on relatedness is available from polymorphic molecular markers.     

Estimation of heritability, evolvability and genetic correlations of two pollen and pistil traits involved in a sexual conflict over timing of stigma receptivity in Collinsia heterophylla (Plantaginaceae)

Background and Aims

Heritable genetic variation is crucial for selection to operate, yet there is a paucity of studies quantifying such variation in interactive male/female sexual traits, especially those of plants. Previous work on the annual plant Collinsia heterophylla, a mixed-mating species, suggests that delayed stigma receptivity is involved in a sexual conflict: pollen from certain donors fertilize ovules earlier than others at the expense of reduced maternal seed set and lower levels of pollen competition.

Methods

Parent–offspring regressions and sib analyses were performed to test for heritable genetic variation and co-variation in male and female interactive traits related to the sexual conflict.

Key Results

Some heritable variation and evolvability were found for the female trait (delayed stigma receptivity in presence of pollen), but no evidence was found for genetic variation in the male trait (ability to fertilize ovules early). The results further indicated a marginally significant correlation between a male''s ability to fertilize early and early stigma receptivity in offspring. However, despite potential indirect selection of these traits, antagonistic co-evolution may not occur given the lack of heritability of the male trait.

Conclusions

To our knowledge, this is the first study of a plant or any hermaphrodite that examines patterns of genetic correlation between two interactive sexual traits, and also the first to assess heritabilities of plant traits putatively involved in a sexual conflict. It is concluded that the ability to delay fertilization in presence of pollen can respond to selection, while the pollen trait has lower evolutionary potential.     

On the sampling variance of intraclass correlations and genetic correlations.

Widely used standard expressions for the sampling variance of intraclass correlations and genetic correlation coefficients were reviewed for small and large sample sizes. For the sampling variance of the intraclass correlation, it was shown by simulation that the commonly used expression, derived using a first-order Taylor series performs better than alternative expressions found in the literature, when the between-sire degrees of freedom were small. The expressions for the sampling variance of the genetic correlation are significantly biased for small sample sizes, in particular when the population values, or their estimates, are close to zero. It was shown, both analytically and by simulation, that this is because the estimate of the sampling variance becomes very large in these cases due to very small values of the denominator of the expressions. It was concluded, therefore, that for small samples, estimates of the heritabilities and genetic correlations should not be used in the expressions for the sampling variance of the genetic correlation. It was shown analytically that in cases where the population values of the heritabilities are known, using the estimated heritabilities rather than their true values to estimate the genetic correlation results in a lower sampling variance for the genetic correlation. Therefore, for large samples, estimates of heritabilities, and not their true values, should be used.     

The effect of scale-free topology on the robustness and evolvability of genetic regulatory networks

We investigate how scale-free (SF) and Erd?s-Rényi (ER) topologies affect the interplay between evolvability and robustness of model gene regulatory networks with Boolean threshold dynamics. In agreement with Oikonomou and Cluzel (2006) we find that networks with SF_in topologies, that is SF topology for incoming nodes and ER topology for outgoing nodes, are significantly more evolvable towards specific oscillatory targets than networks with ER topology for both incoming and outgoing nodes. Similar results are found for networks with SF_both and SF_out topologies. The functionality of the SF_out topology, which most closely resembles the structure of biological gene networks (Babu et al., 2004), is compared to the ER topology in further detail through an extension to multiple target outputs, with either an oscillatory or a non-oscillatory nature. For multiple oscillatory targets of the same length, the differences between SF_out and ER networks are enhanced, but for non-oscillatory targets both types of networks show fairly similar evolvability. We find that SF networks generate oscillations much more easily than ER networks do, and this may explain why SF networks are more evolvable than ER networks are for oscillatory phenotypes. In spite of their greater evolvability, we find that networks with SF_out topologies are also more robust to mutations (mutational robustness) than ER networks. Furthermore, the SF_out topologies are more robust to changes in initial conditions (environmental robustness). For both topologies, we find that once a population of networks has reached the target state, further neutral evolution can lead to an increase in both the mutational robustness and the environmental robustness to changes in initial conditions.     

Experimental evolution: experimental evolution and evolvability

The suggestion that there are characteristics of living organisms that have evolved because they increase the rate of evolution is controversial and difficult to study. In this review, we examine the role that experimental evolution might play in resolving this issue. We focus on three areas in which experimental evolution has been used previously to examine questions of evolvability; the evolution of mutational supply, the evolution of genetic exchange and the evolution of genetic architecture. In each case, we summarize what studies of experimental evolution have told us so far and speculate on where progress might be made in the future. We show that, while experimental evolution has helped us to begin to understand the evolutionary dynamics of traits that affect evolvability, many interesting questions remain to be answered.     

Revisiting Robustness and Evolvability: Evolution in Weighted Genotype Spaces

Robustness and evolvability are highly intertwined properties of biological systems. The relationship between these properties determines how biological systems are able to withstand mutations and show variation in response to them. Computational studies have explored the relationship between these two properties using neutral networks of RNA sequences (genotype) and their secondary structures (phenotype) as a model system. However, these studies have assumed every mutation to a sequence to be equally likely; the differences in the likelihood of the occurrence of various mutations, and the consequence of probabilistic nature of the mutations in such a system have previously been ignored. Associating probabilities to mutations essentially results in the weighting of genotype space. We here perform a comparative analysis of weighted and unweighted neutral networks of RNA sequences, and subsequently explore the relationship between robustness and evolvability. We show that assuming an equal likelihood for all mutations (as in an unweighted network), underestimates robustness and overestimates evolvability of a system. In spite of discarding this assumption, we observe that a negative correlation between sequence (genotype) robustness and sequence evolvability persists, and also that structure (phenotype) robustness promotes structure evolvability, as observed in earlier studies using unweighted networks. We also study the effects of base composition bias on robustness and evolvability. Particularly, we explore the association between robustness and evolvability in a sequence space that is AU-rich – sequences with an AU content of 80% or higher, compared to a normal (unbiased) sequence space. We find that evolvability of both sequences and structures in an AU-rich space is lesser compared to the normal space, and robustness higher. We also observe that AU-rich populations evolving on neutral networks of phenotypes, can access less phenotypic variation compared to normal populations evolving on neutral networks.