Application of network methods for understanding evolutionary dynamics in discrete habitats

In populations occupying discrete habitat patches, gene flow between habitat patches may form an intricate population structure. In such structures, the evolutionary dynamics resulting from interaction of gene‐flow patterns with other evolutionary forces may be exceedingly complex. Several models describing gene flow between discrete habitat patches have been presented in the population‐genetics literature; however, these models have usually addressed relatively simple settings of habitable patches and have stopped short of providing general methodologies for addressing nontrivial gene‐flow patterns. In the last decades, network theory – a branch of discrete mathematics concerned with complex interactions between discrete elements – has been applied to address several problems in population genetics by modelling gene flow between habitat patches using networks. Here, we present the idea and concepts of modelling complex gene flows in discrete habitats using networks. Our goal is to raise awareness to existing network theory applications in molecular ecology studies, as well as to outline the current and potential contribution of network methods to the understanding of evolutionary dynamics in discrete habitats. We review the main branches of network theory that have been, or that we believe potentially could be, applied to population genetics and molecular ecology research. We address applications to theoretical modelling and to empirical population‐genetic studies, and we highlight future directions for extending the integration of network science with molecular ecology.     

Evolution of evolvability in a developmental model

Evolvability, the ability of populations to adapt, can evolve through changes in the mechanisms determining genetic variation and in the processes of development. Here we construct and evolve a simple developmental model in which the pleiotropic effects of genes can evolve. We demonstrate that selection in a changing environment favors a specific pattern of variability, and that this favored pattern maximizes evolvability. Our analysis shows that mutant genotypes with higher evolvability are more likely to increase to fixation. We also show that populations of highly evolvable genotypes are much less likely to be invaded by mutants with lower evolvability, and that this dynamic primarily shapes evolvability. We examine several theoretical objections to the evolution of evolvability in light of this result. We also show that this result is robust to the presence or absence of recombination, and explore how nonrandom environmental change can select for a modular pattern of variability.     

Natural selection. V. How to read the fundamental equations of evolutionary change in terms of information theory

The equations of evolutionary change by natural selection are commonly expressed in statistical terms. Fisher's fundamental theorem emphasizes the variance in fitness. Quantitative genetics expresses selection with covariances and regressions. Population genetic equations depend on genetic variances. How can we read those statistical expressions with respect to the meaning of natural selection? One possibility is to relate the statistical expressions to the amount of information that populations accumulate by selection. However, the connection between selection and information theory has never been compelling. Here, I show the correct relations between statistical expressions for selection and information theory expressions for selection. Those relations link selection to the fundamental concepts of entropy and information in the theories of physics, statistics and communication. We can now read the equations of selection in terms of their natural meaning. Selection causes populations to accumulate information about the environment.     

Gene flow的溯源及其在生物安全和进化研究中的意义

尽管gene flow源于群体遗传学和进化生物学,但已成为环境生物安全文献中常见的科学术语。花粉介导的gene flow在自然界中广泛存在并对物种和群体的进化有着特殊重要的意义。随着转基因生物技术的快速发展和转基因作物在全球范围内的广泛种植,转基因随gene flow发生逃逸及其可能带来的潜在生态进化影响已经成为环境生物安全评价和研究的重要内容,备受全球广泛关注,gene flow这个术语在我国也被频繁引用。但是, gene flow的中文术语在我国各种文献资料中存在着十多种翻译版本,这些不同的翻译版本形式不同且内容略有差异,容易给环境生物安全问题的理解和研究造成不必要的混乱。本文对gene flow的概念及其内涵进行了回顾,并对不同形式的gene flow术语在国内外相关研究领域中使用的历史溯源进行了阐述。笔者建议使用“基因流”作为gene flow在中文应用中的统一术语,这也最接近群体遗传学和进化生物学等相关著作中gene flow的原意。基于此,对基因流在转基因逃逸及其相关的环境生物安全评价以及群体遗传学和进化生物学研究方面的理论和应用意义进行了讨论。     

Emergent buffering balances evolvability and robustness in the evolution of phenotypic flexibility

Evolution of adaptive phenotypic flexibility requires a system that can dynamically restore and update a functional phenotype in response to environmental change. The architecture of such a system evolves under the conflicting demands of versatility and robustness, and resolution of these demands should be particularly evident in organisms that require external inputs for reiterative trait production within a generation, such as in metabolic networks that underlie yearly acquisition of diet‐dependent coloration in birds. Here, we show that a key structural feature of carotenoid networks–redundancy of biochemical pathways–enables these networks to translate variable environmental inputs into consistent phenotypic outcomes. We closely followed life‐long changes in structure and utilization of metabolic networks in a large cohort of free‐living birds and found that greater individual experience with dietary change between molts leads to wider occupancy of the metabolic network and progressive accumulation of redundant pathways in a functionally active network. This generated a regime of emergent buffering whereby greater dietary experience was mechanistically linked to greater robustness of resulting traits and an increasing ability to retain and implement previous adaptive solutions. Thus, experience‐related buffering links evolvability and robustness in carotenoid‐metabolizing networks and we argue that this mechanistic principle facilitates the evolution of phenotypic flexibility.     

Modelling population dynamics in a unicellular social organism community using a minimal model and evolutionary game theory

Most unicellular organisms live in communities and express different phenotypes. Many efforts have been made to study the population dynamics of such complex communities of cells, coexisting as well-coordinated units. Minimal models based on ordinary differential equations are powerful tools that can help us understand complex phenomena. They represent an appropriate compromise between complexity and tractability; they allow a profound and comprehensive analysis, which is still easy to understand. Evolutionary game theory is another powerful tool that can help us understand the costs and benefits of the decision a particular cell of a unicellular social organism takes when faced with the challenges of the biotic and abiotic environment. This work is a binocular view at the population dynamics of such a community through the objectives of minimal modelling and evolutionary game theory. We test the behaviour of the community of a unicellular social organism at three levels of antibiotic stress. Even in the absence of the antibiotic, spikes in the fraction of resistant cells can be observed indicating the importance of bet hedging. At moderate level of antibiotic stress, we witness cyclic dynamics reminiscent of the renowned rock–paper–scissors game. At a very high level, the resistant type of strategy is the most favourable.     

Population dynamics and evolutionary processes: the manifold roles of habitat selection

Summary Any character that has a substantial effect on a species' distribution and abundance can exert a variety of indirect effects on evolutionary processes. It is suggested that an organism's capacity for habitat selection is just such a character. Habitat selection can constrain the selective environment experienced by a population. Habitat selection can also indirectly influence the relative importance of natural selection, drift, and gene flow, through its effect on population size and growth rate. In many circumstances (but not all), habitat selection increases population size and growth rate, and thereby makes selection in a local environment more effective than drift and gene flow.     

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 the B-system of flower development

Background

Gene duplication has often been invoked as a key mechanism responsible for evolution of new morphologies. The floral homeotic B-group gene family has undergone a number of gene duplication events, and yet the functions of these genes appear to be largely conserved. However, detailed comparative analysis has indicated that such duplicate genes have considerable cryptic variability in their functions. In the Solanaceae, two duplicate B-group gene lineages have been retained in three subfamilies. Comparisons of orthologous genes across members of the Solanaceae have demonstrated that the combined function of all four B-gene members is to establish petal and stamen identity, but that this function was partitioned differently in each species. These observations emphasize both the robustness and the evolvability of the B-system.

Scope

We provide an overview of how the B-function genes can robustly specify petal and stamen identity and at the same time evolve through changes in protein–protein interaction, gene expression patterns, copy number variation or alterations in the downstream genes they control. By using mathematical models we explore regulatory differences between species and how these impose constraints on downstream gene regulation.

Conclusions

Evolvability of the B-genes can be understood through the multiple ways in which the B-system can be robust. Quantitative approaches should allow for the incorporation of more biological realism in the representations of these regulatory systems and this should contribute to understanding the constraints under which different B-systems can function and evolve. This, in turn, can provide a better understanding of the ways in which B-genes have contributed to flower diversity.     

The evolvability of herkogamy: Quantifying the evolutionary potential of a composite trait

Accurate estimates of trait evolvabilities are central to predicting the short‐term evolutionary potential of populations, and hence their ability to adapt to changing environments. We quantify and evaluate the evolvability of herkogamy, the spatial separation of male and female structures in flowers, a key floral trait associated with variation in mating systems. We compiled genetic‐variance estimates for herkogamy and related floral traits, computed evolvabilities, and compared these among trait groups and among species differing in their mating systems. When measured in percentage of its own size, the median evolvability of herkogamy was an order of magnitude greater than the evolvability of other floral size measurements, and was generally not strongly constrained by genetic covariance between its components (pistil and stamen lengths). Median evolvabilities were similar across mating systems, with only a tendency toward reduction in highly selfing taxa. We conclude that herkogamy has the potential to evolve rapidly in response to changing environments. This suggests that the extensive variation in herkogamy commonly observed among closely related populations and species may result from rapid adaptive tracking of fitness optima determined by variation in pollinator communities or other selective factors.     

The influence of fluctuating population densities on evolutionary dynamics

The causes and consequences of fluctuating population densities are an important topic in ecological literature. Yet, the effects of such fluctuations on maintenance of variation in spatially structured populations have received little analytic treatment. We analyze what happens when two habitats coupled by migration not only differ in their trade‐offs in selection but also in their demographic stability—and show that equilibrium allele frequencies can change significantly due to ecological feedback arising from locally fluctuating population sizes. When an ecological niche exhibits such fluctuations, these drive an asymmetry in the relative impact of gene flow, and therefore, the equilibrium frequency of the locally adapted type decreases. Our results extend the classic conditions on maintenance of diversity under selection and migration by including the effect of fluctuating population densities. We find simple analytic conditions in terms of the strength of selection, immigration, and the extent of fluctuations between generations in a continent‐island model. Although weak fluctuations hardly affect coexistence, strong recurrent fluctuations lead to extinction of the type better adapted to the fluctuating niche—even if the invader is locally maladapted. There is a disadvantage to specialization to an unstable habitat, as it makes the population vulnerable to swamping from more stable habitats.     

The evolutionary origins of modularity

A central biological question is how natural organisms are so evolvable (capable of quickly adapting to new environments). A key driver of evolvability is the widespread modularity of biological networks—their organization as functional, sparsely connected subunits—but there is no consensus regarding why modularity itself evolved. Although most hypotheses assume indirect selection for evolvability, here we demonstrate that the ubiquitous, direct selection pressure to reduce the cost of connections between network nodes causes the emergence of modular networks. Computational evolution experiments with selection pressures to maximize network performance and minimize connection costs yield networks that are significantly more modular and more evolvable than control experiments that only select for performance. These results will catalyse research in numerous disciplines, such as neuroscience and genetics, and enhance our ability to harness evolution for engineering purposes.     

Simple evolutionary pathways to complex proteins.

A recent paper in this journal has challenged the idea that complex adaptive features of proteins can be explained by known molecular, genetic, and evolutionary mechanisms. It is shown here that the conclusions of this prior work are an artifact of unwarranted biological assumptions, inappropriate mathematical modeling, and faulty logic. Numerous simple pathways exist by which adaptive multi-residue functions can evolve on time scales of a million years (or much less) in populations of only moderate size. Thus, the classical evolutionary trajectory of descent with modification is adequate to explain the diversification of protein functions.     

The role of habitat choice in micro‐evolutionary dynamics: An experimental study on the Mediterranean killifish Aphanius fasciatus (Cyprinodontidae)

Habitat choice is defined as a nonrandom distribution of genotypes in different microhabitats. Therefore, it could exert a great impact on the genetic variance of natural populations by promoting genetic divergence, local adaptation, and may even lead to sympatric speciation. Despite this potential role in micro‐ and macro‐evolutionary processes, there is little empirical evidence that the various genotypes within a population may differ in habitat choice‐related behaviors. Here, we tested whether habitat choice may have contributed to genetic divergence within a local population of the Mediterranean killifish Aphanius fasciatus, which emerged between groups inhabiting microhabitats with different oxygen concentrations during previous field studies. In a first experiment, we studied the distribution of individuals in conditions of hypoxia and normoxia to test whether they had a different ability to shy away from a hypoxic environment; in a second experiment, we analyzed the individual behavior of fish separately in the two conditions, to verify whether they showed peculiar behavioral responses linked to a possible differential distribution. We then analyzed the six allozyme loci, whose allelic and genotypic frequencies were significantly divergent in the previous studies. In the first test, we found that the distribution of the two homozygote genotypes of the glucose‐6‐phosphate isomerase‐1 locus (GPI‐1) was significantly different between the hypoxic and the normoxic conditions. During the second test, all individuals were more active in hypoxic conditions, but the two GPI‐1 homozygotes showed a significant difference in time spent performing surface breathing, which was consistent with their distribution observed in the first experiment. These results provide evidence that individual behavioral traits, related to genetic features, may lead to a nonrandom distribution of genotypes in heterogeneous although contiguous microhabitats and, consequently, that habitat choice can play a significant role in driving the micro‐evolutionary dynamics of this species.     

Eco‐evolutionary dynamics in restored communities and ecosystems

Recent ecological studies have revealed that rapid evolution within populations can have significant impacts on the ecological dynamics of communities and ecosystems. These eco‐evolutionary dynamics (EED) are likely to have substantial and quantifiable effects in restored habitats over timescales that are relevant for the conservation and restoration of small populations and threatened communities. Restored habitats may serve as “hotspots” for EED due to mismatches between transplanted genotypes and the restored environment, and novel interactions among lineages that do not share a coevolutionary history, both of which can generate strong selection for rapid evolutionary change that has immediate demographic consequences. Rapid evolution that influences population dynamics and community processes is likely to have particularly large effects during the establishment phase of restoration efforts. Finally, restoration activities and their associated long‐term monitoring programs provide outstanding opportunities for using eco‐evolutionary experimental approaches. Results from such studies will address questions about the effects of rapid evolutionary change on the ecological dynamics of populations and interacting species, while simultaneously providing critical, but currently overlooked, information for conservation practices.     

Moderate heritability and low evolvability of sperm morphology in a species with high risk of sperm competition,the collared flycatcher Ficedula albicollis

Spermatozoa represent the morphologically most diverse type of animal cells and show remarkable variation in size across and also within species. To understand the evolution of this diversity, it is important to reveal to what degree this variation is genetic or environmental in origin and whether this depends on species’ life histories. Here we applied quantitative genetic methods to a pedigreed multigenerational data set of the collared flycatcher Ficedula albicollis, a passerine bird with high levels of extra‐pair paternity, to partition genetic and environmental sources of phenotypic variation in sperm dimensions for the first time in a natural population. Narrow‐sense heritability (h²) of total sperm length amounted to 0.44 ± 0.14 SE, whereas the corresponding figure for evolvability (estimated as coefficient of additive genetic variation, CV_a) was 0.02 ± 0.003 SE. We also found an increase in total sperm length within individual males between the arrival and nestling period. This seasonal variation may reflect constraints in the production of fully elongated spermatozoa shortly after arrival at the breeding grounds. There was no evidence of an effect of male age on sperm dimensions. In many previous studies on laboratory populations of several insect, mammal and avian species, heritabilities of sperm morphology were higher, whereas evolvabilities were similar. Explanations for the differences in heritability may include variation in the environment (laboratory vs. wild), intensity of sexual selection via sperm competition (high vs. low) and genetic architecture that involves unusual linkage disequilibrium coupled with overdominance in one of the studied species.     

Model with asymptotically stable dynamics for Drosophila gap gene network

We consider a model of gap gene expression during the early development of Drosophila embryo. Parameter values in the model have been obtained by fitting to experimental patterns under an additional condition that the solution be asymptotically stable at large times. The patterns at the beginning of gastrulation in such solutions are very close to an actual attractor in the model. It is shown that such solutions are more robust to perturbations of concentrations and parameter values in the model.     

The evolution of stress-induced hypermutation in asexual populations

Numerous empirical studies show that stress of various kinds induces a state of hypermutation in bacteria via multiple mechanisms, but theoretical treatment of this intriguing phenomenon is lacking. We used deterministic and stochastic models to study the evolution of stress-induced hypermutation in infinite and finite-size populations of bacteria undergoing selection, mutation, and random genetic drift in constant environments and in changing ones. Our results suggest that if beneficial mutations occur, even rarely, then stress-induced hypermutation is advantageous for bacteria at both the individual and the population levels and that it is likely to evolve in populations of bacteria in a wide range of conditions because it is favored by selection. These results imply that mutations are not, as the current view holds, uniformly distributed in populations, but rather that mutations are more common in stressed individuals and populations. Because mutation is the raw material of evolution, these results have a profound impact on broad aspects of evolution and biology.     

How many and when? Optimising targeted gene flow for a step change in the environment

Targeted gene flow is an emerging conservation strategy that involves introducing individuals with particular traits to places where these traits are of benefit. One obvious application is to adapt a recipient population to a known threat, but questions remain as to how best to achieve this. Here, we vary timing and size of the introduction to maximise our objective – survival of the recipient population's genome. We explore a generic population model as well as a specific example – the northern quoll, an Australian marsupial predator threatened by the toxic cane toad. We reveal a trade‐off between preserving the recipient genome and reducing population extinction risk, but key management levers can often optimise this so that nearly 100% of the recipient population's genome is preserved. Any action was better than none but the size of the benefit was sensitive to outbreeding depression, recombination rate, and the timing and size of the introduction.