Patch biogeography under intermittent barriers: macroevolutionary consequences of microevolutionary processes.

The processes that generate biodiversity start on a microevolutionary scale, where each individual's history can impact the species' history. This manuscript presents a theoretical study that examines the macroevolutionary patterns that emerge from the microevolutionary dynamics of populations inhabiting two patches. The model is neutral, meaning that neither survival nor reproduction depends on a fixed genotype, yet individuals must have minimal genetic similarity to reproduce. We used historical sea level oscillation over the past 800 thousand years to hypothesize periods when individuals could migrate from one patch to another. In our study, we keep track of each speciation and extinction event, build the complete and extant phylogenies, and characterize the macroevolutionary patterns regarding phylogeny balance, acceleration of speciation, and crown age. We also evaluate ecological patterns: richness, beta diversity, and species distribution symmetry. The balance of the complete phylogeny can be a sign of the speciation mode, contrasting speciation induced by migration and isolation (vicariance). The acceleration of the speciation process is also affected by the geographical barriers and the duration of the isolation period, with high isolation times leading to accelerated speciation. We report the correlation between ecological and macroevolutionary patterns and show it decreases with the time spent in isolation. We discuss, in light of our results, the challenge of integrating present-time community ecology with macroevolutionary patterns.

The role of epistasis in evolutionary rescue.

The process by which adaptive evolution preserves a population threatened with extinction due to environmental changes is known as evolutionary rescue. Several factors determine the fate of those populations, including demography and genetic factors, such as standing genetic variation, gene flow, availability of de novo mutations, and so on. Despite the extensive debate about evolutionary rescue in the current literature, a study about the role of epistasis and the topography of the fitness landscape on the fate of dwindling populations is missing. In the current work, we aim to fill this gap and study the influence of epistasis on the probability of extinction of populations. We present simulation results, and analytical approximations are derived. Counterintuitively, we show that the likelihood of extinction is smaller when the degree of epistasis is higher. The reason underneath is twofold: first, higher epistasis can promote mutations of more significant phenotypic effects, but also, the incongruence between the maps genotype-phenotype and phenotype-fitness turns the fitness landscape at low epistasis more rugged, thus curbing some of its advantages.

Error catastrophe in populations under similarity-essential recombination.

Organisms are often more likely to exchange genetic information with others that are similar to themselves. One of the most widely accepted mechanisms of RNA virus recombination requires substantial sequence similarity between the parental RNAs and is termed similarity-essential recombination. This mechanism may be considered analogous to assortative mating, an important form of non-random mating that can be found in animals and plants. Here we study the dynamics of haplotype frequencies in populations evolving under similarity-essential recombination. Haplotypes are represented by a genome of B biallelic loci and the Hamming distance between individuals is used as a criterion for recombination. We derive the evolution equations for the haplotype frequencies assuming that recombination does not occur if the genetic distance is larger than a critical value G and that mutation occurs at a rate µ per locus. Additionally, uniform crossover is considered. Although no fitness is directly associated to the haplotypes, we show that frequency-dependent selection emerges dynamically and governs the haplotype distribution. A critical mutation rate µc can be identified as the error threshold transition, beyond which this selective information cannot be stored. For µ<µc the distribution consists of a dominant sequence surrounded by a cloud of closely related sequences, characterizing a quasispecies. For µ>µc the distribution becomes uniform, with all haplotypes having the same frequency. In the case of extreme assortativeness, where individuals only recombine with others identical to themselves (G=0), the error threshold results µc=1/4, independently of the genome size. For weak assortativity (G=B-1)µc=2(-(B+1)) and for the case of no assortativity (G=B) µc=0. We compute the mutation threshold for 0

Understanding evolutionary rescue and parallelism in response to environmental stress.

Evolutionary rescue, the process by which populations facing environmental stress avoid extinction through genetic adaptation, is a critical area of study in evolutionary biology. The order in which mutations arise and get established will be relevant to the population's rescue. This study investigates the degree of parallel evolution at the genotypic level between independent populations facing environmental stress and subject to different demographic regimes. Under density regulation, 2 regimes exist: In the first, the population can restore positive growth rates by adjusting its population size or through adaptive mutations, whereas in the second regime, the population is doomed to extinction unless a rescue mutation occurs. Analytical approximations for the likelihood of evolutionary rescue are obtained and contrasted with simulation results. We show that the initial level of maladaptation and the demographic regime significantly affect the level of parallelism. There is an evident transition between these 2 regimes. Whereas in the first regime, parallelism decreases with the level of maladaptation, it displays the opposite behavior in the rescue/extinction regime. These findings have important implications for understanding population persistence and the degree of parallelism in evolutionary responses as they integrate demographic effects and evolutionary processes.

Evolution of clonal populations approaching a fitness peak.

Populations facing novel environments are expected to evolve through the accumulation of adaptive substitutions. The dynamics of adaptation depend on the fitness landscape and possibly on the genetic background on which new mutations arise. Here, we model the dynamics of adaptive evolution at the phenotypic and genotypic levels, focusing on a Fisherian landscape characterized by a single peak. We find that Fisher's geometrical model of adaptation, extended to allow for small random environmental variations, is able to explain several features made recently in experimentally evolved populations. Consistent with data on populations evolving under controlled conditions, the model predicts that mean population fitness increases rapidly when populations face novel environments and then achieves a dynamic plateau, the rate of molecular evolution is remarkably constant over long periods of evolution, mutators are expected to invade and patterns of epistasis vary along the adaptive walk. Negative epistasis is expected in the initial steps of adaptation but not at later steps, a prediction that remains to be tested. Furthermore, populations are expected to exhibit high levels of phenotypic diversity at all times during their evolution. This implies that populations are possibly able to adapt rapidly to novel abiotic environments.

Evolutionary rescue on genotypic fitness landscapes.

Populations facing adverse environments, novel pathogens or invasive competitors may be destined to extinction if they are unable to adapt rapidly. Quantitative predictions of the probability of survival through adaptation, evolutionary rescue, have been previously developed for one of the most natural and well-studied mappings from an organism's traits to its fitness, Fisher's geometric model (FGM). While FGM assumes that all possible trait values are accessible via mutation, in many applications only a finite set of rescue mutations will be available, such as mutations conferring resistance to a parasite, predator or toxin. We predict the probability of evolutionary rescue, via de novo mutation, when this underlying genetic structure is included. We find that rescue probability is always reduced when its genetic basis is taken into account. Unlike other known features of the genotypic FGM, however, the probability of rescue increases monotonically with the number of available mutations and approaches the behaviour of the classical FGM as the number of available mutations approaches infinity.

Phenotypic evolution as an Ornstein-Uhlenbeck process: The effect of environmental variation and phenotypic plasticity.

Here we investigate phenotypic evolution from the perspective of the Ornstein-Uhlenbeck (OU) process. Evolutionarily speaking, the model assumes the existence of stabilizing selection toward a phenotypic optimum. The standard (OU) model is modified to include environmental variation by taking a moving phenotypic optimum and endowing organisms with phenotypic plasticity. These two processes lead to an effective fitness landscape, which deforms the original. We observe that the simultaneous occurrence of environmental variation and phenotypic plasticity leads to skewed phenotypic distributions. The skewness of the resulting phenotypic distributions strongly depends on the rate of environmental variation and strength of selection. When generalized to more than one trait, the phenotypic distributions are not only affected by the magnitude of the rate of environmental variation but also by its direction. A remarkable feature of our predictions is the existence of an upper bound for the critical rate of environmental variation to allow population persistence, even if there is no cost associated with phenotypic plasticity.

Rate of environmental variation impacts the predictability in evolution.

In the two last decades, we have improved our understanding of the adaptive evolution of natural populations under constant and stable environments. For instance, experimental methods from evolutionary biology have allowed us to explore the structure of fitness landscapes and survey how the landscape properties can constrain the adaptation process. However, understanding how environmental changes can affect adaptation remains challenging. Very little progress has been made with respect to time-varying fitness landscapes. Using the adaptive-walk approximation, we survey the evolutionary process of populations under a scenario of environmental variation. In particular, we investigate how the rate of environmental variation influences the predictability in evolution. We observe that the rate of environmental variation not only changes the duration of adaptive walks towards fitness peaks of the fitness landscape, but also affects the degree of repeatability of both outcomes and evolutionary paths. In general, slower environmental variation increases the predictability in evolution. The accessibility of endpoints is greatly influenced by the ecological dynamics. The dependence of these quantities on the genome size and number of traits is also addressed. To our knowledge, this contribution is the first to use the predictive approach to quantify and understand the impact of the speed of environmental variation on the degree of parallelism of the evolutionary process.

The effect of spatially correlated environments on genetic diversity-area relationships.

Understanding the spatial patterns of genetic diversity and what causes them is an important outstanding question in ecology. Here we investigate the roles of spatial heterogeneity and system area in generating genome diversity, and study its dependence with sampled area. We study an individual-based model that incorporates natural selection on the habitat type and compare the effects of asexual and sexual reproductions. A key ingredient of the model is the possibility to tune the level of spatial heterogeneity among the habitats. Our results corroborate either the bi-phasic or tri-phasic scenarios, one phase corresponding to a power law regime, for the diversity-area relationship in both sexual and asexual populations, being the shape of the curve influenced by mutation rates and spatial correlation. These observations are verified for distinct sets of parameter values.

Robustness and predictability of evolution in bottlenecked populations.

Deterministic and stochastic evolutionary processes drive adaptation in natural populations. The strength of each component process is determined by the population size: deterministic components prevail in very large populations, while stochastic components are the driving mechanisms in small ones. Many natural populations, however, experience intermittent periods of growth, moving through states in which either stochastic or deterministic processes prevail. This growth is often countered by population bottlenecks, which abound in both natural and laboratory populations. Here we investigate how population bottlenecks shape the process of adaptation. We demonstrate that adaptive trajectories in populations experiencing regular bottlenecks can be naturally scaled in time units of generations; with this scaling the time courses of adaptation, fitness variance, and genetic diversity all become relatively insensitive to the timing of population bottlenecks, provided the bottleneck size exceeds a few thousand individuals. We also include analyses at the genotype level to investigate the impact of population bottlenecks on the predictability and distribution of evolutionary pathways. Irrespective of the timing of population bottlenecks, we find that predictability increases with population size. We also find that predictability of the adaptive pathways increases in increasingly rugged fitness landscapes. Overall, our work reveals that both the adaptation rate and the predictability of evolutionary trajectories are relatively robust to population bottlenecks.

Analysis of statistical correlations between properties of adaptive walks in fitness landscapes.

The fitness landscape metaphor has been central in our way of thinking about adaptation. In this scenario, adaptive walks are idealized dynamics that mimic the uphill movement of an evolving population towards a fitness peak of the landscape. Recent works in experimental evolution have demonstrated that the constraints imposed by epistasis are responsible for reducing the number of accessible mutational pathways towards fitness peaks. Here, we exhaustively analyse the statistical properties of adaptive walks for two empirical fitness landscapes and theoretical NK landscapes. Some general conclusions can be drawn from our simulation study. Regardless of the dynamics, we observe that the shortest paths are more regularly used. Although the accessibility of a given fitness peak is reasonably correlated to the number of monotonic pathways towards it, the two quantities are not exactly proportional. A negative correlation between predictability and mean path divergence is established, and so the decrease of the number of effective mutational pathways ensures the convergence of the attraction basin of fitness peaks. On the other hand, other features are not conserved among fitness landscapes, such as the relationship between accessibility and predictability.

Sex and deleterious mutations.

The evolutionary advantage of sexual reproduction has been considered as one of the most pressing questions in evolutionary biology. While a pluralistic view of the evolution of sex and recombination has been suggested by some, here we take a simpler view and try to quantify the conditions under which sex can evolve given a set of minimal assumptions. Since real populations are finite and also subject to recurrent deleterious mutations, this minimal model should apply generally to all populations. We show that the maximum advantage of recombination occurs for an intermediate value of the deleterious effect of mutations. Furthermore we show that the conditions under which the biggest advantage of sex is achieved are those that produce the fastest fitness decline in the corresponding asexual population and are therefore the conditions for which Muller's ratchet has the strongest effect. We also show that the selective advantage of a modifier of the recombination rate depends on its strength. The quantification of the range of selective effects that favors recombination then leads us to suggest that, if in stressful environments the effect of deleterious mutations is enhanced, a connection between sex and stress could be expected, as it is found in several species.

Rate of fixation of beneficial mutations in sexual populations.

We have investigated the rate of substitution of advantageous mutations in populations of haploid organisms where the rate of recombination can be controlled. We have verified that in all the situations recombination speeds up adaptation through recombination of beneficial mutations from distinct lineages in a single individual, and so reducing the intensity of clonal interference. The advantage of sex for adaptation is even stronger when deleterious mutations occur since now recombination can also restore genetic background free of deleterious mutations. However, our simulation results demonstrate that evidence of clonal interference, as increased mean selective effect of fixed mutations and reduced likelihood of fixation of small-effect mutations, are also present in sexual populations. What we see is that this evidence is delayed when compared to asexual populations.

Environmental heterogeneity enhances clonal interference.

Clonal interference (CI) is a phenomenon that may be important in several asexual microbes. It occurs when population sizes are large and mutation rates to new beneficial alleles are of significant magnitude. Here we explore the role of gene flow and spatial heterogeneity in selection strength in the adaptation of asexuals. We consider a subdivided population of individuals that are adapting, through new beneficial mutations, and that migrate between different patches. The fitness effect of each mutation depends on the patch and all mutations considered are assumed to be unconditionally beneficial. We find that spatial variation in selection pressure affects the rate of adaptive evolution and its qualitative effects depend on the level of gene flow. In particular, we find that both low migration and high levels of heterogeneity lead to enhanced CI. In contrast, for high levels of migration the rate of fixation of adaptive mutations is higher when environmental heterogeneity is present. In addition, we observe that the level of fitness variation is higher and simultaneous fixation of multiple mutations tends to occur in the regime of low migration rates and high heterogeneity.

Epistasis and the selective advantage of sex and recombination.

The understanding of the central mechanisms favoring sex and recombination in real populations is one of the fundamental issues in evolutionary biology. Based on a previous stochastic formulation for the study of sex, here we aim to investigate the conditions under which epistasis favors the fixation of the sexual mode of reproduction in a given population. In addition, we try to identify the evolutionary forces which contribute to this process. One considers a finite population model which assumes the existence of a recombination modifier allele that can activate the recombination mechanism. We have found that sex is very little favored in a scenario of antagonistic epistasis, and this advantage only occurs in a narrow range of values of the selection coefficient s_{d} . On the other hand, synergistic epistasis favors recombination in a very broad domain. However, the major mechanism contributing to the spreading of the modifier allele depends on the range of values of s_{d} . At large s_{d} , background selection favors recombination since it increases the efficacy of selection, while at low s_{d} Muller's ratchet is the leading mechanism.

A theoretical approach to the size-complexity rule.

The so-called size-complexity rule claims the existence of a positive correlation between organism size and number of cell types. In this spirit, here we address the relationship between organism size and number of potential tasks that can be performed. The modeling relies on the assumption that the states of the cells within the aggregates are such that the maximum fitness is realized, but also relies on the existence of tradeoffs among the distinct functions. For group sizes larger than the number of potential tasks, fitness maximization is attained when all cells in group specialize in a given task. Under this scenario, the number of potential tasks equals the number of cell types. We have found that the morphology and the topology of aggregates, as well as the developmental mode, strongly influence the dynamics of body formation. Particularly, it has been observed that more compact structures, such as sphere-like structures, are more likely to follow the claim of the size-complexity rule, whereas more fragile structures such as linear chains, which are more vulnerable to drastic changes due to division mechanisms, can, in a broad scenario, violate the size-complexity rule.

Patterns of genetic variation in populations of infectious agents.

BACKGROUND: The analysis of genetic variation in populations of infectious agents may help us understand their epidemiology and evolution. Here we study a model for assessing the levels and patterns of genetic diversity in populations of infectious agents. The population is structured into many small subpopulations, which correspond to their hosts, that are connected according to a specific type of contact network. We considered different types of networks, including fully connected networks and scale free networks, which have been considered as a model that captures some properties of real contact networks. Infectious agents transmit between hosts, through migration, where they grow and mutate until elimination by the host immune system. RESULTS: We show how our model is closely related to the classical SIS model in epidemiology and find that: depending on the relation between the rate at which infectious agents are eliminated by the immune system and the within host effective population size, genetic diversity increases with R0 or peaks at intermediate R0 levels; patterns of genetic diversity in this model are in general similar to those expected under the standard neutral model, but in a scale free network and for low values of R0 a distortion in the neutral mutation frequency spectrum can be observed; highly connected hosts (hubs in the network) show patterns of diversity different from poorly connected individuals, namely higher levels of genetic variation, lower levels of genetic differentiation and larger values of Tajima's D. CONCLUSION: We have found that levels of genetic variability in the population of infectious agents can be predicted by simple analytical approximations, and exhibit two distinct scenarios which are met according to the relation between the rate of drift and the rate at which infectious agents are eliminated. In one scenario the diversity is an increasing function of the level of transmission and in a second scenario it is peaked around intermediate levels of transmission. This is independent of the type of host contact structure. Furthermore for low values of R0, very heterogeneous host contact structures lead to lower levels of diversity.

Muller's ratchet in random graphs and scale-free networks.

Muller's ratchet is an evolutionary process that has been implicated in the extinction of asexual species, the evolution of mitochondria, the degeneration of the Y chromosome, the evolution of sex and recombination and the evolution of microbes. Here we study the speed of Muller's ratchet in a population subdivided into many small subpopulations connected by migration, and distributed on a network. We compare the speed of the ratchet in two distinct types of topologies: scale free networks and random graphs. The difference between the topologies is noticeable when the average connectivity of the network and the migration rate is large. In this situation we observe that the ratchet clicks faster in scale free networks than in random graphs. So contrary to intuition, scale free networks are more prone to loss of genetic information than random graphs. On the other hand, we show that scale free networks are more robust to the random extinction than random graphs. Since these complex networks have been shown to describe well real-life systems, our results open a framework for studying the evolution of microbes and disease epidemics.

Coexistence of competing metabolic pathways in well-mixed populations.

Understanding why strains with different metabolic pathways that compete for a single limiting resource coexist is a challenging issue within a theoretical perspective. Previous investigations rely on mechanisms such as group or spatial structuring to achieve a stable coexistence between competing metabolic strategies. Nevertheless, coexistence has been experimentally reported even in situations where it cannot be attributed to spatial effects [Heredity 100, 471 (2008)HDTYAT0018-067X10.1038/sj.hdy.6801073]. According to that study a toxin expelled by one of the strains can be responsible for the stable maintenance of the two strain types. We propose a resource-based model in which an efficient strain with a slow metabolic rate competes with a second strain type which presents a fast but inefficient metabolism. Moreover, the model assumes that the inefficient strain produces a toxin as a by-product. This toxin affects the growth rate of both strains with different strength. Through an extensive exploration of the parameter space we determine the situations at which the coexistence of the two strains is possible. Interestingly, we observe that the resource influx rate plays a key role in the maintenance of the two strain types. In a scenario of resource scarcity the inefficient is favored, though as the resource influx rate is augmented the coexistence becomes possible and its domain is enlarged.

Competition and fixation of cohorts of adaptive mutations under Fisher geometrical model.

One of the simplest models of adaptation to a new environment is Fisher's Geometric Model (FGM), in which populations move on a multidimensional landscape defined by the traits under selection. The predictions of this model have been found to be consistent with current observations of patterns of fitness increase in experimentally evolved populations. Recent studies investigated the dynamics of allele frequency change along adaptation of microbes to simple laboratory conditions and unveiled a dramatic pattern of competition between cohorts of mutations, i.e., multiple mutations simultaneously segregating and ultimately reaching fixation. Here, using simulations, we study the dynamics of phenotypic and genetic change as asexual populations under clonal interference climb a Fisherian landscape, and ask about the conditions under which FGM can display the simultaneous increase and fixation of multiple mutations-mutation cohorts-along the adaptive walk. We find that FGM under clonal interference, and with varying levels of pleiotropy, can reproduce the experimentally observed competition between different cohorts of mutations, some of which have a high probability of fixation along the adaptive walk. Overall, our results show that the surprising dynamics of mutation cohorts recently observed during experimental adaptation of microbial populations can be expected under one of the oldest and simplest theoretical models of adaptation-FGM.