The role of migration in the evolution of phenotypic switching

Stochastic switching is an example of phenotypic bet hedging, where an individual can switch between different phenotypic states in a fluctuating environment. Although the evolution of stochastic switching has been studied when the environment varies temporally, there has been little theoretical work on the evolution of phenotypic switching under both spatially and temporally fluctuating selection pressures. Here, we explore the interaction of temporal and spatial change in determining the evolutionary dynamics of phenotypic switching. We find that spatial variation in selection is important; when selection pressures are similar across space, migration can decrease the rate of switching, but when selection pressures differ spatially, increasing migration between demes can facilitate the evolution of higher rates of switching. These results may help explain the diverse array of non-genetic contributions to phenotypic variability and phenotypic inheritance observed in both wild and experimental populations.     

THE EVOLUTION OF REVERSIBLE SWITCHES IN THE PRESENCE OF IRREVERSIBLE MIMICS

Reversible phenotypic switching can be caused by a number of different mechanisms including epigenetic inheritance systems and DNA-based contingency loci. Previous work has shown that reversible switching systems may be favored by natural selection. Many switches can be characterized as "on/off" where the "off" state constitutes a temporary and reversible loss of function. Loss-of-function phenotypes corresponding to the "off" state can be produced in many different ways, all yielding identical fitness in the short term. In the long term, however, a switch-induced loss of function can be reversed, whereas many loss-of-function mutations, especially deletions, cannot. We refer to these loss-of-function mutations as "irreversible mimics" of the reversible switch. Here, we develop a model in which a reversible switch evolves in the presence of both irreversible mimics and metapopulation structure. We calculate that when the rate of appearance of irreversible mimics exceeds the migration rate, the evolved reversible switching rate will exceed the bet-hedging rate predicted by panmictic models.     

Haldane's sieve and adaptation from the standing genetic variation

We consider populations that adapt to a sudden environmental change by fixing alleles found at mutation-selection balance. In particular, we calculate probabilities of fixation for previously deleterious alleles, ignoring the input of new mutations. We find that "Haldane's sieve"--the bias against the establishment of recessive beneficial mutations--does not hold under these conditions. Instead probabilities of fixation are generally independent of dominance. We show that this result is robust to patterns of sex expression for both X-linked and autosomal loci. We further show that adaptive evolution is invariably slower at X-linked than autosomal loci when evolution begins from mutation-selection balance. This result differs from that obtained when adaptation uses new mutations, a finding that may have some bearing on recent attempts to distinguish between hitchhiking and background selection by contrasting the molecular population genetics of X-linked vs. autosomal loci. Last, we suggest a test to determine whether adaptation used new mutations or previously deleterious alleles from the standing genetic variation.     

DENSITY DEPENDENCE AND UNPREDICTABLE SELECTION IN A HETEROGENEOUS ENVIRONMENT: COMPROMISE AND POLYMORPHISM IN THE ESS REACTION NORM

In quantitative genetic models of the evolution of reaction norms, an individual is selected in the habitat in which it develops; as a consequence, selection leads to the optimum phenotype in each habitat. Here, individuals are assumed to experience unpredictable habitat change between development and selection, so that the environment in which an individual is selected may differ from the environment in which it developed. The model reveals that unpredictability of the selection an individual actually faces leads to the evolutionarily stable bet-hedging reaction norm constituting a compromise between the phenotypic optima in the different patches. We also examine the effect of local density regulation before selection, in the patches in which the individuals develop, and after selection, in the patches in which they are selected. Density regulation before selection has a much lower influence on the evolution of the reaction norm than density regulation after selection. The source-sink structure of the environment caused by differential productivity of patches strongly affects how the compromise bet-hedging strategy weighs the different phenotypic optima and might compromise the local evolutionary stability of the evolved reaction norm. If the strength and variability among patches of density regulation after selection is sufficiently large, no single reaction norm is evolutionary stable: Polymorphic reaction norms constitute the evolutionarily stable population. We also show that a polymorphic reaction norm is more likely to be observed in a less productive habitat. The relations between the present model and the Dempster and the Levene models are discussed.     

Coreceptor Switching in HIV-1 Subtype B and Subtype C

We use a mathematical model to determine the factors affecting the delayed or rare coreceptor switch in HIV-1 subtype C infected individuals. The model takes into account the two main target cells for the CXCR4-tropic and CCR5-tropic virus and includes the the lytic and non-lytic immune responses. Computer-based simulations and a sensitivity analysis of the model predict that a persistent immune response suppresses the CXCR4-tropic virus to low levels and hence preventing a phenotypic switch. However, not only should the immune response be persistent, but it should have an efficient lytic immune response rather that an efficient non-lytic response. In addition, we also find that the availability of macrophage cells and enhanced viral kinetics are also crucial for the dominance of the R5 strain. We suggest that an altered host environment probably as a result of immune activation may explain the difference in coreceptor switching kinetics between HIV-1 subtype B and subtype C individuals.     

The impact of host-cell dynamics on the fixation probability for lytic viruses

Lytic viruses are obligate parasites whose population dynamics are necessarily coupled to the dynamics of their host-cell population. The adaptation rate of these viruses has attracted considerable scientific interest, as they are a key model organism in experimental evolution. Nevertheless, to date mathematical models of experimental evolution have largely ignored the host-cell population. In this paper we incorporate two important features of host-cell dynamics—the possibility of clearance or death of an infected cell before lysis, and the possibility of changing host-cell density—into previous models for the fixation probability of lytic viruses. We compute the fixation probabilities of rare alleles that confer reproductive benefit through either an increase in attachment rate or burst size, or a reduction in lysis time. We find that host-cell clearance significantly reduces the fixation probabilities of all types of beneficial mutations, having the largest impact on mutations which reduce the lysis time, but has only modest effects on the pattern of fixation probabilities previously observed. We further predict that exponential growth of the host-cell population preferentially selects for mutations that affect burst size or lysis time, and exacerbates the sensitive dependence of fixation probabilities on the time between population bottlenecks. Even when burst size and lysis time are constrained to vary together, our results suggest that lytic viruses should readily adapt to optimize these traits to the timing between population bottlenecks.     

Generalists versus specialists in fluctuating environments: a bet-hedging perspective

Bet-hedging evolves in fluctuating environments because long-term genotype success is determined by geometric (rather than arithmetic) mean fitness across generations. Diversifying bet-hedging produces different specialist offspring, whereas conservative bet-hedging produces similar generalist offspring. However, many fields, such as behavioral ecology and thermal physiology, typically consider specialist versus generalist strategies only in terms of maximizing arithmetic mean fitness benefits to individuals. Here we model how environmental variability affects optimal amounts of phenotypic variation within and among individuals to maximise genotype fitness, and we disentangle the effects of individual-level optimization and genotype-level bet-hedging by comparing long-term arithmetic versus geometric mean fitness. For traits with additive fitness effects within lifetimes (e.g. foraging-related traits), genotypes of similar generalists or diversified specialists perform equally well. However, if fitness effects are multiplicative within lifetimes (e.g. sequential survival probabilities), generalist individuals are always favored. In this case, geometric mean fitness optimization requires even more within-individual phenotypic variation than does arithmetic mean fitness, causing individuals to be more generalist than required to simply maximize their own expected fitness. In contrast to previous results in the bet-hedging literature, this generalist conservative bet-hedging effect is always favored over diversifying bet-hedging. These results link the evolution of behavioral and ecological specialization with earlier models of bet-hedging, and we apply our framework to a range of natural phenomena from habitat choice to host specificity in parasites.     

Bet-hedging as an evolutionary game: the trade-off between egg size and number

Bet-hedging theory addresses how individuals should optimize fitness in varying and unpredictable environments by sacrificing mean fitness to decrease variation in fitness. So far, three main bet-hedging strategies have been described: conservative bet-hedging (play it safe), diversified bet-hedging (don’t put all eggs in one basket) and adaptive coin flipping (choose a strategy at random from a fixed distribution). Within this context, we analyse the trade-off between many small eggs (or seeds) and few large, given an unpredictable environment. Our model is an extension of previous models and allows for any combination of the bet-hedging strategies mentioned above. In our individual-based model (accounting for both ecological and evolutionary forces), the optimal bet-hedging strategy is a combination of conservative and diversified bet-hedging and adaptive coin flipping, which means a variation in egg size both within clutches and between years. Hence, we show how phenotypic variation within a population, often assumed to be due to non-adaptive variation, instead can be the result of females having this mixed strategy. Our results provide a new perspective on bet-hedging and stress the importance of extreme events in life history evolution.     

Switching and Growth for Microbial Populations in Catastrophic Responsive Environments

Phase variation, or stochastic switching between alternative states of gene expression, is common among microbes, and may be important in coping with changing environments. We use a theoretical model to assess whether such switching is a good strategy for growth in environments with occasional catastrophic events. We find that switching can be advantageous, but only when the environment is responsive to the microbial population. In our model, microbes switch randomly between two phenotypic states, with different growth rates. The environment undergoes sudden catastrophes, the probability of which depends on the composition of the population. We derive a simple analytical result for the population growth rate. For a responsive environment, two alternative strategies emerge. In the no-switching strategy, the population maximizes its instantaneous growth rate, regardless of catastrophes. In the switching strategy, the microbial switching rate is tuned to minimize the environmental response. Which of these strategies is most favorable depends on the parameters of the model. Previous studies have shown that microbial switching can be favorable when the environment changes in an unresponsive fashion between several states. Here, we demonstrate an alternative role for phase variation in allowing microbes to maximize their growth in catastrophic responsive environments.     

Phenotype Switching and Mutations in Random Environments

Cell populations can benefit from changing phenotype when the environment changes. One mechanism for generating these changes is stochastic phenotype switching, whereby cells switch stochastically from one phenotype to another according to genetically determined rates, irrespective of the current environment, with the matching of phenotype to environment then determined by selective pressure. This mechanism has been observed in numerous contexts, but identifying the precise connection between switching rates and environmental changes remains an open problem. Here, we introduce a simple model to study the evolution of phenotype switching in a finite population subject to random environmental shocks. We compare the successes of competing genotypes with different switching rates, and analyze how the optimal switching rates depend on the frequency of environmental changes. If environmental changes are as rare as mutations, then the optimal switching rates mimic the rates of environmental changes. If the environment changes more frequently, then the optimal genotype either maximally favors fitness in the more common environment or has the maximal switching rate to each phenotype. Our results also explain why the optimum is relatively insensitive to fitness in each environment.     

Fixation probabilities for the Moran process with three or more strategies: general and coupling results

We study fixation probabilities for the Moran stochastic process for the evolution of a population with three or more types of individuals and frequency-dependent fitnesses. Contrary to the case of populations with two types of individuals, in which fixation probabilities may be calculated by an exact formula, here we must solve a large system of linear equations. We first show that this system always has a unique solution. Other results are upper and lower bounds for the fixation probabilities obtained by coupling the Moran process with three strategies with birth–death processes with only two strategies. We also apply our bounds to the problem of evolution of cooperation in a population with three types of individuals already studied in a deterministic setting by Núñez Rodríguez and Neves (J Math Biol 73:1665–1690, 2016). We argue that cooperators will be fixated in the population with probability arbitrarily close to 1 for a large region of initial conditions and large enough population sizes.

     

Exclusion rules, bottlenecks and the evolution of stochastic phenotype switching

Stochastic phenotype switching--often considered a bet hedging or risk-reducing strategy--can enhance the probability of survival in fluctuating environments. A recent experiment provided direct evidence for an adaptive origin by showing the de novo evolution of switching in bacterial populations propagated under a selective regime that captured essential features of the host immune response. The regime involved strong frequency-dependent selection realized via dual imposition of an exclusion rule and population bottleneck. Applied at the point of transfer between environments, the phenotype common in the current environment was assigned a fitness of zero and was thus excluded from participating in the next round (the exclusion rule). In addition, also at the point of transfer, and so as to found the next bout of selection, a single phenotypically distinct type was selected at random from among the survivors (the bottleneck). Motivated by this experiment, we develop a mathematical model to explore the broader significance of key features of the selective regime. Through a combination of analytical and numerical results, we show that exclusion rules and population bottlenecks act in tandem as potent selective agents for stochastic phenotype switching, such that even when initially rare, and when switching engenders a cost in Malthusian fitness, organisms with the capacity to switch can invade non-switching populations and replace non-switching types. Simulations demonstrate the robustness of our findings to alterations in switching rate, fidelity of exclusion, bottleneck size, duration of environmental state and growth rate. We also demonstrate the relevance of our model to a range of biological scenarios such as bacterial persistence and the evolution of sex.     

The role of phenotypic plasticity in driving genetic evolution

Models of population divergence and speciation are often based on the assumption that differences between populations are due to genetic factors, and that phenotypic change is due to natural selection. It is equally plausible that some of the differences among populations are due to phenotypic plasticity. We use the metaphor of the adaptive landscape to review the role of phenotypic plasticity in driving genetic evolution. Moderate levels of phenotypic plasticity are optimal in permitting population survival in a new environment and in bringing populations into the realm of attraction of an adaptive peak. High levels of plasticity may increase the probability of population persistence but reduce the likelihood of genetic change, because the plastic response itself places the population close to a peak. Moderate levels of plasticity arise whenever multiple traits, some of which are plastic and others not, form a composite trait involved in the adaptive response. For example, altered behaviours may drive selection on morphology and physiology. Because there is likely to be a considerable element of chance in which behaviours become established, behavioural change followed by morphological and physiological evolution may be a potent force in driving evolution in novel directions. We assess the role of phenotypic plasticity in stimulating evolution by considering two examples from birds: (i) the evolution of red and yellow plumage coloration due to carotenoid consumption; and (ii) the evolution of foraging behaviours on islands. Phenotypic plasticity is widespread in nature and may speed up, slow down, or have little effect on evolutionary change. Moderate levels of plasticity may often facilitate genetic evolution but careful analyses of individual cases are needed to ascertain whether plasticity has been essential or merely incidental to population differentiation.     

DYNAMICS OF HYBRID INCOMPATIBILITY IN GENE NETWORKS IN A CONSTANT ENVIRONMENT

After an ancestral population splits into two allopatric populations, different mutations may fix in each. When pairs of mutations are brought together in a hybrid offspring, epistasis may cause reduced fitness. Such pairs are known as Bateson–Dobzhansky–Muller (BDM) incompatibilities. A well-known model of BDM incompatibility due to Orr suggests that the fitness load on hybrids should initially accelerate, and continue to increase as the number of potentially incompatible substitutions increases (the "snowball effect"). In the gene networks model, which violates a key assumption of Orr's model (independence of fixation probabilities), the snowball effect often does not occur. Instead, we describe three possible dynamics in a constant environment: (1) Stabilizing selection can constrain two allopatric populations to remain near-perfectly compatible. (2) Despite constancy of environment, punctuated evolution may obtain; populations may experience rare adaptations asynchronously, permitting incompatibility. (3) Despite stabilizing selection, developmental system drift may permit genetic change, allowing two populations to drift in and out of compatibility. We reinterpret Orr's model in terms of genetic distance. We extend Orr's model to the finite loci case, which can limit incompatibility. Finally, we suggest that neutral evolution of gene regulation in nature, to the point of speciation, is a distinct possibility.     

Advergence in Müllerian mimicry: the case of the poison dart frogs of Northern Peru revisited

Whether the evolution of similar aposematic signals in different unpalatable species (i.e. Müllerian mimicry) is because of phenotypic convergence or advergence continues to puzzle scientists. The poison dart frog Ranitomeya imitator provides a rare example in support of the hypothesis of advergence: this species was believed to mimic numerous distinct model species because of high phenotypic variability and low genetic divergence among populations. In this study, we test the evidence in support of advergence using a population genetic framework in two localities where R. imitator is sympatric with different model species, Ranitomeya ventrimaculata and Ranitomeya variabilis. Genetic analyses revealed incomplete sorting of mitochondrial haplotypes between the two model species. These two species are also less genetically differentiated than R. imitator populations on the basis of both mitochondrial and nuclear DNA comparisons. The genetic similarity between the model species suggests that they have either diverged more recently than R. imitator populations or that they are still connected by gene flow and were misidentified as different species. An analysis of phenotypic variability indicates that the model species are as variable as R. imitator. These results do not support the hypothesis of advergence by R. imitator. Although we cannot rule out phenotypic advergence in the evolution of Müllerian mimicry, this study reopens the discussion regarding the direction of the evolution of mimicry in the R. imitator system.     

The effect of deleterious alleles on adaptation in asexual populations

We calculate the fixation probability of a beneficial allele that arises as the result of a unique mutation in an asexual population that is subject to recurrent deleterious mutation at rate U. Our analysis is an extension of previous works, which make a biologically restrictive assumption that selection against deleterious alleles is stronger than that on the beneficial allele of interest. We show that when selection against deleterious alleles is weak, beneficial alleles that confer a selective advantage that is small relative to U have greatly reduced probabilities of fixation. We discuss the consequences of this effect for the distribution of effects of alleles fixed during adaptation. We show that a selective sweep will increase the fixation probabilities of other beneficial mutations arising during some short interval afterward. We use the calculated fixation probabilities to estimate the expected rate of fitness improvement in an asexual population when beneficial alleles arise continually at some low rate proportional to U. We estimate the rate of mutation that is optimal in the sense that it maximizes this rate of fitness improvement. Again, this analysis relaxes the assumption made previously that selection against deleterious alleles is stronger than on beneficial alleles.     

Diapause and bet-hedging strategies in insects: a meta-analysis of reaction norm shapes

Many organisms escape from lethal climatological conditions by entering a resistant resting stage called diapause, which needs to be optimally timed with seasonal change. As climate change exerts selection pressure on phenology, the evolution of mean diapause timing, but also of phenotypic plasticity and bet-hedging strategies is expected. The potential of the latter strategy as a means of coping with environmental unpredictability has received little attention in the climate change literature. Populations should be adapted to spatial variation in local conditions; contemporary patterns of phenological strategies across a geographic range may hence provide information about their evolvability. We thus extracted 458 diapause reaction norms from 60 studies. First, we correlated mean diapause timing with mean winter onset. Then we partitioned the reaction norm variance into a temporal component (phenotypic plasticity) and among-offspring variance (diversified bet-hedging) and correlated this variance composition with variability of winter onset. Mean diapause timing correlated reasonably well with mean winter onset, except for populations at high latitudes, which apparently failed to track early onsets. Variance among offspring was, however, limited and correlated only weakly with environmental variability, indicating little scope for bet-hedging. The apparent lack of phenological bet-hedging strategies may pose a risk in a less predictable climate, but we also highlight the need for more data on alternative strategies.