QUANTITATIVE GENETICS AND THE EVOLUTION OF REACTION NORMS

We extend methods of quantitative genetics to studies of the evolution of reaction norms defined over continuous environments. Our models consider both spatial variation (hard and soft selection) and temporal variation (within a generation and between generations). These different forms of environmental variation can produce different evolutionary trajectories even when they favor the same optimal reaction norm. When genetic constraints limit the types of evolutionary changes available to a reaction norm, different forms of environmental variation can also produce different evolutionary equilibria. The methods and models presented here provide a framework in which empiricists may determine whether a reaction norm is optimal and, if it is not, to evaluate hypotheses for why it is not.     

Genome‐wide DNA methylation alterations of Alternanthera philoxeroides in natural and manipulated habitats: implications for epigenetic regulation of rapid responses to environmental fluctuation and phenotypic variation

Alternanthera philoxeroides (alligator weed) is an invasive weed that can colonize both aquatic and terrestrial habitats. Individuals growing in different habitats exhibit extensive phenotypic variation but little genetic differentiation in its introduced range. The mechanisms underpinning the wide range of phenotypic variation and rapid adaptation to novel and changing environments remain uncharacterized. In this study, we examined the epigenetic variation and its correlation with phenotypic variation in plants exposed to natural and manipulated environmental variability. Genome‐wide methylation profiling using methylation‐sensitive amplified fragment length polymorphism (MSAP) revealed considerable DNA methylation polymorphisms within and between natural populations. Plants of different source populations not only underwent significant morphological changes in common garden environments, but also underwent a genome‐wide epigenetic reprogramming in response to different treatments. Methylation alterations associated with response to different water availability were detected in 78.2% (169/216) of common garden induced polymorphic sites, demonstrating the environmental sensitivity and flexibility of the epigenetic regulatory system. These data provide evidence of the correlation between epigenetic reprogramming and the reversible phenotypic response of alligator weed to particular environmental factors.     

The fastest evolutionary trajectory

Given two mutants, A and B, separated by n mutational steps, what is the evolutionary trajectory which allows a homogeneous population of A to reach B in the shortest time? We show that the optimum evolutionary trajectory (fitness landscape) has the property that the relative fitness increase between any two consecutive steps is constant. Hence, the optimum fitness landscape between A and B is given by an exponential function. Our result is precise for small mutation rates and excluding back mutations. We discuss deviations for large mutation rates and including back mutations. For very large mutation rates, the optimum fitness landscape is flat and has a single peak at type B.     

Habitat-specific genetic effects on growth rate and morphology across pH and water-level gradients within a population of the moss Sphagnum angustifolium (Sphagnaceae)

To study genetic adaptations in bryophytes on small ecological and spatial scales and to assess the adaptive significance of morphological trait variation, genotypes of Sphagnum angustifolium originating from habitats characterized by different pH and height above water table were clonally propagated and grown along the same gradients that exist in the field. Clones from ombrotrophic habitats grew consistently better ombrotrophically than clones from minerotrophic habitats and vice versa, suggesting that the genotypes were adapted to different pH levels. Genetic variation was found in several morphological traits, but habitat-specific genetic effects were detected only in length of spreading branches. Covariation between morphology and growth was generally environmentally induced. Positive and negative cross-environment genetic correlations suggested the presence of constraints on adaptive reaction norm evolution. The indications of small-scale genetic adaptations suggest either selective establishment of genotypes adapted to specific habitats, strong selective forces operating at the later stages of the life cycle, restricted gene flow over short distances, or a combination of these. In contrast to prevailing views, these results indicate that bryophytes are likely to respond genetically to small-scale environmental gradients.     

The evolution of phenotypic traits in a predator-prey system subject to Allee effect

This paper considers the evolution of phenotypic traits in a community comprising the populations of predators and prey subject to Allee effect. The evolutionary model is constructed from a deterministic approximation of the stochastic process of mutation and selection. Firstly, we investigate the ecological and evolutionary conditions that allow for continuously stable strategy and evolutionary branching. We find that the strong Allee effect of prey facilitates the formation of continuously stable strategy in the case that prey population undergoes evolutionary branching if the Allee effect of prey is not strong enough. Secondly, we show that evolutionary suicide is impossible for prey population when the intraspecific competition of prey is symmetric about the origin. However, evolutionary suicide can occur deterministically on prey population if prey individuals undergo strong asymmetric competition and are subject to Allee effect. Thirdly, we show that the evolutionary model with symmetric interactions admits a stable limit cycle if the Allee effect of prey is weak. Evolutionary cycle is a likely outcome of the process, which depends on the strength of Allee effect and the mutation rates of predators and prey.     

Digestive performance in five Mediterranean lizard species: effects of temperature and insularity

Temperature sensitivity of digestive processes has important ramifications for digestive performance in ectothermic vertebrates. We conducted a comparative analysis of temperature effects on digestive processes [gut passage times (GPTs) and apparent digestive efficiencies (ADEs)] in five lacertid lizards occurring in insular (Podarcis erhardii, P. gaigeae), and mainland (P. muralis, P. peloponnesiaca, Lacerta graeca) Mediterranean environments. GPTs were negatively correlated to temperature with mainland taxa having 10–20% longer GPTs than island taxa. In contrast to previous studies that estimate ADEs using bomb calorimetry, we compare ADEs by analyzing discrete efficiencies for lipids, sugars and proteins at three temperature regimes (20, 25, and 30°C); each of these categories produces different results. ADEs for lipids and sugars showed a monotonic increase with temperature whereas ADEs for proteins decreased with temperature. Island taxa had consistently higher ADEs than their mainland counterparts for lipids and for proteins but not for sugars. They are characterized by superior energy acquisition abilities despite significantly shorter GPTs. Their increased digestive performance relative to the mainland species appears to allow them to maximize energy acquisition in unproductive island environments where food availability is spatially and seasonally clustered.     

Fluctuation in the physical environment as a mechanism for reinforcing evolutionary transitions

We hypothesize a mechanism for reinforcing transitions between levels of selection, involving physiological homeostasis and amplification of variation in the physical environment. Groups experience a stronger selection pressure than individuals for homeostasis with respect to reproductively limiting variables, because their greater longevity exposes them more often to suboptimal physical conditions, and greater physical size means they encompass a larger fraction of any resource/nutrient gradient. Groups achieve homeostasis by differentiation into microcosms with specialist functions, e.g. cell types. Such differentiation is more limited in individuals due to their smaller size and shorter lifespan. Hence tolerance of fluctuation in certain physical variables is proposed to be weaker in individuals than in groups. We show that a trait providing increased tolerance (alpha) to fluctuation (V-V(opt)) in a limiting abiotic variable (V), at relative fitness cost (C), can increase from rarity if the condition alpha.mid R:V-V(opt)|>C is met. Groups also sequester larger absolute quantities of resource than individuals, and group death is less frequent, hence the population dynamics of groups cause resource/nutrient availability to fluctuate with greater amplitude than that of individuals. Increasing the amplitude of fluctuation in a reproductively limiting environmental variable is proposed as a mechanism by which a group can limit reproduction of parasitic "cheat" individuals. Enhancing physical fluctuation is frequency dependent, hence only an increase in tolerance to fluctuation can explain the group's increase from rarity. However, once groups reach intermediate frequencies, a positive feedback process can be initiated in which a differentiated group enhances physical fluctuation beyond the tolerance of any "cheat", and in so doing enhances the selection pressure it experiences for homeostasis. This may help explain the persistence of transitions in individuality, and the coincidence of some such transitions with periods of change and oscillation in global scale environmental variables.     

Fixation probabilities in evolutionary game dynamics with a two-strategy game in finite diploid populations

Fixation processes in evolutionary game dynamics in finite diploid populations are investigated. Traditionally, frequency dependent evolutionary dynamics is modeled as deterministic replicator dynamics. This implies that the infinite size of the population is assumed implicitly. In nature, however, population sizes are finite. Recently, stochastic processes in finite populations have been introduced in order to study finite size effects in evolutionary game dynamics. One of the most significant studies on evolutionary dynamics in finite populations was carried out by Nowak et al. which describes “one-third law” [Nowak, et al., 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 646-650]. It states that under weak selection, if the fitness of strategy α is greater than that of strategy β when α has a frequency , strategy α fixates in a β-population with selective advantage. In their study, it is assumed that the inheritance of strategies is asexual, i.e. the population is haploid. In this study, we apply their framework to a diploid population that plays a two-strategy game with two ESSs (a bistable game). The fixation probability of a mutant allele in this diploid population is derived. A “three-tenth law” for a completely recessive mutant allele and a “two-fifth law” for a completely dominant mutant allele are found; other cases are also discussed.     

Food-web formation with recursive evolutionary branching

A reaction-diffusion model describing the evolutionary dynamics of a food-web was constructed. In this model, predator-prey relationships among organisms were determined by their position in a two-dimensional phenotype space defined by two traits: as prey and as predator. The mutation process is expressed with a diffusion process of biomass in the phenotype space. Numerical simulation of this model showed co-evolutionary dynamics of isolated phenotypic clusters, including various types of evolutionary branching, which were classified into branching as prey, branching as predators, and co-evolutionary branching of both prey and predators. A complex food-web develops with recursive evolutionary branching from a single phenotypic cluster. Biodiversity peaks at the medium strength of the predator-prey interaction, where the food-web is maintained at medium biomass by a balanced frequency between evolutionary branching and extinction.     

Evolution of cooperation under -person snowdrift games

In the animal world, performing a given task which is beneficial to an entire group requires the cooperation of several individuals of that group who often share the workload required to perform the task. The mathematical framework to study the dynamics of collective action is game theory. Here we study the evolutionary dynamics of cooperators and defectors in a population in which groups of individuals engage in N-person, non-excludable public goods games. We explore an N-person generalization of the well-known two-person snowdrift game. We discuss both the case of infinite and finite populations, taking explicitly into consideration the possible existence of a threshold above which collective action is materialized. Whereas in infinite populations, an N-person snowdrift game (NSG) leads to a stable coexistence between cooperators and defectors, the introduction of a threshold leads to the appearance of a new interior fixed point associated with a coordination threshold. The fingerprints of the stable and unstable interior fixed points still affect the evolutionary dynamics in finite populations, despite evolution leading the population inexorably to a monomorphic end-state. However, when the group size and population size become comparable, we find that spite sets in, rendering cooperation unfeasible.     

How inconsistency between attitude and behavior persists through cultural transmission

Individuals tend to conform their behavior to that of the majority. Consequently, an individual's behavior is not always consistent with his or her attitude, and such inconsistency sometimes causes mental distress. Understanding the mechanism of sustaining inconsistency between attitude and behavior is a challenging problem from the viewpoint of evolutionary theory. We constructed an evolutionary game theory model in which each player has an attitude and behavior toward a single social norm, and the players' attitudes and behaviors are affected by three types of cultural transmission: vertical, oblique, and horizontal. We assumed that strategy is a combination of attitude and behavior and that the process of learning or transmitting the social norm depends on the life stage of each player. Adults play a coordination game in which players whose behaviors match those of the majority obtain a high payoff, which is diminished by any inconsistency between attitude and behavior. The adults' strategies are passed to newborns via vertical transmission, and the frequency of a newborn's replication of strategy is proportional to the corresponding adult's payoff. Newborns imitate behaviors of unrelated adults via oblique transmission. Juveniles change their attitudes or behaviors by observing other juveniles' behaviors or inferring other juveniles' attitudes (horizontal transmission). We conclude that the key factor for sustaining inconsistency between attitude and behavior is the ability of players to infer and imitate others' attitudes, and that oblique transmission promotes inconsistency.     

Phenotypic plasticity and population viability: the importance of environmental predictability

Phenotypic plasticity plays a key role in modulating how environmental variation influences population dynamics, but we have only rudimentary understanding of how plasticity interacts with the magnitude and predictability of environmental variation to affect population dynamics and persistence. We developed a stochastic individual-based model, in which phenotypes could respond to a temporally fluctuating environmental cue and fitness depended on the match between the phenotype and a randomly fluctuating trait optimum, to assess the absolute fitness and population dynamic consequences of plasticity under different levels of environmental stochasticity and cue reliability. When cue and optimum were tightly correlated, plasticity buffered absolute fitness from environmental variability, and population size remained high and relatively invariant. In contrast, when this correlation weakened and environmental variability was high, strong plasticity reduced population size, and populations with excessively strong plasticity had substantially greater extinction probability. Given that environments might become more variable and unpredictable in the future owing to anthropogenic influences, reaction norms that evolved under historic selective regimes could imperil populations in novel or changing environmental contexts. We suggest that demographic models (e.g. population viability analyses) would benefit from a more explicit consideration of how phenotypic plasticity influences population responses to environmental change.     

Evolutionary graph theory: breaking the symmetry between interaction and replacement

We study evolutionary dynamics in a population whose structure is given by two graphs: the interaction graph determines who plays with whom in an evolutionary game; the replacement graph specifies the geometry of evolutionary competition and updating. First, we calculate the fixation probabilities of frequency dependent selection between two strategies or phenotypes. We consider three different update mechanisms: birth-death, death-birth and imitation. Then, as a particular example, we explore the evolution of cooperation. Suppose the interaction graph is a regular graph of degree h, the replacement graph is a regular graph of degree g and the overlap between the two graphs is a regular graph of degree l. We show that cooperation is favored by natural selection if b/c>hg/l. Here, b and c denote the benefit and cost of the altruistic act. This result holds for death-birth updating, weak-selection and large population size. Note that the optimum population structure for cooperators is given by maximum overlap between the interaction and the replacement graph (g=h=l), which means that the two graphs are identical. We also prove that a modified replicator equation can describe how the expected values of the frequencies of an arbitrary number of strategies change on replacement and interaction graphs: the two graphs induce a transformation of the payoff matrix.     

The adaptive dynamics of function-valued traits

This study extends the framework of adaptive dynamics to function-valued traits. Such adaptive traits naturally arise in a great variety of settings: variable or heterogeneous environments, age-structured populations, phenotypic plasticity, patterns of growth and form, resource gradients, and in many other areas of evolutionary ecology. Adaptive dynamics theory allows analysing the long-term evolution of such traits under the density-dependent and frequency-dependent selection pressures resulting from feedback between evolving populations and their ecological environment. Starting from individual-based considerations, we derive equations describing the expected dynamics of a function-valued trait in asexually reproducing populations under mutation-limited evolution, thus generalizing the canonical equation of adaptive dynamics to function-valued traits. We explain in detail how to account for various kinds of evolutionary constraints on the adaptive dynamics of function-valued traits. To illustrate the utility of our approach, we present applications to two specific examples that address, respectively, the evolution of metabolic investment strategies along resource gradients, and the evolution of seasonal flowering schedules in temporally varying environments.     

Strategy selection in structured populations

Evolutionary game theory studies frequency dependent selection. The fitness of a strategy is not constant, but depends on the relative frequencies of strategies in the population. This type of evolutionary dynamics occurs in many settings of ecology, infectious disease dynamics, animal behavior and social interactions of humans. Traditionally evolutionary game dynamics are studied in well-mixed populations, where the interaction between any two individuals is equally likely. There have also been several approaches to study evolutionary games in structured populations. In this paper we present a simple result that holds for a large variety of population structures. We consider the game between two strategies, A and B, described by the payoff matrix . We study a mutation and selection process. For weak selection strategy A is favored over B if and only if σa+b>c+σd. This means the effect of population structure on strategy selection can be described by a single parameter, σ. We present the values of σ for various examples including the well-mixed population, games on graphs, games in phenotype space and games on sets. We give a proof for the existence of such a σ, which holds for all population structures and update rules that have certain (natural) properties. We assume weak selection, but allow any mutation rate. We discuss the relationship between σ and the critical benefit to cost ratio for the evolution of cooperation. The single parameter, σ, allows us to quantify the ability of a population structure to promote the evolution of cooperation or to choose efficient equilibria in coordination games.     

Emergence of asymmetry in evolution

We investigate symmetry-breaking bifurcation patterns in evolution in the framework of adaptive dynamics (AD). We define weak and strong symmetry. The former applies for populations where only the simultaneous reflection of all individuals is an invariant transformation. The symmetry is strong in populations where reflection of some, but not all, individuals leaves the situation unchanged. We show that in case of weak symmetry evolutionary branching can lead to the emergence of two asymmetric variants, which are mirror images of each other, and the loss of the symmetric ancestor. We also show that in case of strong symmetry, evolutionary branching can occur into a symmetric and an asymmetric variant, both of which survive. The latter, asymmetric branching differs from the generic branching patterns of AD, which is always symmetric. We discuss biological examples for weak and strong symmetries and a specific model producing the new kind of branching.     

A novel analytical method for evolutionary graph theory problems

Evolutionary graph theory studies the evolutionary dynamics of populations structured on graphs. A central problem is determining the probability that a small number of mutants overtake a population. Currently, Monte Carlo simulations are used for estimating such fixation probabilities on general directed graphs, since no good analytical methods exist. In this paper, we introduce a novel deterministic framework for computing fixation probabilities for strongly connected, directed, weighted evolutionary graphs under neutral drift. We show how this framework can also be used to calculate the expected number of mutants at a given time step (even if we relax the assumption that the graph is strongly connected), how it can extend to other related models (e.g. voter model), how our framework can provide non-trivial bounds for fixation probability in the case of an advantageous mutant, and how it can be used to find a non-trivial lower bound on the mean time to fixation. We provide various experimental results determining fixation probabilities and expected number of mutants on different graphs. Among these, we show that our method consistently outperforms Monte Carlo simulations in speed by several orders of magnitude. Finally we show how our approach can provide insight into synaptic competition in neurology.     

Global mutations and local mutations have very different effects on evolution, illustrated by mixed strategies of asymmetric binary games

We study the evolutionary effect of rare mutations causing global changes in traits. We consider asymmetric binary games between two players. The first player takes two alternative options with probability x and 1−x; and the second player takes options with probability y and 1−y. Due to natural selection and recurrent mutation, the population evolves to have broad distributions of x and y. We analyze three cases showing qualitatively different dynamics, exemplified by (1) vigilance-intrusion game, (2) asymmetric hawk-dove game and (3) cleaner-client game. We found that the evolutionary outcome is strongly dependent upon the distribution of mutants’ traits, more than the mutation rates. For example in the vigilance-intrusion game, the evolutionary dynamics show a perpetual stable oscillation if mutants are always close to the parent (local-mutation mode), whilst the population converges to a stable equilibrium distribution if mutants can be quite different from the parent (global-mutation mode), even for extremely low mutation rate. When common local mutations and rare global mutations occur simultaneously, the evolutionary outcome is controlled by the latter.