The evolution of alternative mating strategies in variable environments

Summary We assessed the influence of phenotypic plasticity in age at maturity on the maintenance of alternative mating strategies in male Atlantic salmon,Salmo salar. We calculated the fitness,r, associated with the parr and the anadromous strategies, using age-specific survival data from the field and strategy-specific fertilization data from the laboratory. The fitness of each strategy depended largely on mate competition (numbers of parr per female, i.e. parr frequency) and on age at maturity. Fitness declined with increasing numbers of parr per female with equilibrium frequencies (at which the fitnesses of each strategy are equal) being within the range observed in the wild. Equilibrium parr frequencies declined with decreasing growth rate and increasing age at maturity. Within populations, the existence of multiple age-specific sets of fitness functions suggests that the fitnesses of alternative strategies are best represented as multidimensional surfaces. The points of intersection of these surfaces, whose boundaries encompass natural variation in age at maturity and mate competition, define an evolutionarily stable continuum (ESC) of strategy frequencies along which the fitnesses associated with each strategy are equal. We propose a simple model that incorporates polygenic thresholds of a largely environmentally-controlled trait (age at maturity) to provide a mechanism by which an ESC can be maintained within a population. An indirect test provides support for the prediction that growth-rate thresholds for parr maturation exist and are maintained by stabilizing selection. Evolutionarily stable continua, maintained by negative frequency-dependent selection on threshold traits, provide a theoretical basis for understanding how alternative life histories can evolve in variable environments.     

Dealing with stochastic environmental variation in space and time: bet hedging by generalist,specialist, and diversified strategies

Building on previous work, we derive an optimization model for a two-state stochastic environment and evaluate the fitnesses of five reproductive strategies across generations. To do this, we characterize spatiotemporal variation and define grain (=patch) size as the scale of fitness autocorrelation. Fitness functions of environmental condition are Gaussian. The strategies include two specialists on each of the environmental conditions; two generalists that each fare equally well under both conditions, but one (a conservative bet hedger) optimizes the shape of the fitness function; and a diversified bet hedger producing an optimal mix of the two specialists within individual broods. When the environment is primarily in one of the two states, the specialist on that state achieves the highest fitness. In the more interesting situation where the two environments are equally prevalent in the long term, with low-moderate environmental variation, a generalist strategy (that copes with both states well) does best. Higher variation favors diversified bet hedgers, or surprisingly, specialists, depending mainly on whether spatial or temporal variation predominates. These strategies reduce variance in fitness and optimize the distribution of offspring among patches differently: specialists by spreading offspring among many independently varying patches, while diversified bet hedgers put all offspring into a few patches or a single patch. We distinguish features consistent with strategies like diversified bet hedgers that spread risk in time from features linked to strategies like specialists that spread risk in space. Finally, we present testable hypotheses arising from this study and suggest directions for future work.     

Multilocus Behavior in Random Environments I. Random Levene Models

In this paper the consequences of natural selection acting on several loci simultaneously in a spatially fluctuating environment are described. The fitnesses of the genotypes are assumed to be additive both within and between loci. The environment is assumed to be made up of a very large (effectively infinite) number of patches in which fitnesses are assigned at random. The resulting deterministic model is called a Random Levene Model and its properties are approximate by a system of differential equations. The main equilibrium properites are that (1) the linkage disequilibrium is zero and (2) the correlations in fitness between alleles at different loci are the principle determinants of the dynamic inter-locus interactions. Although there is no epistasis as conventionally defined, the equilibrium state at the two loci are highly interdependent, the governing principle being that two alleles at different loci whose fitness are negatively correlated across environments have a higher overall fitness due to the reduction in their variance in fitness through the negative correlation. When a large number of loci are considered, they naturally fall into correlation groupings which lead to an enhanced likelihood for polymorphism over that predicted by single-locus theory.     

Evolutionary optimization and neural network models of behavior

One of the main challenges to the adaptionist program in general and the use of optimization models in behavioral and evolutionary ecology, in particular, is that organisms are so constrained' by ontogeny and phylogeny that they may not be able to attain optimal solutions, however those are defined. This paper responds to the challenge through the comparison of optimality and neural network models for the behavior of an individual polychaete worm. The evolutionary optimization model is used to compute behaviors (movement in and out of a tube) that maximize a measure of Darwinian fitness based on individual survival and reproduction. The neural network involves motor, sensory, energetic reserve and clock neuronal groups. Ontogeny of the neural network is the change of connections of a single individual in response to its experiences in the environment. Evolution of the neural network is the natural selection of initial values of connections between groups and learning rules for changing connections. Taken together, these can be viewed as design parameters. The best neural networks have fitnesses between 85% and 99% of the fitness of the evolutionary optimization model. More complicated models for polychaete worms are discussed. Formulation of a neural network model for host acceptance decisions by tephritid fruit flies leads to predictions about the neurobiology of the flies. The general conclusion is that neural networks appear to be sufficiently rich and plastic that even weak evolution of design parameters may be sufficient for organisms to achieve behaviors that give fitnesses close to the evolutionary optimal fitness, particularly if the behaviors are relatively simple.     

Multi-objective behavioural mechanisms are adopted by foraging animals to achieve several optimality goals simultaneously

1. Animals foraging for resources are under a variety of selective pressures, and separate optimality models have been developed predicting the optimal reproductive strategies they should adopt. 2. In most cases, the proximate behavioural mechanisms adopted to achieve such optimality goals have been identified. This is the case, for example, for optimal patch time and sex allocation in insect parasitoids. However, behaviours modelled within this framework have mainly been studied separately, even though real animals have to optimize some behaviours simultaneously. 3. For this reason, it would be better if proximate behavioural rules were designed to attain several goals simultaneously. Despite their importance, such multi-objective proximate rules remain to be discovered. 4. Based on experiments on insect parasitoids that simultaneously examine their optimal patch time and sex allocation strategies, it is shown here that animals can adopt multi-objective behavioural mechanisms that appear consistent with the two optimal goals simultaneously. 5. Results of computer simulations demonstrate that these behavioural mechanisms are indeed consistent with optimal reproductive strategies and have thus been most likely selected over the course of the evolutionary time.     

Retirement investment theory explains patterns in songbird nest-site choice

When opposing evolutionary selection pressures act on a behavioural trait, the result is often stabilizing selection for an intermediate optimal phenotype, with deviations from the predicted optimum attributed to tracking a moving target, development of behavioural syndromes or shifts in riskiness over an individual''s lifetime. We investigated nest-site choice by female golden-winged warblers, and the selection pressures acting on that choice by two fitness components, nest success and fledgling survival. We observed strong and consistent opposing selection pressures on nest-site choice for maximizing these two fitness components, and an abrupt, within-season switch in the fitness component birds prioritize via nest-site choice, dependent on the time remaining for additional nesting attempts. We found that females consistently deviated from the predicted optimal behaviour when choosing nest sites because they can make multiple attempts at one fitness component, nest success, but only one attempt at the subsequent component, fledgling survival. Our results demonstrate a unique natural strategy for balancing opposing selection pressures to maximize total fitness. This time-dependent switch from high to low risk tolerance in nest-site choice maximizes songbird fitness in the same way a well-timed switch in human investor risk tolerance can maximize one''s nest egg at retirement. Our results also provide strong evidence for the adaptive nature of songbird nest-site choice, which we suggest has been elusive primarily due to a lack of consideration for fledgling survival.     

The use of conspecific reproductive success for breeding patch selection in terrestrial migratory species

Classical models of breeding habitat selection rarely deal with the question of information gathering for patch quality assessment. In this paper, we present two models comparing the fitness outcomes of behavioural strategies based on conspecific reproductive success as a cue to assess local environmental quality before selecting a new breeding habitat. The models deal with two phases of the life-cycle of a territorial migratory species: recruitment to a breeding population (model 1) and breeding site fidelity of subsequent breeding attempts (model 2). The first model shows that prospecting breeding patches before recruiting is the best strategy if the environment is predictable and contains a low proportion of good patches, even if it implies losing a breeding opportunity. The second model shows that dispersing after a breeding attempt according to the patch's breeding success rather than the individual's own success is the bests own success is the best strategy if the environment is patchy. These results underline the importance of studying the spatio-temporal variations of factors affecting reproductive success when considering the importance of habitat selection strategies based on conspecifics. Moreover, they allow the understanding of individual behaviour patterns observed in natural populations and their potential consequences at the metapopulation level.     

A complex adaptive systems approach to the kinetic folding of RNA

The kinetic folding of RNA sequences into secondary structures is modeled as a complex adaptive system, the components of which are possible RNA structural rearrangements (SRs) and their associated bases and base pairs. RNA bases and base pairs engage in local stacking interactions that determine the probabilities (or fitnesses) of possible SRs. Meanwhile, selection operates at the level of SRs; an autonomous stochastic process periodically (i.e., from one time step to another) selects a subset of possible SRs for realization based on the fitnesses of the SRs. Using examples based on selected natural and synthetic RNAs, the model is shown to reproduce characteristic (nonlinear) RNA folding dynamics such as the attainment by RNAs of alternative stable states. Possible applications of the model to the analysis of properties of fitness landscapes, and of the RNA sequence-to-structure mapping are discussed.     

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.     

Theory of evolutionary molecular engineering through simultaneous accumulation of advantageous mutations

We examined the effectiveness of an "adaptive leap" strategy using the "mutation scrambling" method as an efficient optimization technique (Uchiyama, 2000;J. Biochem.128, 441-447) for cases where mutational (rough) additivity holds in fitness. The mutation scrambling method is composed of the following three processes: (1) preliminary selection of several advantageous single-point mutations introduced in a wild-type sequence; (2) preparation of various multiple-point mutants incorporating the advantageous mutant residue or wild-type residue at each of the selected sites, by scrambling the mutant residues and wild-type residues (this process is called mutation scrambling); and (3) selection of the fittest through screening of the mutant pool. The fitness distribution in the mutant pool is controlled by the mixing ratio of the mutant residues to the wild-type residues. We focused on the mutant fitness distribution and obtained the optimal mixing ratio which efficiently generates superior multiple-point mutants with high fitnesses. As a result, we found that the optimal ratio lies between 7/3 and 9/1 in realistic cases. Particularly, this strategy works well in cases where the number of component mutations is large and the size of the population to be screened is small. Analysis of the mutant fitness distributions with various mixing ratios is also useful to explore local fitness landscapes.     

Relative Fitness, Teleology, and the Adaptive Landscape

The metaphor of the adaptive landscape, introduced by Sewall Wright in 1932, has played, and continues to play, a central role in much evolutionary thought. I argue that the use of this metaphor is tied to a teleological view of the evolutionary process, in which natural selection directs evolution toward an improved future state. I argue further that the use of “relative fitnesses” standardized to an arbitrary value, which is closely connected with the metaphor of an adaptive landscape, produces a disconnect between the mean fitness of a population and any real property of that population. This allows for a vague and ill-defined improvement to occur under the influence of selection. Instead, I suggest that relative fitnesses should be standardized by the mean absolute fitness (expected population growth rate), so that they express the expected rate of increase in frequency, rather than number. Under this definition, the mean relative fitness of all populations is always 1.0, and never changes as long as the population continues to exist.     

Models of Frequency-Dependent Selection with Mutation from Parental Alleles

Frequency-dependent selection (FDS) remains a common heuristic explanation for the maintenance of genetic variation in natural populations. The pairwise-interaction model (PIM) is a well-studied general model of frequency-dependent selection, which assumes that a genotype’s fitness is a function of within-population intergenotypic interactions. Previous theoretical work indicated that this type of model is able to sustain large numbers of alleles at a single locus when it incorporates recurrent mutation. These studies, however, have ignored the impact of the distribution of fitness effects of new mutations on the dynamics and end results of polymorphism construction. We suggest that a natural way to model mutation would be to assume mutant fitness is related to the fitness of the parental allele, i.e., the existing allele from which the mutant arose. Here we examine the numbers and distributions of fitnesses and alleles produced by construction under the PIM with mutation from parental alleles and the impacts on such measures due to different methods of generating mutant fitnesses. We find that, in comparison with previous results, generating mutants from existing alleles lowers the average number of alleles likely to be observed in a system subject to FDS, but produces polymorphisms that are highly stable and have realistic allele-frequency distributions.     

Identifying fitness and optimal life-history strategies for an asexual filamentous fungus

Filamentous fungi are ubiquitous and ecologically important organisms with rich and varied life histories, however, there is no consensus on how to identify or measure their fitness. In the first part of this study we adapt a general epidemiological model to identify the appropriate fitness metric for a saprophytic filamentous fungus. We find that fungal fitness is inversely proportional to the equilibrium density of uncolonized fungal resource patches which, in turn, is a function of the expected spore production of a fungus. In the second part of this study we use a simple life history model of the same fungus within a resource patch to show that a bang-bang resource allocation strategy maximizes the expected spore production, a critical fitness component. Unlike bang-bang strategies identified in other life-history studies, we find that the optimal allocation strategy for saprophytes does not entail the use of all of the resources within a patch.     

sOAR: a tool for modelling optimal animal life‐history strategies in cyclic environments

Periodic environments determine the life cycle of many animals across the globe and the timing of important life history events, such as reproduction and migration. These adaptive behavioural strategies are complex and can only be fully understood (and predicted) within the framework of natural selection in which species adopt evolutionary stable strategies. We present sOAR, a powerful and user‐friendly implementation of the well‐established framework of optimal annual routine modelling. It allows determining optimal animal life history strategies under cyclic environmental conditions using stochastic dynamic programming. It further includes the simulation of population dynamics under the optimal strategy. sOAR provides an important tool for theoretical studies on the behavioural and evolutionary ecology of animals. It is especially suited for studying bird migration. In particular, we integrated options to differentiate between costs of active and passive flight into the optimal annual routine modelling framework, as well as options to consider periodic wind conditions affecting flight energetics. We provide an illustrative example of sOAR where food supply in the wintering habitat of migratory birds significantly alters the optimal timing of migration. sOAR helps improving our understanding of how complex behaviours evolve and how behavioural decisions are constrained by internal and external factors experienced by the animal. Such knowledge is crucial for anticipating potential species’ response to global environmental change.     

Selection and Neutrality in Lactose Operons of Escherichia Coli

The kinetics of the permeases and beta-galactosidases of six lactose operons which had been transduced into a common genetic background from natural isolates of Escherichia coli were investigated. The fitnesses conferred by the operons were determined using chemostat competition experiments in which lactose was the sole growth-limiting factor. The cell wall is demonstrated to impose a resistance to the diffusion of galactosides at low substrate concentrations. A steady state model of the flux of lactose through the metabolic pathway (diffusion, uptake and hydrolysis) is shown to be proportional to fitness. This metabolic model is used to explain why an approximately twofold range in activity among the permease alleles confers a 13% range in fitness, whereas a similar range in activity among alleles of the beta-galactosidase confers a 0.5% range in fitness. This metabolic model implies that selection need not be maximized when a resource is scarce.     

Evolutionarily stable strategies in food selection models with fitness sets

Most current models for optimal food selection apply to ecological and behavioural optimization. In this paper optimal food selection theory is extended to apply to evolutionary optimization. A general evolutionary model for optimal food selection must incorporate the concept of fitness sets--or that variables, changing as a result of natural selection in evolutionary time, cannot, in general, vary independently of each other. A "Charnov type" optimal food selection model with a fitness set is investigated, and evolutionarily stable strategy (ESS) solutions of the evolutionary variables (i.e., the efficiencies of using available food types) are found. From this analysis it follows that the relative frequency of various food types in the environment may, under specified conditions, influence the evolutionarily optimal diet. Secondly, the analysis demonstrates that a food type not in the optimal diet may, in evolutionary time, be added to this by becoming more abundant. Thirdly, it follows from the analysis that the ecological result of MacArthur and Pianka, that food types are worth eating even if there is competition for them, is not generally applicable when referring to an evolutionary time scale. Finally, it is pointed out that for the diet to be an ESS, it is necessary that the consumer's density is stable and that the consumer's population dynamics are subjected to some density-dependent factor.     

Genetic variation in patch time allocation in a parasitic wasp

1. The intra-patch experience acquired by foraging parasitoid females has often been considered to have a strong influence on their tendency to leave a patch, and thus on their total patch residence time. Most studies that have been performed on this subject suggest that the patch-leaving rules observed are adaptive because they enable the females to adjust their patch residence time to local environmental conditions.
2. Considering a behavioural rule as being adaptive supposes that it has been progressively settled by natural selection, and thus that there is, in the population, genetic variation on which the natural selection could act.
3. Therefore, this study aimed to discover whether there was indeed genetic variability in the patch-leaving decision rules in a population of the egg parasitoid species Telenomus busseolae , which attacks patches of its hosts, the eggs of Sesamia nonagrioides . Different wasp families were compared using the isofemale lines method, and the behavioural records were analysed by means of a modified version of the Cox's proportional hazards model proposed by Haccou et al . (1991 ) and Hemerik, Driessen & Haccou (1993 ).
4. The results obtained show that T. busseolae females increase their tendency to leave the patch after each successful oviposition. Each host rejection also led to an increase in the tendency to leave the patch, but this effect was smaller when host rejections were observed between two ovipositions occurring in rapid succession. Subsequent visits to the patch also increased the patch-leaving tendency.
5. Genetic variability was found in both the global patch-leaving tendency and in the effect that successful ovipositions and host rejections have on this tendency.
6. The adaptive and evolutionary consequences of these results are discussed.     

Evolutionary stability of optimal foraging: Partial preferences in the diet and patch models

In this article the patch and diet choice models of the optimal foraging theory are reanalyzed with respect to evolutionary stability of the optimal foraging strategies. In their original setting these fundamental models consider a single consumer only and the resulting fitness functions are both frequency and density independent. Such fitness functions do not allow us to apply the classical game theoretical methods to study an evolutionary stability of optimal foraging strategies for competing animals. In this article frequency and density dependent fitness functions of optimal foraging are derived by separation of time scales in an underlying population dynamical model and corresponding evolutionarily stable strategies are calculated. Contrary to the classical foraging models the results of the present article predict that partial preferences occur in optimal foraging strategies as a consequence of the ecological feedback of consumer preferences on consumer fitness. In the case of the patch occupation model these partial preferences correspond to the ideal free distribution concept while in the case of the diet choice model they correspond to the partial inclusion of the less profitable prey type in predators diet.     

Maynard Smith,optimization, and evolution

Maynard Smith’s defenses of adaptationism and of the value of optimization theory in evolutionary biology are both criticized. His defense does not adequately respond to the criticism of adaptationism by Gould and Lewontin. It is also argued here that natural selection cannot be interpreted as an optimization process if the objective function to be optimized is either (i) interpretable as a fitness, or (ii) correlated with the mean population fitness. This result holds even if fitnesses are frequency-independent; the problem is further exacerbated in the frequency-dependent context modeled by evolutionary game theory. However, Eshel and Feldman’s new results on “long-term” evolution may provide some hope for the continuing relevance of the game-theoretic framework. These arguments also demonstrate the irrelevance of attempts by Intelligent Design creationists to use computational limits on optimization algorithms as evidence against evolutionary theory. It is pointed out that adaptation, natural selection, and optimization are not equivalent processes in the context of biological evolution. It is a pleasure to dedicate this paper to the memory of John Maynard Smith. Thanks are due to James Justus and Samir Okasha for comments on an earlier draft.