Evolution of unstable and stable biparental care

Evolutionarily stable strategy models suggest that biparentalcare will be stable when parents partially compensate for changesin care by the other parent. Previous work has emphasized therelationship between parental expenditure and the current componentof fitness (e. g., offspring survival and fecundity) in causingpartial compensation. This study shows that partial compensationdepends critically on the effect of current parental expenditureon a parent's future fitness (e. g., survival to and fecundityin subsequent breeding seasons). Partial compensation is favoredand biparental care is stable when future fitness is a concave-downfunction of expenditure (i. e., each increment of expenditureis more costly than the previous). However, when future fitnessis a convex-down function of expenditure (i. e., each incrementof expenditure is less costly) biparental care is unstable.(BehavEcol 7: 490–493(1996)]     

Evolutionarily stable strategies in differential and difference equation models

Summary A definition for an evolutionarily stable strategy (ESS) is given which is applicable to a general differential equation population model and two difference equation analogs. With the introduction of a fitnessgenerating function, it is possible to develop necessary conditions for the determination of an ESS for each of these systems. In most situations, an ESS for one system will also be an ESS for the other. Necessary conditions for an ESS are obtained. Under certain restrictions, they are shown to be valid, even under an unstable equilibrium in population density. the results are illustrated with an example which has the same ESS solution whether a continuous or discrete model is used. The behavior of the ESS for the discrete model is then examined under unstable equilibrium conditions in population density.     

The evolution of fitness in life-history theory

Theory concerning the evolution of life history (the schedule of reproduction and survival) focuses on describing the life history which maximises fitness. Although there is an intuitive link between life history and fitness, there are in fact several measures of the 'black box' concept of fitness. There has been a debate in the bio-mathematical literature on the predictive difference between the two most commonly used measures; intrinsic rate of increase r and net reproductive ratio R0. Although both measures aim to describe fitness, models using one of the measures may predict the opposite of similar models using the other measure, which is clearly undesirable. Here, I review the evolution of these fitness measures over the last four decades, the predictive differences between these measures and the resulting shift of the fitness concept. I focus in particular on some recent developments, which have solved the dilemma of predictive differences between these fitness measures by explicitly acknowledging the game-theoretical nature of life-history evolution.     

Evolutionarily stable strategies of migration in heterogeneous environments

By means of a simulation model we are showing that the rates of migration can be related to avoidance of competition between relatives, especially in clonal organisms. This could result in a strong selective pressure for migration, even at a high cost. In addition, if the habitat is fragmented, migration can strongly affect local dynamics and result in a dramatic decrease of the densities in some places. In parthenogenetically reproducing organisms like aphids, the level of relatedness in local populations is expected to be very high and therefore they can serve as a good model group for testing these hypotheses. This revised version was published online in July 2006 with corrections to the Cover Date.     

Evolutionarily stable germination strategies with time-correlated yield

We investigate the effect of auto-correlated yield on the evolutionarily stable germination fraction of dormant seeds. By using both analytics and numerics, we first show that in a regime of small fluctuations a positive correlation reduces dormancy and a negative correlation enhances dormancy. By extending the numerical analysis we also show that in the regime of large fluctuations a more complex picture emerges where also negative correlations can reduce dormancy.     

Evolutionarily stable kleptoparasitism: consequences of different prey types

We present two elaborations of the model of Broom and Ruxtonthat found evolutionarily stable kleptoparasitic strategiesfor foragers. These elaborations relax the assumption that thedistribution of times required to handle discovered food itemsis exponential. These changes increase the complexity of themodel but represent a significant improvement in biologicalrealism. In one elaboration, handling takes a fixed interval,t_h, at the end of which the whole value of the food item isobtained. We liken this to peeling then consuming a small orange.The other elaboration also assumes that handling takes a fixedinterval, t_h, but this time the reward from the food item isextracted continuously throughout the handling period. We likenthis to eating an apple. Both models predict that increasingfood density, the ease with which food items can be discovered,or the length of aggressive contests all act to make kleptoparasitismless common. The difference between the evolutionarily stablestrategy solutions of the apple and orange models provides aclear prediction of our theory. When prey items require handlingbefore yielding a lump sum at the end, then kleptoparasiticattacks will be focused on prey items near the end of theirhandling period. However, if prey items yield reward continuouslyduring handling, then attacks should be biased toward newlydiscovered food items. Another key difference between the modelpredictions is that kleptoparasitism increases with foragerdensity in the apple model, but decreases in the orange model.     

Maximization of fitness through limiting the number of offspring in the evolution ofHomo sapiens

It is proposed that the concealment of ovulation and the extension of sexual receptivity of the hominid female is a fitness maximizing adaptation resulting in limiting the number of offspring. To support this hypothesis a probability model is introduced. For a specific set of parameter values (including maternal mortality during delivery) through a formal deduction, it is shown that keeping the number of offspring below the physiological limit is a fitness maximizing strategy.     

Evolutionarily stable dispersal of a waterstrider in a temporally and spatially heterogeneous environment

Summary Evolutionary stable dispersal and wing muscle histolysis strategies are studied in the waterstriderGerris thoracicus. These strategies relate to spreading reproductive risk. Overwintering individuals have the choice of dispersing to either a brackish sea bay or a rock pool habitat. The former is reproductively more favorable than the latter during warm dry years and less favorable during cool wet years. After spring migration, individuals may histolyse their flight muscles and lay all their eggs in one pool or they may retain their flight ability and lay fewer eggs in total but spread them in several pools. We use a simple two-habitat model to examine the question of habitat dispersal. Our results indicate that, although the value of the evolutionary stable dispersal depends on the degree of variability in the environment and on the probability of local extinctions in either habitat, the population always disperses to both habitats as a consequence of density dependent growth. We use a more detailed multiple-rockpool habitat model to examine the question of wing muscle histolysis as a response to density dependence. Our results indicate that a wing muscle histolysis response to population density is an evolutionarily stable strategy when compared with the two alternatives of females always histolysing or never histolysing their flight muscles. The application of evolutionarily stable theory to stochastic problems presents a number of difficulties. We discuss these difficulties in the context of computing evolutionarily stable strategies for the problems at hand.     

Evolutionarily stable stealing: game theory applied to kleptoparasitism

We present an individual-based model of a group of foraginganimals. Individuals can obtain food either by discovering itthemselves or by stealing it from others (kleptoparasitism).Given that challenging another individual for a discovered fooditem costs time (which could otherwise be spent searching foran undiscovered item), attempting to steal from another maynot always be efficient We show that there is generally a uniquestrategy that maximizes uptake rate—always or never challengingothers. For any combination of parameter values, we can identifywhich strategy is appropraite. As a corollary to this, we predictthat small changes in ecolgical conditions can, under some circumstances,cause a dramatic change in the aggressive behavior of individuals.Further, we investigate situations where searching for undiscoveredfood and searching for potential opportunities for stealingare mutually exclusive activities (i.e., success at one canonly be improved at the expense of the other). Using game theory,we are able to find the evolutionarily stable strategy for investmentin these two activities in terms of the ecological parametersof the model.     

Evolutionarily stable seasonal timing for insects with competition for renewable resource

Summary I study the evolutionarily stable seasonal patterns of hatching and pupation for herbivorous insects that engage in exploitative competition for a renewable resource. A longer larval feeding period enhances female fecundity, but also causes a higher mortality by predation and parasitism. Previously, it was shown that the evolutionarily stable population exhibits asynchronous starting and ending of the larval feeding period in a model in which larval growth rate decreases with the total larval biomass in the population due presumably to interference competition. Here I study the case in which resource availability changes not only with environmental seasonality but with the depletion by the feeding of larvae. I find that if the impact of the herbivory is strong, both hatching and pupation should occur asynchronously in the evolutionarily stable population. And if the favourable season for the host plant is short the ESS population may include synchronous timing of pupation. If the timing of hatching and pupation occurs asynchronously, in the first day of each interval some fraction of the population hatch or pupate, respectively and the rest do so gradually over the interval. In addition, if the environmental variable changes as a symmetric function of time, the length of the period in which hatching occurs tends to be much shorter than the period in which pupation occurs.     

Evolutionarily stable resource allocation for production of wind-dispersed seeds

We developed a game-theoretic model for wind-dispersed seed production to examine the seed mass–dispersal ability relationship and the evolutionarily stable distance of seed dispersal in terms of exploitation of safe sites. We assumed trade-offs between masses of the embryo (including albumen) and the wind-dispersal structures per seed, and also between seed mass and number of seeds per parent. We showed that ESS wing-loading is independent of embryo mass; that is, heavy seeds are not poor dispersers if the cost of producing wind-dispersal structures per unit area is constant. The ESS embryo mass per seed depends only on the factors which determine the probability of a seedling being established from a seed. However, wing-loading was found to increase with embryo mass when the change in length was isometric and there was a negative correlation between seed mass and dispersal ability. Thus, the area–mass relationship in wind-dispersal structures may have large effects on the ESS production of wind-dispersed seeds. On the other hand, given that only a limited number of adults can be established at a safe site, the ESS seed dispersal distance depends on the relative degree of sib to non-sib competition. A parent disperses its seeds over a wide area to exploit many safe sites if sib competition is strong. However, it disperses its seeds within a narrow area if the mean number of parents per unit area is large, or if non-sib competition is strong. Thus, in addition to an upper limit on the number of adults per safe site, the degree of sib and non-sib competition may be important for the ESS dispersal distance in wind-dispersed seeds. This revised version was published online in July 2006 with corrections to the Cover Date.     

Positive feedback and alternative stable states in inbreeding, cooperation, sex roles and other evolutionary processes

A large proportion of studies in systems science focus on processes involving a mixture of positive and negative feedbacks, which are also common themes in evolutionary ecology. Examples of negative feedback are density dependence (population regulation) and frequency-dependent selection (polymorphisms). Positive feedback, in turn, plays a role in Fisherian 'runaway' sexual selection, the evolution of cooperation, selfing and inbreeding tolerance under purging of deleterious alleles, and the evolution of sex differences in parental care. All these examples feature self-reinforcing processes where the increase in the value of a trait selects for further increases, sometimes via a coevolutionary feedback loop with another trait. Positive feedback often leads to alternative stable states (evolutionary endpoints), making the interpretation of evolutionary predictions challenging. Here, we discuss conceptual issues such as the relationship between self-reinforcing selection and disruptive selection. We also present an extension of a previous model on parental care, focusing on the relationship between the operational sex ratio and sexual selection, and the influence of this relationship on the evolution of biparental or uniparental care.     

Modelling the adaptive dynamics of traits involved in inter- and intraspecific interactions: An assessment of three methods

In recent years, three related methods have been used to model the phenotypic dynamics of traits under the influence of natural selection. The first is based on an approximation to quantitative genetic recursion equations for sexual populations. The second is based on evolution in asexual lineages with mutation-generated variation. The third method finds an evolutionarily stable set of phenotypes for species characterized by a given set of fitness functions, assuming that the mode of reproduction places no constraints on the number of distinct types that can be maintained in the population. The three methods share the property that the rate of change of a trait within a homogeneous population is approximately proportional to the individual fitness gradient. The methods differ in assumptions about the potential magnitude of phenotypic differences in mutant forms, and in their assumptions about the probability that invasion or speciation occurs when a species has a stable, yet invadable phenotype. Determining the range of applicability of the different methods is important for assessing the validity of optimization methods in predicting the evolutionary outcome of ecological interactions. Methods based on quantitative genetic models predict that fitness minimizing traits will often be evolutionarily stable over significant time periods, while other approaches suggest this is likely to be rare. A more detailed study of cases of disruptive selection might reveal whether fitness-minimizing traits occur frequently in natural communities.     

An inclusive fitness analysis of synergistic interactions in structured populations

We study the evolution of a pair of competing behavioural alleles in a structured population when there are non-additive or ‘synergistic’ fitness effects. Under a form of weak selection and with a simple symmetry condition between a pair of competing alleles, Tarnita et al. provide a surprisingly simple condition for one allele to dominate the other. Their condition can be obtained from an analysis of a corresponding simpler model in which fitness effects are additive. Their result uses an average measure of selective advantage where the average is taken over the long-term—that is, over all possible allele frequencies—and this precludes consideration of any frequency dependence the allelic fitness might exhibit. However, in a considerable body of work with non-additive fitness effects—for example, hawk–dove and prisoner''s dilemma games—frequency dependence plays an essential role in the establishment of conditions for a stable allele-frequency equilibrium. Here, we present a frequency-dependent generalization of their result that provides an expression for allelic fitness at any given allele frequency p. We use an inclusive fitness approach and provide two examples for an infinite structured population. We illustrate our results with an analysis of the hawk–dove game.     

The importance of the timescale of the fitness metric for estimates of selection on phenotypic traits during a period of demographic change

Although fitness is central to the evolutionary process, metrics vary by timescale. Different timescales may give rise to different estimates of selection, especially during demographic transitions caused by rapid environmental and socioeconomic change. In this study, we used a dataset of a human population in Finland from 1775 to 1950 to compare two fitness metrics and their estimates of selection pressures, before and during a demographic transition. Both metrics, lifetime reproductive success and an annual metric of individual performance, declined while selection on the ages at first and last reproduction remained nearly constant, favouring individuals with wider reproductive windows. The ability to partition the annual metric into contributions from reproduction and survival revealed the short‐term effects of a famine and the reversal of selection pressure via the survival component of annual fitness. Although the metrics generally agreed, the annual metric detected the effects of environmental variation and demographic change occurring within a generation.     

Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree

We present a general framework for modelling adaptive trait dynamics in which we integrate various concepts and techniques from modern ESS-theory. The concept of evolutionarily singular strategies is introduced as a generalization of the ESS-concept. We give a full classification of the singular strategies in terms of ESS-stability, convergence stability, the ability of the singular strategy to invade other populations if initially rare itself, and the possibility of protected dimorphisms occurring within the singular strategy's neighbourhood. Of particular interest is a type of singular strategy that is an evolutionary attractor from a great distance, but once in its neighbourhood a population becomes dimorphic and undergoes disruptive selection leading to evolutionary branching. Modelling the adaptive growth and branching of the evolutionary tree can thus be considered as a major application of the framework. A haploid version of Levene's soft selection model is developed as a specific example to demonstrate evolutionary dynamics and branching in monomorphic and polymorphic populations.     

Multigenerational versus single generation studies to estimate herbicide resistance fitness cost in Arabidopsis thaliana

The evolution of resistance in response to pesticide selection is expected to be delayed if fitness costs are associated with resistance genes. The estimate of fitness costs usually involves comparing major growth traits of resistant versus susceptible individuals in the absence of pesticide. Ideally, a measure of changes in resistance allele frequency over several generations would allow the best estimate of the overall fitness cost of a resistance gene. In greenhouse conditions, we monitored the dynamics of the evolution of the frequencies of six herbicide-resistant mutations (acetolactate synthase, cellulose synthase, and auxin-induced target genes) in the model species Arabidopsis thaliana in a multigenerational study covering five to seven nonoverlapping generations. The microevolutionary dynamics in experimental populations indicated a mean fitness cost of 38%, 73%, and 94% for the ixr1-2, axr1-3, and axr2-1 resistances, respectively; no fitness cost for the csr1-1, and ixr2-1 resistances; and a transient advantage for the aux1-7 resistance. The result for the csr1-1 resistance contrasts with a cost of 37% based on total seed number in a previous study, demonstrating that single generation studies could have limitation for detecting cost. A positive frequency dependence for the fitness cost was also detected for the ixr1-2 resistance. The results are discussed in relation to the maintenance of polymorphism at resistance loci.     

The evolution of traits that determine ability in competitive contests

Summary We analyse mathematical models of the evolution of a trait that determines ability in contest competition. We assume that the value of the competitive trait affects two different components of fitness, one measuring the benefit of winning contests and the other measuring the cost of developing the competitive trait. Unlike previous analyses, we include the population dynamical consequences of larger competitive trait values. Exaggeration of the competitive trait reduces the mean probability of survival during the non-competitive stage of the life cycle. The resulting lower population density reduces competition and, therefore, reduces the advantages of greater competitive ability. Models without population dynamics often predict dimorphism in the competitive trait when resource possession is decided by interactions with many other individuals. If the competition involves a contest with a single other individual, models without population dynamics often predict cycles of increase and collapse in the trait or a continual increase, possibly resulting in extinction. When population dynamics are included, both of these results become less likely and a single stable trait value becomes more likely. Population dynamics also make it possible to have dimorphism when individuals have a single pairwise contest and alternative stable trait values when an individual has many contests. Increases in the value of the resource being contested may increase or decrease the evolutionarily stable size of the trait. Competition between very differently sized species will often decrease size in the larger species (character convergence).     

Expected relative fitness and the adaptive topography of fluctuating selection

Wright's adaptive topography describes gene frequency evolution as a maximization of mean fitness in a constant environment. I extended this to a fluctuating environment by unifying theories of stochastic demography and fluctuating selection, assuming small or moderate fluctuations in demographic rates with a stationary distribution, and weak selection among the types. The demography of a large population, composed of haploid genotypes at a single locus or normally distributed phenotypes, can then be approximated as a diffusion process and transformed to produce the dynamics of population size, N, and gene frequency, p, or mean phenotype, . The expected evolution of p or is a product of genetic variability and the gradient of the long-run growth rate of the population, , with respect to p or . This shows that the expected evolution maximizes , the mean Malthusian fitness in the average environment minus half the environmental variance in population growth rate. Thus, as a function of p or represents an adaptive topography that, despite environmental fluctuations, does not change with time. The haploid model is dominated by environmental stochasticity, so the expected maximization is not realized. Different constraints on quantitative genetic variability, and stabilizing selection in the average environment, allow evolution of the mean phenotype to undergo a stochastic maximization of . Although the expected evolution maximizes the long-run growth rate of the population, for a genotype or phenotype the long-run growth rate is not a valid measure of fitness in a fluctuating environment. The haploid and quantitative character models both reveal that the expected relative fitness of a type is its Malthusian fitness in the average environment minus the environmental covariance between its growth rate and that of the population.     

Effects of B chromosomes and supernumerary segments on morphometric traits and adult fitness components in the grasshopper, Dichroplus elongatus (Acrididae)

The South American species, Dichroplus elongatus, is polymorphic for B chromosomes and supernumerary segments in chromosome pairs M6 (SS6), S9 (SS9) and S10 (SS10). Both forms of supernumerary heterochromatin shape chiasma frequency and distribution and B chromosomes also affect male fertility. Here, we analysed the effects of these polymorphisms on morphometric traits (total, 3rd femur, 3rd tibia, thorax and tegmen lengths) and several adult fitness components, including male and female mating success, and female reproductive potential. B chromosomes tend to decrease, and SS6 segments to increase the body size of carriers. The analysis of reproductive potential suggested that B chromosome carrying females have higher numbers of embryos per clutch and ovarioles per ovary. The uni- and multivariate analysis of mating success revealed that sexual selection favours larger individuals of both sexes and males with standard karyotype. B chromosomes may have accumulation mechanisms, which involve preferential transmission of B chromosomes to germ cells or functional gametes. The maintenance of Bs might be explained by interactions among accumulation mechanisms and trade-offs between detrimental and favourable effects on different fitness components.