Evolutionarily stable strategy in a sex- and frequency-dependent selection model

In this paper, a sex-dependent matrix game haploid model is investigated. For this model, since the phenotypes of female and male individuals are determined by alleles located at a single locus and are sex dependent, any given genotype corresponds to a strategy pair. Thus, a strategy pair is an ESS if and only if the allele corresponding to this strategy pair cannot be invaded by any mutant allele. We show that an ESS equilibrium must be locally asymptotically stable if it exists.     

Evolutionarily stable age at first reproduction in a density-dependent model.

We develop a new model of life history evolution to investigate the evolution of age at first reproduction. Density dependence is taken into account. For a given "species", age of maturity, offspring survival, immature survival, adult survival, fecundity, immature age-classes entering in competition with adults and immature competitive ability are traits adjustable by natural selection, and constitute a particular strategy. On the contrary, the type of intraspecific competition (scramble or contest), strength of competition and inherent net reproductive rate Ro(inh) are fixed (specific) characteristics. As a consequence of fixing Ro(inh), the evolution of any trait will affect trade-offs between others. Evolutionarily stable strategies are determined numerically by using the mathematical concept of Lyapunov exponents. Altogether, we consider 960 different hypothetical "species" (i.e. different combinations of fixed traits). Corresponding ESSs are analyzed with respect to their age at first reproduction, adult survival and immature competitive ability components. They appear to be gathered in three groups. One is intuitive and characterized by a reduction of immature competitive ability and a correlation of age of maturity with adult survival; populations reach mainly equilibria. The two other groups respectively include "species" with low age of maturity but high adult survival, and "species" close to semelparity with delayed maturity; immature competitive ability may not be minimized, and populations possibly exhibit complex dynamics. In conclusion, the hypothesis that the evolution of a demographic parameter modifies trade-offs between others turns out to have important consequences. We argue that life history theory cannot ignore the source and mode-of-operation of density dependence and must regard potential short-term instability as essential.     

The truthful signalling hypothesis: an explicit general equilibrium model

In mating competition, the truthful signalling hypothesis (TSH), sometimes known as the handicap principle, asserts that higher-quality males signal while lower-quality males do not (or else emit smaller signals). Also, the signals are "believed", that is, females mate preferentially with higher-signalling males. Our analysis employs specific functional forms to generate analytic solutions and numerical simulations that illuminate the conditions needed to validate the TSH. Analytic innovations include: (1) A Mating Success Function indicates how female mating choices respond to higher and lower signalling levels. (2) A congestion function rules out corner solutions in which females would mate exclusively with higher-quality males. (3) A Malthusian condition determines equilibrium population size as related to per-capita resource availability. Equilibria validating the TSH are achieved over a wide range of parameters, though not universally. For TSH equilibria it is not strictly necessary that the high-quality males have an advantage in terms of lower per-unit signalling costs, but a cost difference in favor of the low-quality males cannot be too great if a TSH equilibrium is to persist. And although the literature has paid less attention to these points, TSH equilibria may also fail if: the quality disparity among males is too great, or the proportion of high-quality males in the population is too large, or if the congestion effect is too weak. Signalling being unprofitable in aggregate, it can take off from a no-signalling equilibrium only if the trait used for signalling is not initially a handicap, but instead is functionally useful at low levels. Selection for this trait sets in motion a bandwagon, whereby the initially useful indicator is pushed by male-male competition into the domain where it does indeed become a handicap.     

Evolutionarily stable sets in the single-locus frequency-dependent model of natural selection

Recent developments in the static theory of evolutionarily stable sets (ESSets) are applied to the single-locus frequency-dependent model of natural selection. Particular emphasis is paid to the ESSet properties of the preimage of an ESS (or ESSet) under the genotype-phenotype map. When an ESS is realized in genetic equilibrium with redundancy in a diploid sexual population, the basic problem in biological terms is whether the corresponding set of allele frequencies is an evolutionarily stable set. The interesting question of the dynamic stability of this preimage is also discussed and a geometric condition developed which implies its evolutionary and dynamic stability.The authors appreciate detailed suggestions for improvement made by the reviewers of the original version of this paper. Financial assistance from the Natural Sciences and Engineering Research Council of Canada and from the Hungarian National Scientific Research Fund (OTKA Projects T029320 and T037271) is also gratefully acknowledged.     

Evolutionarily stable strategies of mutual help between relatives having unequal fertilities

The evolutionarily stable strategy of mutual help between relatives having unequal fertilities is studied in a kin selection model, which also takes into account competition between kins and the possibility of reciprocation. It turns out that competition and reciprocation can establish ESSs which are completely different from those expected by Hamilton's basic theory.     

Evolutionarily stable nesting strategy in a digger wasp.

Two alternative “strategies” will not coexist in a population unless on average they are equally successful. The most likely way for such an equilibrium to be maintained is through something equivalent to frequency-dependent selection. Females of the digger wasp Sphex ichneumoneus (Sphecidae) nest in underground burrows. They usually dig and provision these by themselves but occasionally a nest is jointly occupied. The two wasps fight whenever they meet and in the end only one of the two females lays an egg in the shared nest. Two models based on the theory of mixed evolutionarily stable strategies were developed and tested on comprehensive field data from two North American populations of these wasps. The first model proposes two strategies called founding and joining. Founders start burrows alone, but they are more successful when they are joined by a joiner. At equilibrium founders and joiners are equally successful, which amounts to an amicable, sharing relationship. The predictions of this amicable model are decisively rejected by the data. The second model proposes two strategies called digging and entering. Diggers dig their own burrows but they often have to abandon these burrows because of temporary unsuitability. Enterers move in later, thereby exploiting abandoned burrows as a valuable resource. They do not distinguish an adandoned burrow from one that is still occupied. Therefore sharing of burrows arises as an unfortunate by product of selection for entering abandoned burrows, and Model 2 is not an amicable model. Its quantitative predictions are impressively fulfilled in one population, though not in another population. This is one of the only examples yet known of a mixed evolutionarily stable strategy in nature. Yet the word strategy itself can confuse, and this paper tries the experiment of substituting “decision”, defined as a moment at which the animal commits future time to a course of action.     

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 [corrected] stable strategies: a review of basic theory

Widely successful in applied population biology, the Evolutionarily Stable Strategy concept remains controversial because of the severe restrictions present in its original formulation. We review theory which explores and relaxes these restrictions, finding the concept to be quite robust and adaptable, incorporating considerations such as genetics, population diversity, environmental variability, and mutation.     

Evolutionarily stable mixed mating in a variety of genetic systems

Many species display a mixture of close inbreeding and outbreeding which is referred to as mixed mating. For selfing species, models predict that such mixed mating systems can be stable. Conversely, models considering separate sex species have not been able to explain mixed mating systems. This failure may be a result of the unrealistic assumption that recurrent inbreeding does not increase the inbreeding coefficient. Here we show that mixed mating is expected in separate sex systems when recurrent inbreeding is taken into account. A female that allows her brother to sibmate with her gives an extra mating opportunity to said brother. This kin selective advantage should be strongest in genetic systems where the male is more related to the female. In support of this idea, we find that inbreeding evolves most easily in selfers, followed by diploid sibmating, followed by haplodiploid sibmating. Consideration of published values for the regression of fitness on inbreeding coefficient suggests that many species fall in a range where some selfing/sibmating is optimal.     

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.     

Indirect genetic effects and kin recognition: estimating IGEs when interactions differ between kin and strangers

Social interactions among individuals are widespread, both in natural and domestic populations. As a result, trait values of individuals may be affected by genes in other individuals, a phenomenon known as indirect genetic effects (IGEs). IGEs can be estimated using linear mixed models. The traditional IGE model assumes that an individual interacts equally with all its partners, whether kin or strangers. There is abundant evidence, however, that individuals behave differently towards kin as compared with strangers, which agrees with predictions from kin-selection theory. With a mix of kin and strangers, therefore, IGEs estimated from a traditional model may be incorrect, and selection based on those estimates will be suboptimal. Here we investigate whether genetic parameters for IGEs are statistically identifiable in group-structured populations when IGEs differ between kin and strangers, and develop models to estimate such parameters. First, we extend the definition of total breeding value and total heritable variance to cases where IGEs depend on relatedness. Next, we show that the full set of genetic parameters is not identifiable when IGEs differ between kin and strangers. Subsequently, we present a reduced model that yields estimates of the total heritable effects on kin, on non-kin and on all social partners of an individual, as well as the total heritable variance for response to selection. Finally we discuss the consequences of analysing data in which IGEs depend on relatedness using a traditional IGE model, and investigate group structures that may allow estimation of the full set of genetic parameters when IGEs depend on kin.     

Evolutionarily stable transition rates in a stage-structured model. An application to the analysis of size distributions of badges of social status

This paper deals with the adaptive dynamics associated to a hierarchical non-linear discrete population model with a general transition matrix. In the model, individuals are categorized into n dominance classes, newborns lie in the subordinate class, and it is considered as evolutionary trait a vector eta of probabilities of transition among classes. For this trait, we obtain the evolutionary singular strategy and prove its neutral evolutionary stability. Finally, we obtain conditions for the invading potential of such a strategy, which is sufficient for the convergence stability of the latter. With the help of the previous results, we provide an explanation for the bimodal distribution of badges of status observed in the Siskin (Carduelis spinus). In the Siskin, as in several bird species, patches of pigmented plumage signal the dominance status of the bearer to opponents, and central to the discussion on the evolution of status signalling is the understanding of which should be the frequency distribution of badge sizes. Though some simple verbal models predicted a bimodal distribution, up to now most species display normal distributions and bimodality has only been described for the Siskin. In this paper, we give conditions leading to one of these two distributions in terms of the survival, fecundity and aggression rates in each dominance class.     

Evolutionarily stable growth of a sapling which waits for future gap formation under closed canopy

Summary A model was developed to examine the ESS sapling growth waiting for future gap formation under closed canopy. Assumptions are: a sapling has two parts, a trunk and a photosynthetic part, and allocates annual photosynthates to these two parts; and a sapling with a larger photosynthetic part has a larger production rate, but a sapling with a larger trunk is more successful in competition after gap formation. The ESS growth schedule of a sapling typically consists of three phases: (1) the sapling first allocates all annual photosynthates to the photosynthetic part, then (2) it allocates annual photosynthates both to its trunk and to photosynthetic part, and both parts grow simultaneously, and finally (3) it also allocates annual photosynthates to both parts, but the size of the photosynthetic part stays constant due to annual loss, and only the trunk size increases. A sapling should allocate photosynthates more to the trunk if mortality or probability of gap formation is large. However, a sapling should allocate photosynthates more to the photosynthetic part if large trunks are strongly advantageous in competition after gap formation.     

Evolutionarily stable infection by a male-killing endosymbiont in Drosophila innubila: molecular evidence from the host and parasite genomes

Maternally inherited microbes that spread via male-killing are common pathogens of insects, yet very little is known about the evolutionary duration of these associations. The few examples to date indicate very recent, and thus potentially transient, infections. A male-killing strain of Wolbachia has recently been discovered in natural populations of Drosophila innubila. The population-level effects of this infection are significant: approximately 35% of females are infected, infected females produce very strongly female-biased sex ratios, and the resulting population-level sex ratio is significantly female biased. Using data on infection prevalence and Wolbachia transmission rates, infected cytoplasmic lineages are estimated to experience a approximately 5% selective advantage relative to uninfected lineages. The evolutionary history of this infection was explored by surveying patterns of polymorphism in both the host and parasite genomes, comparing the Wolbachia wsp gene and the host mtDNA COI gene to five host nuclear genes. Molecular data suggest that this male-killing infection is evolutionarily old, a conclusion supported with a simple model of parasite and mtDNA transmission dynamics. Despite a large effective population size of the host species and strong selection to evolve resistance, the D. innubila-Wolbachia association is likely at a stable equilibrium that is maintained by imperfect maternal transmission of the bacteria rather than partial resistance in the host species.     

When kinases meet mathematics: the systems biology of MAPK signalling

The mitogen activated protein kinase/extracellular signal regulated kinase pathway regulates fundamental cellular function such as cell proliferation, survival, differentiation and motility, raising the question how these diverse functions are specified and coordinated. They are encoded through the activation kinetics of the pathway, a multitude of feedback loops, scaffold proteins, subcellular compartmentalisation, and crosstalk with other pathways. These regulatory motifs alone or in combination can generate a multitude of complex behaviour. Systems biology tries to decode this complexity through mathematical modelling and prediction in order to gain a deeper insight into the inner works of signalling networks.     

RhoGTPase signalling at epithelial tight junctions: Bridging the GAP between polarity and cancer

The establishment and maintenance of epithelial polarity must be correctly controlled for normal development and homeostasis. Tight junctions (TJ) in vertebrates define apical and basolateral membrane domains in polarized epithelia via bi-directional, complex signalling pathways between TJ themselves and the cytoskeleton they are associated with. RhoGTPases are central to these processes and evidence suggests that their regulation is coordinated by interactions between GEFs and GAPs with junctional, cytoplasmic adapter proteins. In this InFocus review we determine that the expression, localization or stability of a variety of these adaptor proteins is altered in various cancers, potentially representing an important mechanistic link between loss of polarity and cancer. We focus here, on two well characterized RhoGTPases Cdc42 and RhoA who's GEFs and GAPs are predominantly localized to TJ via cytoplasmic adaptor proteins.     

Evolutionarily stable strategies and the evolution of life history strategies: I. Density dependent models

The evolution of life history strategies in density dependent situations is considered in both continuous time and discrete time models. The question of equilibrium and of competitively stable strategies, the “invasion” question, are shown to be completely determined by the number of offspring left at a fixed population size. Evolutionarily stable strategies are shown to maximize population size in a certain sense.