A theory of natural selection incorporating interaction among individuals. VII. Use of groups consisting of one sire and one dam

A previous study, (V), in this series dealt with the problem of interaction among individuals in a population by utilizing a conceptual life-history model that assumed the synchronization of fitness components (viability and fecundity) for members within groups of interacting individuals. The model also assumed that the group members were not differentiated in any way. It was shown that these assumptions of synchronization and homogeneity of group members resulted in overall symmetric fitness values, and that selection operating on these symmetric values produced optimum short- and long-term results.Since the idealized model of paper (V) yields optimum selection results, it is of interest to consider specific biological mechanisms which can be used to fulfill the conceptual assumptions involved. The solution adopted in this study is to, first, require survival to occur at the group level. This forces the viability parameters to be identical for all group members.Second, the group composition is restricted to a single pair mating. This forces the fecundity parameters to be identical for members (sire and dam) of the same group. However, this solution causes a complication. Since each individual is identified as belonging to one of the two sexual types, it is necessary to extend the previous analysis in paper (V), to accommodate differentiated group members. It is shown that this differentiation leads to a non-symmetric fitness matrix. However, it is further shown that the selection results can be obtained by use of a ‘combined’ fitness matrix that is symmetric. Therefore, the important result is demonstrated that selection involving differentiated sire-dam groups possesses all of the optimum short- and long-term properties inherent in the original non-differentiated selection procedure developed in paper (V). It is speculated that these results could be of some significance with regard to the evolution of a monogamous, pair-bonding family structure.     

A theory of natural selection incorporating interaction among individuals. V. Use of random synchronized groups

In the first paper of the current series, (I), a complex interaction model capable of describing any kind of interaction among individuals was developed. However, selection operating on random groups with regard to this model yielded short- and long-term results which were unbalanced. In subsequent kin-selection papers (II, III, and IV), a systematic analysis demonstrated that use of non-random groups could partially solve the balance problem.The present study is the first of several to employ a different approach to the problem of accommodating interaction. This approach involves changing the life-history model itself in such a way that the fitness components of individuals within groups are synchronized. Synchronization of fitness components produces total fitness values which are symmetrical. In the present study, selection operating on random groups for a model having symmetrical fitness values is evaluated for both balance and efficiency. It is demonstrated that the selection response is balanced and yields short- and long-term optimum results, but under a variety of conditions the efficiency can be low.     

A theory of natural selection incorporating interaction among individuals. VIII. Use of groups consisting of a sire and several dams

The previous paper, (VII), in this series dealt with a group structure that consisted of a single mating pair. It was demonstrated that selection operating on such groups produced optimum short- and long-term results. The present study extends this group structure to include a single sire and several, (n ? 1), dams. The objective of the present study is to determine whether or not the optimum evolutionary results inherent with groups consisting of a single mating pair extend to groups consisting of multiple matings.It is demonstrated that extending the group from a single mating pair to include multiple matings converts the strictly symmetric into a modified-symmetric selection procedure that combines symmetric and non-symmetric properties. Thus the optimum evolutionary results of groups consisting of a single mating pair do not extend completely to groups consisting of multiple matings.     

Apparent directional selection by biased pleiotropic mutation

Pleiotropic effects of deleterious mutations are considered to be among the factors responsible for genetic constraints on evolution by long-term directional selection acting on a quantitative trait. If pleiotropic phenotypic effects are biased in a particular direction, mutations generate apparent directional selection, which refers to the covariance between fitness and the trait owing to a linear association between the number of mutations possessed by individuals and the genotypic values of the trait. The present analysis has shown how the equilibrium mean value of the trait is determined by a balance between directional selection and biased pleiotropic mutations. Assuming that genes act additively both on the trait and on fitness, the total variance-standardized directional selection gradient was decomposed into apparent and true components. Experimental data on mutation bias from the bristle traits of Drosophila and life history traits of Daphnia suggest that apparent selection explains a small but significant fraction of directional selection pressure that is observed in nature; the data suggest that changes induced in a trait by biased pleiotropic mutation (i.e., by apparent directional selection) are easily compensated for by (true) directional selection.     

Evolution in fine-grained environments. II. Habitat selection as a homeostatic mechanism

A model of genotype specific habitat selection is developed for an organism subject to within-lifetime environmental fluctuations. Habitat selection is first overlaid upon both hard and soft selection Levene models with either discrete or continuous habitats. It is shown that even if all genotypes have identical physiological and fitness responses within a habitat, habitat selection can still maintain a polymorphism. In other words, physiological divergence is not a necessary prerequisite for divergence in habitat preferences. Within-lifetime environmental variability is then assumed to occur within each chosen habitat. It is shown that habitat selection acts as an evolutionary filter that can enhance the fitness impact of some niches and effectively eliminate the impact of others such that it generally increases the chances for a polymorphism under soft selection. However, density-dependent effects obscure the relationship between physiological fitness and evolutionary outcome. Indeed, it is possible for selection to favor an allele causing its bearers to preferentially go to the niche to which they are least physiologically adapted. Hence, changes in habitat preference can evolve before an organism has completely adapted physiologically to a new habitat. The fitness impact of habitat selection interacts with both homeostatic avoidance mechanisms (i.e., short-term buffering) and with tolerance (long-term) mechanisms. In general, habitat selection will be most favored in those organisms deficient in long-term tolerance. Moreover, habitat selection tends to accentuate selection favoring short-term avoidance mechanisms. Thus, organisms displaying much habitat selection should have poor physiological long-term tolerances but effective physiological short-term avoidance mechanisms. Finally, if the fitness costs associated with habitat selection are too large to be ignored and are comparable for all genotypes, habitat selection directs the selective pressures back onto the physiological homeostatic capabilities. Hence, the very existence and extent of habitat selection depends critically upon the physiological capabilities of the organism.     

Antagonistic multilevel selection on size and architecture in variable density settings

In some ecological settings, an individual's fitness depends on both its own phenotype (individual-level selection) as well as the phenotype of the individuals with which it interacts (group-level selection). Using contextual analysis to measure multilevel selection in experimental stands of Arabidopsis thaliana, we detected significant linear selection that reversed across individual versus group levels for two composite phenotypic traits, "size" and "elongation." In both cases, selection at the individual level acted to increase values of these traits, presumably due to their positive effect on resource acquisition. Group selection favored decreased values of the same traits. Nonlinear selection was weak but significant in several cases, including stabilizing selection on developmental rate; individuals with very rapid development likely had lower than average fitness due to their reduced resource level at reproduction, while very delayed reproduction may have resulted in lower fitness if prolonged competition for resources reduced overall environmental quality and fitness of all individuals in a group. Under this scenario, stabilizing selection on individual traits is evidence of selection at the group level. Significant density-dependent selection suggests that a threshold density must be reached before group selection acts. Below this threshold, selection at the individual level affects phenotypic evolution more strongly than group selection. A second experiment measured multilevel selection in progeny stands of the original experimental plants. Multilevel selection again acted antagonistically on a composite trait that included size and elongation as well as on an architectural trait, branch production. The magnitude of individual versus group selection was relatively similar in the progeny generation, and the observed balance of individual versus group selection across densities is generally consistent with the hypotheses that multilevel selection can contribute to phenotypic evolution and to important demographic phenomena, including soft selection and the "law of constant yield."     

Symmetric competition as a general model for single-species adaptive dynamics

Adaptive dynamics is a widely used framework for modeling long-term evolution of continuous phenotypes. It is based on invasion fitness functions, which determine selection gradients and the canonical equation of adaptive dynamics. Even though the derivation of the adaptive dynamics from a given invasion fitness function is general and model-independent, the derivation of the invasion fitness function itself requires specification of an underlying ecological model. Therefore, evolutionary insights gained from adaptive dynamics models are generally model-dependent. Logistic models for symmetric, frequency-dependent competition are widely used in this context. Such models have the property that the selection gradients derived from them are gradients of scalar functions, which reflects a certain gradient property of the corresponding invasion fitness function. We show that any adaptive dynamics model that is based on an invasion fitness functions with this gradient property can be transformed into a generalized symmetric competition model. This provides a precise delineation of the generality of results derived from competition models. Roughly speaking, to understand the adaptive dynamics of the class of models satisfying a certain gradient condition, one only needs a complete understanding of the adaptive dynamics of symmetric, frequency-dependent competition. We show how this result can be applied to number of basic issues in evolutionary theory.     

SELECTION ON MOTHERS AND OFFSPRING: WHOSE PHENOTYPE IS IT AND DOES IT MATTER?

Reproductive and early life-history traits can be considered aspects of either offspring or maternal phenotype, and their evolution will therefore depend on selection operating through offspring and maternal components of fitness. Furthermore, selection at these levels may be antagonistic, with optimal offspring and maternal fitness occurring at different phenotypic values. We examined selection regimes on the correlated traits of birth weight, birth date, and litter size in Soay sheep (Ovis aries) using data from a long-term study of a free-living population on the archipelago of St. Kilda, Scotland. We tested the hypothesis that selective constraints on the evolution of the multivariate phenotype arise through antagonistic selection, either acting at offspring and maternal levels, or on correlated aspects of phenotype. All three traits were found to be under selection through variance in short-term and lifetime measures of fitness. Analysis of lifetime fitness revealed strong positive directional selection on birth weight and weaker selection for increased birth date at both levels. However, there was also evidence for stabilizing selection on these traits at the maternal level, with reduced fitness at high phenotypic values indicating lower phenotypic optima for mothers than for offspring. Additionally, antagonistic selection was found on litter size. From the offspring's point of view it is better to be born a singleton, whereas maternal fitness increases with average litter size. The decreased fitness of twins is caused by their reduced birth weight; therefore, this antagonistic selection likely results from trade-offs between litter size and birth weight that have different optimal resolutions with respect to offspring and maternal fitness. Our results highlight how selection regimes may vary depending on the assignment of reproductive and early life-history traits to either offspring or maternal phenotype.     

The significance of over- and underdominance for the maintenance of genetic polymorphisms. I. Underdominance and stability

It is pointed out that the standard selection models in population genetics all require some form of heterozygote advantage in fitness in order to guarantee the maintenance or stability of genetic polymorphisms. Even more recent results demonstrating the existence of stable two-locus polymorphisms with marginal underdominance at both loci are based on certain epistatically acting heterosis assumptions. This raises the question as to whether heterozygote advantage in fitness is indeed a generally valid principle of maintaining polymorphisms. To avoid ambiguity in definition of heterozygote advantage (overdominance) as it appears in multiallele or multilocus systems, a one-locus-two-allele model is considered. This model allows for sexually asymmetric selection and random mating. It is shown that the model produces globally stable polymorphisms exhibiting underdominance in fitness for a considerable and biologically reasonable range of selection values. Having thus properly refuted the general validity of the common overdominance principle, a modified version is suggested which covers the classical viability selection model and its extension to arbitrary, sexually asymmetric viability and fertility selection. This modified overdominance principle is based on the notion of fractional fitnesses and relates protectedness of biallelic polymorphisms to the extent to which each genotype reproduces its own type. The fact that the model treated displays frequency dependent fitnesses which may change in ranking while approaching equilibrium is discussed in relation to problems of the evolution of overdominance and underdominance.     

Diffusion approximations for one-locus multi-allele kin selection,mutation and random drift in group-structured populations: a unifying approach to selection models in population genetics

Diffusion approximations are ascertained from a two-time-scale argument in the case of a group-structured diploid population with scaled viability parameters depending on the individual genotype and the group type at a single multi-allelic locus under recurrent mutation, and applied to the case of random pairwise interactions within groups. The main step consists in proving global and uniform convergence of the distribution of the group types in an infinite population in the absence of selection and mutation, using a coalescent approach. An inclusive fitness formulation with coefficient of relatedness between a focal individual J affecting the reproductive success of an individual I, defined as the expected fraction of genes in I that are identical by descent to one or more genes in J in a neutral infinite population, given that J is allozygous or autozygous, yields the correct selection drift functions. These are analogous to the selection drift functions obtained with pure viability selection in a population with inbreeding. They give the changes of the allele frequencies in an infinite population without mutation that correspond to the replicator equation with fitness matrix expressed as a linear combination of a symmetric matrix for allozygous individuals and a rank-one matrix for autozygous individuals. In the case of no inbreeding, the mean inclusive fitness is a strict Lyapunov function with respect to this deterministic dynamics. Connections are made between dispersal with exact replacement (proportional dispersal), uniform dispersal, and local extinction and recolonization. The timing of dispersal (before or after selection, before or after mating) is shown to have an effect on group competition and the effective population size. In memory of Sam Karlin.     

Horn asymmetry and fitness in gemsbok, Oryx g. gazella

The relationship between fluctuating asymmetry in horns of gemsbok(Oryx g. gazella) and a number of fitness components was determinedin a field study in Etosha National Park, Namibia. The lengthand width of horns and skull length demonstrated fluctuatingasymmetry. Both males and females with asymmetric horns werein poorer condition than symmetric individuals. Individualsof both sexes with symmetric horns more often won aggressiveinteractions at waterholes. Although symmetric individuals spentmore time in dense vegetation, their vigilance rate was nothigher than that of asymmetric individuals. Territorial, singlemales had more symmetric horns than males in herds, suggestingthat mating success was inversely related to horn asymmetry.Females with symmetric horns more often had calves than asymmetricfemales. Horn asymmetry thus appears to reliably reveal phenotypicquality as demonstrated by a suite of fitness components.[BehavEcol 7: 247-253 (1996)]     

Good genes and old age: Do old mates provide superior genes?

It has been suggested that female preference for older mates in species without parental care has evolved in response to an alleged higher genetic quality of older individuals. This is based on the widespread assumption that viability selection produces older individuals that are genetically superior to younger individuals. In contrast, we propose that the oldest individuals rarely are genetically superior. Quantitative genetic models of life history evolution indicate that young to intermediately aged individuals are likely to possess the highest breeding values of fitness. This conclusion is based on four arguments: 1) Viability selection on older individuals may decrease or at least not substantially increase breeding values of fitness, because there may exist negative genetic correlations between late-age and early-age life history parameters, 2) Fertility selection is likely to raise the fitness of gametes produced by young individuals more than those produced by old individuals, because the covariance between fertility and fitness often decreases with age, 3) The history of selection on their parents makes younger individuals more fit than older individuals, 4) Germ-line mutations, which are generally deleterious, significantly decrease the breeding value of fitness of an individual throughout its lifespan, especially in males. Therefore, females that mate with the oldest males in a population are doing so for reasons other than to obtain offspring of high genetic quality.     

Why breeding time has not responded to selection for earlier breeding in a songbird population

A crucial assumption underlying the breeders' equation is that selection acts directly on the trait of interest, and not on an unmeasured environmental factor which affects both fitness and the trait. Such an environmentally induced covariance between a trait and fitness has been repeatedly proposed as an explanation for the lack of response to selection on avian breeding time. We tested this hypothesis using a long-term dataset from a Dutch great tit (Parus major) population. Although there was strong selection for earlier breeding in this population, egg-laying dates have changed only marginally over the last decades. Using a so-called animal model, we quantified the additive genetic variance in breeding time and predicted breeding values for females. Subsequently, we compared selection at the phenotypic and genetic levels for two fitness components, fecundity and adult survival. We found no evidence for an environmentally caused covariance between breeding time and fitness or counteracting selection on the different fitness components. Consequently, breeding time should respond to selection but the expected response to selection was too small to be detected.     

Conditions for the evolution of altruism under darwinian selection

A model of population structure is discussed which under certain circumstances allows for evolution of altruistic traits, beyond the classical restrictions imposed by kin selection theory and related concepts such as reciprocal altruism. Essentially, the model sees a large population as socially subdivided into small groups without any barriers, however, to free random mating. An altruistic trait is defined as lowering, locally, the fitness of a carrier below that of noncarriers within the same group; but the local fitness of an individual randomly chosen in a group increases with the number of altruists. It is shown that altruism can evolve even if the groups are randomly formed. The conditions for such evolution are contrasted with those prevailing when the groups are formed either with some phenotypic assortment between the members or on the basis of kinship. It is shown that any possibility of evolution tends to rapidly disappear as groups become large, unless there is complete positive assortment or individuals in the groups are kin. The example of alarm calls is also considered, and the two extremes of random and sib-groups are contrasted, using a model by Maynard Smith. It is shown that alarm calls can evolve in small groups of unrelated individuals under conditions qualitatively similar but quantitatively more rigorous than those prevailing for sib-groups.     

A theory of natural selection incorporating interaction among individuals. III. Use of random groups of inbred individuals

The present series of studies attempts to accommodate interaction among individuals in evolutionary theory. The interaction phenomenon is characterized by two dimensions (direct and associate) of gene activity. For optimal selection results, a balance between the two dimensions must occur. In the first paper of the series, it was shown that random interactions resulted in an unbalanced selection response in that the direct, but not associate, effects were included in the expression for gene frequency change. The next three papers of the series (II, III and IV) were designed to determine whether or not selection with life-history models that involved non-random interactions would be useful in ameliorating the problem of selection balance.In the present study, non-randomness is generated by restricting interactions to inbred individuals. It is demonstrated that this form of non-random gene association within interacting genotypes does not improve selection balance. Thus restricting interaction to groups of inbred individuals does not result in the introduction of associate effects into the expression for gene frequency change. It is shown that inbreeding in the base population merely accelerates the unbalanced response normally occurring when selection operates on random, non-inbred individuals.     

Selection and Biased Gene Conversion in a Multigene Family: Consequences of Interallelic Bias and Threshold Selection

In a previous paper, I investigated the interactions in a gene family of additive selection and biased gene conversion in a finite population when conversion events are rare. Here I extend my "weak-conversion limit" model by allowing biased interallelic conversion (conversion between alleles at the same locus) of arbitrary frequency and various threshold selection schemes for rare interlocus conversion events. I suggest that it is not unreasonable for gene families to experience threshold fitness functions, and show that certain types of thresholds can greatly constrain the rate at which advantageous alleles are fixed as compared to other fitness schemes, such as additive selection. It is also shown that the double sampling process operating on a gene family in a finite population (sampling over the number of genes in the gene family and over the number of individuals in the population) can have interesting consequences. For selectively neutral alleles that experience interallelic bias, the probability of fixation at each single locus may be essentially neutral, but the cumulative effects on the entire gene family of small departures from neutrality can be significant, especially if the gene family is large. Thus, in some situations, gene families can respond to directional forces that are weak in comparison to drift at single loci.     

Selection on viability of individuals heterozygous for the temperature-sensitive lethal mutation l(2)M167(DTS) in experimental populations of Drosophila melanogaster

In experiments on introduction of mutation l(2)M167(DTS) in Drosophila melanogaster populations, larval and pupal viability and developmental rate are limiting factors determining the intensity of selection on the l(2)M167(DTS) mutation. Notwithstanding the rapid elimination of the mutation from the population, positive selection for viability was shown, which increased fitness of the mutation carriers in generations. The fitness component viability was estimated in individuals l(2)M167(DTS)/+; relative to that of wild-type individuals, it varied from 0.1 to 1. Factors affecting this trait in overcrowded populations were found.     

Structure and function in mammalian societies

Traditional interpretations of the evolution of animal societies have suggested that their structure is a consequence of attempts by individuals to maximize their inclusive fitness within constraints imposed by their social and physical environments. In contrast, some recent re-interpretations have argued that many aspects of social organization should be interpreted as group-level adaptations maintained by selection operating between groups or populations. Here, I review our current understanding of the evolution of mammalian societies, focusing, in particular, on the evolution of reproductive strategies in societies where one dominant female monopolizes reproduction in each group and her offspring are reared by other group members. Recent studies of the life histories of females in these species show that dispersing females often have little chance of establishing new breeding groups and so are likely to maximize their inclusive fitness by helping related dominants to rear their offspring. As in eusocial insects, increasing group size can lead to a progressive divergence in the selection pressures operating on breeders and helpers and to increasing specialization in their behaviour and life histories. As yet, there is little need to invoke group-level adaptations in order to account for the behaviour of individuals or the structure of mammalian groups.     

Prediction of rates of inbreeding in populations selected on best linear unbiased prediction of breeding value

Predictions for the rate of inbreeding (DeltaF) in populations with discrete generations undergoing selection on best linear unbiased prediction (BLUP) of breeding value were developed. Predictions were based on the concept of long-term genetic contributions using a recently established relationship between expected contributions and rates of inbreeding and a known procedure for predicting expected contributions. Expected contributions of individuals were predicted using a linear model, u(i)(()(x)()) = alpha + betas(i), where s(i) denotes the selective advantage as a deviation from the contemporaries, which was the sum of the breeding values of the individual and the breeding values of its mates. The accuracy of predictions was evaluated for a wide range of population and genetic parameters. Accurate predictions were obtained for populations of 5-20 sires. For 20-80 sires, systematic underprediction of on average 11% was found, which was shown to be related to the goodness of fit of the linear model. Using simulation, it was shown that a quadratic model would give accurate predictions for those schemes. Furthermore, it was shown that, contrary to random selection, DeltaF less than halved when the number of parents was doubled and that in specific cases DeltaF may increase with the number of dams.