Multilevel Selection 4: Modeling the Relationship of Indirect Genetic Effects and Group Size

Indirect genetic effects (IGE) occur when individual trait values depend on genes in others. With IGEs, heritable variance and response to selection depend on the relationship of IGEs and group size. Here I propose a model for this relationship, which can be implemented in standard restricted maximum likelihood software.SOCIAL interactions among individuals are abundant in life (Frank 2007). Trait values of individuals may, therefore, depend on genes in other individuals, a phenomenon known as indirect genetic effects (IGE; Wolf et al. 1998) or associative effects (Griffing 1967; Muir 2005). IGEs may have drastic effects on the rate and direction of response to selection. Moreover, with IGEs, heritable variance and response to selection depend on the size of the interaction group, hereafter denoted group size (Griffing 1967; Bijma et al. 2007; McGlothlin et al. 2010). The magnitude of the IGEs themselves, however, may also depend on group size, because interactions between a specific pair of individuals are probably less intense in larger groups (Arango et al. 2005). The relationship between the magnitude of IGEs and group size is relevant because it affects the dynamics of response to selection, heritable variation, and group size, determining, e.g., whether or not selection is more effective with larger groups. Moreover, a model for this relationship is required to estimate IGEs from data containing varying group sizes. Hadfield and Wilson (2007) proposed a model for the relationship between IGEs and group size. Here I present an alternative.With IGEs, the trait value of focal individual i is the sum of a direct effect rooted in the focal individual itself, P_D,i, and the sum of the indirect effects, P_S,j, of each of its n − 1 group mates j,(1)where A and E represent the heritable and nonheritable component of the full direct and indirect effect, respectively, and n denotes group size (Griffing 1967). When IGEs are independent of group size, total heritable variance in the trait equals (Bijma et al. 2007)(2)For a fixed becomes very large with large groups. This is unrealistic because an individual''s IGE on a single recipient probably becomes smaller in larger groups. The decrease of IGEs with group size, referred to as dilution here, will depend on the trait of interest. With competition for a finite amount of feed per group, for example, an individual consuming 1 kg has an average indirect effect of P_S,i = −1/(n − 1) on feed intake of each of its group mates. Hence, the indirect effect is inversely proportional to the number of group mates, indicating full dilution. The other extreme of no dilution may be illustrated by alarm-calling behavior, where an individual may warn all its group mates when a predator appears, irrespective of group size. Here the indirect effect each group mate receives is independent of group size, indicating no dilution. The degree of dilution is an empirical issue, which may be trait and population specific, and needs to be estimated.Here I propose to model dilution of indirect effects as(3)where P_S,i,n is the indirect effect of individual i in a group of n members, P_S,i,2 the indirect effect of i in a group of two members, and d the degree of dilution. With no dilution, d = 0, indirect effects do not depend on group size, P_S,i,n = P_S,i,2, as with alarm-calling behavior. With full dilution, d = 1, indirect effects are inversely proportional to the number of group mates, P_S,i,n = P_S,i,2/(n − 1), as with competition for a finite amount of feed. Equation 3 is an extension of the model of Arango et al. (2005), who used d = 1.Assuming that IGEs are diluted in the same manner as the full indirect effect, the indirect genetic variance for groups of n members equals(4)and total heritable variance equals(5)Hence, for σ_ADS = 0, total heritable variance increases with group size as long as dilution is incomplete (d < 1). Total heritable variance is independent of group size with full dilution (d = 1). Phenotypic variance also depends on group size. With unrelated group members,(6)which increases with group size for d < 0.5, is independent of group size for d = 0.5, and decreases with group size for d > 0.5.The degree of dilution can be estimated from data containing variation in group size, by using a mixed model with restricted maximum likelihood and evaluating the likelihood for different fixed values of d (Arango et al. 2005; Canario et al. 2010). With Equation 3, however, the estimated genetic (co)variances and breeding values for indirect effect refer to a group size of two individuals, which is inconvenient when actual group size differs considerably. Estimates of A_S, , and σ_ADS referring to the average group size may be obtained from the following mixed model,(7)where z is a vector of observations, Xb are the usual fixed effects, Z_Da_D are the direct genetic effects, Z_gg are random group effects, and e is a vector of residuals. The is a vector of IGEs referring to the average group size, and Z_S(d) is the incidence matrix for IGEs, which depends on the degree of dilution; dilution being specified relative to the average group size. Elements of Z_S(d) are(8)where denotes average group size. This model is equivalent to Equation 3, but yields estimates of genetic parameters and breeding values referring to the average group size because for . When the magnitude of IGEs depends on group size, the group and residual variance in Equation 7 will depend on group size:(9a)(9b)Hence, to obtain unbiased estimates of the genetic parameters and d, it may be required to fit a separate group and residual variance for each group size.To account for the relationship between IGEs and group size, Hadfield and Wilson (2007; HW07) proposed including an additional IGE. In their model, an individual''s full IGE is the sum of an effect independent of group size, and an effect regressed by the reciprocal of the number of group mates,(10)There are a number of differences between both models. First, Equation 3 specifies the relationship between the magnitude of IGEs and group size on the population level, which is sufficient to remedy the problem of increasing variance with group size. The HW07 model, in contrast, specifies the relationship between the magnitude of IGEs and group size on the individual level. In the HW07 model, the absolute value of (1/(n − 1))A_SR,_i decreases with group size, while A_S,i is constant. Consequently, the relationship between an individual''s full IGE and group size depends on the relative magnitudes of its A_S,i and A_SR,_i; the IGEs of individuals with greater |A_SR| show greater change when group size varies. This alters the IGE ranking of individuals when group size varies. The HW07 model, therefore, not only scales IGEs with group size, but also allows for IGE-by-group-size interaction, whereas Equation 3 scales IGEs of all individuals in the same way. Second, the interpretation of the genetic parameters differs between both models. In the HW07 model, lim_n→∞ A_S,i,HW07 = A_S,i, meaning that Var(A_S) represents the variance in IGEs when group size is infinite. With Equation 3 or 7, in contrast, refers to groups of two individuals or to the average group size. Third, in the HW07 model, the dilution of IGEs with group size is implicitly incorporated in the magnitudes of Var(A_S) and Var(A_SR), greater Var(A_SR) implying greater dilution. Equation 3, in contrast, has a single parameter for the degree of dilution, expressed on a 0–1 scale. Finally, implementing the HW07 model involves estimating three additional covariance parameters, Var(A_SR), Cov(A_D, A_SR), and Cov(A_S, A_SR), whereas implementing the model proposed here involves estimating a single additional fixed effect, which is simpler. In conclusion, the HW07 model has greater flexibility than the model proposed here, but is also more difficult to implement and interpret.     

Social Effects of Genetic Counselling

In a follow-up study of 104 subjects referred for genetic counselling between 1965 and 1969 all were at risk of having children with a variety of serious genetic disorders. Most subjects were in social classes III and IV, were married, in their late 20s, and already had an affected child. Sixty-three per cent. were referred by hospital consultants, 27% by their general practitioners, and 10% were self-referrals. All of those counselled appeared to have appreciated the genetic implications, although four overestimated the risks and 11 underestimated the risks.Of those at high risk (greater than 1 in 10) of having an affected child 10 out of 55 couples “planned” further pregnancies despite the risks. In two this was because they had been unable to adopt a child, in four because they had no living children and the disorders in question usually resulted in stillbirth or death in infancy so that the “burden” of an affected child would be of relatively short duration, and one mother had had antenatal diagnosis and selective abortion. Most of the couples in the low-risk group (less than 1 in 20) were reassured and planned further pregnancies.     

Selection Based on Indirect Genetic Effects for Growth,Environmental Enrichment and Coping Style Affect the Immune Status of Pigs

Pigs living in intensive husbandry systems may experience both acute and chronic stress through standard management procedures and limitations in their physical and social environment, which may have implications for their immune status. Here, the effect of a new breeding method where pigs were selected on their heritable influence on their pen mates'' growth, and environmental enrichment on the immune status of pigs was investigated. Hereto, 240 pigs with a relatively positive genetic effect on the growth of their pen mates (+SBV) and 240 pigs with a relatively negative genetic effect on the growth of their pen mates (−SBV) were housed in barren or straw-enriched pens from 4 to 23 weeks of age (n  =  80 pens in total). A blood sample was taken from the pigs before, three days after a 24 h regrouping test, and at week 22. In addition, effects of coping style, as assessed in a backtest, and gender were also investigated. Mainly, +SBV were found to have lower leukocyte, lymphocyte and haptoglobin concentrations than -SBV pigs. Enriched housed pigs had a lower neutrophil to lymphocyte (N:L) ratio and lower haptoglobin concentrations, but had higher antibody titers specific for Keyhole Limpet Hemocyanin (KLH) than barren housed pigs. No interactions were found between SBV class and housing. Furthermore, pigs with a proactive coping style had higher alternative complement activity and, in the enriched pens, higher antibody titers specific for KLH than pigs with a reactive coping style. Lastly, females tended to have lower leukocyte, but higher haptoglobin concentrations than castrated males. Overall, these results suggest that +SBV pigs and enriched housed pigs were less affected by stress than -SBV and barren housed pigs, respectively. Moreover, immune activation might be differently organized in individuals with different coping styles and to a lesser extent in individuals of opposite genders.     

Individualist and Multi-level Perspectives on Selection in Structured Populations

Recent years have seen a renewed debate over the importance of groupselection, especially as it relates to the evolution of altruism. Onefeature of this debate has been disagreement over which kinds ofprocesses should be described in terms of selection at multiple levels,within and between groups. Adapting some earlier discussions, we presenta mathematical framework that can be used to explore the exactrelationships between evolutionary models that do, and those that donot, explicitly recognize biological groups as fitness-bearing entities.We show a fundamental set of mathematical equivalences between these twokinds of models, one of which applies a form of multi-level selectiontheory and the other being a form of ``individualism.' However, we alsoargue that each type of model can have heuristic advantages over theother. Indeed, it can be positively useful to engage in a kind ofback-and-forth switching between two different perspectives on theevolutionary role of groups. So the position we defend is a``gestalt-switching pluralism.'     

Indirect Genetic Effects from Competition in the Clonal Herb Sedum album (Crassulaceae)

Recent years have seen increasing interest in indirect genetic effects, i.e. influences on the phenotype that depend on the genotype of other conspecific individuals; however, the empirical evidence for such effects is still limited, especially in wild plant species. The present study of the clonal herb Sedum album assessed direct and indirect genetic effects on performance-related traits in a 4-year experiment with clonally replicated genotypes, grown in pairs and differing in anthocyanin pigmentation to allow separation of individuals during data collection. In agreement with the existence of indirect genetic effects, the experimentally-paired plants not only expressed their own genotype but were also affected by the genotype of their pair mate. The effect of neighbour genotype explained up to one-fourth of the variation in performance and most likely resulted from competition, imposed by the close physical contact between paired individuals and the limiting conditions used in the garden environment. Indirect genetic effects from competition have the potential to enhance the efficacy of group-level selection relative to individual selection, given the nutrient-poor and spatially-confined substrate available to plants of S. album in the natural habitat.     

Genetic structuring in fluctuating populations

The effect of genetic drift in spatially distributed dispersal-linked and density-regulated populations is studied in a classical one-locus two-allele system. We analyse emergence of genetic differentiation assuming random drift only, where the noise-like variability is due to demographic stochasticity. We find emergence of clusters of sub-units with local allele fixation and persistence of both alleles in lengthy simulations. We demonstrate that local allele fixation (extending over a number of adjoining spatial sub-units) – without global loss of alleles – may occur when the carrying capacities of local patches are small, under a full range population dynamic regimes, when dispersal rate is small, and when redistribution (through dispersal) does not act as global mixer. These results are novel. The key to the observations is that drift is simultaneously influenced by distance-dependent dispersal, demographic stochasticity and autocorrelated population fluctuations due to delayed-density dependence. These are standard elements of contemporary population models in spatially structured context. With stable large populations, no stochasticity and dispersal limited to neighbours only, our model collapses to the stepping-stone model, while with dispersal being random and global, the model collapses to Wright's island model.     

Genetic relatedness in viscous populations

Summary Hamilton's inclusive fitness rule shows that the evolution of altruism is facilitated by high genetic relatedness of altruists to their beneficiaries. But the evolution of altruism is inhibited when the beneficiaries are also close competitors of the altruist, as will often be true in structured or viscous populations. However, Hamilton's rule still gives the correct condition for the evolution of altruism if relatedness is measured with respect to the local competitive neighbourhood.     

Selection for recombination in structured populations

In finite populations, linkage disequilibria generated by the interaction of drift and directional selection (Hill-Robertson effect) can select for sex and recombination, even in the absence of epistasis. Previous models of this process predict very little advantage to recombination in large panmictic populations. In this article we demonstrate that substantial levels of linkage disequilibria can accumulate by drift in the presence of selection in populations of any size, provided that the population is subdivided. We quantify (i) the linkage disequilibrium produced by the interaction of drift and selection during the selective sweep of beneficial alleles at two loci in a subdivided population and (ii) the selection for recombination generated by these disequilibria. We show that, in a population subdivided into n demes of large size N, both the disequilibrium and the selection for recombination are equivalent to that expected in a single population of a size intermediate between the size of each deme (N) and the total size (nN), depending on the rate of migration among demes, m. We also show by simulations that, with small demes, the selection for recombination is stronger than both that expected in an unstructured population (m = 1 - 1/n) and that expected in a set of isolated demes (m = 0). Indeed, migration maintains polymorphisms that would otherwise be lost rapidly from small demes, while population structure maintains enough local stochasticity to generate linkage disequilibria. These effects are also strong enough to overcome the twofold cost of sex under strong selection when sex is initially rare. Overall, our results show that the stochastic theories of the evolution of sex apply to a much broader range of conditions than previously expected.     

Genetic Drift Suppresses Bacterial Conjugation in Spatially Structured Populations

Conjugation is the primary mechanism of horizontal gene transfer that spreads antibiotic resistance among bacteria. Although conjugation normally occurs in surface-associated growth (e.g., biofilms), it has been traditionally studied in well-mixed liquid cultures lacking spatial structure, which is known to affect many evolutionary and ecological processes. Here we visualize spatial patterns of gene transfer mediated by F plasmid conjugation in a colony of Escherichia coli growing on solid agar, and we develop a quantitative understanding by spatial extension of traditional mass-action models. We found that spatial structure suppresses conjugation in surface-associated growth because strong genetic drift leads to spatial isolation of donor and recipient cells, restricting conjugation to rare boundaries between donor and recipient strains. These results suggest that ecological strategies, such as enforcement of spatial structure and enhancement of genetic drift, could complement molecular strategies in slowing the spread of antibiotic resistance genes.     

Genetic Drift Suppresses Bacterial Conjugation in Spatially Structured Populations

Conjugation is the primary mechanism of horizontal gene transfer that spreads antibiotic resistance among bacteria. Although conjugation normally occurs in surface-associated growth (e.g., biofilms), it has been traditionally studied in well-mixed liquid cultures lacking spatial structure, which is known to affect many evolutionary and ecological processes. Here we visualize spatial patterns of gene transfer mediated by F plasmid conjugation in a colony of Escherichia coli growing on solid agar, and we develop a quantitative understanding by spatial extension of traditional mass-action models. We found that spatial structure suppresses conjugation in surface-associated growth because strong genetic drift leads to spatial isolation of donor and recipient cells, restricting conjugation to rare boundaries between donor and recipient strains. These results suggest that ecological strategies, such as enforcement of spatial structure and enhancement of genetic drift, could complement molecular strategies in slowing the spread of antibiotic resistance genes.     

Genetic variability in wild cherry populations in France. Effects of colonizing processes

 Isoenzymes were used to evaluate gene diversity and genetic differentiation among six populations of wild cherry (Prunus avium L.) in France. We contrast the genetic characteristics of a population resulting from a recent colonization with those of a much older population of the same species. No significant genetic structure was observed among populations; in this respect wild cherry does not differ from other forest trees. No founder effects could be detected in the newly colonized population. To explain the results, we discuss classic explanations for the lack of genetic differentiation among populations, including balancing selection and neutral drift/migration. In order to account for the absence of founder effects, we propose a hypothesis based on the life cycle of forest trees, namely that the length of the juvenile phase reduces the impact of small numbers of initial founders. Received : 26 November 1996 / Accepted : 20 December 1996     

Structured populations of the oriental fruit moth in an agricultural ecosystem

Intercontinental trade has led to multiple introductions of invasive pest species at a global scale. Molecular analyses of the structure of populations support the understanding of ecological strategies and evolutionary patterns that promote successful biological invasions. The oriental fruit moth, Grapholita (=Cydia) molesta, is a cosmopolitan and economically destructive pest of stone and pome fruits, expanding its distribution range concomitantly with global climate warming. We used ten newly developed polymorphic microsatellite markers to examine the genetic structure of G. molesta populations in an agricultural ecosystem in the Emilia‐Romagna region of northern Italy. Larvae collected in eight sampling sites were assigned to a mosaic of five populations with significant intra‐regional structure. Inferred measures of gene flow within populations implicated both active dispersal, and passive dispersal associated with accidental anthropogenic displacements. Small effective population sizes, coupled with high inbreeding levels, highlighted the effect of orchard management practices on the observed patterns of genetic variation within the sampling sites. Isolation by distance did not appear to play a major role at the spatial scale considered. Our results provide new insights into the population genetics and dynamics of an invasive pest species at a regional scale.     

Genetic studies in south Balkan populations

Within a study of the genetics of Balkan populations, four DNA-STR systems and 19 classical markers were examined in seven samples: Romanians (two groups), Albanians, Greeks and Aromuns (three groups). The results for the DNA-STR systems have been compared with data from the literature. The results show four clear separated groups: sub-Saharan black populations, North-African, Japanese and European populations. The large Balkan populations, except the Greek sample, are genetically more homogenous than the Aromun populations. A second Neighbor-joining tree based on all 23 analyzed systems, show a particular trend of the Aromun groups, which indicates a particular genetic structure.     

Genetic distance and species formation in evolving populations

Summary We compare the behavior of the genetic distance between individuals in evolving populations for three stochastic models.In the first model reproduction is asexual and the distribution of genetic distances reflects the genealogical tree of the population. This distribution fluctuates greatly in time, even for very large populations.In the second model reproduction is sexual with random mating allowed between any pair of individuals. In this case, the population becomes homogeneous and the genetic distance between pairs of individuals has small fluctuations which vanish in the limit of an infinitely large population.In the third model reproduction is still sexual but instead of random mating, mating only occurs between individuals which are genetically similar to each other. In that case, the population splits spontaneously into species which are in reproductive isolation from one another and one observes a steady state with a continual appearance and extinction of species in the population. We discuss this model in relation to the biological theory of speciation and isolating mechanisms.We also point out similarities between these three models of evolving populations and the theory of disordered systems in physics. Offprint requests to: P.G. Higgs     

Social recognition in wild fish populations

The ability of animals to gather information about their social and physical environment is essential for their ecological function. Odour cues are an important component of this information gathering across taxa. Recent laboratory studies have revealed the importance of flexible chemical cues in facilitating social recognition of fishes. These cues are known to be mediated by recent habitat experience and fishes are attracted to individuals that smell like themselves. However, to be relevant to wild populations, where animals may move and forage freely, these cues would have to be temporally flexible and allow spatial resolution. Here, we present data from a study of social recognition in wild populations of three-spined sticklebacks (Gasterosteus aculeatus). Focal fish preferentially associated with conspecifics from the same habitat as themselves. These preferences were changed and updated following translocation of the focal fish to a different site. Further investigation revealed that association preferences changed after 3 h of exposure to different habitat cues. In addition to temporal flexibility, the cues also allowed a high degree of spatial resolution: fish taken from sites 200 m apart produced cues that were sufficiently different to enable the focal fish to discriminate and associate with fish captured near their own home site. The adaptive benefits of this social recognition mechanism remain unclear, though they may allow fish to orient within their social environment and gain current local information.     

Indirect Effects of Antibiotics in the Aquatic Environment: A Laboratory Study on Detritivore Food Selection Behavior

With regard to possible detrimental effects of human and veterinary antibiotics in the aquatic environment, most research in this field assesses direct impacts of pharmaceuticals on vertebrate or invertebrate test organisms. Another related area of concern is the possible development of antibiotic-resistant bacteria by introducing antimicrobials into the aquatic compartment. However, indirect effects of antibacterials on the trophic cascade have rarely been investigated. This study contributes with an example of how indirect effects of antibiotics on leaf litter decay can be measured and to what extent shredder organisms might be affected. Results from food-selection experiments using Gammarus pulex (Amphipoda) demonstrated clear preferences for leaves conditioned in the absence versus those conditioned in the presence of two antibiotics, oxytetracycline and sulfadiazine. Although this result suggested that microbial and fungal colonisation during leaf litter conditioning might be adversely affected in the antibiotic-treated groups, analyses of total carbon and nitrogen content of conditioned leaf discs did not reveal differences among the treatments.