There is no fitness but fitness,and the lineage is its bearer

Inclusive fitness has been the cornerstone of social evolution theory for more than a half-century and has matured as a mathematical theory in the past 20 years. Yet surprisingly for a theory so central to an entire field, some of its connections to evolutionary theory more broadly remain contentious or underappreciated. In this paper, we aim to emphasize the connection between inclusive fitness and modern evolutionary theory through the following fact: inclusive fitness is simply classical Darwinian fitness, averaged over social, environmental and demographic states that members of a gene lineage experience. Therefore, inclusive fitness is neither a generalization of classical fitness, nor does it belong exclusively to the individual. Rather, the lineage perspective emphasizes that evolutionary success is determined by the effect of selection on all biological and environmental contexts that a lineage may experience. We argue that this understanding of inclusive fitness based on gene lineages provides the most illuminating and accurate picture and avoids pitfalls in interpretation and empirical applications of inclusive fitness theory.     

Very low levels of direct additive genetic variance in fitness and fitness components in a red squirrel population

A trait must genetically correlate with fitness in order to evolve in response to natural selection, but theory suggests that strong directional selection should erode additive genetic variance in fitness and limit future evolutionary potential. Balancing selection has been proposed as a mechanism that could maintain genetic variance if fitness components trade off with one another and has been invoked to account for empirical observations of higher levels of additive genetic variance in fitness components than would be expected from mutation–selection balance. Here, we used a long‐term study of an individually marked population of North American red squirrels (Tamiasciurus hudsonicus) to look for evidence of (1) additive genetic variance in lifetime reproductive success and (2) fitness trade‐offs between fitness components, such as male and female fitness or fitness in high‐ and low‐resource environments. “Animal model” analyses of a multigenerational pedigree revealed modest maternal effects on fitness, but very low levels of additive genetic variance in lifetime reproductive success overall as well as fitness measures within each sex and environment. It therefore appears that there are very low levels of direct genetic variance in fitness and fitness components in red squirrels to facilitate contemporary adaptation in this population.     

A reconciliation of inclusive fitness and personal fitness approaches: a proposed correcting term for the inclusive fitness formula

Hamilton implicitly defined the inclusive fitness of an individual as the number of genomes, identical by descent to its own, but not in its own body, which owe their existence to expression of genes in said individual. Hamilton regarded inclusive fitness as the true metric of evolutionary success and the thin- maximized by selection. Williams, Stern and Orlove either claimed this property for mean reproductive success, or stated that expected reproductive success equals expected inclusive fitness. These statements are reconciled if a correcting term is added to Hamilton's inclusive fitness formula.This change completely accounts for inclusive fitness in personal fitness terminology. The use of ? in place of r renders the new formula exact. This has less numerical impact than the addition of the correcting term to begin with, but helps show inclusive fitness theory holds exactly.     

Inclusive fitness is an indispensable approximation for understanding organismal design

For some decades most biologists interested in design have agreed that natural selection leads to organisms acting as if they are maximizing a quantity known as “inclusive fitness.” This maximization principle has been criticized on the (uncontested) grounds that other quantities, such as offspring number, predict gene frequency changes accurately in a wider range of mathematical models. Here, we adopt a resolution offered by Birch, who accepts the technical difficulties of establishing inclusive fitness maximization in a fully general model, while concluding that inclusive fitness is still useful as an organizing framework. We set out in more detail why inclusive fitness is such a practical and powerful framework, and provide verbal and conceptual arguments for why social biology would be more or less impossible without it. We aim to help mathematicians understand why social biologists are content to use inclusive fitness despite its theoretical weaknesses. Here, we also offer biologists practical advice for avoiding potential pitfalls.     

Natural selection on age-specific fertilities in human females: comparison of individual-level fitness measures.

Lifetime reproductive success and timing of reproduction are key components of life-history evolution. To understand the evolution of reproductive schedules, it is important to use a measure of fitness that is sensitive both to reproductive quantity and reproductive timing. There is a contradiction between the theory, which mainly focuses on the rate measures of fitness (r and lambda), and empirical studies, which mainly use lifetime reproductive success (LRS), or some of its correlates, as a fitness measure. We measured phenotypic selection on age-specific fertilities in three pre-modern human populations using individually estimated finite rate of increase, er (lambda). We found that lambda and lifetime reproductive success ranked individuals differently according to their fitness: for example, a female giving birth to four children at a young age may actually have a higher fitness than a female giving birth to six children at a greater age. Increase in fertility at the young age classes (15-19 years) was favoured by selection, but the intensity of selection on fertility was higher in the older age classes (20-30 years), where the variance in fertility was highest. Hence, variation in fertility in the older age classes (20-30) was actually responsible for most of the observed variation in fitness among the individuals. Additionally, more than 90% of variation in fitness (lambda) was attributable to individual differences in LRS, whereas only about 5% of all variation in fitness was due to differences in the reproductive schedule. The rate-sensitive fitness measure did not significantly challenge the importance of total fertility as a component of fitness in humans. However, the rate-sensitive measure clearly allowed more accurate estimation of individual fitness, which may be important for answering some more specific questions.     

Does evolution lead to maximizing behavior?

A long‐standing question in biology and economics is whether individual organisms evolve to behave as if they were striving to maximize some goal function. We here formalize this “as if” question in a patch‐structured population in which individuals obtain material payoffs from (perhaps very complex multimove) social interactions. These material payoffs determine personal fitness and, ultimately, invasion fitness. We ask whether individuals in uninvadable population states will appear to be maximizing conventional goal functions (with population‐structure coefficients exogenous to the individual's behavior), when what is really being maximized is invasion fitness at the genetic level. We reach two broad conclusions. First, no simple and general individual‐centered goal function emerges from the analysis. This stems from the fact that invasion fitness is a gene‐centered multigenerational measure of evolutionary success. Second, when selection is weak, all multigenerational effects of selection can be summarized in a neutral type‐distribution quantifying identity‐by‐descent between individuals within patches. Individuals then behave as if they were striving to maximize a weighted sum of material payoffs (own and others). At an uninvadable state it is as if individuals would freely choose their actions and play a Nash equilibrium of a game with a goal function that combines self‐interest (own material payoff), group interest (group material payoff if everyone does the same), and local rivalry (material payoff differences).     

Mating frequency and inclusive fitness in Drosophila melanogaster

In many species, increased mating frequency reduces maternal survival and reproduction. In order to understand the evolution of mating frequency, we need to determine the consequences of increased mating frequency for offspring. We conducted an experiment in Drosophila melanogaster in which we manipulated the mating frequency of mothers and examined the survival and fecundity of the mothers and their daughters. We found that mothers with the highest mating frequency had accelerated mortality and more rapid reproductive senescence. On average, they had 50% shorter lives and 30% lower lifetime reproductive success (LRS) than did mothers with the lowest mating frequency. However, mothers with the highest mating frequency produced daughters with 28% greater LRS. This finding implies that frequent mating stimulates cross-generational fitness trade-offs such that maternal fitness is reduced while offspring fitness is enhanced. We evaluate these results using a demographic metric of inclusive fitness. We show that the costs and benefits of mating frequency depend on the growth rate of the population. In an inclusive fitness context, there was no evidence that increased mating frequency results in fitness costs for mothers. These results indicate that cross-generational fitness trade-offs have an important role in sexual selection and life-history evolution.     

Female mating decisions: maximizing fitness?

Sexual selection theory assumes that maximizing fitness is the ultimate goal in every mating decision. Fitness can be maximized directly by increasing the number of offspring (direct benefits) or indirectly by maximizing offspring's lifetime reproductive success (indirect benefits). Whereas there is considerable evidence in the literature for the influence of mating decisions on direct benefits, indirect benefits have been more elusive. Here, we review the variables that influence mating decisions made by females of freshwater fish and how these affect their fitness directly, as well as indirectly. Females enhance their fitness by matching their mating decisions to current environmental conditions, using a wide range of pre- and post-copulation mechanisms that enable them to maximize benefits from mating. Male sexual traits and courtship displays are signals used by females as a way of assessing male quality in terms of both direct and indirect benefits. Polyandry is very common among freshwater fish species, and indirect benefits have been hypothesized as drivers of its predominance. Despite intensive theoretical work, and multiple suggestions of the effects of indirect benefits, to date no study has been able to demonstrate experimentally the existence of indirect benefits in freshwater fish species. Additionally, most studies of direct benefits measure short-term benefits of mating decisions. In both cases, lifetime reproductive success is not assessed. Therefore, we are led to conclude that evidence as to whether female mating decisions result in direct and/or indirect benefits in freshwater fish species is still lacking. These results should be considered in light of the ongoing debate about the significance of indirect benefits in female mating decisions.     

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.     

Inclusive Fitness from Multitype Branching Processes

I use multitype branching processes to study genetic models for the evolution of social behaviour, i.e. behaviours that, when acted out, affect the success of the actor’s neighbours. Here, I suppose an individual bearing a mutant copy of a gene influences the reproductive success of a neighbour by altering its own competitive ability. Approximations based on assumptions about the rareness of the mutant allele and the strength of selection allow me to formulate statements concerning the probability of mutant extinction in terms of inclusive fitness. Inclusive fitness is an idea well known to biologists and can be thought of as a sum of an individual’s fitness and the fitness of each of its relatives, weighted by some measure of genetic relatedness. Previous work has led to some confusion surrounding the definition of the inclusive-fitness effect of a mutant allele when individuals carrying that allele experience demographic conditions that fluctuate randomly. In this paper, I emphasise the link between inclusive fitness and the probability of mutant extinction. I recover standard results for populations of constant size, and I show that inclusive fitness can be used to determine the short-term fate of mutants in the face of stochastic demographic fluctuations. Overall, then, I provide a connection between certain inclusive-fitness-based approaches routinely applied in theoretical studies of social evolution.     

Inclusive fitness and reproductive strategies in dwarf mongooses

Dwarf mongooses (Helogale parvula) are small, communally breedingcarnivores found in woodland and tree-savanna throughout Africa.Within a pack, socially subordinate mongooses do not normallybreed, yet they invariably participate in all aspects of parentalcare. The primary alternative to tolerating reproductive suppressionis dispersal, which shortens the wait for dominance and breeding.Here, we calculate the annual inclusive fitness payoffs to thedispersing and nondispersing strategies for males and femalesof ages one to seven, using data from a 14-year study in SerengetiNational Park, Tanzania. Factors with effects on inclusive fitnessincluded relatedness to pack mates before and after dispersal,the effect of help on recipients' reproductive success, theprobability of dispersing successfully, the probability of attainingdominance, and reproductive success after attaining dominance.All of these factors differed between male and female dwarfmongooses. We compared the contributions of direct and indirectfitness to the total fitness of mongooses pursuing each of thestrategies, across a range of ages. In our population, dispersaland nondispersal both yielded direct and indirect payoffs atmost ages. For dispersers of both sexes, direct fitness wasthe primary component of total fitness but indirect fitnesswas substantial for young (< 2 years old) dispersers. Fornondispersers of both sexes, indirect fitness was the majorcomponent of total fitness among young mongooses (up to 2 or3 years), but direct fitness was the major component among oldermongooses. By comparing the inclusive fitness payoffs for thetwo strategies, we determined the range of ages at which dispersalshould be favored for each sex. These comparisons correctlypredicted that males should be more dispersive than femalesat all ages, and that males should disperse over a broader rangeof ages.     

Kinship,sex, and fitness in a Caribbean community

Patterns of human kinship commonly involve preferential treatment of relatives based on lineal descent (lineages) rather than degree of genetic relatedness (kindreds), presenting a challenge for inclusive fitness theory. Here, we examine effects of lineage and kindred characteristics on reproductive success (RS) and number of grandchildren for 130 men and 124 women in a horticultural community on Dominica. Kindreds had little effect on fitness independently of lineage characteristics. Fitness increased with the number of lineal relatives residing in the community but decreased beyond an apparently optimal lineage size, suggesting resource enhancement and competition among kin. Female-biased patrilineage sex ratio was positively associated with men’s fitness, while male-biased matrilineage sex ratio was positively associated with women’s fitness. Number of brothers in the community was negatively associated with men’s, but not women’s, fitness. Parents and number of sisters had no effect on either male or female reproduction; however, women with younger sisters had higher RS, suggesting benefits of kin support for childcare. In sum, imposed norms for lineage social organization may enhance lineal ancestors’ inclusive fitness at a cost to individual inclusive fitness. Research was supported by grants from the National Science Foundation (BNS 8920569 and SBR 9205373); the University of Missouri Research Board to MVF; the Earthwatch Center for Field Research to MVF, Marsha B. Quinlan, and RJQ; and the B.S.U. Center for International Programs and Office of Academic Research and Sponsored Programs to RJQ. Marsha Quinlan and Napoleon Chagnon provided valuable advice on earlier drafts. Ed Hagen gave generous help with Descent software for kinship analysis. Many friends, teachers, and consultants in Bwa Mawego contributed generously to this study: the Durand clan—Juranie, Jonah, Elford, Induria, Margelia, Eugenia, Lillia, Elquimedo, Zexia, Delfine, Wilford, Nathalie, and Sarah; the Warringtons—Martina, Amatus, Onia, Belltina, Zabius, Sarah-Gene, and Heckery; the Laudats—Eddie, Benedict, and Dellie; the Laurents—Aron and Tito; the Lewises—Eddie, Melanie, Eulina, Spliffy, Ganjala, Julina, Jalina, and Marietta; Franklin Vigilante; Lawrence Prosper; Edmund Sanderson; Alex and Tita Alie; and especially Mistress Didi and Mr. McField Coipel. Rob Quinlan is Assistant Professor of Anthropology at Ball State University. His main interests include human evolutionary ecology, reproductive development, parental care, kinship, and medical anthropology. He has conducted fieldwork in Dominica since 1993. Mark Flinn is Associate Professor of Anthropology and Psychological Sciences at the University of Missouri-Columbia. His main interests include evolutionary theory, childhood stress, family relationships, and health. He has conducted fieldwork in Dominica every year since 1987.     

An inclusive fitness model for the evolutionary advantage of sibmating

Summary We construct an inclusive fitness model of the relative selective advantage of sibmating and outbreeding behaviour, under the assumption that inbred offspring pay a fitness penalty. We are particularly interested in the question of whether such inbreeding depression is enough to generate a stable phenotypic polymorphism, with both kinds of breeding observed. The model predicts that, under diploidy, such a polymorphism is never found, but under haplodiploidy, it exists for a narrow range of parameter values. The inclusive fitness argument is technically interesting because care must be taken with reproductive values. We also present a corrected version of a one-locus genetic model for sibmating and find that the inclusive fitness and genetic models give identical results when selection is weak.     

Lower reproductive success in hybrid fur seal males indicates fitness costs to hybridization

Hybridization among organisms can potentially contribute to the processes of evolution, but this depends on the fitness of hybrids relative to parental species. A small, recently formed population of fur seals on subantarctic Macquarie Island contains a high proportion of hybrids (17-30%) derived from combinations of three parental species: Antarctic, subantarctic and New Zealand fur seals. Mitochondrial control-region data (restriction fragment length polymorphisms) and nine microsatellites were used to determine the species composition of breeding adults, and hybrid male fitness was measured by comparing reproductive success (number of genetically inferred paternities) of hybrid and pure-species territory males over 6 years. No correlations were found between male reproductive success and three genetic measures of outbreeding, but this may be due to a relatively small number of dominant males analysed. Territory males fathered 63% of pups, but hybrid males had lower reproductive success than pure-species males despite having the same ability to hold territories. A greater proportion of females in hybrid male territories conceived extra-territorially than those in territories of pure-species males, and most (70 of 82) mated with conspecifics. This suggests the presence of reproductive isolating mechanisms that promote positive assortative mating and reduce the production of hybrid offspring. Although we found no evidence for male sterility in the population, mechanisms that reduce lifetime reproductive success may act to decrease the frequency of hybrids. Our study has identified a disadvantage of hybridization - reduced reproductive success of hybrid sons - that may be contributing to the persistence of pure lineages at Macquarie Island and the temporal decline in hybridization observed there.     

A simple fitness proxy for structured populations with continuous traits, with case studies on the evolution of haplo-diploids and genetic dimorphisms

For structured populations in equilibrium with everybody born equal, ln(R (0)) is a useful fitness proxy for evolutionarily steady strategy (ESS) and most adaptive dynamics calculations, with R (0) the average lifetime number of offspring in the clonal and haploid cases, and half the average lifetime number of offspring fathered or mothered for Mendelian diploids. When individuals have variable birth states, as is, for example, the case in spatial models, R (0) is itself an eigenvalue, which usually cannot be expressed explicitly in the trait vectors under consideration. In that case, Q(Y| X):=-det (I-L(Y| X)) can often be used as fitness proxy, with L the next-generation matrix for a potential mutant characterized by the trait vector Y in the (constant) environment engendered by a resident characterized by X. If the trait space is connected, global uninvadability can be determined from it. Moreover, it can be used in all the usual local calculations like the determination of evolutionarily singular trait vectors and their local invadability and attractivity. We conclude with three extended case studies demonstrating the usefulness of Q: the calculation of ESSs under haplo-diploid genetics (I), of evolutionarily steady genetic dimorphisms (ESDs) with a priori proportionality of macro- and micro-gametic outputs (an assumption that is generally made but the fulfilment of which is a priori highly exceptional) (II), and of ESDs without such proportionality (III). These case studies should also have some interest in their own right for the spelled out calculation recipes and their underlying modelling methodology.     

Susceptibility of the male fitness phenotype to spontaneous mutation

Adult reproductive success can account for a large fraction of male fitness, however, we know relatively little about the susceptibility of reproductive traits to mutation-accumulation (MA). Estimates of the mutational rate of decline for adult fitness and its components are controversial in Drosophila melanogaster, and post-copulatory performance has not been examined. We therefore separately measured the consequences of MA for total male reproductive success and its major pre-copulatory and post-copulatory components: mating success and sperm competitive success. We also measured juvenile viability, an important fitness component that has been well studied in MA experiments. MA had strongly deleterious effects on both male viability and adult fitness, but the latter declined at a much greater rate. Mutational pressure on total fitness is thus much greater than would be predicted by viability alone. We also noted a significant and positive correlation between all adult traits and viability in the MA lines, suggesting pleiotropy of mutational effect as required by 'good genes' models of sexual selection.     

Inclusive fitness in finite populations—effects of heterogeneity and synergy

I review recent results concerning the relationship between the inclusive fitness (IF) effect and standard measures of allele fitness in a finite‐population, with attention to the effect of heterogeneity in population structure and nonadditive fitness effects. In both cases, existing theoretical work is somewhat technical and I try to provide a more transparent account. In a heterogeneous population it is known that inclusive fitness will generally fail to incorporate the effects of selection on the distribution of alleles among states unless a reproductive‐value weighting is used. But even given that, recent work shows that under certain updating rules, the IF effect can fail to be equivalent to standard measures such as fixation probability. In terms of synergistic fitness effects, I review the result that in the finite population model, the IF effect can be calculated using only “additive” relatedness coefficients so that computational difficulties found in the infinite‐population model do not arise. In my own work, there is an interaction here in that my 2012 work on synergy with Maciejewski made an assumption about inclusive fitness that my 2014 work on heterogeneity with Tarnita showed to be wrong. I include (Appendix C) a corrected argument for the 2012 result.     

Clutch size, offspring performance, and intergenerational fitness

It is now generally recognized that clutch size affects morethan offspring number. In particular, clutch size affects asuite of traits associated with offspring reproductive performance.Optimal clutch size is therefore determined not by the numericallymost productive clutch but by the clutch that maximizes collectiveoffspring reproductive success. Calculation of optimal clutchsize thus requires a consideration of ecological factors operatingduring an intergenerational time frame, spanning the lifetimeof the egglaying adult and the lifetimes of her offspring. Theoptimal clutch cannot define reproductive values in advance,but instead requires that the strategy chosen is the best responseto the set of reproductive values that it itself generates.In this article, we introduce methods for solving this problem,based on an iterative solution of the equation characterizingexpected lifetime reproductive success. We begin by consideringa semelparous organism, in which case lifetime reproductivesuccess is a function only of the state of the organism. Foran iteroparous organism, lifetime reproductive success dependsupon both state and time, so that our methods extend the usualstochastic dynamic programming approach to the evaluation oflifetime reproductive success. The methods are intuitive andeasily used. We consider both semelparous and iteroparous organisms,stable and varying environments, and describe how our methodscan be employed empirically.     

Host density impacts relative fitness of bacteriophage Phi6 genotypes in structured habitats

Spatially structured environments may impact evolution by restricting population sizes, limiting opportunities for genetic mixis, or weakening selection against deleterious genotypes. When habitat structure impedes dispersal, low-productivity (less virulent) infectious parasites may benefit from their prudent exploitation of local hosts. Here we explored the combined ability for habitat structure and host density to dictate the relative reproductive success of differentially productive parasites. To do so, we allowed two RNA bacteriophage Phi6 genotypes to compete in structured and unstructured (semi-solid versus liquid) habitats while manipulating the density of Pseudomonas hosts. In the unstructured habitats, the more-productive phage strain experienced a relatively constant fitness advantage regardless of starting host density. By contrast, in structured habitats, restricted phage dispersal may have magnified the importance of local productivity, thus allowing the relative fitness of the less-productive virus to improve as host density increased. Further data suggested that latent period (duration of cellular infection) and especially burst size (viral progeny produced per cell) were the phage "life-history" traits most responsible for our results. We discuss the relevance of our findings for selection occurring in natural phage populations and for the general evolutionary epidemiology of infectious parasites.