Pedigree-Based Estimation of Reproductive Value

Allele frequency dynamics under sex-biased demography and sex-specific inheritance in a pedigreed jay population

Sex-biased demography, including sex-biased survival or migration, can alter allele frequency changes across the genome. In particular, we can expect different patterns of genetic variation on autosomes and sex chromosomes due to sex-specific differences in life histories, as well as differences in effective population size, transmission modes, and the strength and mode of selection. Here, we demonstrate the role that sex differences in life history played in shaping short-term evolutionary dynamics across the genome. We used a 25-year pedigree and genomic dataset from a long-studied population of Florida Scrub-Jays (Aphelocoma coerulescens) to directly characterize the relative roles of sex-biased demography and inheritance in shaping genome-wide allele frequency trajectories. We used gene dropping simulations to estimate individual genetic contributions to future generations and to model drift and immigration on the known pedigree. We quantified differential expected genetic contributions of males and females over time, showing the impact of sex-biased dispersal in a monogamous system. Due to female-biased dispersal, more autosomal variation is introduced by female immigrants. However, due to male-biased transmission, more Z variation is introduced by male immigrants. Finally, we partitioned the proportion of variance in allele frequency change through time due to male and female contributions. Overall, most allele frequency change is due to variance in survival and births. Males and females make similar contributions to autosomal allele frequency change, but males make higher contributions to allele frequency change on the Z chromosome. Our work shows the importance of understanding sex-specific demographic processes in characterizing genome-wide allele frequency change in wild populations.

Multi-generation genetic contributions of immigrants reveal cryptic elevated and sex-biased effective gene flow within a natural meta-population

Impacts of immigration on micro-evolution and population dynamics fundamentally depend on net rates and forms of resulting gene flow into recipient populations. Yet, the degrees to which observed rates and sex ratios of physical immigration translate into multi-generational genetic legacies have not been explicitly quantified in natural meta-populations, precluding inference on how movements translate into effective gene flow and eco-evolutionary outcomes. Our analyses of three decades of complete song sparrow (Melospiza melodia) pedigree data show that multi-generational genetic contributions from regular natural immigrants substantially exceeded those from contemporary natives, consistent with heterosis-enhanced introgression. However, while contributions from female immigrants exceeded those from female natives by up to three-fold, male immigrants' lineages typically went locally extinct soon after arriving. Both the overall magnitude, and the degree of female bias, of effective gene flow therefore greatly exceeded those which would be inferred from observed physical arrivals, altering multiple eco-evolutionary implications of immigration.

The estimation of reproductive values from pedigrees

Quantifying fitness is important to understand adaptive evolution. Reproductive values are useful for making fitness comparisons involving different categories of individuals, like males and females. By definition, the reproductive value of a category is the expected per capita contribution of the members of that category to the gene pool of future generations. Life history theory reveals how reproductive values can be determined via the estimation of life-history parameters, but this requires an adequate life-history model and intricate algebraic calculations. Recently, an alternative pedigree-based method has become popular, which estimates the expected genetic contribution of individuals to future generations by tracking their descendants down the pedigree. This method is versatile and intuitively appealing, but it is unknown if the method produces estimates of reproductive values that are accurate and precise. To investigate this, we implement various life-history scenarios (for which the "true" reproductive values can be calculated) in individual-based simulations, use the simulation data to estimate reproductive values with the pedigree method, and compare the results with the true target values. We show that the pedigree-based estimation of reproductive values is either biased (in the short term) or imprecise (in the long term). This holds even for simple life histories and under idealized conditions. We conclude that the pedigree method is not a good substitute for the traditional method to quantify reproductive values.

The long-lasting legacy of reproduction: lifetime reproductive success shapes expected genetic contributions of humans after 10 generations

An individual's lifetime reproductive success (LRS) measures its realized genetic contributions to the next generation, but how well does it predict this over longer periods? Here we use human genealogical data to estimate expected individual genetic contributions (IGC) and quantify the degree to which LRS, relative to other fitness proxies, predicts IGC over longer periods. This allows an identification of the life-history stages that are most important in shaping variation in IGC. We use historical genealogical data from two non-isolated local populations in Switzerland to estimate the stabilized IGC for 2230 individuals approximately 10 generations after they were born. We find that LRS explains 30% less variation in IGC than the best predictor of IGC, the number of grandoffspring. However, albeit less precise than the number of grandoffspring, we show that LRS does provide an unbiased prediction of IGC. Furthermore, it predicts IGC better than lifespan, and accounting for offspring survival to adulthood does not improve the explanatory power. Overall, our findings demonstrate the value of human genealogical data to evolutionary biology and suggest that reproduction-more than lifespan or offspring survival-impacts the long-term genetic contributions of historic humans, even in a population with appreciable migration.

Reproductive isolation via polygenic local adaptation in sub-divided populations: Effect of linkage disequilibria and drift

This paper considers how polygenic local adaptation and reproductive isolation between hybridizing populations is influenced by linkage disequilibria (LD) between loci, in scenarios where both gene flow and genetic drift counteract selection. It shows that the combined effects of multi-locus LD and genetic drift on allele frequencies at selected loci and on heterozygosity at neutral loci are predicted accurately by incorporating (deterministic) effective migration rates into the diffusion approximation (for selected loci) and into the structured coalescent (for neutral loci). Theoretical approximations are tested against individual-based simulations and used to investigate conditions for the maintenance of local adaptation on an island subject to one-way migration from a differently adapted mainland, and in an infinite-island population with two habitats under divergent selection. The analysis clarifies the conditions under which LD between sets of locally deleterious alleles allows these to be collectively eliminated despite drift, causing sharper and (under certain conditions) shifted migration thresholds for loss of adaptation. Local adaptation also has counter-intuitive effects on neutral (relative) divergence: F_ST is highest for a pair of subpopulations belonging to the same (rare) habitat, despite the lack of reproductive isolation between them.

Environmental adaptation often involves spatially heterogeneous selection at many genetic loci. Thus, the evolutionary consequences of hybridisation between populations adapted to different environments depend on the coupled dynamics of multiple loci under selection, migration and genetic drift, making them challenging to predict. Here, I introduce theoretical approximations that accurately capture the effect of such coupling on allele frequencies at individual loci, while also accounting for the stochastic effects of genetic drift. I then use these approximations to study hybridisation in a metapopulation consisting of many interconnected subpopulations, where each subpopulation belongs to one of two habitats under divergent selection. The analysis clarifies how subpopulations belonging to a rare habitat can maintain local adaptation despite high levels of migration if net selection against multi-locus genotypes is stronger than a threshold which depends on the relative abundances of the two habitats. Further, local adaptation in a metapopulation can significantly elevate F_ST between subpopulations belonging to the same habitat, even though these are not reproductively isolated. These findings highlight the importance of carefully considering the genetic architecture and spatial context of divergence when interpreting patterns of genomic differentiation between speciating populations.

What is the best fitness measure in wild populations? A case study on the power of short-term fitness proxies to predict reproductive value

Fitness is at the core of evolutionary theory, but it is difficult to measure accurately. One way to measure long-term fitness is by calculating the individual’s reproductive value, which represents the expected number of allele copies an individual passes on to distant future generations. However, this metric of fitness is scarcely used because the estimation of individual’s reproductive value requires long-term pedigree data, which is rarely available in wild populations where following individuals from birth to death is often impossible. Wild study systems therefore use short-term fitness metrics as proxies, such as the number of offspring produced. This study compared two frequently used short-term metrics for fitness obtained at different offspring life stages (eggs, hatchlings, fledglings and recruits), and compared their ability to predict reproductive values derived from the genetic pedigree of a wild passerine bird population. We used twenty years of precise field observations and a near-complete genetic pedigree to calculate reproductive success, individual growth rate and de-lifed fitness as lifetime fitness measures, and as annual de-lifed fitness. We compared the power of these metrics to predict reproductive values and lineage survival to the end of the study period. The three short-term fitness proxies predict the reproductive values and lineage survival only when measured at the recruit stage. There were no significant differences between the different fitness proxies at the same offspring stages in predicting the reproductive values and lineage survival. Annual fitness at one year old predicted reproductive values equally well as lifetime de-lifed fitness. However, none of the short-term fitness proxies were strongly associated with the reproductive values. The commonly used short-term fitness proxies best predict long-term fitness when measured at recruitment stage. Thus, because lifetime fitness measured at recruit stage and annual fitness in the first year of life were the best proxies of long-term fitness in short-lived birds, we encourage their future use.

The relevance of pedigrees in the conservation genomics era

Over the past 50 years conservation genetics has developed a substantive toolbox to inform species management. One of the most long‐standing tools available to manage genetics—the pedigree—has been widely used to characterize diversity and maximize evolutionary potential in threatened populations. Now, with the ability to use high throughput sequencing to estimate relatedness, inbreeding, and genome‐wide functional diversity, some have asked whether it is warranted for conservation biologists to continue collecting and collating pedigrees for species management. In this perspective, we argue that pedigrees remain a relevant tool, and when combined with genomic data, create an invaluable resource for conservation genomic management. Genomic data can address pedigree pitfalls (e.g., founder relatedness, missing data, uncertainty), and in return robust pedigrees allow for more nuanced research design, including well‐informed sampling strategies and quantitative analyses (e.g., heritability, linkage) to better inform genomic inquiry. We further contend that building and maintaining pedigrees provides an opportunity to strengthen trusted relationships among conservation researchers, practitioners, Indigenous Peoples, and Local Communities.

A simple completion of Fisher's fundamental theorem of natural selection

Fisher's fundamental theorem of natural selection shows that the part of the rate of change of mean fitness that is due to natural selection equals the additive genetic variance in fitness. Fisher embedded this result in a model of total fitness, adding terms for deterioration of the environment and density dependence. Here, a quantitative genetic version of this neglected model is derived that relaxes its assumptions that the additive genetic variance in fitness and the rate of deterioration of the environment do not change over time, allows population size to vary, and includes an input of mutational variance. The resulting formula for total rate of change in mean fitness contains two terms more than Fisher's original, representing the effects of stabilizing selection, on the one hand, and of mutational variance, on the other, making clear for the first time that the fundamental theorem deals only with natural selection that is directional (as opposed to stabilizing) on the underlying traits. In this model, the total (rather than just the additive) genetic variance increases mean fitness. The unstructured population allows an explanation of Fisher's concept of fitness as simply birth rate minus mortality rate, and building up to the definition in structured populations.