In this paper we study genetic variation at a highly polymorphic locus of a monoecious or dioecious population whose census and effective sizes differ and possibly vary independently over time. More specifically, we develop a general framework for the allele frequency spectrum (AFS) at this locus, and functions of the AFS. Examples of such functions are number of alleles, number of common and rare alleles, allelic diversity, gene diversity, higher order gene diversity and Hill numbers. We develop exact recursions for the expected AFS, and its functionals, with particular interest in populations that experience a rapid (a few generations) bottleneck followed by approaching a new equilibrium between mutation and drift. A grid-based numerical algorithm is developed, which is exact for small populations and approximate for large populations. This algorithm is exemplified with exact calculations for small populations that undergo a bottleneck, and approximate calculations for a moderately large population that rapidly decreases in size.

Traditional mathematical models of population genetics have generally assumed discrete generations, but most species have overlapping generations. It is necessary to estimate generation length with overlapping generations for purposes of comparison with discrete-generation models. In populations with overlapping generations, generation length is the average age of parents at the time their progeny are born. Genetic risks associated with small populations depend on both effective population size and elapsed time in generations. In some cases, populations with larger effective size can lose heterozygosity more quickly than populations with smaller effective size because they have shorter generation length. Therefore, estimates of effective size alone cannot be used to predict the loss of heterozygosity over calendar time. Generation length is also required to estimate effective population size from the rate of loss of heterozygosity, to estimate the time of divergence between species using molecular data, and to use coalescent models for historical demographic analyses. Generation length is often not carefully defined or estimated in these cases. In some papers, authors have used the generation length only for females and have ignored males. A review of the literature indicates that the generation length for males and females can be substantially different in some species. In addition, a variety of proxies have been used in the literature for generation length. Many of these proxies do not provide reliable estimates of generation length. Accurate estimates of generation length require detailed life-history information that is unfortunately not available for many species. Analyses using these proxies for generation length should be treated with some skepticism. Most population genetics textbooks do not define generation length. It is hard to understand why such an important parameter in population genetics has been so ignored.

How species time reproduction and adapt to environmental conditions are key topics in ecology and evolutionary biology. Here, we conducted a high-resolution population genetic analysis of Baltic herring, a subspecies of Atlantic herring (Clupea harengus). Genotypes at >4,500 SNPs were generated from >4,500 spawning individuals, sampled from 150 locations spanning Swedish’s eastern coast. Abiotic factors—week of spawning, latitude, temperature, salinity—were used to assess how genetic variation is shaped by temporal, spatial, and environmental gradients. Our results reaffirm strong genetic differentiation between spring- and autumn-spawning ecotypes, despite hybridization suggesting ongoing gene flow between the two ecotypes. We document significant substructuring within the spring-spawning ecotype, delineating three main, previously unidentified, genetic clusters underpinned by adaptative genetic variation associated with latitude, salinity, temperature, and spawning time. Complementary linkage disequilibrium (LD) partitioning showed that adaptive loci—especially those in inversion regions—exhibit strong elevated among-population LD, consistent with divergence maintained by local selection despite ongoing gene flow. Clinal variation in allele frequencies indicated regionally distinct selection pressures, including shifts in allele frequencies at two major supergenes (inversions) and at a suite of genes correlated with abiotic factors. Importantly, rare genetic outlier populations are identified within each geographic region which further illustrates the unexpected fine-grained population structure of Baltic herring and implies a strong homing behavior in this abundant marine fish. Overall, this study demonstrates the capacity for targeted population genetic studies to detect adaptive variation in natural populations, the outcomes of which have direct implications for sustainable fisheries and biodiversity management.

Translocations are carried out either unintentionally or intentionally for conservation or management reasons. In both cases, translocated populations may genetically impact natural populations via introgression. Understanding how genetic background may affect an establishment in a novel environment and the potential risks for native populations is important for biodiversity conservation. Here, using a panel of 96 SNPs, we monitor the establishment of two genetically and ecologically distinct brown trout populations released into a mountain lake system in central Sweden where trout did not occur prior to the release. The release was carried out in 1979, and we monitor the establishment over the first three decades (5–6 generations) in seven lakes downstream of the release site. We find that extensive hybridization has occurred, and genes from both populations exist in all lakes examined. Genes from the population that was nonmigratory in its native environment have remained to a higher degree in the area close to the release site, while genes from the population that was more migratory in its native habitat have spread further downstream. All established populations exhibit higher levels of genetic diversity than the released populations. Natural, stream-resident brown trout populations occur ~15 km downstream of the release site and below a waterfall that acts as an upstream migration barrier. Released fish have spread genes to these populations but with low introgression rates of 3%–8%. Recently adopted indicators for monitoring genetic diversity were partly able to detect this introgression, emphasizing the usefulness of genetic indicators in management. The SNP panel used in this study provides a similar picture as previously used allozymes, showing that older marker systems with fewer loci may still be useful for describing the population structure.

Salmonids have a remarkable ability to form sympatric morphs after postglacial colonisation of freshwater lakes. These morphs often differ in morphology, feeding and spawning behaviour. Here, we explored the genetic basis of morph differentiation in Arctic charr (n = 283) by first establishing a high-quality reference genome and then using this in whole genome sequencing of distinct morphs present in two Norwegian and two Icelandic lakes. The four lakes represent the spectrum of genetic differentiation between morphs from one lake with no genetic differentiation between morphs, implying phenotypic plasticity, to two lakes with locus-specific genetic differentiation, implying incomplete reproductive isolation, and one lake with strong genome-wide divergence consistent with complete reproductive isolation. As many as 12 putative inversions ranging from 0.45 to 3.25 Mbp in size segregated among the four morphs present in one lake, Thingvallavatn, and these contributed significantly to the genetic differentiation among morphs. None of the putative inversions were found in any of the other lakes, but there were cases of partial haplotype sharing in similar morph contrasts in other lakes. Our findings are consistent with a highly polygenic basis of morph differentiation with population-specific selection on alleles linked to the development of similar morph phenotypes. The results support a model where morph differentiation is first established through phenotypic plasticity, leading to niche expansion and separation. This may be followed by gradual development of reproductive isolation, locus-specific differentiation and eventually complete reproductive isolation and genome-wide divergence.

Genetic diversity is fundamental to the adaptive potential and survival of species. Although its importance has long been recognized in science, it has a history of neglect within policy, until now. The new Global Biodiversity Framework recently adopted by the Convention on Biological Diversity, states that genetic diversity must be maintained at levels assuring adaptive potential of populations, and includes metrics for systematic monitoring of genetic diversity in so called indicators. Similarly, indicators for genetic diversity are being developed at national levels. Here, we apply new indicators for Swedish national use to one of the northernmost salmonid fishes, the Arctic charr (Salvelinus alpinus). We sequence whole genomes to monitor genetic diversity over four decades in three landlocked populations inhabiting protected alpine lakes in central Sweden. We find levels of genetic diversity, inbreeding and load to differ among lakes but remain stable over time. Effective population sizes are generally small (< 500), suggesting a limited ability to maintain adaptive variability if genetic exchange with nearby populations became eliminated. We identify genomic regions potentially shaped by selection; SNPs exhibiting population divergence exceeding expectations under drift and a putative selective sweep acting within one lake to which the competitive brown trout (Salmo trutta) was introduced during the sampling period. Identified genes appear involved in immunity and salinity tolerance. Present results suggest that genetically vulnerable populations of Arctic charr have maintained neutral and putatively adaptive genetic diversity despite small effective sizes, attesting the importance of continued protection and assurance of gene flow among populations.

International policy recently adopted commitments to maintain genetic diversity in wild populations to secure their adaptive potential, including metrics to monitor temporal trends in genetic diversity – so-called indicators. A national programme for assessing trends in genetic diversity was recently initiated in Sweden. Relating to this effort, we systematically assess contemporary genome-wide temporal trends (40 years) in wild populations using the newly adopted indicators and whole genome sequencing (WGS). We use pooled and individual WGS data from brown trout (Salmo trutta) in eight alpine lakes in protected areas. Observed temporal trends in diversity metrics (nucleotide diversity, Watterson's ϴ and heterozygosity) lie within proposed acceptable threshold values for six of the lakes, but with consistently low values in lakes above the tree line and declines observed in these northern-most lakes. Local effective population size is low in all lakes, highlighting the importance of continued protection of interconnected systems to allow genetic connectivity for long-term viability of these populations. Inbreeding (F_ROH) spans 10%–30% and is mostly represented by ancient (<1 Mb) runs of homozygosity, with observations of little change in mutational load. We also investigate adaptive dynamics over evolutionarily short time frames (a few generations); identifying putative parallel selection across all lakes within a gene pertaining to skin pigmentation as well as candidates of selection unique to specific lakes and lake systems involved in reproduction and immunity. We demonstrate the utility of WGS for systematic monitoring of natural populations, a priority concern if genetic diversity is to be protected.

There are two primary measures of the amount of genetic variation in a population at a locus: heterozygosity and the number of alleles. Effective population size (Ne) provides both an expectation of the amount of heterozygosity in a population at drift-mutation equilibrium and the rate of loss of heterozygosity because of genetic drift. In contrast, the number of alleles in a population at drift-mutation equilibrium is a function of both Ne and census size (NC). In addition, populations with the same Ne can lose allelic variation at very different rates. Allelic variation is generally much more sensitive to bottlenecks than heterozygosity. Expressions used to adjust for the effects of violations of the ideal population on Ne do not provide good predictions of the loss of allelic variation. These effects are much greater for loci with many alleles, which are often important for adaptation. We show that there is a linear relationship between the reduction of NC and the corresponding reduction of the expected number of alleles at drift-mutation equilibrium. This makes it possible to predict the expected effect of a bottleneck on allelic variation. Heterozygosity provides good estimates of the rate of adaptive change in the short-term, but allelic variation provides important information about long-term adaptive change. The guideline of long-term Ne being greater than 500 is often used as a primary genetic metric for evaluating conservation status. We recommend that this guideline be expanded to take into account allelic variation as well as heterozygosity.

The variance effective population size (N-eV) is frequently used to quantify the expected rate at which a population's allele frequencies change over time. The purpose of this paper is to find expressions for the global N-eV of a spatially structured population that are of interest for conservation of species. Since N-eV depends on allele frequency change, we start by dividing the cause of allele frequency change into genetic drift within subpopulations (I) and a second component mainly due to migration between subpopulations (II). We investigate in detail how these two components depend on the way in which subpopulations are weighted as well as their dependence on parameters of the model such a migration rates, and local effective and census sizes. It is shown that under certain conditions the impact of II is eliminated, and N-eV of the metapopulation is maximized, when subpopulations are weighted proportionally to their long term reproductive contributions. This maximal N-eV is the sought for global effective size, since it approximates the gene diversity effective size N-eGD, a quantifier of the rate of loss of genetic diversity that is relevant for conservation of species and populations. We also propose two novel versions of N-eV, one of which (the backward version of N-eV) is most stable, exists for most populations, and is closer to N-eGD than the classical notion of N-eV. Expressions for the optimal length of the time interval for measuring genetic change are developed, that make it possible to estimate any version of N-eV with maximal accuracy.

Population extinction is ubiquitous in all taxa. Such extirpations can reduce intraspecific diversity, but the extent to which genetic diversity of surviving populations are affected remains largely unclear. A key concept in this context is the effective population size (N_e), which quantifies the rate at which genetic diversity within populations is lost. N_e was developed for single, isolated populations while many natural populations are instead connected to other populations via gene flow. Recent analytical approaches and software permit modelling of N_e of interconnected populations (metapopulations). Here, we apply such tools to investigate how extinction of subpopulations affects N_e of the metapopulation (N_eMeta) and of separate surviving subpopulations (N_eRx) under different rates and patterns of genetic exchange between subpopulations. We assess extinction effects before and at migration-drift equilibrium. We find that the effect of extinction on N_eMeta increases with reduced connectivity, suggesting that stepping stone models of migration are more impacted than island-migration models when the same number of subpopulations are lost. Furthermore, in stepping stone models, after extinction and before a new equilibrium has been reached, N_eRx can vary drastically among surviving subpopulations and depends on their initial spatial position relative to extinct ones. Our results demonstrate that extinctions can have far more complex effects on the retention of intraspecific diversity than typically recognized. Metapopulation dynamics need heightened consideration in sustainable management and conservation, e.g., in monitoring genetic diversity, and are relevant to a wide range of species in the ongoing extinction crisis.