| 1. |
- Hössjer, Ola, et al.
(författare)
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A new general analytical approach for modeling patterns of genetic differentiation and effective size of subdivided populations over time
- 2014
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Ingår i: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 258, s. 113-133
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Tidskriftsartikel (refereegranskat)abstract
- The main purpose of this paper is to develop a theoretical framework for assessing effective population size and genetic divergence in situations with structured populations that consist of various numbers of more or less interconnected subpopulations. We introduce a general infinite allele model for a diploid, monoecious and subdivided population, with subpopulation sizes varying overtime, including local subpopulation extinction and recolonization, bottlenecks, cyclic census size changes or exponential growth. Exact matrix analytic formulas are derived for recursions of predicted (expected) gene identities and gene diversities, identity by descent and coalescence probabilities, and standardized variances of allele frequency change. This enables us to compute and put into a general framework a number of different types of genetically effective population sizes (N-e) including variance, inbreeding, nucleotide diversity, and eigenvalue effective size. General expressions for predictions (g(ST)) of the coefficient of gene differentiation G(ST) are also derived. We suggest that in order to adequately describe important properties of a subdivided population with respect to allele frequency change and maintenance of genetic variation over time, single values of g(ST) and N-e are not enough. Rather, the temporal dynamic patterns of these properties are important to consider. We introduce several schemes for weighting subpopulations that enable effective size and expected genetic divergence to be calculated and described as functions of time, globally for the whole population and locally for any group of subpopulations. The traditional concept of effective size is generalized to situations where genetic drift is confounded by external sources, such as immigration and mutation. Finally, we introduce a general methodology for state space reduction, which greatly decreases the computational complexity of the matrix analytic formulas.
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| 2. |
- Hössjer, Ola, 1964-, et al.
(författare)
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Assessment of the Global Variance Effective Size of Subdivided Populations, and Its Relation to Other Effective Sizes
- 2023
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Ingår i: Acta Biotheoretica. - 0001-5342 .- 1572-8358. ; 71:3
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 3. |
- Hössjer, Ola, et al.
(författare)
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Effective sizes and time to migration-drift equilibrium in geographically subdivided populations
- 2016
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Ingår i: Theoretical Population Biology. - : Elsevier BV. - 0040-5809 .- 1096-0325. ; 112, s. 139-156
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Tidskriftsartikel (refereegranskat)abstract
- Many versions of the effective population size (N-e) exist, and they are important in population genetics in order to quantify rates of change of various characteristics, such as inbreeding, heterozygosity, or allele frequencies. Traditionally, N-e was defined for single, isolated populations, but we have recently presented a mathematical framework for subdivided populations. In this paper we focus on diploid populations with geographic subdivision, and present new theoretical results. We compare the haploid and diploid versions of the inbreeding effective size (N-ei) with novel expression for the variance effective size (N-ev), and conclude that for local populations N-ev is often much smaller than both versions of Nei, whenever they exist. Global N(ev)of the metapopulation, on the other hand, is close to the haploid Net and much larger than the diploid Nei. We introduce a new effective size, the additive genetic variance effective size Neill', which is of particular interest for long term protection of species. It quantifies the rate at which additive genetic variance is lost and we show that this effective size is closely related to the haploid version of Nei. Finally, we introduce a new measure of a population's deviation from migration-drift equilibrium, and apply it to quantify the time it takes to reach this equilibrium. Our findings are of importance for understanding the concept of effective population size in substructured populations and many of the results have applications in conservation biology.
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| 4. |
- Hössjer, Ola, et al.
(författare)
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Metapopulation inbreeding dynamics, effective size and subpopulation differentiation-A general analytical approach for diploid organisms
- 2015
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Ingår i: Theoretical Population Biology. - : Elsevier BV. - 0040-5809 .- 1096-0325. ; 102, s. 40-59
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by problems in conservation biology we study genetic dynamics in structured populations of diploid organisms (monoecious or dioecious). Our analysis provides an analytical framework that unifies substantial parts of previous work in terms of exact identity by descent (IBD) and identity by state (IBS) recursions. We provide exact conditions under which two structured haploid and diploid populations are equivalent, and some sufficient conditions under which a dioecious diploid population can be treated as a monoecious diploid one. The IBD recursions are used for computing local and metapopulation inbreeding and coancestry effective population sizes and for predictions of several types of fixation indices over different time horizons.
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| 5. |
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| 6. |
- Kurland, Sara, 1989-, et al.
(författare)
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Effects of subpopulation extinction on effective size (Ne) of metapopulations
- 2023
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Ingår i: Conservation Genetics. - : Springer Science and Business Media LLC. - 1566-0621 .- 1572-9737. ; 24:4, s. 417-433
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Tidskriftsartikel (refereegranskat)abstract
- 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 (Ne), which quantifies the rate at which genetic diversity within populations is lost. Ne 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 Ne of interconnected populations (metapopulations). Here, we apply such tools to investigate how extinction of subpopulations affects Ne of the metapopulation (NeMeta) and of separate surviving subpopulations (NeRx) 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 NeMeta 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, NeRx 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.
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| 7. |
- Laikre, Linda, et al.
(författare)
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Metapopulation effective size and conservation genetic goals for the Fennoscandian wolf (Canis lupus) population
- 2016
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Ingår i: Heredity. - : Springer Science and Business Media LLC. - 0018-067X .- 1365-2540. ; 117:4, s. 279-289
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Tidskriftsartikel (refereegranskat)abstract
- The Scandinavian wolf population descends from only five individuals, is isolated, highly inbred and exhibits inbreeding depression. To meet international conservation goals, suggestions include managing subdivided wolf populations over Fennoscandia as a metapopulation; a genetically effective population size of N-e >= 500, in line with the widely accepted long-term genetic viability target, might be attainable with gene flow among subpopulations of Scandinavia, Finland and Russian parts of Fennoscandia. Analytical means for modeling N-e of subdivided populations under such non-idealized situations have been missing, but we recently developed new mathematical methods for exploring inbreeding dynamics and effective population size of complex metapopulations. We apply this theory to the Fennoscandian wolves using empirical estimates of demographic parameters. We suggest that the long-term conservation genetic target for metapopulations should imply that inbreeding rates in the total system and in the separate subpopulations should not exceed Delta f = 0.001. This implies a meta-Ne of N-eMeta >= 500 and a realized effective size of each subpopulation of N-eRx >= 500. With current local effective population sizes and one migrant per generation, as recommended by management guidelines, the meta-Ne that can be reached is similar to 250. Unidirectional gene flow from Finland to Scandinavia reduces meta-N-e to similar to 130. Our results indicate that both local subpopulation effective sizes and migration among subpopulations must increase substantially from current levels to meet the conservation target. Alternatively, immigration from a large (N-e >= 500) population in northwestern Russia could support the Fennoscandian metapopulation, but immigration must be substantial (5-10 effective immigrants per generation) and migration among Fennoscandian subpopulations must nevertheless increase.
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| 8. |
- Olsson, Fredrik, et al.
(författare)
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Characteristics of the variance effective population size over time using an age structured model with variable size
- 2013
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Ingår i: Theoretical Population Biology. - : Elsevier BV. - 0040-5809 .- 1096-0325. ; 90, s. 91-103
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Tidskriftsartikel (refereegranskat)abstract
- The variance effective population size (N-ev) is a key concept in population biology, because it quantifies the microevolutionary process of random genetic drift, and understanding the characteristics of N-ev is thus of central importance. Current formulas for Nev for populations with overlapping generations weight age classes according to their reproductive values (i.e. reflecting the contribution of genes from separate age classes to the population growth) to obtain a correct measure of genetic drift when computing the variance of the allele frequency change over time. In this paper, we examine the effect of applying different weights to the age classes using a novel analytical approach for exploring N-ev. We consider a haploid organism with overlapping generations and populations of increasing, declining, or constant expected size and stochastic variation with respect to the number of individuals in the separate age classes. We define Nov, as a function of how the age classes are weighted, and of the span between the two points in time, when measuring allele frequency change. With this model, time profiles for N-ev can be calculated for populations with various life histories and with fluctuations in life history composition, using different weighting schemes. We examine analytically and by simulations when Nei, using a weighting scheme with respect to reproductive contribution of separate age classes, accurately reflect the variance of the allele frequency change due to genetic drift over time. We show that the discrepancy of N-ev, calculated with reproductive values as weights, compared to when individuals are weighted equally, tends to a constant when the time span between the two measurements increases. This constant is zero only for a population with a constant expected population size. Our results confirm that the effect of ignoring overlapping generations, when empirically assessing Nell from allele frequency shifts, gets smaller as the time interval between samples increases. Our model has empirical applications including assessment of (i) time intervals necessary to permit ignoring the effect of overlapping generations for N-ev estimation by means of the temporal method, and (ii) effects of life table manipulation on N-ev over varying time periods.
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| 9. |
- Olsson, Fredrik, et al.
(författare)
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GESP : A computer program for modelling genetic effective population size, inbreeding and divergence in substructured populations
- 2017
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Ingår i: Molecular Ecology Resources. - : Wiley. - 1755-098X .- 1755-0998. ; 17:6, s. 1378-1384
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Tidskriftsartikel (refereegranskat)abstract
- The genetically effective population size (N-e) is of key importance for quantifying rates of inbreeding and genetic drift and is often used in conservation management to set targets for genetic viability. The concept was developed for single, isolated populations and the mathematical means for analysing the expected N-e in complex, subdivided populations have previously not been available. We recently developed such analytical theory and central parts of that work have now been incorporated into a freely available software tool presented here. gesp (Genetic Effective population size, inbreeding and divergence in Substructured Populations) is R-based and designed to model short- and long-term patterns of genetic differentiation and effective population size of subdivided populations. The algorithms performed by gesp allow exact computation of global and local inbreeding and eigenvalue effective population size, predictions of genetic divergence among populations (G(ST)) as well as departures from random mating (F-IS, F-IT) while varying (i) subpopulation census and effective size, separately or including trend of the global population size, (ii) rate and direction of migration between all pairs of subpopulations, (iii) degree of relatedness and divergence among subpopulations, (iv) ploidy (haploid or diploid) and (v) degree of selfing. Here, we describe gesp and exemplify its use in conservation genetics modelling.
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| 10. |
- Ryman, Nils, et al.
(författare)
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Do estimates of contemporary effective population size tell us what we want to know?
- 2019
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Ingår i: Molecular Ecology. - : Wiley. - 0962-1083 .- 1365-294X. ; 28:8, s. 1904-1918
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Tidskriftsartikel (refereegranskat)abstract
- Estimation of effective population size (N-e) from genetic marker data is a major focus for biodiversity conservation because it is essential to know at what rates inbreeding is increasing and additive genetic variation is lost. But are these the rates assessed when applying commonly used N-e estimation techniques? Here we use recently developed analytical tools and demonstrate that in the case of substructured populations the answer is no. This is because the following: Genetic change can be quantified in several ways reflecting different types of N-e such as inbreeding (N-eI), variance (N-eV), additive genetic variance (N-eAV), linkage disequilibrium equilibrium (N-eLD), eigenvalue (N-eE) and coalescence (N-eCo) effective size. They are all the same for an isolated population of constant size, but the realized values of these effective sizes can differ dramatically in populations under migration. Commonly applied N-e-estimators target N-eV or N(eLD )of individual subpopulations. While such estimates are safe proxies for the rates of inbreeding and loss of additive genetic variation under isolation, we show that they are poor indicators of these rates in populations affected by migration. In fact, both the local and global inbreeding (N-eI) and additive genetic variance (N-eAV) effective sizes are consistently underestimated in a subdivided population. This is serious because these are the effective sizes that are relevant to the widely accepted 50/500 rule for short and long term genetic conservation. The bias can be infinitely large and is due to inappropriate parameters being estimated when applying theory for isolated populations to subdivided ones.
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