| 1. |
- Aguilar, Elliot, et al.
(författare)
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Modeling the genealogy of a cultural trait
- 2015
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Ingår i: Theoretical Population Biology. - : Elsevier BV. - 0040-5809 .- 1096-0325. ; 101, s. 1-8
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Tidskriftsartikel (refereegranskat)abstract
- The mathematical study of genealogies has yielded important insights in population biology, such as the ability to estimate the time to the most recent common ancestor (MRCA) of a sample of genetic sequences or of a group of individuals. Here we introduce a model of cultural genealogies that is a step toward answering similar questions for cultural traits. In our model individuals can inherit from a variable, potentially large number of ancestors, rather than from a fixed, small number of ancestors (one or two) as is typical of genetic evolution. We first show that, given a sample of individuals, a cultural common ancestor does not necessarily exist. We then introduce a related concept: the most recent unique ancestor (MRUA), i.e., the most recent single individual who is the earliest cultural ancestor of the sample. We show that, under neutral evolution, the time to the MRUA can be staggeringly larger than the time to MRCA in a single ancestor model, except when the average number of learning opportunities per individuals is small. Our results point out that the properties of cultural genealogies may be very different from those of genetic genealogies, with potential implications for reconstructing the histories of cultural traits.
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| 2. |
- 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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| 3. |
- 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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| 4. |
- Kaj, Ingemar, et al.
(författare)
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The non-equilibrium allele frequency spectrum in a Poisson random field framework
- 2016
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Ingår i: Theoretical Population Biology. - : Elsevier BV. - 0040-5809 .- 1096-0325. ; 111, s. 51-64
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Tidskriftsartikel (refereegranskat)abstract
- In population genetic studies, the allele frequency spectrum (AFS) efficiently summarizes genome-wide polymorphism data and shapes a variety of allele frequency-based summary statistics. While existing theory typically features equilibrium conditions, emerging methodology requires an analytical understanding of the build-up of the allele frequencies over time. In this work, we use the framework of Poisson random fields to derive new representations of the non-equilibrium AFS for the case of a Wright-Fisher population model with selection. In our approach, the AFS is a scaling-limit of the expectation of a Poisson stochastic integral and the representation of the non-equilibrium AFS arises in terms of a fixation time probability distribution. The known duality between the Wright-Fisher diffusion process and a birth and death process generalizing Kingman's coalescent yields an additional representation. The results carry over to the setting of a random sample drawn from the population and provide the non-equilibrium behavior of sample statistics. Our findings are consistent with and extend a previous approach where the non-equilibrium AFS solves a partial differential forward equation with a non-traditional boundary condition. Moreover, we provide a bridge to previous coalescent-based work, and hence tie several frameworks together. Since frequency-based summary statistics are widely used in population genetics, for example, to identify candidate loci of adaptive evolution, to infer the demographic history of a population, or to improve our understanding of the underlying mechanics of speciation events, the presented results are potentially useful for a broad range of topics.
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| 5. |
- Olsson, Fredrik, et al.
(författare)
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Estimation of the variance effective population size in age structured populations
- 2015
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Ingår i: Theoretical Population Biology. - : Elsevier BV. - 0040-5809 .- 1096-0325. ; 101, s. 9-23
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Tidskriftsartikel (refereegranskat)abstract
- The variance effective population size for age structured populations is generally hard to estimate and the temporal method often gives biased estimates. Here, we give an explicit expression for a correction factor which, combined with estimates from the temporal method, yield approximately unbiased estimates. The calculation of the correction factor requires knowledge of the age specific offspring distribution and survival probabilities as well as possible correlation between survival and reproductive success. In order to relax these requirements, we show that only first order moments of these distributions need to be known if the time between samples is large, or individuals from all age classes which reproduce are sampled. A very explicit approximate expression for the asymptotic coefficient of standard deviation of the estimator is derived, and it can be used to construct confidence intervals and optimal ways of weighting information from different markers. The asymptotic coefficient of standard deviation can also be used to design studies and we show that in order to maximize the precision for a given sample size, individuals from older age classes should be sampled since their expected variance of allele frequency change is higher and easier to estimate. However, for populations with fluctuating age class sizes, the accuracy of the method is reduced when samples are taken from older age classes with high demographic variation. We also present a method for simultaneous estimation of the variance effective and census population size.
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| 6. |
- Sainudiin, Raazesh, et al.
(författare)
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Full likelihood inference from the site frequency spectrum based on the optimal tree resolution
- 2018
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Ingår i: Theoretical Population Biology. - : ACADEMIC PRESS INC ELSEVIER SCIENCE. - 0040-5809 .- 1096-0325. ; 124, s. 1-15
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Tidskriftsartikel (refereegranskat)abstract
- We develop a novel importance sampler to compute the full likelihood function of a demographic or structural scenario given the site frequency spectrum (SFS) at a locus free of intra-locus recombination. This sampler, instead of representing the hidden genealogy of a sample of individuals by a labelled binary tree, uses the minimal level of information about such a tree that is needed for the likelihood of the SFS and thus takes advantage of the huge reduction in the size of the state space that needs to be integrated. We assume that the population may have demographically changed and may be non-panmictically structured, as reflected by the branch lengths and the topology of the genealogical tree of the sample, respectively. We also assume that mutations conform to the infinitely-many-sites model. We achieve this by a controlled Markov process that generates 'particles' in the hidden space of SFS histories which are always compatible with the observed SFS. To produce the particles, we use Aldous' Beta-splitting model for a one parameter family of prior distributions over genealogical topologies or shapes (including that of the Kingman coalescent) and allow the branch lengths or epoch times to have a parametric family of priors specified by a model of demography (including exponential growth and bottleneck models). Assuming independence across unlinked loci, we can estimate the likelihood of a population scenario based on a large collection of independent SFS by an importance sampling scheme, using the (unconditional) distribution of the genealogies under this scenario when the latter is available. When it is not available, we instead compute the joint likelihood of the tree balance parameter beta assuming that the tree topology follows Aldous' Beta splitting model, and of the demographic scenario determining the distribution of the inter-coalescence times or epoch times in the genealogy of a sample, in order to at least distinguish different equivalence classes of population scenarios leading to different tree balances and epoch times. Simulation studies are conducted to demonstrate the capabilities of the approach with publicly available code.
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| 7. |
- Svardal, Hannes, et al.
(författare)
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A general condition for adaptive genetic polymorphism in temporally and spatially heterogeneous environments
- 2015
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Ingår i: Theoretical Population Biology. - : Elsevier BV. - 0040-5809 .- 1096-0325. ; 99, s. 76-97
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Tidskriftsartikel (refereegranskat)abstract
- Both evolution and ecology have long been concerned with the impact of variable environmental conditions on observed levels of genetic diversity within and between species. We model the evolution of a quantitative trait under selection that fluctuates in space and time, and derive an analytical condition for when these fluctuations promote genetic diversification. As ecological scenario we use a generalized island model with soft selection within patches in which we incorporate generation overlap. We allow for arbitrary fluctuations in the environment including spatio-temporal correlations and any functional form of selection on the trait. Using the concepts of invasion fitness and evolutionary branching, we derive a simple and transparent condition for the adaptive evolution and maintenance of genetic diversity. This condition relates the strength of selection within patches to expectations and variances in the environmental conditions across space and time. Our results unify, clarify, and extend a number of previous results on the evolution and maintenance of genetic variation under fluctuating selection. Individual-based simulations show that our results are independent of the details of the genetic architecture and whether reproduction is clonal or sexual. The onset of increased genetic variance is predicted accurately also in small populations in which alleles can go extinct due to environmental stochasticity.
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