| 1. |
- Bartoszek, Krzysztof, et al.
(författare)
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A consistent estimator of the evolutionary rate
- 2015
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Ingår i: Journal of Theoretical Biology. - : Elsevier BV. - 0022-5193 .- 1095-8541. ; 371, s. 69-78
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Tidskriftsartikel (refereegranskat)abstract
- We consider a branching particle system where particles reproduce according to the pure birth Yule process with the birth rate 2, conditioned on the observed number of particles to be equal to n. Particles are assumed to move independently on the real line according to the Brownian motion with the local variance sigma(2). In this paper we treat n particles as a sample of related species. The spatial Brownian motion of a particle describes the development of a trait value of interest (e.g. log-body-size). We propose an unbiased estimator 4 of the evolutionary rate rho(2) - sigma(2)/lambda. The estimator R-n(2) is proportional to the sample variance S-n(2) computed from n trait values. We find an approximate formula for the standard error of R-n(2), based on a neat asymptotic relation for the variance of S-n(2). (C) 2015 Elsevier Ltd. All rights reserved.
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| 2. |
- Bartoszek, Krzysztof, 1984-, et al.
(författare)
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Phylogenetic confidence intervals for the optimal trait value
- 2015
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 52:4, s. 1115-1132
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Tidskriftsartikel (refereegranskat)abstract
- We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree is modelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to evolve along lineages as an Ornstein-Uhlenbeck process. As a result, the trait values of the n species form a sample with dependent observations. We establish three limit theorems for the sample mean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean is approximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.
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| 3. |
- Bartoszek, Krzysztof, 1984-, et al.
(författare)
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Time to a single hybridization event in a group of species with unknown ancestral history
- 2013
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Ingår i: Journal of Theoretical Biology. - : Elsevier BV. - 0022-5193 .- 1095-8541. ; 322, s. 1-6
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Tidskriftsartikel (refereegranskat)abstract
- We consider a stochastic process for the generation of species which combines a Yule process with a simple model for hybridization between pairs of co-existent species. We assume that the origin of the process, when there was one species, occurred at an unknown time in the past, and we condition the process on producing n species via the Yule process and a single hybridization event. We prove results about the distribution of the time of the hybridization event. In particular we calculate a formula for all moments, and show that under various conditions, the distribution tends to an exponential with rate twice that of the birth rate for the Yule process.
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| 4. |
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| 5. |
- Eriksson, Anders, 1975, et al.
(författare)
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An accurate model for genetic hitchhiking
- 2008
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Ingår i: Genetics. - : Oxford University Press (OUP). - 0016-6731 .- 1943-2631. ; 178:1, s. 439-451
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Tidskriftsartikel (refereegranskat)abstract
- We suggest a simple deterministic approximation for the growth of the favored-allele frequency during a selective sweep. Using this approximation we introduce an accurate model for genetic hitchhiking. Only when Ns < 10 (N is the population size and s denotes the selection coefficient) are discrepancies between our approximation and direct numerical simulations of a Moran model notable. Our model describes the gene genealogies of a contiguous segment of neutral loci close to the selected one, and it does not assume that the selective sweep happens instantaneously. This enables us to compute SNP distributions on the neutral segment without bias.
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| 6. |
- Eriksson, Anders, 1975, et al.
(författare)
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The total branch length of sample genealogies in populations of variable size
- 2010
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Ingår i: Genetics. - : Oxford University Press (OUP). - 0016-6731 .- 1943-2631. ; 186:2, s. 601-611
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Tidskriftsartikel (refereegranskat)abstract
- We consider neutral evolution of a large population subject to changes in its population size. For a population with a time-variable carrying capacity we study the distribution of the total branch lengths of its sample genealogies. Within the coalescent approximation we have obtained a general expression— Equation 20—for the moments of this distribution with a given arbitrary dependence of the population size on time. We investigate how the frequency of population-size variations alters the total branch length.
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| 7. |
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| 8. |
- Jagers, Peter, 1941, et al.
(författare)
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Convergence to the coalescent in populations of substantially varying size.
- 2004
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Ingår i: J. Appl. Probab.. - 0021-9002. ; 41:2, s. 368-378
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Tidskriftsartikel (refereegranskat)abstract
- Kingman's classical coalescent uncovers the basic pattern of genealogical trees of random samples of individuals in large but time-constant populations. Time is viewed as discrete and identified with non-overlapping generations. Reproduction can be very generally taken as exchangeable (meaning that the labelling of individuals in each generation carries no significance). Recent generalisations have dealt with population sizes exhibiting given deterministic or (minor) random fluctuations. We consider population sizes which constitute a stationary Markov chain, explicitly allowing large fluctuations in short times. Convergence of the genealogical tree, as population size tends to infinity, towards the (time-scaled) coalescent is simply proved under minimal conditions. As a result, a formula for effective population size obtains, generalising the well-knownharmonic mean expression for effective size.
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| 9. |
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| 10. |
- Jagers, Peter, 1941, et al.
(författare)
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General branching processes in discrete time as random trees.
- 2008
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Ingår i: Bernoulli. - 1350-7265. ; 14:4, s. 949-962
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Tidskriftsartikel (refereegranskat)abstract
- The simple Galton-Watson process describes populations where individuals live one season and are then replaced by a random number of children. It can also be viewed as a way of generating random trees, each vertex being an individual of the family tree. This viewpoint has led to new insights and a revival of classical theory. We show how a similar reinterpretation can shed new light on the more interesting forms of branching processes that allow repeated bearings and, thus, overlapping generations. In particular, we use the stable pedigree law to give a transparent description of a size-biased version of general branching processes in discrete time. This allows us to analyse the xlog x condition for exponential growth of supercritical general processes, and also the relation between simple Galton-Watson and more general branching processes.
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