scholarly journals A Branching Process Model of Evolutionary Rescue

2021 ◽  
Author(s):  
Peter Olofsson ◽  
Ricardo B. R. Azevedo
Keyword(s):  
Population Growth ◽  
Mutation Rate ◽  
Discrete Time ◽  
Growth Curve ◽  
Process Model ◽  
Branching Process ◽  
Selective Advantage ◽  
Population Declines ◽  
Beneficial Mutations ◽  
Evolutionary Rescue

Evolutionary rescue is the process whereby a declining population may start growing again, thus avoiding extinction, via an increase in the frequency of beneficial genotypes. These genotypes may either already be present in the population in small numbers, or arise by mutation as the population declines. We present a simple two-type discrete-time branching process model and use it to obtain results such as the probability of rescue, the shape of the population growth curve of a rescued population, and the time until the first rescuing mutation occurs. Comparisons are made to existing results in the literature in cases where both the mutation rate and the selective advantage of the beneficial mutations are small.

scholarly journals Dynamics and fate of beneficial mutations under lineage contamination by linked deleterious mutations

2016 ◽  
Author(s):  
Sophie Pénisson ◽  
Tanya Singh ◽  
Paul Sniegowski ◽  
Philip Gerrish
Keyword(s):  
Mutation Rate ◽  
Branching Process ◽  
Deleterious Mutation ◽  
Selective Advantage ◽  
Single Type ◽  
Deleterious Mutations ◽  
Beneficial Mutations ◽  
Multitype Branching Process ◽  
Fitness Effects ◽  
Adaptive Substitution

ABSTRACTBeneficial mutations drive adaptive evolution, yet their selective advantage does not ensure their fixation. Haldane’s application of single-type branching process theory showed that genetic drift alone could cause the extinction of newly-arising beneficial mutations with high probability. With linkage, deleterious mutations will affect the dynamics of beneficial mutations and might further increase their extinction probability. Here, we model the lineage dynamics of a newly-arising beneficial mutation as a multitype branching process; this approach allows us to account for the combined effects of drift and the stochastic accumulation of linked deleterious mutations, which we call lineage contamination. We first study the lineage contamination phenomenon in isolation, deriving extinction times and probabilities of beneficial lineages. We then put the lineage contamination phenomenon into the context of an evolving population by incorporating the effects of background selection. We find that the survival probability of beneficial mutations is simply Haldane’s classical formula multiplied by the correction factor , where U is deleterious mutation rate, is mean selective advantage of beneficial mutations, κ ∈ (1, ε], and ε = 2 – e−1. We also find there exists a genomic deleterious mutation rate, , that maximizes the rate of production of surviving beneficial mutations, and that . Both of these results, and others, are curiously independent of the fitness effects of deleterious mutations. We derive critical mutation rates above which: 1) lineage contamination alleviates competition among beneficial mutations, and 2) the adaptive substitution process all but shuts down.

scholarly journals The Probability of Fixation in Populations of Changing Size

Genetics ◽  
1997 ◽  
Vol 146 (2) ◽  
pp. 723-733 ◽  
Author(s):  
Sarah P Otto ◽  
Michael C Whitlock
Keyword(s):  
Diffusion Equation ◽  
Adaptive Evolution ◽  
Process Model ◽  
Branching Process ◽  
Approximate Solutions ◽  
Logistic Growth ◽  
Beneficial Mutations ◽  
Demographic Models ◽  
Deleterious Alleles ◽  
Probability Of Fixation

The rate of adaptive evolution of a population ultimately depends on the rate of incorporation of beneficial mutations. Even beneficial mutations may, however, be lost from a population since mutant individuals may, by chance, fail to reproduce. In this paper, we calculate the probability of fixation of beneficial mutations that occur in populations of changing size. We examine a number of demographic models, including a population whose size changes once, a population experiencing exponential growth or decline, one that is experiencing logistic growth or decline, and a population that fluctuates in size. The results are based on a branching process model but are shown to be approximate solutions to the diffusion equation describing changes in the probability of fixation over time. Using the diffusion equation, the probability of fixation of deleterious alleles can also be determined for populations that are changing in size. The results developed in this paper can be used to estimate the fixation flux, defined as the rate at which beneficial alleles fix within a population. The fixation flux measures the rate of adaptive evolution of a population and, as we shall see, depends strongly on changes that occur in population size.

MODELING THE ROLE OF MUTATIONS AND DENSITY INDEPENDENT DISPERSAL IN EVOLUTIONARY RESCUE

2014 ◽  
Vol 22 (01) ◽  
pp. 123-132
Author(s):  
MELKIOR ORNIK
Keyword(s):  
Experimental Research ◽  
Discrete Time ◽  
Environmental Changes ◽  
Discrete Space ◽  
Time Model ◽  
Beneficial Mutations ◽  
Discrete Time Model ◽  
Population Dispersal ◽  
Evolutionary Rescue

Faced with a strong and sudden deterioration of environment, a population encounters two possible options — adapt or perish. In general, it is not known which of those outcomes the environmental changes will lead to. Building on experimental research, we introduce a discrete-space, discrete-time model for environmental rescue based on the influence of population dispersal, as well as, potentially beneficial mutations. Numerical results obtained by the model are shown to correspond well to experimentally obtained data.

scholarly journals Evolutionary rescue by beneficial mutations in environments that change in space and time

2013 ◽  
Vol 368 (1610) ◽  
pp. 20120082 ◽  
Author(s):  
Mark Kirkpatrick ◽  
Stephan Peischl
Keyword(s):  
Branching Processes ◽  
Selective Advantage ◽  
Maximum Speed ◽  
Selection Coefficient ◽  
Beneficial Mutations ◽  
Changing Environments ◽  
Classic Theory ◽  
Evolutionary Rescue ◽  
Effective Selection ◽  
Establishment Probability

A factor that may limit the ability of many populations to adapt to changing conditions is the rate at which beneficial mutations can become established. We study the probability that mutations become established in changing environments by extending the classic theory for branching processes. When environments change in time, under quite general conditions, the establishment probability is approximately twice the ‘effective selection coefficient’, whose value is an average that gives most weight to a mutant's fitness in the generations immediately after it appears. When fitness varies along a gradient in a continuous habitat, increased dispersal generally decreases the chance a mutation establishes because mutations move out of areas where they are most adapted. When there is a patch of favourable habitat that moves in time, there is a maximum speed of movement above which mutations cannot become established, regardless of when and where they first appear. This critical speed limit, which is proportional to the mutation's maximum selective advantage, represents an absolute constraint on the potential of locally adapted mutations to contribute to evolutionary rescue.

scholarly journals THE SURVIVAL OF MUTANTS AT VERY LOW FREQUENCIES IN TRIBOLIUM POPULATIONS

Genetics ◽  
1974 ◽  
Vol 77 (4) ◽  
pp. 805-818
Author(s):  
Robert R Sokal ◽  
Aykut Kence ◽  
David E McCauley
Keyword(s):  
Process Model ◽  
Branching Process ◽  
Tactile Stimulation ◽  
Selective Advantage ◽  
Developmental Period ◽  
Extinction Rate ◽  
Wild Type ◽  
Gene Frequencies ◽  
Low Frequencies ◽  
Average Gene

ABSTRACT Forty population cages, each with 499 adult T. castaneum of the wild-type UPF strain, received a bb female newly mated with UPF males. Half of the immigrants had a Chicago Black genetic background, the other half a UPF background. These conditions simulate, respectively, the fate of a rare, genetically differing immigrant or the fate of a mutation in populations of considerable size. Adults were censused for 11 discrete generations. The semi-dominant autosomal black gene survived in 26 out of 40 cultures by the end of the experiment, demonstrating its selective advantage at these very low frequencies. The gene increased from an initial frequency of 0.002 to 0.055 (at generation 11) in at least one replicate. Although frequency-dependent fitness has been shown for black at higher frequencies, no such dependence could be demonstrated at the low frequencies of this study. The cultures simulating mutations (immigrants with native backgrounds) had a higher average gene frequency, different distribution of gene frequencies across replicates, and a lower extinction rate of black than did the cultures with alien background immigrants. The observations only partially fitted expectation based on a branching process model. The data show a tendency for the persistence of a few heterozygotes in cultures and for a deficiency of cultures that lost the mutant or those with many heterozygotes. The increase in frequency of black cannot be attributed to increased reproductive success of heterozygotes. The advantage of heterozygotes appears due to delayed developmental period as a result of tactile stimulation and probable differential cannibalism among pupae.

scholarly journals A branching process model of evolutionary rescue

2021 ◽  
pp. 108708
Author(s):  
Ricardo B.R. Azevedo ◽  
Peter Olofsson
Keyword(s):  
Process Model ◽  
Branching Process ◽  
Evolutionary Rescue

scholarly journals A branching process model for the analysis of abortive colony size distributions in carbon ion-irradiated normal human fibroblasts

2014 ◽  
Vol 55 (3) ◽  
pp. 423-431 ◽  
Author(s):  
T. Sakashita ◽  
N. Hamada ◽  
I. Kawaguchi ◽  
T. Hara ◽  
Y. Kobayashi ◽  
...  
Keyword(s):  
Colony Size ◽  
Process Model ◽  
Branching Process ◽  
Human Fibroblasts ◽  
Size Distributions ◽  
Carbon Ion ◽  
Normal Human
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