Reproductive Value and the Stochastic Demography of Age‐Structured Populations

2009 ◽  
Vol 174 (6) ◽  
pp. 795-804 ◽  
Author(s):  
Steinar Engen ◽  
Russell Lande ◽  
Bernt‐Erik Sæther ◽  
F. Stephen Dobson
Keyword(s):  
Structured Populations ◽  
Reproductive Value ◽  
Stochastic Demography ◽  
Age Structured

scholarly journals Towards a replicator dynamics model of age structured populations

2021 ◽  
Vol 82 (5) ◽  
Author(s):  
K. Argasinski ◽  
M. Broom
Keyword(s):  
Sex Ratio ◽  
Age Structure ◽  
Replicator Dynamics ◽  
Structured Populations ◽  
Reproductive Value ◽  
Leslie Matrix ◽  
Age Classes ◽  
Structured Population Model ◽  
Age Class ◽  
Age Structured

AbstractWe present a new modelling framework combining replicator dynamics, the standard model of frequency dependent selection, with an age-structured population model. The new framework allows for the modelling of populations consisting of competing strategies carried by individuals who change across their life cycle. Firstly the discretization of the McKendrick von Foerster model is derived. We show that the Euler–Lotka equation is satisfied when the new model reaches a steady state (i.e. stable frequencies between the age classes). This discretization consists of unit age classes where the timescale is chosen so that only a fraction of individuals play a single game round. This implies a linear dynamics and individuals not killed during the round are moved to the next age class; linearity means that the system is equivalent to a large Bernadelli–Lewis–Leslie matrix. Then we use the methodology of multipopulation games to derive two, mutually equivalent systems of equations. The first contains equations describing the evolution of the strategy frequencies in the whole population, completed by subsystems of equations describing the evolution of the age structure for each strategy. The second contains equations describing the changes of the general population’s age structure, completed with subsystems of equations describing the selection of the strategies within each age class. We then present the obtained system of replicator dynamics in the form of the mixed ODE-PDE system which is independent of the chosen timescale, and much simpler. The obtained results are illustrated by the example of the sex ratio model which shows that when different mortalities of the sexes are assumed, the sex ratio of 0.5 is obtained but that Fisher’s mechanism, driven by the reproductive value of the different sexes, is not in equilibrium.

Using reproductive value to estimate key parameters in density-independent age-structured populations

2007 ◽  
Vol 244 (2) ◽  
pp. 308-317 ◽  
Author(s):  
Steinar Engen ◽  
Russell Lande ◽  
Bernt-Erik Sæther ◽  
Marco Festa-Bianchet
Keyword(s):  
Structured Populations ◽  
Reproductive Value ◽  
Age Structured

scholarly journals Frequency responses of age-structured populations: Pacific salmon as an example

2010 ◽  
Vol 78 (4) ◽  
pp. 239-249 ◽  
Author(s):  
Lee Worden ◽  
Louis W. Botsford ◽  
Alan Hastings ◽  
Matthew D. Holland
Keyword(s):  
Pacific Salmon ◽  
Structured Populations ◽  
Frequency Responses ◽  
Age Structured

scholarly journals The effect of life-history and mode of inheritance on neutral genetic variability

2001 ◽  
Vol 77 (2) ◽  
pp. 153-166 ◽  
Author(s):  
BRIAN CHARLESWORTH
Keyword(s):  
Sequence Variation ◽  
Adult Mortality ◽  
Structured Populations ◽  
Human Populations ◽  
Effective Population ◽  
Transmission Modes ◽  
Population Sizes ◽  
Age Structured ◽  
Infinite Sites Model ◽  
Site Diversity

Formulae for the effective population sizes of autosomal, X-linked, Y-linked and maternally transmitted loci in age-structured populations are developed. The approximations used here predict both asymptotic rates of increase in probabilities of identity, and equilibrium levels of neutral nucleotide site diversity under the infinite-sites model. The applications of the results to the interpretation of data on DNA sequence variation in Drosophila, plant, and human populations are discussed. It is concluded that sex differences in demographic parameters such as adult mortality rates generally have small effects on the relative effective population sizes of loci with different modes of inheritance, whereas differences between the sexes in variance in reproductive success can have major effects, either increasing or reducing the effective population size for X-linked loci relative to autosomal or Y-linked loci. These effects need to be accounted for when trying to understand data on patterns of sequence variation for genes with different transmission modes.

Evolution in Age-Structured Populations.

1995 ◽  
Vol 83 (3) ◽  
pp. 548
Author(s):  
Tom J. de Jong ◽  
B. Charlesworth
Keyword(s):  
Structured Populations ◽  
Age Structured

scholarly journals Towards a better understanding of the dynamics of Aphis spiraecola Patch (Homoptera: Aphididae) populations in commercial alpine yarrow fields

2010 ◽  
Vol 42 (2) ◽  
pp. 103 ◽  
Author(s):  
Zulfaidah Penata Gama ◽  
Pablo Morlacchi ◽  
Giuseppe Carlo Lozzia ◽  
Johann Baumgärtner ◽  
Anna Giorgi
Keyword(s):  
Natural Enemy ◽  
Distributed Delay ◽  
Structured Populations ◽  
Temperature Dependent ◽  
Optimum Sample Size ◽  
Aphis Spiraecola ◽  
Different Temperatures ◽  
Mechanistic Basis ◽  
Age Structured ◽  
Optimum Sample

The spatial distribution of Aphis spiraecola Patch was studied in two commercial yarrow fields located in the Swiss and Italian Alps and represented by Taylor’s (1961) power law. The respective parameters indicate a highly aggregated distribution and lead to a high optimum sample size of 400-500 plants in the design of a sampling program. Opportunities for reducing the sampling efforts are discussed. The infestation patterns were studied on the basis of Vansickle’s (1977) time varying distributed delay adequate for modelling the dynamics of age-structured populations. Published literature data were used to parametrize the functions representing the temperature-dependent duration and survival of the nymphal and adult stage. Likewise, literature data were available to obtain reliable estimates for the parameters of the fecundity function comprising the reproductive profile and the number of nymphs produced at different temperatures. The field data were used to parametrize the functions for wing formation and a compound mortality compromising the effects of plant senescence, stem cutting and natural enemies. The model satisfactorily represented the observed infestation patterns. However, there are opportunities for improving parameter estimation and validation. Moreover, the separation of the compound mortality into host plant and natural enemy effects would improve the mechanistic basis of the model and lead towards a tool that could be used to study bottom-up and top-down effects in the yarrow-aphid-natural enemy system.

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