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.

scholarly journals When does selection favor learning from the old? Social Learning in age-structured populations

2020 ◽  
Author(s):  
Dominik_Deffner ◽  
Richard McElreath
Keyword(s):  
Social Learning ◽  
Adaptive Behavior ◽  
Age Structure ◽  
Cultural Transmission ◽  
Empirical Work ◽  
Structured Populations ◽  
Older Age ◽  
Age Classes ◽  
Demographic Processes ◽  
Age Structured

Culture and demography jointly facilitate flexible human adaptation, yet it still remains unclear how social learning operates in populations with age structure. Specifically, how do demographic processes affect the adaptive value of culture, cultural adaptation and population growth and when does selection favor copying the behavior of older vs. younger individuals? Here, we develop and analyze a mathematical model of the evolution of social learning in a population with different age classes. We find that adding age structure alone does not resolve Rogers' paradox, i.e. the finding that social learning can evolve without increasing population fitness. Cultural transmission in combination with demographic filtering, however, can lead to much higher adaptation levels. This is because by increasing proportions of adaptive behavior in older age classes, demographic filtering constitutes an additional adaptive force that social learners can benefit from. Moreover, older age classes tend to have higher proportions of adaptive behavior when the environment is relatively stable and adaptive behavior is hard to acquire but confers large survival advantages. Through individual-based simulations comparing temporal and spatial variability in the environment, we find a ``copy older over younger models''-strategy only evolves readily when social learning is erroneous. The opposite ``copy the younger''-strategy is adaptive when the environment fluctuates frequently but still maintains large proportions of social learners. Our results demonstrate that age structure can substantially alter cultural dynamics and should be addressed in further theoretical and empirical work.

scholarly journals Unreported cases for Age Dependent COVID-19 Outbreak in Japan

2020 ◽  
Author(s):  
Quentin Griette ◽  
Pierre Magal ◽  
Ousmane Seydi
Keyword(s):  
Mathematical Model ◽  
Age Structure ◽  
Early Stage ◽  
Structured Data ◽  
Computational Method ◽  
Mitigation Measures ◽  
Age Classes ◽  
The Social ◽  
Age Dependent ◽  
Age Structured

AbstractWe investigate the age structured data for the COVID-19 outbreak in Japan. We consider a mathematical model for the epidemic with unreported infectious patient with and without age structure. In particular, we build a new mathematical model and a new computational method to fit the data by using age classes dependent exponential growth at the early stage of the epidemic. This allows to take into account differences in the response of patients to the disease according to their age. This model also allows for a heterogeneous response of the population to the social distancing measures taken by the local government. We fit this model to the observed data and obtain a snapshot of the effective transmissions occurring inside the population at different times, which indicates where and among whom the disease propagates after the start of public mitigation measures.

Contributions of adult mortality to declines of Puget Sound Pacific herring

2017 ◽  
Vol 75 (1) ◽  
pp. 319-329 ◽  
Author(s):  
Margaret C Siple ◽  
Andrew O Shelton ◽  
Tessa B Francis ◽  
Dayv Lowry ◽  
Adam P Lindquist ◽  
...  
Keyword(s):  
Age Structure ◽  
Puget Sound ◽  
Adult Mortality ◽  
Forage Fish ◽  
Pacific Herring ◽  
Natural Mortality ◽  
Structured Population Model ◽  
Adult Age ◽  
Age Structured

Abstract Forage fish undergo dramatic changes in abundance through time. Long-term fluctuations, which have historically been attributed to changes in recruitment, may also be due to changes in adult mortality. Pacific herring, a lightly exploited forage fish in Puget Sound, WA, have exhibited shifts in age structure and decreases in spawning biomass during the past 30 years. Here, we investigate changes in adult mortality as a potential explanation for these shifts. Using a hierarchical, age-structured population model, we indicate that adult natural mortality for Puget Sound Pacific herring has increased since 1973. We find that natural mortality has increased for every age class of adult (age 3+), especially age 4 fish, whose estimated mortality has doubled over the survey time period (from M = 0.84–1.76). We demonstrate that long-term shifts in mortality explain changes in age structure, and may explain biomass declines and failure to reach management thresholds for two spawning sites in Puget Sound (Cherry Point and Squaxin Pass). Temporal shifts in natural adult mortality could have negative implications for herring and herring predators. We demonstrate that adult mortality, in addition to recruitment variation, is an important driver for forage fish, which face exceptionally high natural mortality compared with other fishes.

scholarly journals Studi Kelompok Siamang (Hylobates Syndactylus) Di Repong Damar Pahmungan Pesisir Barat

2015 ◽  
Vol 3 (3) ◽  
pp. 85 ◽  
Author(s):  
Erna Maya Sari ◽  
Sugeng P. Harianto
Keyword(s):  
Sex Ratio ◽  
National Park ◽  
Local Community ◽  
Agroforestry Systems ◽  
Age Classes ◽  
Adult Age ◽  
Age Class ◽  
Hylobates Syndactylus ◽  
The Individual ◽  
Coastal District

Repong Damar in Pahmungan, West Coastal District is a buffer of Bukit Barisan Selatan National Park (TNBBS).  Repong Damar is one example of the success of agroforestry systems managed by local community that is still very traditional.  This area was identified as a component of siamang (Hylobates syndactylus) habitat.  The absence of data and the latest information about the siamang groups in Pekon Pahmungan were reasons of this research.  The purpose of this research was to determine the siamang groups in Repong Damar, used concentrated area methode.  The research was done on April 2015.  The results showed that the existence of siamang group in Repong Damar Pahmungan were 4 individuals/group.  The distribution of age classes in the individual phases of adult siamang were 2 individuals and the individual of adolescent phase were 2 individuals.  The sex ratio in the adult age class phase was 1:1 and at adolescent age class phase was 1:1.  Keywords: siamang, groups, repong damar

scholarly journals An Analysis of a Semelparous Population Model with Density-Dependent Fecundity and Density-Dependent Survival Probabilities

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Arild Wikan
Keyword(s):  
Density Dependence ◽  
Chaotic Dynamics ◽  
Leslie Matrix ◽  
Age Classes ◽  
Density Dependent ◽  
Survival Probabilities ◽  
Leslie Matrix Model ◽  
Periodic Dynamics ◽  
Age Structured ◽  
Nonstationary Dynamics

A discrete age-structured semelparous Leslie matrix model where density dependence is included both in the fecundity and in the survival probabilities is analysed. Depending on strength of density dependence, we show in the precocious semelparous case that the nonstationary dynamics may indeed be rich, ranging from SYC (a dynamical state where the whole population is in one age class only) dynamics to cycles of low period where all age classes are populated. Quasiperiodic and chaotic dynamics have also been identified. Moreover, outside parameter regions where SYC dynamics dominates, we prove that the transfer from stability to instability goes through a supercritical Neimark−Sacker bifurcation, and it is further shown that when the population switches from possessing a precocious to a delayed semelparous life history both stability properties and the possibility of periodic dynamics become weaker.

Reproductive value and analyses of population dynamics of age-structured populations

2021 ◽  
pp. 285-298
Author(s):  
Bernt-Erik Sæther ◽  
Steinar Engen
Keyword(s):  
Growth Rate ◽  
Population Dynamics ◽  
Age Structure ◽  
Good Description ◽  
Age Distribution ◽  
Reproductive Rate ◽  
Environmental Stochasticity ◽  
Reproductive Value ◽  
Long Run ◽  
Age Structured

Many populations of especially long-lived species show large temporal variation in age structure, which can complicate estimating of important population parameters. This occurs because it can be difficult to disentangle whether variation in numbers is due to fluctuations in the environment or caused by changes in the age distribution. This chapter shows that fluctuations in the total reproductive value of the population, that is, the sum of all individual reproductive values, often provide a good description of the population dynamics but still is not confounded by fluctuations in age structure. Because the change in the total reproductive rate is exactly equal to the growth rate of the population, this quantity enables decomposition of the long-run growth rate into stochastic components caused by age-specific variation in demographic and environmental stochasticity. The chapter illustrates the practical application of this approach in stochastic demography by analyses of the dynamics of several populations of birds and mammals. It puts a strong focus on these methods being particularly useful in viability analyses of small populations of vulnerable or endangered species.

scholarly journals Importance of age structure in models of the response of upper trophic levels to fishing and climate change

2011 ◽  
Vol 68 (6) ◽  
pp. 1270-1283 ◽  
Author(s):  
Louis W. Botsford ◽  
Matthew D. Holland ◽  
Jameal F. Samhouri ◽  
J. Wilson White ◽  
Alan Hastings
Keyword(s):  
Climate Change ◽  
Age Structure ◽  
Life Histories ◽  
Resonance Effect ◽  
Population Data ◽  
Ecosystem Model ◽  
Structured Populations ◽  
Trophic Levels ◽  
Ecosystem Models ◽  
Age Structured

Abstract Botsford, L. W., Holland, M. D., Samhouri, J. F., White, J. W., and Hastings, A. 2011. Importance of age structure in models of the response of upper trophic levels to fishing and climate change. – ICES Journal of Marine Science, 68: 1270–1283. There is a growing effort to use predictions of the physical state of the ocean under climate change to forecast the response of marine ecosystems. Many of these forecasts use ecosystem models rather than age-structured population models to describe upper trophic level (UTL) species. We illustrate the potential effects of climate on age-structured populations, then illustrate the ways in which ecosystem models might not depict adequately: (i) long-term changes in abundance, and (ii) variability attributable to cohort resonance. We simulated two generic species with different life histories, a short-lived semelparous species (e.g. salmon), and a long-lived iteroparous species (e.g. cod). For both species, juvenile survival was varied, first with white noise, then with the Pacific Decadal Oscillation as environmental signals. Variability in recruitment increased with fishing and became particularly sensitive to forcing at time-scales near the mean age of reproduction, consistent with the cohort resonance effect. Ecosystem models without age structure do not predict this behaviour, particularly when the ecosystem model incorrectly predicts the effective steepness of the stock–recruitment relationship, or the age structure is approximated by a stage-structured model. We suggest that ecosystem models of UTLs include full representations of age structure, fitted to available population data.

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