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.

Consequences of potential density-dependent mechanisms on recovery of ocean-type chinook salmon (Oncorhynchus tshawytscha)

2004 ◽  
Vol 61 (4) ◽  
pp. 590-602 ◽  
Author(s):  
Correigh M Greene ◽  
Timothy J Beechie
Keyword(s):  
Density Dependence ◽  
Chinook Salmon ◽  
Habitat Restoration ◽  
Oncorhynchus Tshawytscha ◽  
High Sensitivity ◽  
Leslie Matrix ◽  
Relative Importance ◽  
Density Dependent ◽  
Habitat Area ◽  
Leslie Matrix Model

Restoring salmon populations depends on our ability to predict the consequences of improving aquatic habitats used by salmon. Using a Leslie matrix model for chinook salmon (Oncorhynchus tshawytscha) that specifies transitions among spawning nests (redds), streams, tidal deltas, nearshore habitats, and the ocean, we compared the relative importance of different habitats under three density-dependent scenarios: juvenile density independence, density-dependent mortality within streams, delta, and nearshore, and density-dependent migration among streams, delta, and nearshore. Each scenario assumed density dependence during spawning. We examined how these scenarios influenced priorities for habitat restoration using a set of hypothetical watersheds whose habitat areas could be systematically varied, as well as the Duwamish and Skagit rivers. In all watersheds, the three scenarios shared high sensitivity to changes in in nearshore and ocean mortality and produced similar responses to changes in other parameters controlling mortality (i.e., habitat quality). However, the three scenarios exhibited striking variation in population response to changes in habitat area (i.e., capacity). These findings indicate that nearshore habitat relationships may play significant roles for salmon populations and that the relative importance of restoring habitat area will depend on the mechanism of density dependence influencing salmon stocks.

An experimental and theoretical study of the dynamics of a mouse – nematode (Heligmosomoides polygyrus) interaction

Parasitology ◽  
1990 ◽  
Vol 101 (1) ◽  
pp. 75-92 ◽  
Author(s):  
M. E. Scott
Keyword(s):  
Leslie Matrix ◽  
Uninfected Mouse ◽  
Heligmosomoides Polygyrus ◽  
Mouse Population ◽  
Dependent Effect ◽  
Density Dependent ◽  
Sex Structure ◽  
Leslie Matrix Model ◽  
Survival And Reproduction ◽  
Age Structured

SUMMARYThe population dynamics of outbred laboratory mice in indoor enclosures in the absence and presence of a naturally transmitted direct life-cycle nematode Heligmosomoides polygyrus Dujardin 1845 were reported previously. This manuscript presents further information on the age and sex structure of the populations, results of experiments designed to estimate the density-dependent effect of the parasite on host survival and reproduction, and a mathematical model of both uninfected and infected mouse populations. In the uninfected mouse population, survival of female mice was age- and density-independent, survival of male mice was age-dependent and density-independent, and recruitment was density-dependent. Independent experiments revealed that the parasite had no density-dependent effect on mouse reproduction, but had density-dependent effects on both acute and chronic survival of mice. An age-structured Leslie matrix model captured the exponential growth and plateau of the uninfected mouse population. Modification of the model to incorporate the effects of the parasite provided a good fit to the data from the infected populations, supporting the hypothesis that density-dependent effects of the parasite on host survival could lead to regulation of host abundance.

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.

About Chaotic Dynamics in the Twisted Horseshoe Map

2016 ◽  
Vol 26 (06) ◽  
pp. 1650092 ◽  
Author(s):  
Elisa Sovrano
Keyword(s):  
Chaotic Dynamics ◽  
Population Models ◽  
Rigorous Proof ◽  
Age Classes ◽  
Density Dependent ◽  
Mathematical Literature

The twisted horseshoe map was developed in order to study a class of density dependent Leslie population models with two age classes. From the beginning, scientists have tried to prove that this map presents chaotic dynamics. Some demonstrations that have appeared in mathematical literature present some difficulties or delicate issues. In this paper, we give a simple and rigorous proof based on a different approach. We also highlight the possibility of getting chaotic dynamics for a broader class of maps.

scholarly journals Density dependence in an age-structured population of great tits: identifying the critical age classes

Ecology ◽  
2016 ◽  
Vol 97 (9) ◽  
pp. 2479-2490 ◽  
Author(s):  
Marlène Gamelon ◽  
Vidar Grøtan ◽  
Steinar Engen ◽  
Eirin Bjørkvoll ◽  
Marcel E. Visser ◽  
...  
Keyword(s):  
Density Dependence ◽  
Age Classes ◽  
Structured Population ◽  
Critical Age ◽  
Age Structured ◽  
Age Structured Population

Linear, age-structured models and their long-term dynamics

2019 ◽  
pp. 54-86
Author(s):  
Louis W. Botsford ◽  
J. Wilson White ◽  
Alan Hastings
Keyword(s):  
Density Dependence ◽  
Continuous Time ◽  
Linear Models ◽  
Leslie Matrix ◽  
Linear Matrix ◽  
Introduced Populations ◽  
Primary Model ◽  
Age Structured ◽  
Linear Matrix Equations

The chapter describes age-structured models that are linear (i.e. without density dependence). Like simple (non-age-structured) linear models they eventually either increase to infinity or decrease to zero. They are only appropriate when density dependence is not an important factor, such as recently introduced populations or those that have declined to low abundance. The chapter steps through several different ways of formulating such models. First are Lotka’s renewal equation and the M’Kendrick/von Foerster equation, both continuous time, continuous age models. Next is the Leslie matrix, which operates in discrete age and time. Solutions to linear matrix equations, such as the Leslie matrix, can be written in a general way in terms of eigenvalues and eigenvectors. These form the basis of analyses of dynamic stability throughout the book. Practically speaking, the Leslie matrix approach is the primary model used in modern ecology.

scholarly journals An Approximate Bayesian Method Applied to Estimating the Trajectories of Four British Grey Seal (Halichoerus grypus) Populations from Pup Counts

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Mike Lonergan ◽  
Dave Thompson ◽  
Len Thomas ◽  
Callan Duck
Keyword(s):  
Bayesian Method ◽  
Adult Population ◽  
Population Monitoring ◽  
Leslie Matrix ◽  
Density Dependent ◽  
Leslie Matrix Model ◽  
Pinniped Species ◽  
Pup Survival ◽  
Species Population ◽  
Approximate Bayesian

For British grey seals, as with many pinniped species, population monitoring is implemented by aerial surveys of pups at breeding colonies. Scaling pup counts up to population estimates requires assumptions about population structure; this is straightforward when populations are growing exponentially but not when growth slows, since it is unclear whether density dependence affects pup survival or fecundity. We present an approximate Bayesian method for fitting pup trajectories, estimating adult population size and investigating alternative biological models. The method is equivalent to fitting a density-dependent Leslie matrix model, within a Bayesian framework, but with the forms of the density-dependent effects as outputs rather than assumptions. It requires fewer assumptions than the state space models currently used and produces similar estimates. We discuss the potential and limitations of the method and suggest that this approach provides a useful tool for at least the preliminary analysis of similar datasets.

Sign in / Sign up

Export Citation Format

Share Document