scholarly journals Dynamic modes of the Ricker model with periodic Malthusian parameter

2017 ◽  
Vol 13 (3) ◽  
pp. 363-380 ◽  
Author(s):  
К.В. Шлюфман ◽  
◽  
Г.П. Неверова ◽  
Е.Я. Фрисман ◽  
◽  
...  
Keyword(s):  
Malthusian Parameter ◽  
Ricker Model

scholarly journals Phase Multistability of Dynamics Modes of the Ricker Model with Periodic Malthusian Parameter

2018 ◽  
Vol 13 (1) ◽  
pp. 68-83
Author(s):  
K.V. Shlufman ◽  
G.P. Neverova ◽  
E.Ya. Frisman
Keyword(s):  
Phase Shift ◽  
Dynamic Mode ◽  
Threshold Values ◽  
Attraction Basin ◽  
Malthusian Parameter ◽  
Ricker Model ◽  
Short Period ◽  
Tangent Bifurcation ◽  
Attraction Basins ◽  
Model Trajectory

The paper investigates the phase multistability of dynamical modes of the Ricker model with 2-year periodic Malthusian parameter. It is shown that both the variable perturbation and the phase shift of the Malthusian parameter can lead to a phase shift or a change in the dynamic mode observed. The possibility of switches between different dynamic modes is due to multistability, since the model has two different stable 2-cycles. The first stable 2-cycle is the result of transcritical bifurcation and is synchronous to the oscillations of the Malthusian parameter. The second stable 2-cycle arises as a result of the tangent bifurcation and is asynchronous to the oscillations of the Malthusian parameter. This indicates that two-year fluctuations in the population size can be both synchronous and asynchronous to the fluctuations in the environment. The phase shift of the Malthusian parameter causes a phase shift in the stable 4-cycle of the first bifurcation series to one or even three elements of the 4-cycle. The phase shift to two elements of this 4-cycle is possible due to a change in the half-amplitude of the Malthusian parameter oscillation or the variable perturbation. At the same time, the longer period of the cycle, the more phases with their attraction basins it has, and the smaller the threshold values above which shift from the attraction basin to another one occur. As a result, in the case of cycles with long period (for example, 8-cycle) perturbations, that stable cycles with short period are able to "absorb", can cause different phase transitions, which significantly complicates the dynamics of the model trajectory and, as a consequence, the identification of the dynamic mode observed.

scholarly journals Two-cycles of the Ricker model with the periodic Malthusian parameter: stability and multistability

2016 ◽  
pp. 553-565 ◽  
Author(s):  
К.В. Шлюфман ◽  
◽  
Г.П. Неверова ◽  
Е.Я. Фрисман ◽  
◽  
...  
Keyword(s):  
Malthusian Parameter ◽  
Parameter Stability ◽  
Ricker Model

Alternative Recruitment Models of Adams River Sockeye Salmon, Oncorhynchus nerka

1987 ◽  
Vol 44 (9) ◽  
pp. 1551-1561 ◽  
Author(s):  
Jeremy S. Collie ◽  
Carl J. Walters
Keyword(s):  
Sockeye Salmon ◽  
Oncorhynchus Nerka ◽  
Status Quo ◽  
Management Policy ◽  
Best Management ◽  
Interaction Terms ◽  
Ricker Model ◽  
The Status ◽  
Stock Recruitment ◽  
High Yields

Despite evidence of depensatory interactions among year-classes of Adams River sockeye salmon (Oncorhynchus nerka), the best management policy is one of equal escapement for all year-classes. We fit alternative models (Ricker model and Larkin model) to 32 yr of stock–recruitment data and checked, using simulation tests, that the significant interaction terms in the Larkin model are not caused by biases in estimating the parameters. We identified a parameter set (Rationalizer model) for which the status quo cyclic escapement policy is optimal, but this set fits the observed data very poorly. Thus it is quite unlikely that the Rationalizer model is correct or that the status quo escapement policy is optimal. Using the fitted stock–recruitment parameters, we simulated the sockeye population under several management policies. The escapement policy optimal under the Ricker model is best overall because of the high yields if it should be correct. If the three stock–recruitment models are equally likely to be correct, the simulations predict that adopting a constant-escapement policy would increase long-term yield 30% over the current policy and that an additional 15% increase in yield could be obtained if the policy were actively adaptive.

A note on the subcritical generalized age-dependent branching process

1976 ◽  
Vol 13 (4) ◽  
pp. 798-803 ◽  
Author(s):  
R. A. Doney
Keyword(s):  
Branching Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Malthusian Parameter ◽  
Age Dependent ◽  
The Mean ◽  
Mean Function ◽  
Necessary And Sufficient

For a subcritical Bellman-Harris process for which the Malthusian parameter α exists and the mean function M(t)∼ aeat as t → ∞, a necessary and sufficient condition for e–at (1 –F(s, t)) to have a non-zero limit is known. The corresponding condition is given for the generalized branching process.

scholarly journals Extension of the Haldane-Muller principle of mutation load with application for estimating a possible range of relative evolution rate

1985 ◽  
Vol 46 (1) ◽  
pp. 75-84 ◽  
Author(s):  
Kazushige Ishii ◽  
Hirotsugu Matsuda
Keyword(s):  
Mutation Rate ◽  
Time Variation ◽  
Evolution Rate ◽  
Mutation Load ◽  
Weak Selection ◽  
Diploid Population ◽  
Malthusian Parameter ◽  
Haploid Population ◽  
Range Of Values

SUMMARYThe Haldane-Muller principle of mutation load is generalized so as to be applicable to both cases of strong and very weak selection with any time variation. It is proved that in an infinite asexual haploid population, the average Malthusian parameter m¯ of a population, the evolution rate ν, and the total mutation rate μ satisfy the relation ∂m¯/∂/∂μ = ν/μ−1, so long as each Malthusian parameter is independent of μ. A similar result is also true in a diploid population under genie selection. It is discussed how the above relation gives a restriction on the possible range of values of relative evolution rate ν/μ.

scholarly journals The evolution of Daphnia pulex in a temporally varying environment

1998 ◽  
Vol 72 (1) ◽  
pp. 25-37 ◽  
Author(s):  
SAMUEL M. SCHEINER ◽  
LEV Yu YAMPOLSKY
Keyword(s):  
Genetic Variation ◽  
Temperature Change ◽  
Local Population ◽  
Daphnia Pulex ◽  
Selection Response ◽  
Clonal Variation ◽  
Offspring Size ◽  
Malthusian Parameter ◽  
Offspring Number ◽  
Variable Environments

We investigated three aspects of adaptation to variable environments in Daphnia pulex (Cladocera: Crustacea): (1) effects of temporal variation on the evolution of phenotypic plasticity ; (2) plasticity in sexual versus asexual lineages; (3) maintenance of genetic variation in variable environments. We performed a 72-day quasi-natural selection experiment comparing three patterns of variation: constant temperatures, varying but predictable temperature change, and unpredictable temperature change. All populations were begun with an identical array of 34 clones. During selection clonal variation declined in all populations and different patterns of environmental variation had little effect on amounts of genetic variation. Sexual and asexual lineages differed in size and growth rate, but did not differ in amounts of plasticity or in adaptation to variable environments. The primary target of selection was the Malthusian parameter (r) and life history traits of development time, offspring size and offspring number. The heritability of plasticity was generally lower than trait heritability. Because of this difference, the selection response on the mean of the traits overwhelmed the selection response on plasticity. Lower heritabilities of plasticity are very typical, suggesting that our results will be typical of responses to selection in nature. Our results suggest that selection will act mostly on trait means within environments and that plasticity will evolve often as a correlated trait. Because selection on plasticity is based on its across-deme, global fitness, this process will usually be slow. Comparative studies need to shift from closely related, local population differences to those of more distantly related populations or even different species.

Malthusian behaviour of the critical and subcritical age-dependent branching processes with arbitrary state space

1976 ◽  
Vol 13 (3) ◽  
pp. 455-465
Author(s):  
D. I. Saunders
Keyword(s):  
State Space ◽  
Branching Process ◽  
Branching Processes ◽  
Rates Of Convergence ◽  
Expected Number ◽  
Subcritical Case ◽  
Arbitrary State ◽  
Malthusian Parameter ◽  
Age Dependent ◽  
Number Of Individuals

For the age-dependent branching process with arbitrary state space let M(x, t, A) be the expected number of individuals alive at time t with states in A given an initial individual at x. Subject to various conditions it is shown that M(x, t, A)e–at converges to a non-trivial limit where α is the Malthusian parameter (α = 0 for the critical case, and is negative in the subcritical case). The method of proof also yields rates of convergence.

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