scholarly journals Bistability and Bifurcations in Modified Nicholson-Bailey Model with Age-Structure for Prey

2019 ◽  
Vol 14 (1) ◽  
pp. 257-278 ◽  
Author(s):  
O.L. Revutskaya ◽  
M.P. Kulakov ◽  
E.Ya. Frisman
Keyword(s):  
Survival Rate ◽  
Population Size ◽  
Age Structure ◽  
Birth Rate ◽  
System Stability ◽  
Dynamic Mode ◽  
Interacting Species ◽  
Predator Prey Model ◽  
Saddle Node ◽  
Age Dependent

The paper investigates dynamic modes of the predator-prey model with age structure for prey. We use a slight modification of the Nicholson-Bailey model to describe the interaction between predator and prey. We assume the population size is regulated by decreasing juvenile survival rate with growth of age class sizes. Conditions for sustainable coexistence of interacting species are described. It is shown that the coexistence of species becomes possible if there are a transcritical or saddle-node (tangential) bifurcations. Due to the saddle-node bifurcation there is bistability in the system of interacting species: predator either coexists with prey or dies depending on the initial conditions. It is shown that the range of demographic parameters, for which the prey and predator coexist, can significantly increase with growth of survival of adult prey or the proportion of predators born or the prey consumption rate of the predator. We studied the oscillation scenarios of interacting population, influences of reproduction, survival and self-regulation rates of population prey and age-dependent predation as well as variations in the current number on transitions between different dynamic modes. It is shown that an increase in the birth rate of the prey under intraspecific competition can lead to a dynamics destabilization and to oscillations appearance in numbers. Age-dependent predation is shown to be a stabilizing influence. At the same time, with a high birth rate of the prey, the system stability is ensured by the high survival rate of adult prey. It was found that in the model parametric space, both bistability and multistability arises, which are not related to each other. Consequently, even a small variation of the current population size leads to more complex behavior of the interacting species, and can give a significant change in both the observed dynamic mode and the coexistence scenario of the species.

Dynamic modes of exploited limited population: results of modeling and numerical study

2016 ◽  
Vol 11 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Г.П. Неверова ◽  
G.P. Neverova
Keyword(s):  
Population Dynamics ◽  
Density Dependence ◽  
Population Size ◽  
Age Structure ◽  
Birth Rate ◽  
Numerical Study ◽  
Dynamic Regime ◽  
Demographic Parameters ◽  
Current Population

The paper investigates the model of population dynamics with age structure and density dependence of birth rate. We consider two situations: 1) the population develops freely and 2) the population is exploited. It was shown that harvesting leads to the stabilization of the dynamics. There is multiregimism, i.e. different dynamic regimes are possible with the same values of demographic parameters. It is shown that even a single harvesting in the current population size could lead to a change of the observed dynamic regime.

scholarly journals The Sex Ratio Influence on the Dynamics of Structured Population

2017 ◽  
Vol 12 (2) ◽  
pp. 237-255 ◽  
Author(s):  
О.Л. Ревуцкая ◽  
O.L. Revutskaya
Keyword(s):  
Survival Rate ◽  
Sex Ratio ◽  
Population Size ◽  
Self Regulation ◽  
Small Variation ◽  
Dynamic Mode ◽  
Sex Structure ◽  
Offspring Number ◽  
Parametric Space ◽  
Harem Size

This article develops and investigates a simple mathematical model that simultaneously studies influence of age and sex structure formation and sex ratio on demographic and evolutionary processes. We assume fertility depends on the population sex ratio and is described by the modified harmonic mating function with switching. The population size is regulated by limiting the juvenile survival rate when immature individual survival decreases with growth of sex-age class sizes. We received the conditions for sustainable development of the population in the parametric space of the model. The relationships between the group sizes of newborns and mature females and males are analyzed. The growth of the harem size is shown to result in higher the newborn group size in case of female numerical dominance. The offspring number demonstrates the same tendency as the sex group with the smallest number in the cases of higher female survival rate and higher newborn female proportion, and lower male survival rate. Excessive asymmetry of the sexes is shown to lead to a decrease in reproduction of polygamous species. Complex scenarios of population dynamics are studied. Transitions between different dynamic modes are caused by changes in both population parameters determining birth, survival and self-regulation rates, and the formation process of the mating pairs. The model parametric space is shown to have multistability areas in which the initial condition variation can lead to the realization of one dynamic mode or the other. The multistability is the result of both the system nonlinearity and the complex bifurcation mechanisms, and the changing pair formation principle. Consequently, even a small variation of the current population size changing the sex ratio complicates the population behavior and can give significant change in the dynamic mode observed.

scholarly journals MODELING THE DYNAMICS OF THE PREDATOR- PREY COMMUNITY WITH THE PREY AGE STRUCTURE AND THE WITHDRAWAL

2021 ◽  
Vol 24 (2-3) ◽  
pp. 209-212
Author(s):  
O.L. Revutskaya
Keyword(s):  
Population Size ◽  
Discrete Time ◽  
Age Structure ◽  
Older Age ◽  
Predator Population ◽  
Age Classes ◽  
Time Model ◽  
Predator Prey ◽  
Discrete Time Model ◽  
Interacting Species

The paper studies the dynamic modes of the predator-prey community discrete-time model taking into account the prey age structure and the withdrawal. The investigated system is a modification of the Nicholson-Bailey model. The author has considered the cases of withdrawal from the prey younger or older age class, or from the prey population of two- age classes, or from the predator population. It is studied conditions of stable coexistence of interacting species and scenarios of the population size oscillatory modes occurrence.

Lamb survival in two hill flocks

1959 ◽  
Vol 1 (1) ◽  
pp. 85-91 ◽  
Author(s):  
A. F. Purser ◽  
G. B. Young
Keyword(s):  
Birth Weight ◽  
Survival Rate ◽  
Age Structure ◽  
Maternal Age ◽  
Mortality Rates ◽  
The Mean ◽  
Lamb Survival

The effects of birth weight, maternal age and parity on survival of single lambs have been studied in a Blackface and a Welsh Mountain flock.In both flocks the maximum survival rate was found to occur among lambs with birth weights just above the mean. Mortality increased as lambs' birth weight increased or decreased from the optimum, but was especially heavy at the lower extreme of the range of birth weights.Mortality decreased with age of dam to 14·3% for lambs from 4- to 6-year-old Blackface ewes and to 9·4% for lambs of 3- to 4-year-old Welsh ewes. Ewes having their first lambs gave mortality rates twice as great as for the mature ewes in the same flocks. The lower chances of survival of first born lambs irrespective of dam's age accounts for the apparent trend of mortality with maternal age in the Blackface.Changes in mortality rates associated with variation in lamb's birth weight and with the age structure of the ewe flock were estimated. Possible means of improvement of survival rate are discussed.

Effect of Orthene® on an unconfined population of the meadow vole (Microtus pennsylvanicus)

1986 ◽  
Vol 64 (1) ◽  
pp. 243-250 ◽  
Author(s):  
David A. Jett ◽  
James D. Nichols ◽  
James E. Hines
Keyword(s):  
Survival Rate ◽  
Population Size ◽  
Weight Change ◽  
Relative Weight ◽  
Reproductive Activity ◽  
Microtus Pennsylvanicus ◽  
Field Application ◽  
Meadow Vole ◽  
Old Field ◽  
Insecticide Treatment

The possible impact on Microtus pennsylvanicus of ground applications of Orthene® insecticide was investigated in old-field habitats in northern Maryland during 1982 and 1983. The treatment grids in 1982 and 1983 were sprayed at 0.62 and 0.82 kg active ingredient/ha, respectively. A capture–recapture design robust to unequal capture probabilities was utilized to estimate population size, survival, and recruitment. Data on reproductive activity and relative weight change were also collected to investigate the effect of the insecticide treatment. There were no significant differences in population size or recruitment between control and treatment grids which could be directly related to the treatment. Survival rate was significantly lower on the treatment grid than on the control grid after spraying in 1983; however, survival rate was higher on the treatment grid after spraying in 1982. Significantly fewer pregnant adults were found on the treatment grid after spraying in 1982, whereas the proportions of voles lactating or with perforate vaginas or open pubic symphyses were slightly higher or remained unchanged during this period. Relative weight change was not affected by the treatment. Results do not indicate any pattern of inhibitory effects from the insecticide treatment. Field application of Orthene® did not have an adverse effect on this Microtus population.

scholarly journals Statistical Estimation of Modern Trends and Prospects of the Size and Structure Population of Ukraine

2017 ◽  
pp. 65-72
Author(s):  
Z. О. Palian ◽  
I. H. Bondarenko
Keyword(s):  
Population Size ◽  
Age Structure ◽  
Structural Changes ◽  
Age Groups ◽  
Natural Increase ◽  
Reproductive Age ◽  
Structural Factors ◽  
Forecast Horizon ◽  
The Crimea ◽  
Size And Structure

A balanced change in demographic processes should be considered as a prerequisite and, at the same time, as a result of the stable development of the state. Reproduction intensity depends not only on the character of demographic behavior, but also on the presence of contingents of the population, providing or potentially able to provide for its replacement. The dynamics of Ukrainian population, the transformation of its gender-age structure during the period of independence, taking into account the intensive and structural factors of natural increase and migration, is considered. During 2002-2015, the regime of survival and fertility improved in Ukraine, due to which the depopulation slowed down somewhat. But even these positive changes do not compensate for the loss of population size as a result of systematic aging, reducing the proportion of reproductive contingent and its aging. Significant demographic losses, direct and indirect, were caused by a hybrid war from Russia. Alienation of the territory of the Crimea and parts of Donbas is not only a minus 2.5 million citizens of Ukraine. This is a change in the structure of the population - a decrease in the proportion of older age groups that increase the demographic load and worsen the characteristics of survival and fertility of the maternal generation. In this work are presented the results of the short-term simulation of population size and structure taking into account modern trends of replacements components and existing administrative-territorial changes. Two scenarios of the forecast for 2018 have been developed, and the base year it was taken in 2013, when the Crimea was part of Ukraine. The first, realistic scenario was based on the preservation of the current situation - Ukraine without the annexed Crimea and the occupied part of the Donbas. The second scenario imitates the return to Ukraine of all the lost territories. Simulation showed that the population of Ukraine will be reduced by both scenarios, but to 41.9 million people under the scenario without the occupied and annexed territories and to 44.7 million people in the second scenario. The finish of war will due to slow down the death rate to 14.9%0. The age structure of the population does not differ significantly in two scenarios, because the forecast horizon is very short (4 years). The share of generation of parents and women of reproductive age in both variants of the forecast decreases. However, in the case of returning Crimea, it will be even lower (47.4% vs. 47.5% in the first scenario). The reason for this is the emigration of young and middle-aged people to the mainland of Ukraine and to the Russian Federation, which provided some preferences to the settlers from Ukraine. Expected structural changes combined with the modern life and fertility regime will worsen natural population growth rates in both scenarios. In further research is planned to build trend models of births and deaths that will allow the artificially restore the interrupted time series due to administrative-territorial incomparability of data on demographic events

A linear birth-and-death predator–prey process

1995 ◽  
Vol 32 (01) ◽  
pp. 274-277
Author(s):  
John Coffey
Keyword(s):  
Death Rate ◽  
Birth Rate ◽  
Prey Population ◽  
Death Process ◽  
Predator Population ◽  
Birth And Death Process ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

A new stochastic predator-prey model is introduced. The predator population X(t) is described by a linear birth-and-death process with birth rate λ 1 X and death rate μ 1 X. The prey population Y(t) is described by a linear birth-and-death process in which the birth rate is λ 2 Y and the death rate is . It is proven that and iff

The age structure of a striped maple population

1979 ◽  
Vol 9 (4) ◽  
pp. 504-508 ◽  
Author(s):  
David E. Hibbs
Keyword(s):  
Structure Analysis ◽  
High Mortality ◽  
Age Structure ◽  
Mortality Rates ◽  
Population Age Structure ◽  
Survivorship Curve ◽  
Age Dependent ◽  
Gap Phase ◽  
Annual Mortality

Cohort and population age structure analysis showed that, after the initially high mortality rates of the 1st year (87.5%), striped maple seedlings (Acerpensylvanicum L.) underwent practically no mortality until the age of 15. Annual mortality was up (3.8%) between the ages of 16 and 40, then dropped to a lower level (1.6%). Mortality was age dependent and generally density independent. The survivorship curve agrees well with a pattern that could be expected of a species whose strategy is gap phase replacement.

Sign in / Sign up

Export Citation Format

Share Document