scholarly journals The impact of management on the behavior of an isolated logistics population

2021 ◽  
pp. 81-84
Author(s):  
T. V. Kolianova
Keyword(s):  
Population Size ◽  
Initial Conditions ◽  
Stationary Points ◽  
Initial Population ◽  
Isolated Population ◽  
Initial Value ◽  
The Third ◽  
First Case ◽  
Initial Population Size ◽  
The Impact

The article considers the isolated population described by the logistic equation and studies the influence of management on the change of its number. Depending on the value of the control parameter, there are three different cases of behavior of an isolated population. In the first case, when the quota is equal to the corresponding value, depending on the initial value, the population either goes to a stationary value, or dies out. In the second case, when the quota does not exceed the established value, depending on the initial population size, the population either goes to the largest stationary point, or dies out. And in the third case, when the quota exceeds the established value, regardless of the initial population size, the population dies out. Stationary points for stability in all three cases are studied and graphs of population behavior depending on different initial conditions are presented.

scholarly journals Agglomeration economies, congestion diseconomies, and fertility dynamics in a two-region economy

2021 ◽  
Author(s):  
Madoka Muroishi ◽  
Akira Yakita
Keyword(s):  
Population Size ◽  
Stability Condition ◽  
Fertility Rate ◽  
Model Parameters ◽  
Initial Population ◽  
Interregional Migration ◽  
Stable Path ◽  
Regional Population ◽  
Initial Population Size

AbstractUsing a small, open, two-region economy model populated by two-period-lived overlapping generations, we analyze long-term agglomeration economy and congestion diseconomy effects of young worker concentration on migration and the overall fertility rate. When the migration-stability condition is satisfied, the distribution of young workers between regions is obtainable in each period for a predetermined population size. Results show that migration stability does not guarantee dynamic stability of the economy. The stationary population size stability depends on the model parameters and the initial population size. On a stable trajectory converging to the stationary equilibrium, the overall fertility rate might change non-monotonically with the population size of the economy because of interregional migration. In each period, interregional migration mitigates regional population changes caused by fertility differences on the stable path. Results show that the inter-regional migration-stability condition does not guarantee stability of the population dynamics of the economy.

Estimation of the parameters of a branching process from migrating binomial observations

1998 ◽  
Vol 30 (4) ◽  
pp. 948-967 ◽  
Author(s):  
C. Jacob ◽  
J. Peccoud
Keyword(s):  
Confidence Interval ◽  
Asymptotic Behaviour ◽  
Population Size ◽  
Branching Process ◽  
Total Population ◽  
Initial Population ◽  
Asymptotic Confidence Interval ◽  
Total Population Size ◽  
Initial Population Size ◽  
Watson Process

This paper considers a branching process generated by an offspring distribution F with mean m < ∞ and variance σ2 < ∞ and such that, at each generation n, there is an observed δ-migration, according to a binomial law Bpvn*Nnbef which depends on the total population size Nnbef. The δ-migration is defined as an emigration, an immigration or a null migration, depending on the value of δ, which is assumed constant throughout the different generations. The process with δ-migration is a generation-dependent Galton-Watson process, whereas the observed process is not in general a martingale. Under the assumption that the process with δ-migration is supercritical, we generalize for the observed migrating process the results relative to the Galton-Watson supercritical case that concern the asymptotic behaviour of the process and the estimation of m and σ2, as n → ∞. Moreover, an asymptotic confidence interval of the initial population size is given.

scholarly journals Experimental demonstration of a two-phase population extinction hazard

2011 ◽  
Vol 8 (63) ◽  
pp. 1472-1479 ◽  
Author(s):  
John M. Drake ◽  
Jeff Shapiro ◽  
Blaine D. Griffen
Keyword(s):  
Population Size ◽  
Time Distribution ◽  
Proportional Hazards ◽  
Initial Population ◽  
Extinction Time ◽  
Habitat Size ◽  
Two Phase ◽  
Population Extinction ◽  
Initial Population Size ◽  
Phase Population

Population extinction is a fundamental biological process with applications to ecology, epidemiology, immunology, conservation biology and genetics. Although a monotonic relationship between initial population size and mean extinction time is predicted by virtually all theoretical models, attempts at empirical demonstration have been equivocal. We suggest that this anomaly is best explained with reference to the transient properties of ensembles of populations. Specifically, we submit that under experimental conditions, many populations escape their initially vulnerable state to reach quasi-stationarity, where effects of initial conditions are erased. Thus, extinction of populations initialized far from quasi-stationarity may be exposed to a two-phase extinction hazard. An empirical prediction of this theory is that the fit Cox proportional hazards regression model for the observed survival time distribution of a group of populations will be shown to violate the proportional hazards assumption early in the experiment, but not at later times. We report results of two experiments with the cladoceran zooplankton Daphnia magna designed to exhibit this phenomenon. In one experiment, habitat size was also varied. Statistical analysis showed that in one of these experiments a transformation occurred so that very early in the experiment there existed a transient phase during which the extinction hazard was primarily owing to the initial population size, and that this was gradually replaced by a more stable quasi-stationary phase. In the second experiment, only habitat size unambiguously displayed an effect. Analysis of data pooled from both experiments suggests that the overall extinction time distribution in this system results from the mixture of extinctions during the initial rapid phase, during which the effects of initial population size can be considerable, and a longer quasi-stationary phase, during which only habitat size has an effect. These are the first results, to our knowledge, of a two-phase population extinction process.

The extinction time of a birth, death and catastrophe process and of a related diffusion model

1985 ◽  
Vol 17 (01) ◽  
pp. 42-52 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Population Size ◽  
Diffusion Processes ◽  
Death Process ◽  
Arbitrary Distribution ◽  
Initial Population ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Expected Time ◽  
Time To Extinction ◽  
Initial Population Size

The distribution of the extinction time for a linear birth and death process subject to catastrophes is determined. The catastrophes occur at a rate proportional to the population size and their magnitudes are random variables having an arbitrary distribution with generating function d(·). The asymptotic behaviour (for large initial population size) of the expected time to extinction is found under the assumption that d(.) has radius of convergence greater than 1. Corresponding results are derived for a related class of diffusion processes interrupted by catastrophes with sizes having an arbitrary distribution function.

scholarly journals Mapping Mendelian traits in asexual progeny using changes in marker allele frequency

2011 ◽  
Vol 93 (3) ◽  
pp. 221-232 ◽  
Author(s):  
SAYANTHAN LOGESWARAN ◽  
NICK H. BARTON
Keyword(s):  
Population Size ◽  
Allele Frequency ◽  
Inbred Lines ◽  
Initial Population ◽  
Marker Allele ◽  
Major Locus ◽  
Multiple Generations ◽  
Marker Allele Frequency ◽  
Initial Population Size ◽  
Marker Frequency

SummaryLinkage between markers and genes that affect a phenotype of interest may be determined by examining differences in marker allele frequency in the extreme progeny of a cross between two inbred lines. This strategy is usually employed when pooling is used to reduce genotyping costs. When the cross progeny are asexual, the extreme progeny may be selected by multiple generations of asexual reproduction and selection. We analyse this method of measuring phenotype in asexual progeny and examine the changes in marker allele frequency due to selection over many generations. Stochasticity in marker frequency in the selected population arises due to the finite initial population size. We derive the distribution of marker frequency as a result of selection at a single major locus, and show that in order to avoid spurious changes in marker allele frequency in the selected population, the initial population size should be in the low to mid hundreds.

scholarly journals Population viability analysis and conservation of Chinese Grouse Bonasa sewerzowi in Lianhuashan Nature Reserve, north-west China

2010 ◽  
Vol 21 (1) ◽  
pp. 49-58 ◽  
Author(s):  
NAN LU ◽  
YUE-HUA SUN
Keyword(s):  
Population Size ◽  
Human Activity ◽  
Western China ◽  
Management Tool ◽  
Initial Population ◽  
Current Population ◽  
Initial Population Size ◽  
Bonasa Sewerzowi ◽  
Nest Loss ◽  
Chinese Grouse

SummaryChinese Grouse Bonasa sewerzowi is threatened by human activity, especially during the breeding season, in the Lianhuashan Mountains, Gansu Province, north-western China. We conducted a series of simulations on the viability of this population using the computer program VORTEX. The simulations suggested that the population had an extinction probability of 17% in 100 years using data gathered from current field work. Sensitivity analysis revealed that the predicted population trend was most sensitive to chick mortality, offspring per female per year, and adult male mortality. The first two parameters are correlated with human activity such as nest loss due to egg collecting by local people. When we set initial population size to the same size as carrying capacity, 2,500 individuals would constitute a minimum viable population (MVP). This would require a forest area of about 3,780 ha, which is smaller than the size of the Lianhuashan reserve, but the current population does not constitute an MVP due to the small initial population size. Furthermore, we found that if chick mortality declined by 5% or the number of offspring produced per female increased by 5% (i.e. reducing nest loss) under the current situation, local reserve size and current population would constitute an MVP. Therefore, the most practical and simple conservation management tool would be to increase the breeding success of Chinese Grouse, especially by limiting human activity during the incubation period.

Modified Leslie–DeLury Population Models of the Long-Finned Pilot Whale (Globicephala melaena) and Annual Production of the Short-Finned Squid (Illex illecebrosus) Based upon their Interaction at Newfoundland

1975 ◽  
Vol 32 (7) ◽  
pp. 1145-1154 ◽  
Author(s):  
M. C. Mercer
Keyword(s):  
Population Size ◽  
Closed System ◽  
Population Models ◽  
Annual Production ◽  
Initial Population ◽  
Pilot Whale ◽  
Seasonal Movements ◽  
System Models ◽  
Initial Population Size ◽  
Pilot Whales

Distributions and seasonal movements of Globicephala melaena and Illex illecebrosus evince similar patterns and the cetacean feeds almost exclusively on the cephalopod while inshore at Newfoundland. Peaks in Newfoundland landings of both species are coincident and this is taken to indicate that availability of pilot whales inshore depends on that of short-finned squid. Progressively higher peaks in squid landings with progressively lower peaks in whale landings are interpreted to indicate depletion of the whale populations. Utilizing squid landings as a correction for availability of whales, closed system models are generated to estimate the initial population size of the exploited pilot whales at less than 60,000. Estimates of potential squid consumption by these stocks indicate that annual squid production may be in the order of several hundred thousand tons.

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