scholarly journals Noise-Induced Transitions in a Population Growth Model Based on Size-Dependent Carrying Capacity

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Neeme Lumi ◽  
Ain Ainsaar ◽  
Romi Mankin
Keyword(s):  
Population Growth ◽  
Population Size ◽  
Growth Model ◽  
Carrying Capacity ◽  
Stochastic Dynamics ◽  
Exact Analytical Solution ◽  
Probability Distributions ◽  
Stationary Probability Distribution ◽  
Size Dependent ◽  
Stochastic Case

The stochastic dynamics of a population growth model with size-dependent carrying capacity is considered. The effect of a fluctuating environment on population growth is modeled as a multiplicative dichotomous noise. At intermediate values of population size the deterministic counterpart of the model behaves similarly to the Von Foerster model for human population, but at small and very large values of population size substantial differences occur. In the stochastic case, an exact analytical solution for the stationary probability distribution is found. It is established that variation of noise correlation time can cause noise-induced transitions between three different states of the system characterized by qualitatively different behaviors of the probability distributions of the population size. Also, it is shown that, in some regions of the system parameters, variation of the amplitude of environmental fluctuations can induce single unidirectional abrupt transitions of the mean population size.

scholarly journals Population prediction of purwanegara village, Indonesia using modified logistic model with migration factor

2018 ◽  
Vol 7 (3) ◽  
pp. 1962
Author(s):  
Diandra Chika Fransisca ◽  
Padosroha Marbun
Keyword(s):  
Population Growth ◽  
Equilibrium Point ◽  
Growth Model ◽  
Carrying Capacity ◽  
Logistic Model ◽  
Central Java ◽  
Migration Factor ◽  
Central Java Province ◽  
Population Prediction ◽  
Birth Death

Population growth model is a widely been used model to do an estimation and forecasting towards the population of peoples, animals, bac-teria and even in economics growth. Many studies have been carried out on population growth model concerning the factors of birth, death and carrying capacity in order to predict the number of population at certain area. From these studies there is only one study involved the constant value factor of migration as an input in the logistic model. Therefore contradicting with the above modified logistic model, in this study logistic model is modified by adding a migration factor as a function of population. This function takes into account the migration and the interaction between peoples that is limited to the carrying capacity of the environment. This model can be solved qualitatively using the analysis of equilibrium point and quantitatively using the separable variables method. This modified logistic model with migration factor has been applied in the population prediction of Purwanegara village in Central Java Province, Indonesia. Throughout the results, the modified logistic model with migration factor as a function of population gives a better result for population prediction of Purwanegara village in Central Java Province, Indonesia compared with logistic model.  

scholarly journals Population-size-dependent, age-structured branching processes linger around their carrying capacity

2011 ◽  
Vol 48 (A) ◽  
pp. 249-260
Author(s):  
Peter Jagers ◽  
Fima C. Klebaner
Keyword(s):  
Population Size ◽  
Carrying Capacity ◽  
Branching Process ◽  
Branching Processes ◽  
Critical Threshold ◽  
Small Populations ◽  
Size Dependent ◽  
Large Populations ◽  
Age Structured ◽  
Process Context

Dependence of individual reproduction upon the size of the whole population is studied in a general branching process context. The particular feature under scrutiny is that of reproduction changing from supercritical in small populations to subcritical in large populations. The transition occurs when the population size passes a critical threshold, known in ecology as the carrying capacity. We show that populations either die out directly, never coming close to the carrying capacity, or grow quickly towards the carrying capacity, subsequently lingering around it for a time that is expected to be exponentially long in terms of a carrying capacity tending to infinity.

The Size of the Stag Determines the Level of Cooperation

2021 ◽  
Author(s):  
Eric Schnell ◽  
Robin Schimmelpfennig ◽  
Michael Muthukrishna
Keyword(s):  
Population Growth ◽  
Population Size ◽  
Carrying Capacity ◽  
Large Scale ◽  
Growth Dynamics ◽  
Stag Hunt ◽  
Low Levels

ABSTRACTIn the last 12,000 years, human societies have scaled up from small bands to large states of millions and even billions. Many modern societies and even groups of societies cooperate on large-scale projects with relatively low levels of conflict, but the scale and intensity of cooperation varies dramatically between societies. Here we attempt to formalize dynamics that may be driving this rapid increase in cooperation and the differences we see between societies. Our model extends an N-person stag hunt to include population growth dynamics, “stags” with different sized payoffs, and competition for these stags. An increasing number of cooperators is required to access larger stags. The payoff from these stags in turn increases carrying capacity, which increases competition for the stag. As population size increases, new cooperative thresholds are attainable, and as population size shrinks, previously attainable thresholds fall out of reach. Among other predictions, we show that when a new threshold is accessible to a population, the level of cooperation will increase to reach this threshold. However, when the next threshold is out of reach, cooperation decreases as individuals refrain from costly cooperation, preferring a smaller stag. This model offers a framework for understanding the rapid increase in the scale of human cooperation and decline of violence, differences between societies, and challenges to future cooperation.

scholarly journals Penerapan Persamaan Diferensial Verhulst dalam Menentukan Proyeksi Penduduk di Kabupaten Tulungagung

2018 ◽  
Vol 7 (2) ◽  
pp. 87-102
Author(s):  
Dewi Anggreini
Keyword(s):  
Growth Rate ◽  
Population Growth ◽  
Growth Model ◽  
Carrying Capacity ◽  
Applied Mathematics ◽  
Logistic Growth ◽  
Second Stage ◽  
The Subject ◽  
Logistic Growth Model ◽  
To Come

Penelitian ini bertujuan menentukan proyeksi pertumbuhan penduduk di Kabupaten Tulungagung provinsi Jawa Timur dengan model persamaan diferensial Verhulst berdasarkan laju pertumbuhan dan daya tampung (carrying capacity). Target khusus dari hasil penelitian ini adalah model pertumbuhan logistik bisa digunakan sebagai alat untuk mengetahui proyeksi pertumbuhan penduduk berdasarkan laju pertumbuhan dan daya tampung dibeberapa daerah di Indonesia. Metode riset yang digunakan pada tahap pertama adalah menentukan subjek penelitian dan tahap Kedua adalah (1) mengumpulkan data penelitian (2) analisis data dan terakhir menarik kesimpulan. Data penelitian ini diperoleh dari BPS Kabupaten Tulungagung yaitu jumlah penduduk dari tahun 2010-2016. Hasil Penelitian menunjukkan bahwa: 1) Besarnya nilai carrying capacity yang membatasi penduduk di Kabupaten Tulungagung adalah sebesar 1.089.103,3. 2) Laju pertumbuhan intrinsik penduduk di kabupaten Tulungagung dengan menggunakan Model pertumbuhan logistik adalah sebesar r = 0,07480. 3) Jumlah penduduk di Kabupaten Tulungagung pada tahun 2025 dari hasil estimasi menggunakan model pertumbuhan logistik adalah sebesar 1.055.578 jiwa. 4) Proyeksi jumlah penduduk di Kabupaten Tulungagung  lebih tepat menggunakan model logistik I dengan persamaannya . Penelitian ini diharapkan dapat bermanfaat bagi semua pihak khususnya pada bidang matematika terapan serta metode dalam  menghitung pertumbuhan populasi di suatu daerah pada periode yang akan datang. [This study aims to determine the projected population growth in Tulungagung Regency of East Java province with a model of Verhulst differential equations based on growth rate and carrying capacity. The specific target of this research is logistic growth model can be used as a tool to know the projection of population growth based on growth rate and capacity in some regions in Indonesia. Research methods used in the first stage is to determine the subject of research and the second stage is (1) collect research data (2) data analysis and last draw conclusions. The data of this research is obtained from BPS of Tulungagung Regency that is population from 2010-2016. The results showed that: 1) The amount of carrying capacity that limits the population in Tulungagung Regency is equal 1.089.103,3. 2) The intrinsic growth rate of the population in Tulungagung district using the logistic growth model is r = 0,07480 3) The population in Tulungagung District in 2025 from the estimation using the logistic growth model is 1.055.578 soul, 4) The projection of population in Tulungagung is more appropriate using the logistic model I with the equation .  This study is expected to be useful for all parties, especially in the field of applied mathematics and methods in calculating population growth in an area in the period to come.]

scholarly journals Population-size-dependent, age-structured branching processes linger around their carrying capacity

2011 ◽  
Vol 48 (A) ◽  
pp. 249-260 ◽  
Author(s):  
Peter Jagers ◽  
Fima C. Klebaner
Keyword(s):  
Population Size ◽  
Carrying Capacity ◽  
Branching Process ◽  
Branching Processes ◽  
Critical Threshold ◽  
Small Populations ◽  
Size Dependent ◽  
Large Populations ◽  
Age Structured ◽  
Process Context

Dependence of individual reproduction upon the size of the whole population is studied in a general branching process context. The particular feature under scrutiny is that of reproduction changing from supercritical in small populations to subcritical in large populations. The transition occurs when the population size passes a critical threshold, known in ecology as the carrying capacity. We show that populations either die out directly, never coming close to the carrying capacity, or grow quickly towards the carrying capacity, subsequently lingering around it for a time that is expected to be exponentially long in terms of a carrying capacity tending to infinity.

Stochastic Dynamical Theta-Logistic Population Growth Model

2014 ◽  
Vol 2014 (3) ◽  
pp. 1-15
Author(s):  
Morteza Khodabin ◽  
◽  
Neda Kiaee ◽  
Keyword(s):  
Population Growth ◽  
Growth Model

scholarly journals Can we reestablish a self-sustaining population? A case study on reintroduced Crested Ibis with population viability analysis

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Yashuai Zhang ◽  
Fang Wang ◽  
Zhenxia Cui ◽  
Min Li ◽  
Xia Li ◽  
...  
Keyword(s):  
Sex Ratio ◽  
Population Size ◽  
Carrying Capacity ◽  
Wild Population ◽  
Population Viability Analysis ◽  
Population Viability ◽  
Viability Analysis ◽  
Crested Ibis ◽  
Reintroduced Population

Abstract Background One of the most challenging tasks in wildlife conservation and management is clarifying which and how external and intrinsic factors influence wildlife demography and long-term viability. The wild population of the Crested Ibis (Nipponia nippon) has recovered to approximately 4400, and several reintroduction programs have been carried out in China, Japan and Korea. Population viability analysis on this endangered species has been limited to the wild population, showing that the long-term population growth is restricted by the carrying capacity and inbreeding. However, gaps in knowledge of the viability of the reintroduced population and its drivers in the release environment impede the identification of the most effective population-level priorities for aiding in species recovery. Methods The field monitoring data were collected from a reintroduced Crested Ibis population in Ningshan, China from 2007 to 2018. An individual-based VORTEX model (Version 10.3.5.0) was used to predict the future viability of the reintroduced population by incorporating adaptive patterns of ibis movement in relation to catastrophe frequency, mortality and sex ratio. Results The reintroduced population in Ningshan County is unlikely to go extinct in the next 50 years. The population size was estimated to be 367, and the population genetic diversity was estimated to be 0.97. Sensitivity analysis showed that population size and extinction probability were dependent on the carrying capacity and sex ratio. The carrying capacity is the main factor accounting for the population size and genetic diversity, while the sex ratio is the primary factor responsible for the population growth trend. Conclusions A viable population of the Crested Ibis can be established according to population viability analysis. Based on our results, conservation management should prioritize a balanced sex ratio, high-quality habitat and low mortality.

R&D Heterogeneity and the Impact of R&D Subsidies*

2021 ◽  
Author(s):  
Sigurd M⊘lster Galaasen ◽  
Alfonso Irarrazabal
Keyword(s):  
Economic Impact ◽  
Growth Model ◽  
Relative Size ◽  
Schumpeterian Growth ◽  
Size Dependent ◽  
Investment Growth ◽  
The Impact ◽  
D Investment ◽  
Model Fits

Abstract This paper studies the determinants of R&D heterogeneity and the economic impact of R&D subsidies. We estimate a Schumpeterian growth model featuring firms with heterogeneous innovation efficiencies. The model fits well the R&D investment distribution, and the frequency and relative size of R&D performers. Using the model we study the impact of a Norwegian R&D reform targeting firms with R&D spending below a certain threshold. The size-dependent subsidy increases aggregate R&D investment by 11.7%, but reduces growth and welfare. In contrast, a uniform subsidy stimulates investment, growth and welfare.

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