+ Site Statistics
+ Search Articles
+ Subscribe to Site Feeds
Most Shared
PDF Full Text
+ PDF Full Text
Request PDF Full Text
+ Follow Us
Follow on Facebook
Follow on Twitter
Follow on LinkedIn
+ Translate
+ Recently Requested

A simple saddlepoint approximation for the equilibrium distribution of the stochastic logistic model of population growth

A simple saddlepoint approximation for the equilibrium distribution of the stochastic logistic model of population growth

Ecological Modelling15: 239-248

The deterministic logistic model of population growth and its notion of an equilibrium 'carrying capacity' are widely used in the ecological sciences. Leading texts also present a stochastic formulation of the model and discuss the concept and calculation of an equilibrium population size distribution. This paper describes a new method of finding accurate approximating distributions. Recently, cumulant approximations for the equilibrium distribution of this model were derived [Biometrics 52 (1996) 980], and separately a simple saddlepoint (SP) method of approximating distributions using exact cumulants was presented [J. Math. Appl. Med. Biol. 15 (1998) 41]. This paper proposed using the SP method with the new approximate cumulants, which are readily obtained from the assumed birth and death rates. The method is shown to be quite accurate with three test cases, namely on a classic model proposed by Pielou [Mathematical Ecology, New York, Wiley, p. 304] and on two African bee models proposed previously by the authors [Biometrics 52 (1996) 980; Theor. Popul. Biol. 53 (1998) 16]. Because the new method is also relatively simple to apply, it is expected that its use will lead to a more widespread utilization of the stochastic model in ecological modeling.

(PDF emailed within 0-6 h: $19.90)

Accession: 010098514

Download citation: RISBibTeXText

DOI: 10.1016/s0304-3800(02)00344-7

Related references

A simple approximation of moments of the quasi-equilibrium distribution of an extended stochastic theta-logistic model with non-integer powers. Mathematical Biosciences 271: 96-112, 2017

On the moments of the equilibrium distribution of a logistic population growth model. Bulletin of the Ecological Society of America 76(3 SUPPL ): 362, 1995

On approximating the moments of the equilibrium distribution of a stochastic logistic model. Biometrics 52(3): 980-991, 1996

Applying the saddlepoint approximation to bivariate stochastic processes. Mathematical Biosciences 168(1): 57-75, 2000

Saddlepoint Approximations of the Distribution of the Person Parameter in the Two Parameter Logistic Model. Psychometrika 80(3): 665-688, 2016

Application of the Simple Saddlepoint Approximation to Estimate Probability Distributions in Wildlife Research. The Journal of Wildlife Management 75(3): 740-746, 2011

Application of the simple saddlepoint approximation to estimate probability distributions in wildlife research. Journal of Wildlife Management 75(3): 740-746, 2011

Saddlepoint Approximation to Cumulative Distribution Function for Poisson–Exponential Distribution. 2013

A perturbation approximation to the simple stochastic epidemic in a large population. Biometrika 55(1): 199-209, 1968

The growth of Scottish salmon ( Salmo salar ) aquaculture 19792016 fits a simple two-phase logistic population model. Aquaculture 496: 146-152, 2018

Stochastic growth models with logistic mean population. Journal of Theoretical Biology 82(1): 167-169, 1980

Stochastic dynamics and logistic population growth. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 91(6): 062133, 2016

A Saddlepoint Approximation to the Distribution of Inhomogeneous Discounted Compound Poisson Processes. Methodology and Computing in Applied Probability 12(3): 533-551, 2010

On the cumulants of population size for the stochastic power law logistic model. Theoretical Population Biology 53(1): 16-29, 1998

Saddlepoint approximations of marginal densities and confidence intervals in the logistic regression measurement error model. Biometrics 52(3): 1096-1102, 1996