Stochastic von Bertalanffy models, with applications to fish recruitment

Qiming Lv; Jonathan W. Pitchford

doi:10.1016/j.jtbi.2006.09.009

Stochastic von Bertalanffy models, with applications to fish recruitment

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Abstract

We consider three individual-based models describing growth in stochastic environments. Stochastic differential equations (SDEs) with identical von Bertalatiffy deterministic parts are formulated, with a stochastic term which decreases, remains constant, or increases with organism size, respectively. Probability density functions for hitting times are evaluated in the context of fish growth and mortality. Solving the hitting time problem analytically or numerically shows that stochasticity can have a large positive impact on fish recruitment probability. It is also demonstrated that the observed mean growth rate of surviving individuals always exceeds the mean population growth rate, which itself exceeds the growth rate of the equivalent deterministic model. The consequences of these results in more general biological situations are discussed. (c) 2006 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	640-655
Number of pages	16
Journal	Journal of Theoretical Biology
Volume	244
Issue number	4
DOIs	https://doi.org/10.1016/j.jtbi.2006.09.009
Publication status	Published - 21 Feb 2007

Keywords

individual-based models
stochastic differential equations
first hitting time density
ENVIRONMENTAL VARIABILITY
GROWTH
LARVAE

Access to Document

10.1016/j.jtbi.2006.09.009

http://dx.doi.org/10.1016/j.jtbi.2006.09.009

Cite this

@article{8041d857e14948f3ac8672c072399075,

title = "Stochastic von Bertalanffy models, with applications to fish recruitment",

abstract = "We consider three individual-based models describing growth in stochastic environments. Stochastic differential equations (SDEs) with identical von Bertalatiffy deterministic parts are formulated, with a stochastic term which decreases, remains constant, or increases with organism size, respectively. Probability density functions for hitting times are evaluated in the context of fish growth and mortality. Solving the hitting time problem analytically or numerically shows that stochasticity can have a large positive impact on fish recruitment probability. It is also demonstrated that the observed mean growth rate of surviving individuals always exceeds the mean population growth rate, which itself exceeds the growth rate of the equivalent deterministic model. The consequences of these results in more general biological situations are discussed. (c) 2006 Elsevier Ltd. All rights reserved.",

keywords = "individual-based models, stochastic differential equations, first hitting time density, ENVIRONMENTAL VARIABILITY, GROWTH, LARVAE",

author = "Qiming Lv and Pitchford, {Jonathan W.}",

year = "2007",

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doi = "10.1016/j.jtbi.2006.09.009",

language = "English",

volume = "244",

pages = "640--655",

journal = "Journal of Theoretical Biology",

issn = "0022-5193",

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TY - JOUR

T1 - Stochastic von Bertalanffy models, with applications to fish recruitment

AU - Lv, Qiming

AU - Pitchford, Jonathan W.

PY - 2007/2/21

Y1 - 2007/2/21

N2 - We consider three individual-based models describing growth in stochastic environments. Stochastic differential equations (SDEs) with identical von Bertalatiffy deterministic parts are formulated, with a stochastic term which decreases, remains constant, or increases with organism size, respectively. Probability density functions for hitting times are evaluated in the context of fish growth and mortality. Solving the hitting time problem analytically or numerically shows that stochasticity can have a large positive impact on fish recruitment probability. It is also demonstrated that the observed mean growth rate of surviving individuals always exceeds the mean population growth rate, which itself exceeds the growth rate of the equivalent deterministic model. The consequences of these results in more general biological situations are discussed. (c) 2006 Elsevier Ltd. All rights reserved.

AB - We consider three individual-based models describing growth in stochastic environments. Stochastic differential equations (SDEs) with identical von Bertalatiffy deterministic parts are formulated, with a stochastic term which decreases, remains constant, or increases with organism size, respectively. Probability density functions for hitting times are evaluated in the context of fish growth and mortality. Solving the hitting time problem analytically or numerically shows that stochasticity can have a large positive impact on fish recruitment probability. It is also demonstrated that the observed mean growth rate of surviving individuals always exceeds the mean population growth rate, which itself exceeds the growth rate of the equivalent deterministic model. The consequences of these results in more general biological situations are discussed. (c) 2006 Elsevier Ltd. All rights reserved.

KW - individual-based models

KW - stochastic differential equations

KW - first hitting time density

KW - ENVIRONMENTAL VARIABILITY

KW - GROWTH

KW - LARVAE

U2 - 10.1016/j.jtbi.2006.09.009

DO - 10.1016/j.jtbi.2006.09.009

M3 - Article

SN - 0022-5193

VL - 244

SP - 640

EP - 655

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

IS - 4

ER -