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Abstract Filipe+Braumann IWSM 2008

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Modelling Individual Animal Growth in Random Environments

Patr´ıcia A. Filipe

1

and Carlos A. Braumann

1

1 Universidade de ´Evora, Centro de Investiga¸c˜ao em Matem´atica e Aplica¸c˜oes Rua Rom˜ao Ramalho, 59, 7000-671 ´Evora, Portugal

[email protected], [email protected]

Abstract:We have considered, as general models for the evolution of animal size in a random environment, stochastic differential equations of the formdY(t) = b(A−Y(t))dt+σdW(t), whereY(t) =g(X(t)),X(t) is the size of an animal at timet,gis a strictly increasing function,A=g(a) whereais the asymptotic size, σ measures the effect of random environmental fluctuations on growth, andWt

is the Wiener process. We have considered the stochastic Bertalanffy-Richards model (g(x) = xc with c > 0) and the stochastic Gompertz model (g(x) = lnx). We have studied the problems of parameter estimation for one path and also considered the extension to several paths. We also used bootstrap methods.

Results and methods are illustrated using bovine growth data.

Keywords: growth models; stochastic differential equations; estimation; cattle weight.

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