On a Stochastic Model of Gulping Behavior of Larval Fish to Planktonic Prey

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  • On a Stochastic Model of Gulping Behavi

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We present a stochastic model that describes the gulping behavior of fish larva to planktonic prey. The model basically deploys the Yule's process, for it conveysthe situation that the previous experience on feeding bouts is influential to the sequential volition of gulping.<br> Let Px (t) indicate the probability of how larval fish gulp x prey during the time interval [0, t], and λx(t)w+o(w)(o(w)/w→0) the conditional probability that larval fish gulped x preys by the time t and the next gulping behavior occurs once duringthe time interval [t, t+w]. In order to characterize λx(t), λx(t)=λx+k (λ, k: constants) is adopted. This arrangement shows that the gulping behavior is dependent upon conditional experiences (λx)and non-conditional potential (k). Then, the differential equation system with respect to Px(t) is solved under an initialcondition.<br> When λ>0, Px(t) shapes theprobability distribution function of the negative binomial type;when λ=0, Px(t) shapes of the Poisson's type; and when λ<0, Px(t) shapes of the binomial type, respectively.Thus, the parameter λ may operate asan indicator which distinguishes the dietetic maneuvers of larval fish and itsramifications.

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