ON A STOCHASTIC-MODEL OF GULPING BEHAVIOR OF LARVAL FISH TO PLANKTONIC PREY

We present a stochastic model that describes the gulping behavior of f ish larva to planktonic prey. The model basically deploys the Yule's p rocess, for it conveys the situation that the previous experience on f eeding bouts is influential to the sequential volition of gulping. Let P-x(t) indicate the probability of how larval fish gulp x prey during the time interval [0, t], and lambda(x)(t)w+o(w) (o(w)/w-->0) the con ditional probability that larval fish gulped x preys by the time t and the next gulping behavior occurs once during the time interval [t, t + w]. In order to characterize lambda(x)(t), lambda(x)(t)=lambda x+k ( lambda, k: constants) is adopted. This arrangement shows that the gulp ing behavior is dependent upon conditional experiences (lambda x) and non-conditional potential(k). Then, the differential equation system w ith respect to P,(t) is solved under an initial condition. When lambda >0, P-x(t) shapes the probability distribution function of the negati ve binomial type; when lambda=0, P-x(t) shapes of the Poisson's type; and when lambda<0, P-x(t) shapes of the binomial type, respectively. T hus, the parameter A may operate as an indicator which distinguishes t he dietetic maneuvers of larval fish and its ramifications.