Six series of ten repeated net hauls were made to examine the variation in catches of eggs and pre-larvae among the repeated hauls. The obtained results show that catches of eggs and pre-larvae of
Engraulis japonicus were slightly over-dispersed or randomly distributed.
A poisson mixture model is applied to explain these results. Suppose plankton organisms of some definite types, distributed at random with a mean
M. Let the mean
M be variable and set
Q(M)dM be probability that
M lies between
M and
M+
dM. Then the probability of catching n organisms is
P(n)=∫
∞0Q(M)e
-MM
n/n!dM.
Consequently, we can obtain following relation between the variance σn2 and mean μn of catch n;
σn
2=μn+μn
2(σM/μM)
2where σM
2 and μM are the variance and mean of
M respectively. This relation is equivalentto the one of the variance to the mean in a negative binomial model(NBM). But NBM is a special case that
Q(M)is Gamma distribution in this model.
Apparently, when σM≠0, then σn
2>μn. But there is no reason why aggregation always occurred because variation of
M is caused from many sources, for example, aggregation, prey-predator relation, transport by current, etc. Additional researches should be directed to-ward the causal factors inducing variation of
M.
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