Ecology of the burrowing amphipod, Pontoporeia affinis, in Lake Michigan / by Wayne Paul Alley.

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bution. The theoretical curve for the normal distribution was calculated
for small and total Pontoporeia utilizing the equation: m= (N i/ S/2r.)
e-(X-X)2 /b2S The theoretical curve for the Poisson distribution was
-2 2 3
calculated for large Pontoporeia by: m=Ne-X(1, X, X /2!,X /3!,..
XJ/j!). Inthe above equations N represents the number of observations,
X the average number of amphipods per category, i the size of the class
interval, S2 the variance, S the standard deviation, e the base of the
natural logarithm, and m the expected number of individuals in an interval.
The theoretical curves were superimposed on their respective histograms.
The chi square test for goodness of fit comparing the theoretical
values with the observed values was calculated for each amphipod category. Because the probability of occurrence is exceedingly slight at the
extreme ends of these curves and the 88 samples were not enough to
represent adequately the distal areas of these curves, it was necessary
to pool the extreme observed and expected values. The terminal intervals of the observed and expected values for each tail were combined
until their sum approximated 3 organisms for the combined intervals.
The following intervals were combined: 0-10 and 75-85 for small amphipods, 6-8 for large amphipods, and 0-10 and 75-85 for total amphipods.
In computing the normal distribution curves, the mean and standard
deviation were estimated, thus the degrees of freedom for these curves
are k - 3 where k represents the number of intervals. One degree of
freedom is lost in estimating the chi square distribution. The degrees