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

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samples possessing considerably more variability than others with no
apparent relation between means and variances, Regular heterogeneity
usually arises from some type of nonnormality in the data with the variability of the samples being related to the sample means (Steel and
Torrie 1960).
It is often difficult to interpret the causes of variance-mean interaction but the variance of either the Poisson or binomial distribution is
functionally related to the mean. Evans (1952) pointed out that if density
is defined as the number of individuals per quadrat, density becomes
directly proportional to quadrat size with a doubling in value occurring
for each two-fold increase of quadrat area. The larger the quadrat the
more likely it will contain many individuals and less likely to contain
fewer individuals. A population sampled with one quadrat size may have
its members distributed at random, yet the same individuals may be consindered highly aggregated when another quadrat size is usedo The
Pontoporeia sampled in the long-term study area were converted to
individuals A4 because the two samplers used had different grab areaso
If samples are multiplied by a constant, the mean of these samples is
increased by the multiple of the constant while the variance is increased
by the square of the constant, which can affect the variance-mean relationship. It was indicated earlier that different size groups of Pontoporeia
were either contagiously or randomly distributed. The relative proportion of these size groups will affect the distributional patterns.