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

64

The general multiple regression equation is written Y = a.+ blXl+
bZXZ +... bjXj where X1 represents an independent variable such as
depth, b1 the regression coefficient, a the intercept, and Y the dependent variable. The dependent variable in this study is the density of
Pontoporeia/mz while the independent variables include surface and
bottom temperature, depth, depth squared, sediment type, day of the
year, percent carbon in the sediment, distance from shore, and the
densities of oligochaetes, sphaeriids, and chironomids.
An initial examination of the depth distribution of Pontoporeia
(Fig. 31) indicated this was a curvilinear relationship which could possibly be satisfied by a second order polynomial equation. Depth was
squared and this value was treated as the additional variable that would
possibly satisfy this curvilinear relationship. In another study involving
the stations of the C, D, and E transects an additional parameter, wave
height, was added to the previously discussed independent variables.
In the first section of the following analysis, a two dimensional
presentation is made showing the effects of environmental parameters on
the abundance of Pontoporeia. This is accomplished by comparing the
geometric mean number of Pontoporeia with the environmental factors
and also by examining the correlation coefficients of these relationships.
Stepwise multiple regression analysis was employed in the second part
of this section to show how the environmental factors, acting together,
affect the quantity of Pontoporeia.