Hierarchal logistic regression models using both feeding vs. non-feeding and moving vs. stationary activities as the response variable were fitted with tests of significant effects based on the mean deviance. For feeding vs. non-feeding activities, the probability of feeding was explained by quadratic regressions in size for each combination of time of day and depth; the fitted curves together with 95% approximate confidence intervals and the observed proportions are shown in Figs. 2(a) and (b). The interaction between time of day and size of starfish is extremely strong for both depths, with small starfish tending to feed predominantly at night, whereas larger starfish tend to feed more frequently during the day. For the largest starfish (.50 cm) time of day does not appear to influence feeding behaviour, though few observations were available as reflected in the comparatively wide confidence intervals. Though there were significant interactions between depth and both time of day and the quadratic polynomials in size, the pattern of size and time of day effects is of similar form for both depths though more obtained by averaging the parameter estimates from the two quadratic polynomials in Fig. 2(c). Note the results (Fig. 2(d)) differ substantially from those obtained by simply fitting size to the overall proportions of feeding starfish in each size category. This is due to the larger number of daytime observations which biases the estimates in favour of the daytime feeding pattern. Over the whole size range, the estimates adjusted for bias are lower than the unadjusted ones (Fig. 2(d)), with a substantial difference of 10–20% for starfish .40 cm. The estimated probabilities of feeding vary little with size, with all starfish feeding for about 45% of the 24 h period. For moving vs. stationary activities, quadratic regressions in size were required for each combination of size and depth. The overall patterns were similar to the feeding vs. non-feeding activities with smaller animals being on the move more frequently during the night, whereas medium size starfish tended to move more during the day (Figs. 3(a)
and (b)). The effects of depth entered the models additively (i.e. there were no interactions between depth and size and/or time of day) representing an increase of 2.22 (95% CI5(1.82, 2.71)) in the relative odds of the starfish moving when at depths .3 m. As was the case with feeding vs. non-feeding activity, depth had less effect than size or time of day and the curves pooled over depth are shown in Fig. 3(c). The probability of motion as a function of size was estimated in the same manner as for feeding activity, and shows a steady increase from |5% for small animals (10 cm), up to | 20% for large animals (60 cm) (Fig. 3(d)).