Semiparametric generalized estimating equations for repeated measurements in cross-over designs.

A model for cross-over designs with repeated measures within each period was developed. It was obtained using an extension of generalized estimating equations that includes a parametric component to model treatment effects and a non-parametric component to model time and carry-over effects; the estimation approach for the non-parametric component is based on splines. A simulation study was carried out to explore the model properties. Thus, when there is a carry-over effect or a functional temporal effect, the proposed model presents better results than the standard models. Among the theoretical properties, the solution is found to be analogous to weighted least squares. Therefore, model diagnostics can be made by adapting the results from a multiple regression. The proposed methodology was implemented in the data sets of the cross-over experiments that motivated the approach of this work: systolic blood pressure and insulin in rabbits.

Larval traits carry over to affect post-settlement behaviour in a common coral reef fish.

Most reef fishes begin life as planktonic larvae before settling to the reef, metamorphosing and entering the benthic adult population. Different selective forces determine survival in the planktonic and benthic life stages, but traits established in the larval stage may carry over to affect post-settlement performance. We tested the hypothesis that larval traits affect two key post-settlement fish behaviours: social group-joining and foraging. Certain larval traits of reef fishes are permanently recorded in the rings in their otoliths. In the bluehead wrasse (Thalassoma bifasciatum), prior work has shown that key larval traits recorded in otoliths (growth rate, energetic condition at settlement) carry over to affect post-settlement survival on the reef, with higher-larval-condition fish experiencing less post-settlement mortality. We hypothesized that this selective mortality is mediated by carry-over effects on post-settlement antipredator behaviours. We predicted that better-condition fish would forage less and be more likely to join groups, both behaviours that would reduce predation risk. We collected 550 recently settled bluehead wrasse (Thalassoma bifasciatum) from three reef sites off St. Croix (USVI) and performed two analyses. First, we compared each settler's larval traits to the size of its social group to determine whether larval traits influenced group-joining behaviour. Secondly, we observed foraging behaviour in a subset of grouped and solitary fish (n = 14) for 1-4 days post-settlement. We then collected the fish and tested whether larval traits influenced the proportion of time spent foraging. Body length at settlement, but not condition, affected group-joining behaviour; smaller fish were more likely to remain solitary or in smaller groups. However, both greater length and better condition were associated with greater proportions of time spent foraging over four consecutive days post-settlement. Larval traits carry over to affect post-settlement behaviour, although not as we expected: higher quality larvae join groups more frequently (safer) but then forage more. Foraging is risky but may allow faster post-settlement growth, reducing mortality risk in the long run. This shows that behaviour likely serves as a mechanistic link connecting larval traits to post-settlement selective mortality.