A trend test for the analysis of multiple paternity

The aquatic warbler, Acrocephalus paludicola, is one of a few species in which nestlings from a single nest can be sired by up to four different fathers. Data from a DNA fingerprinting study suggest that there is a trend: the larger the number of fathers in a brood the larger is the number of nestlings. However, the number of young within a single nest cannot be smaller than the number of fathers. This restriction causes an inherent trend and, consequently, can lead to a false-positive trend test result. For this nonstandard situation, we propose a trend test that differentiates between the inherent trend and a "real" trend, that is, a larger brood size through multiple paternity. Using DNA fingerprinting data, we performed a randomization test using the proposed new trend test statistic and obtained a significant result (P = 0.047). This indicates that a larger number of fathers per brood is associated with a larger brood size. In addition, we consider an umbrella alternative, that is, a downturn in effect may occur after the optimal number of fathers per brood is exceeded. An appropriate test for this alternative also leads to a significance (P = 0.011) .