No abstract

Vocal repertoire size is an important behavioural measure in songbirds and mammals with complex vocal communication systems, and has traditionally been used as an indicator of individual fitness, cognitive ability, and social structure. Estimates of asymptotic repertoire size have typically been made using curve fitting techniques. However, the exponential model usually applied in these techniques has never been provided with a theoretical justification based on probability theory, and the model has led to inaccurate estimates. We derived the precise expression for the expected number of distinct signal types observed for a fixed sampling effort: a variation of what is known in the statistical literature as the "Coupon Collector׳s problem". We used empirical data from three species (northern mockingbird, Carolina chickadee, and rock hyrax) to assess the performance of the Coupon Collector model compared to commonly used techniques, such as exponential fitting and repertoire enumeration, and also tested the different models against simulated artificial data sets with the statistical properties of the empirical data. We found that when signal probabilities are dissimilar, the Coupon Collector model provides far more accurate estimates of repertoire size than traditional techniques. Enumeration and exponential curve fitting greatly underestimated repertoire size, despite appearing to have reached saturation. Application of the Coupon Collector model can generate more accurate estimates of repertoire size than the commonly used exponential model of repertoire discovery, and could go a long way towards re-establishing repertoire size as a useful indicator in animal communication research.

No abstract

Most previous attempts to model the geographical range expansion of an invading species assume random dispersal of organisms through a homogeneous environment. These models result in a series of uniformly increasing circles radiating out from the centre of origin over time. Although these models often give reasonable fits to available data, they do not typically include mechanisms of dispersal. Alternatively, models that include assumptions of non‐random dispersal and a heterogeneous environment inevitably result in an anisotropic or jagged invasion front. This front will include propagules of pioneer individuals for the expanding species. Existing data from biological invasions reveal that the spatial structure of an invading species usually exhibits these propagules. Using population data gathered from the past century, we investigated the propagules of two North American invading bird species: the European starling (Sturnus vulgaris Linnaeus), and the house finch (Carpodacus mexicanus Müller), and found a correlation between propagule location and habitat quality. These results suggest that dispersing individuals seek out favourable habitat and remain there, thus introducing a possible mechanism for explaining non‐uniform dispersal during invasions. When combined with results from other studies, our results suggest that propagules provide starting points for future population expansion of an invading species.