Trapline foraging by bumble bees .2. Definition and detection from sequence data

Trapline foraging-repeated sequential visits to a series of feeding locations-presents interesting problems seldom treated in foraging models. Work on traplining is hampered by the lack of statistical, operational approaches for detecting its existence and measuring its strength. We propose several statistical procedures, illustrating them with records of interplant flight sequences by bumble bees visiting penstemon flowers. An asymmetry test detects deviations from binomial expectation in the directionality of visits between pairs of plants. Several tests compare data from one bee to another: frequencies of visits to plants and frequencies of departures to particular destinations are compared using contingency tables; similarities of repeated sequences within bees are compared to those between bees by means of sequence alignment and Mantel tests. We also compared observed movement patterns to those generated by null models designed to represent realistic foraging by ono-traplining bees, examining: temporal patterns of the bee's spatial displacement from its starting point using spectral analysis; the variance of return times to particular plants; and the sequence alignment of repeated cycles within sequences. We discuss the different indications and the relative strengths of these approaches.