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Hierarchical population structure, where individuals are aggregated into colonies or similar groups that themselves grow, survive or perish, and potentially produce offspring groups, is an important feature of many biological systems, most notably eusocial organisms such as the honey bee, Apis mellifera. Despite this hierarchical structure, there is a paucity of analytical models and theory linking the dynamics of individuals within colonies to the dynamics of a population of colonies. We present an analytical framework that provides a simple, robust, and predictive theory for the population dynamics of hierarchical organisms. Our framework explicitly describes and links demographic dynamics for the different levels in the hierarchy (individuals, groups, population). We illustrate the application of the framework by developing a model for honey bees and analyzing the effects of life history traits such as worker life span and size at swarming on the growth rate of populations. We conclude by discussing possible extensions of the model that increase its realism and expand its usefulness beyond swarm-founding, monogynous, eusocial insects. Key words: Apis mellifera; bees; demography; eusocial insects; hierarchical population; multilevel selection population model.

Honey bees (Apis mellifera) are regularly faced with the task of navigating back to their hives from remote food sources. They have evolved several methods to do this, including compass-directed 'vector' flights and the use of landmarks. If these hive-centered mechanisms are disrupted, bees revert to searching for the hive, but the nature and efficiency of their searching strategy have hitherto been unknown. We used harmonic radar to record the flight paths of honey bees that were searching for their hives. Our subsequent analysis of these paths revealed that they can be represented by a series of straight line segments that have a scale-free, Levy distribution with an inverse-square-law tail. We show that these results, combined with the 'no preferred direction' characteristic of the segments, demonstrate that the bees were flying an optimal search pattern. Levy movements have already been identified in a number of other animals. Our results are the best reported example where the movements are mostly attributable to the adoption of an optimal, scale-free searching strategy. Key words: flight pattern; harmonic radar; honey bees; Levy flights; optimal searching strategy; scale

The distance that pollen is dispersed has important ecological and evolutionary implications. Nevertheless, our understanding of the mechanism that generates spatial patterns of pollen dispersal in animal-pollinated plants, namely the combined processes of pollinator movement and pollen deposition, is at present qualitative. I show how easily measured characteristics of pollinator movement and pollen deposition can be used to build models that generate quantitative predictions about pollen dispersal distance. A field experiment in which I followed honey bees (Apis mellifera) foraging on one-dimensional arrays of mustard plants (Brassica campestris) indicated that individual honeybees have a biased direction of movement and alter their movement patterns in response to plant spacing. I used the model to explore the potential consequences of biased movement and plant spacing for pollen dispersal. Biased movement results in an increase in the expected pollen dispersal distance. In addition, the predicted dispersal distance increased with increasing interplant distance. These results demonstrate that models of pollen spatial dynamics based on individual pollinator behavior can be used to explore the consequences of plant spatial arrangement for gene flow in plant populations.

Three Asian honey bee species (Apis florea, A. cerana, and A. dorsata) were studied in Thailand, and compared with the European honey bee A. mellifera, to explore the energy implications of interspecific differences in worker body size and nesting behavior. From previous work on these four species, we know that several measures of the energy-related performance of foragers (body temperature, flight speed, wing loading, and mass-specific metabolic rate) deviate from predicted size-dependent patterns. Instead, workers in the two species intermediate in body size, A. cerana and A. mellifera, appear to be high-powered relative to those of the largest species (A. dorsata) and the smallest species (A. florea). Among the Asian species, A. cerana's colonies also show a disproportionately high mass-specific metabolic rate, and their foragers make many more trips per in the same habitat than do foragers of the other species. These various traits seem to be functionally related, and to represent evolved differences among species in worker 'tempo,' i.e., in the rate of performance of colony tasks. Correlated with the dichotomy in worker tempo is a dichotomy in nest architecture and intracolony demography. The low-tempo species (Apis florea and A. dorsata) nest in the open, protecting the comb and its contents with a thick curtain of young worker bees. The high-tempo species build their nests in enclosed cavities, which allows the workers to protect and provision a relatively larger area of comb. Worker life-span is longer in the open-nesting species; this allows colonies to maintain the work force needed for the curtain, even though the rate of worker production (per capita) is lower than that of cavity nesters because of the relatively small number of brood cells available. With the assumption that there is a fundamental relationship across species among tempo, foraging performance, and the rate of mortality, we propose that the relatively high tempo of cavity-nesting workers has been favored for two reasons. First, a benefit of higher tempo (enhanced ability to provision brood) is better realized owing to the greater brood-rearing capacity of their nests. Second, a cost of higher tempo (shorter life-span, resulting in fewer workers available for nest protection) is less important for the cavity nesters because the cavity walls reduce the need for protection by workers.