Confidence Intervals for Population Allele Frequencies: The General Case of Sampling from a Finite Diploid Population of Any Size

The estimation of population allele frequencies using sample data forms a central component of studies in population genetics. These estimates can be used to test hypotheses on the evolutionary processes governing changes in genetic variation among populations. However, existing studies frequently do not account for sampling uncertainty in these estimates, thus compromising their utility. Incorporation of this uncertainty has been hindered by the lack of a method for constructing confidence intervals containing the population allele frequencies, for the general case of sampling from a finite diploid population of any size. In this study, we address this important knowledge gap by presenting a rigorous mathematical method to construct such confidence intervals. For a range of scenarios, the method is used to demonstrate that for a particular allele, in order to obtain accurate estimates within 0.05 of the population allele frequency with high probability (%), a sample size of is often required. This analysis is augmented by an application of the method to empirical sample allele frequency data for two populations of the checkerspot butterfly (Melitaea cinxia L.), occupying meadows in Finland. For each population, the method is used to derive % confidence intervals for the population frequencies of three alleles. These intervals are then used to construct two joint % confidence regions, one for the set of three frequencies for each population. These regions are then used to derive a % confidence interval for Jost''s D, a measure of genetic differentiation between the two populations. Overall, the results demonstrate the practical utility of the method with respect to informing sampling design and accounting for sampling uncertainty in studies of population genetics, important for scientific hypothesis-testing and also for risk-based natural resource management.     

The Optimal Foraging Analysis of Horticultural Production

This paper extends the application of optimal foraging theory to horticultural economies. The Machiguenga, a native Amazonian population of southeastern Peru, are used as a test case. The results demonstrate the theory's utility in structuring questions and predicting the outcome of horticultural production. By extending the range of foraging theory the evolution of subsistence strategies from hunting-gathering to agriculture can be examined in quantitative terms. The evolutionary sequence is illustrated with a hypothetical population. Additional insights are gained when the theory is used to structure specific production decisions. Disagreements concerning the scarcity of protein in Amazonian economies are shown to be a consequence of the measurement units employed.     

Data Quality and the Comparative Method: The Case of Primate Group Size

The comparative method is frequently employed to study primate behavior and evolution. The method is used to infer adaptations, and considerable improvements have been made with respect to its implementation. Despite these advances, scant attention has been given to the nature of the data that are used in comparative analyses. This creates a potential problem as data are often compiled from studies conducted by multiple researchers, whose methods may differ, resulting in variation in data quality. In this article, we investigate the quality of data employed in studies of primate group size. Several issues concerning data quality arise when assembling data on group size. For example, data quality may be compromised if group sizes are estimated from censuses, unhabituated groups, or groups with unrecognized individuals. To mitigate these and other data quality issues, we gathered data from the literature on 23 monkeys and apes using well-defined and biologically relevant criteria for inclusion. We compare our results with those of eight published compilations of group size. Most studies did not provide details regarding the criteria for including data. We found that our group size values were uncorrelated or weakly correlated with those from three other studies and differed in a consistent fashion from those of one other study. Because conclusions derived from comparative analyses are only as accurate as the data that they use, future studies should provide details regarding data collection to ensure their reliability.     

The Effective Size of a Subdivided Population

This paper derives the long-term effective size, N(e), for a general model of population subdivision, allowing for differential deme fitness, variable emigration and immigration rates, extinction, colonization, and correlations across generations in these processes. We show that various long-term measures of N(e) are equivalent. The effective size of a metapopulation can be expressed in a variety of ways. At a demographic equilibrium, N(e) can be derived from the demography by combining information about the ultimate contribution of each deme to the future genetic make-up of the population and Wright's F(ST)'s. The effective size is given by N(e) = 1/(1 + var ( &))<(1 - f(STi))/N(i)n>, where n is the number of demes, &(i) is the eventual contribution of individuals in deme i to the whole population (scaled such that σ(i) &(i) = n), and < > denotes an average weighted by &(i)(2). This formula is applied to a catastrophic extinction model (where sites are either empty or at carrying capacity) and to a metapopulation model with explicit dynamics, where extinction is caused by demographic stochasticity and by chaos. Contrary to the expectation from the standard island model, the usual effect of population subdivision is to decrease the effective size relative to a panmictic population living on the same resource.     

Home Range in a Patchy Environment: Optimal Foraging Predictions

Optimal foraging rules are used to simulate the home range ofa central place forager in an environment with a patchy resourcedistribution. The model makes the following predictions: (1)Home range size is inversely related to maximum resource densityand resource renewal rate. It is positively related to the animal'srate of movement. (2) The optimal home range shape in a patchyenvironment is elongate rather than circular, with a major tominor axisratio of about 2:1. This agrees well with observedvalues. (3) The proportion of the total home range used perforaging bout is positively related to the renewal rate of theenvironment. (4) The tendency of an animal to concentrate itsactivity in a subregion of the home range (rather than distributingits activity uniformly) will increase with the maximum resourcedensity. This tendency is measured as the ratio of the areawhich will contain 65% of the occurrences of an animal to thearea required to contain 95% of its occurrences. The valuesof the ratio predicted by this model agree closely with observedvalues.     

相关风险因子对高原鼠兔摄食行为的影响

研究了捕食风险环境中集和洞口距离对高原鼠兔摄食行为的影响。结果表明,集群数量的增加不仅降低了警觉行为,同时也减少了摄食行为,在高风险环境中,集群为1时的取食行为强度最大,低风险环境中,为0时最大,警觉行为主要出现在距洞口2m的范围内,其行为强度与洞口踪影职责负相关,当洞口距离大于3m时,风险处理区的高原鼠兔几乎无警觉行为出现,且该处理区的取食区域几乎压缩的洞口旁,研究结果表明,在捕食风险环境中,高原鼠兔摄食行为与集群和洞口距离之间具有复杂的关系,其行为决策反映了降低风险与摄取食物间的权衡,行为目标是在降低捕食风险的同时尽可能地取食食物。     

The Abundance and Pollen Foraging Behaviour of Bumble Bees in Relation to Population Size of Whortleberry (Vaccinium uliginosum)

Habitat fragmentation can have severe effects on plant pollinator interactions, for example changing the foraging behaviour of pollinators. To date, the impact of plant population size on pollen collection by pollinators has not yet been investigated. From 2008 to 2010, we monitored nine bumble bee species (Bombus campestris, Bombus hortorum s.l., Bombus hypnorum, Bombus lapidarius, Bombus pascuorum, Bombus pratorum, Bombus soroensis, Bombus terrestris s.l., Bombus vestalis s.l.) on Vaccinium uliginosum (Ericaceae) in up to nine populations in Belgium ranging in size from 80 m² to over 3.1 ha. Bumble bee abundance declined with decreasing plant population size, and especially the proportion of individuals of large bumble bee species diminished in smaller populations. The most remarkable and novel observation was that bumble bees seemed to switch foraging behaviour according to population size: while they collected both pollen and nectar in large populations, they largely neglected pollen collection in small populations. This pattern was due to large bumble bee species, which seem thus to be more likely to suffer from pollen shortages in smaller habitat fragments. Comparing pollen loads of bumble bees we found that fidelity to V. uliginosum pollen did not depend on plant population size but rather on the extent shrub cover and/or openness of the site. Bumble bees collected pollen only from three plant species (V. uliginosum, Sorbus aucuparia and Cytisus scoparius). We also did not discover any pollination limitation of V. uliginosum in small populations. We conclude that habitat fragmentation might not immediately threaten the pollination of V. uliginosum, nevertheless, it provides important nectar and pollen resources for bumble bees and declining populations of this plant could have negative effects for its pollinators. The finding that large bumble bee species abandon pollen collection when plant populations become small is of interest when considering plant and bumble bee conservation.     

The Homozygosity Test after a Change in Population Size

The homozygosity of a population will be influenced by any recent change in the population size. The "homozygosity test" of the neutral mutation hypothesis might also be influenced by a population change. A computer simulation method is described that establishes the significance levels of observed homozygosities after a change in population size. Some numerical examples are given.     

Complexity and Human Health: The Case for a Transdisciplinary Paradigm

Transdisciplinary thinking is an emerging philosophy underpinning health social science. We advance a definition of transdisciplinary thinking and link it with complexity theory. Complexity theory's concern with non-linear relationships, interactive causality and emergent properties of systems compels researchers to adopt a transdisciplinary perspective. We construct a generic framework for analyzing health processes from diverse disciplines and apply it to coronary heart disease in the Australian Coalfields. Insights from this analysis support our argument that transdisciplinary thinking maximizes understanding of the complexity of human health.     

Optimal phenology and body-size of Orb-weaving spiders: Foraging constrains

Summary Large orb-weaving spiders in temperate zones always mature in Autumn. A model based on laboratory feeding experiments and insect trap samples from an old-field in Michigan was used to simulate orb-weaver foraging behavior in various habitats and seasons. Seasons of peak energy return rates in habitats used by old-field orb-weavers indicate that prey availability plays a role in determining phenologies of large spiders. The minimum body-size to which the constraint applies in the model corresponds to the lower size-range of strictly Autumn-maturing orb-weaver species.     

A Life-Cycle Model of Human Social Groups Produces a U-Shaped Distribution in Group Size

One of the central puzzles in the study of sociocultural evolution is how and why transitions from small-scale human groups to large-scale, hierarchically more complex ones occurred. Here we develop a spatially explicit agent-based model as a first step towards understanding the ecological dynamics of small and large-scale human groups. By analogy with the interactions between single-celled and multicellular organisms, we build a theory of group lifecycles as an emergent property of single cell demographic and expansion behaviours. We find that once the transition from small-scale to large-scale groups occurs, a few large-scale groups continue expanding while small-scale groups gradually become scarcer, and large-scale groups become larger in size and fewer in number over time. Demographic and expansion behaviours of groups are largely influenced by the distribution and availability of resources. Our results conform to a pattern of human political change in which religions and nation states come to be represented by a few large units and many smaller ones. Future enhancements of the model should include decision-making rules and probabilities of fragmentation for large-scale societies. We suggest that the synthesis of population ecology and social evolution will generate increasingly plausible models of human group dynamics.     

Optimal Foraging: Field Tests of Diet Choice and Habitat Switching

The application of optimal foraging theory to questions of predatorbehavior, and evidence bearing on the utility of this construct,are reviewed. Experimental tests of simple models predictingprey choice are examined with particular reference to the size-selectionof prey by fish. Laboratory estimates of model parameters arethen used to predict prey choice in the field and data fromseveral field tests are presented which corroborate these predictions.When parameters are habitat specific this permits predictionsof net return from foraging in different habitats and consequentlypredictions of habitat use and switching. Field data gatheredto test these predictions demonstrate that fish feed in thericher habitats and switch habitats when the profitability ofone drops below that of another. Examples are provided showinghow these models can then be used to relate behavioral and morphologicaldifferences between species and questions at higher levels suchas the nature of species interactions and community structure.It is suggested that this may be one of the more useful applicationsof optimal foraging theory. Finally, some of the criticismsof the theory and important questions requiring further studyare discussed.     

The Effects of Predation Risk, Food Abundance, and Population Size on Group Size of Brown-Headed Cowbirds (Molothrus ater)

Social and ecological conditions can influence flock formation (e.g. number of flocks, flock size, etc.) depending on the degree of social attraction of a species. We studied group formation in brown‐headed cowbirds (Molothrus ater) over short time periods (30 min) in two semi‐natural experiments conducted under controlled conditions. First, we determined the shape of the relationship between intake rate and flock size by manipulating group size in a single enclosure. Second, we assessed the role of population size, food abundance, and predation risk, and their interactions, in flock size formation in a system of four enclosures (two with and two without food) connected to a central refuge patch. In the first experiment, we found that pecking rates peaked at intermediate flock sizes (three to six individuals), which was influenced by greater availability of foraging time and more aggressive interactions in large groups. In the second experiment, flock sizes in the patches with food increased with population size likely due to the benefits of patch exploitation in groups. Flock size decreased after predator attack probably because refuge availability reduced perceived predation risk more than flocking in larger groups. Food abundance had minor effects, varying flock sizes between the two patches with food, under high food availability conditions when population size was high, probably due to social cohesion effects. Our results suggest that: (1) this species has an inverted‐U food intake–group size relationship with a range of intake‐maximizing flock sizes rather than a single peak, (2) the presence of a near refuge modifies the expected benefits of group patch exploitation under high predation risk, and (3) an increase in population size would more likely be translated into rapid increases in the size of the flocks rather than in more new flocks.     

Possible Mechanisms for the Formation of Flower Size Preferences by Foraging Bumblebees

Large flowers often contain larger nectar rewards, and receive more pollinator visits, than small flowers. We studied possible behavioral mechanisms underlying the formation of flower size preferences in bumblebees, using a two-phase laboratory experiment. Experimentally naive Bombus terrestris (L.) foraged on artificial flowers that bore either a large (3.8 cm diameter) or a small (2.7 cm diameter) display of a uniform color. Only flowers of one display size contained nectar rewards. We changed the display color and the locations of large and small flowers in the second experimental phase. We recorded the bees' choices in both phases. Almost half of the bees (41%) made their first visit to a small flower. The bees learned to associate display size with food reward, and chose rewarding flowers with >85% accuracy by the end of each experimental phase. Some learning occurred within the bees' first three flower visits. Learning of the size–reward association was equally good for large and small displays in the first experimental phase, but better for small displays in the second phase. Formation of size–reward associations followed a similar course in both phases. This suggests that the bees did not apply their experience from the first learning phase to the new situation of the second phase. Rather, they treated each phase of the experiment as an independent learning task. Our results suggest that associative learning is involved in the formation of preferences for large displays by bees. Moreover, bees that had learned to prefer large displays in one foraging situation may not transfer this preference to a novel situation that is sufficiently different. We propose that this feature of the bees' behavior can select for honest advertising in flowers.     

The Effect of Variability on the Optimal Size of a Feeding Territory

Previous empirical and theoretical work has focused on how feedingterritory size is governed by average levels of food availabilityand intrusion pressure; the potentially important effects ofvariability have not yet been studied in detail. Here I incorporatevariation in food availability and intrusion pressure in somesimple optimality models of territory size. The results showthat the possible effects of variability are diverse, includingboth increase and decrease in territory size. And in some cases,variation in food availability produces qualitatively differenteffects than variation in intrusion pressure.     

Optimal Foraging Theory: A Review of Some Models and Their Applications

Hunter-Gatherer Foraging Strategies: Ethnographic and Archeological Analyses . Bruce Winterhalter and Eric Alden Smith , eds. Chicago: University of Chicago Press, 1981. x + 268 pp. $18.00 (cloth), $7.50 (paper).