Predicting the economic impact of an invasive species on an ecosystem service.

Quantifying the impact of alien invasive species on ecosystem services is an essential step in developing effective practices and policy for invasive species management. Here we develop a stochastic bioeconomic model that enables the economic impact of an invasive pest to be estimated before its arrival, based on relatively poorly specified ecological and economic parameters. We developed the model by using a hypothetical invasion of the varroa bee mite (Varroa destructor) into Australia and the negative flow-on effects that it would have on pollination by reducing honey bee populations, giving rise to a loss of pollination services, reduced crop yields, and additional production costs. If the mite were to continue to be prevented from entering the country over the next 30 years, we estimate that the economic costs avoided would be U.S. $16.4-38.8 million (Aus $21.3-50.5 million) per year. We suggest that current invasion response funding arrangements in Australia, which do not acknowledge these avoided damages, require amendment.     

Condition-dependent response to changes in pollen stores by honey bee (Apis mellifera) colonies with different parasitic loads

The impact of a parasitic infestation may be influenced by nutritional state, in both individuals and colonies. This study examined the interaction between pollen storage and the effects of an infestation by the mite, Varroa jacobsoni Oudemans, in colonies of the honey bee, Apis mellifera L. We manipulated the pollen storage and mite infestation levels of colonies, and measured pollen foraging and brood rearing. Increased pollen stores decreased both the number of pollen foragers and pollen load size, while initially at least foragers from colonies with moderate infestations carried smaller pollen loads than those from lightly infested colonies. Over the course of the experiment, all colonies significantly increased pollen-foraging rates and pollen consumption, which was presumably a seasonal effect. Lightly infested colonies exhibited a larger increase in pollen forager number than moderately infested colonies, suggesting that more intense mite infestations compromised forager recruitment. Brood production was not affected by the addition of pollen, but moderately infested colonies were rearing significantly less brood by the end of the experiment than lightly infested colonies. Furthermore, the efficiency with which colonies converted pollen to brood decreased as the pollen storage level decreased and the infestation level increased. The results of this study may indicate that honey bee colonies adaptively alter brood-production efficiency in response to parasitic infestations and seasonal changes. Received: 3 May 1999 / Received in revised form: 14 September 1999 / Accepted: 25 September 1999     

Predicting reproduction rate of varroa

A single equation is derived to predict population-density effects on the reproduction rate of the honey bee parasite Varroa destructor Anderson and Trueman. This equation provides a simpler alternative to the approach currently used in the literature, and additionally corrects an anomaly in that approach. The method is then extended to the case of co-existing haplotypes of Varroa. It thus derives an equation used without proof for modelling biocontrol of Varroa, and examines the error caused by an approximation necessary for a closed form solution. Additionally a varroa population model incorporating the derived equation is described.     

Behavioral attributes and parental care of Varroa mites parasitizing honeybee brood

Varroa jacobsoni, an ectoparasite of the Asian honeybeeApis cerana, has been introduced world-wide, and is currently decimating colonies of the European honeybeeApis mellifera.Varroa's reproductive cycle is tuned to that of drone cells, those mainly parasitized in the original host. We describe here how a single fertilized female, infesting a brood cell, can produce two to four adult fertilized females within the limited time span of bee development (270 h in worker and 320 h in drone cells), despite the disturbance caused by cocoon spinning and subsequent morphological changes of the bee. From observations on transparent artificial cells we were able to show how the mite combats these problems with specialized behaviors that avoid destruction by the developing bee, prepares a feeding site for the nymphs on the bee pupa, and constructs a fecal accumulation on the cell wall which serves as a rendezvous site for matings between its offspring. The proximity of the fecal accumulation to the feeding site facilitates feeding by the maturing progeny. However, communal use of the feeding site leads to competition between individuals, and protonymphs are most disadvantaged. This competition is somewhat compensated by the timing of oviposition by the mites. Use of a common rendezvous and feeding site by two or moreVarroa mothers in multiinfested cells may have developed from the parental care afforded to them as nymphs.     

An estimating function approach to the inference of catch-effort models

A class of catch-effort models, which allows for heterogeneous removal probabilities, is proposed for closed populations. The model includes three types of removal probabilities: multiplicative, Poisson and logistic. The usual removal and generalized removal models then become special cases. The equivalence of the proposed model and a special type of capture-recapture model is discussed. A unified estimating function approach is used to estimate the initial population size. For the homogeneous model, the resulting population size estimator based on optimal estimating functions is asymptotically equivalent to the maximum likelihood estimator. One advantage for our approach is that it can be extended to handle the heterogeneous populations in which the maximum likelihood estimators do not exist. The bootstrap method is applied to construct variance estimators and confidence intervals. We illustrate the method by two real data examples. Results of a simulation study investigating the performance of the proposed estimation procedure are presented.     

An engineering model for countercurrent flow under wind-induced waves and current

A general model for the phase-averaged velocity field in wind-induced countercurrent flow is proposed. The influence of waves on the time-averaged velocity is accounted for by introducing a skewness factor in a parabolic eddy viscosity model. The skewness factor represents the net effect of the wavy surface in the engineering model for velocity. The coherent velocity components are described separately by an orbital velocity obtained from linear wave theory and are added to the time-averaged components to give a complete model for the phase-averaged velocity field. The proposed model collapses to the standard model for deep-water conditions, but is also shown to yield the correct behavior for intermediate conditions. Moreover, the bed shear stress, derived from the proposed velocity model, is also shown to be in agreement with experiments.     

Migration effects in a stochastic multipopulation model for African bee population dynamics

The rate of northern migration of the Africanized honey bee (AHB) in the United States has recently slowed dramatically. This paper investigates the impact of migration on the equilibrium size distributions of a particular stochastic multipopulation model, namely a coupled logistic power law model. The bivariate equilibrium size distribution of the model is derived and illustrated with parameter values used to describe AHB population dynamics. In the model, the difference between the equilibrium sizes of the two populations is a measure of the effect of migration. The distribution of this difference may be approximated by a normal distribution. The mean and variance parameters for the normal are predicted accurately by a second-order regression model based on the migration rate and the maximum size of the first population. The methodology is general, and should be useful in studying the migration effect in many other applications with one-way migration.     

Population dynamics models based on cumulative density dependent feedback: A link to the logistic growth curve and a test for symmetry using aphid data

Density dependent feedback, based on cumulative population size, has been advocated to explain and mathematically characterize “boom and bust” population dynamics. Such feedback results in a bell-shaped population trajectory of the population density. Here, we note that this trajectory is mathematically described by the logistic probability density function. Consequently, the cumulative population follows a time trajectory that has the same shape as the cumulative logistic function. Thus, the Pearl–Verhulst logistic equation, widely used as a phenomenological model for density dependent population growth, can be interpreted as a model for cumulative rather than instantaneous population. We extend the cumulative density dependent differential equation model to allow skew in the bell-shaped population trajectory and present a simple statistical test for skewness. Model properties are exemplified by fitting population trajectories of the soybean aphid, Aphis glycines. The linkage between the mechanistic underpinnings of the logistic probability density function and cumulative distribution function models could open up new avenues for analyzing population data.     

On stochastic differential equations and equilibrium distribution: a conditional moment approach

In the recent past there have been several attempts to obtain the equilibrium distribution of multiple populations and their moments in the context of some biological or ecological processes (e.g., Matis and Kiffe in Biometrics 52:155, 1996; Matis and Kiffe in Environ Ecol Stat 9:237, 2002; Renshaw in J Math Appl Med Biol, 15:1, 1998). In particular, the method of cumulant truncation (Matis and Kiffe in Biometrics 52:155, 1996) is a pioneering work in this field. However it requires solving a large number of cumulant functions even in the case of two simultaneous differential equations. Besides the solutions are approximate and depend on the precision of the software. Renshaw (Math Biosci 168:57, 2000) provided a nice extension of the univariate truncated saddle point procedure to multivariate scenarios. But this approach involves a multivariate Newton-Raphson type iterative algorithm whose performance and convergence are critically dependent on the choice of the initial values. In the present paper we propose a new and simple approach to obtain the equilibrium distribution of populations and their conditional moments in a system of differential equations of any dimension. Our proposed method, which is a natural extension of the classical variational matrix approach, has several advantages which are discussed in detail in the paper; among other things it includes the derivation of additional conditions which can be interpreted as environmental surrogates.     

Why do Varroa mites invade worker brood cells of the honey bee despite lower reproductive success?

Varroa jacobsoni reproduces both in drone and worker brood cells of honey bees, but in drone cells reproductive success is higher than in worker cells. A simple model using clonal population growth as a fitness measure has been developed to study the circumstances under which specialization on drone brood would be a better strategy than reproduction in both types of cell. For European Apis mellifera, the model suggests that if mites have to wait less than 7 days on average before they can invade a drone cell, specialization on drone brood would be a better strategy. This is close to the estimated waiting time of 6 days. Hence, small differences in reproductive success in drone and worker cells and in the rate of mortality may determine whether specialization on drone brood will be promoted or not. In European A. mellifera colonies, Varroa mites invade both drone and worker cells, but specialization on drone brood cells seems to occur to some extent because drone cells are more frequently invaded than worker cells. In the parasite-host association of V. jacobsoni with African or Africanized A. mellifera or with A. cerana, the mites also invade both drone and worker cells, but the mites specialize on drone brood for reproduction since a large percentage of the mites in worker brood do not reproduce. Only in the parasite-host association of Euvarroa sinhai, a mite closely resembling V. jacobsoni, and A. forea is specialization complete, because these mites only invade drone brood.     

Cuticular volatiles,attractivity of worker larvae and invasion of brood cells by Varroa mites. A comparison of Africanized and European honey bees

Summary. Africanized honey bees (AHBs) of Brazil and Mexico have proven to be tolerant to Varroa destructor mites. In contrast, European honey bees (EHBs: Apis mellifera carnica) at the same tropical study site are highly intolerant to these ectoparasites. A lower attractiveness of Varroa-tolerant AHB larvae has been hypothesised to be an important trait in reducing the susceptibitlity of AHBs to these mites. Thus, selection for EHB brood that is less attractive to mites is thought to be one possibility for limiting mite population growth and thus increase the tolerance of EHBs to the mite.?In Ribeir?o Preto, Brazil, European A. m. carnica bees and AHBs were tested with respect to their rate of brood infestation and brood attractiveness to Varroa mites. For the comparison of brood infestation rates, we introduced combs with pieces of EHB and AHB brood into honey bee colonies (18 repetitions). The relative infestation rate of EHB brood was significantly higher compared to AHB brood.?The preference behaviour of single Varroa mites was tested in a laboratory bioassay where either living host stages were offered or host extracts were presented on dummies. By these tests we could confirm the preference of Varroa females for certain developmental host stages and for their corresponding extracts. In contrast to the within-colony results, Varroa mites in the laboratory bioassay showed a slight preference for AHB compared to EHB larvae.?The gas chromatographic analysis revealed differences in the chemical spectrum of extracts obtained from different larvae. In accord with the results of the bioassays, we could detect stage-specific odour differences in larval cuticular compounds, including methyl esters and hydrocarbons that have been described as kairomones. None of these substances, however, revealed significant race-specific differences. Therefore, the quantity and composition of certain cuticular compounds seem to be responsible only for the recognition of a suitable host stage by Varroa females. The different infestation rates in the colonies, however, seem to be caused neither by race-specific differences in attractiveness of bee larvae nor by an extended attractive period of EHB larvae: both AHB and EHB larvae become attractive approximately 21 h before capping of the brood cell, and thus have the same window of time when they can be parasitised.?Therefore differential Varroa-infestation rates are not related to larval attraction but probably are determined by other race-specific and colony-related factors. Received 11 June 2001; accepted 19 November 2001.     

Resampling methods for estimating dispersion indices in random and adaptive designs

In many surveys in environmental and natural phenomena the aim is to evaluate the heterogeneity, and the skewness of the distribution of the number point-objects in the study area opportunely partitioned in sub-regions. For this purpose, in this paper the estimation of dispersion indices is considered by using simple random sampling and adaptive sampling with initial simple random sampling selected with replacement or without replacement. The jackknife and the bootstrap procedures are proposed in both cases for reducing bias. Finally, both a simulation study and a case study on biological population referred to a Oidium tuckeri contamination in a growing vineyard is performed to assess the accuracy of the proposed estimators.     

Modeling scale up of anthropogenic impacts from individual pollinator behavior to pollination systems

Understanding how anthropogenic disturbances affect plant–pollinator systems has important implications for the conservation of biodiversity and ecosystem functioning. Previous laboratory studies show that pesticides and pathogens, which have been implicated in the rapid global decline of pollinators over recent years, can impair behavioral processes needed for pollinators to adaptively exploit floral resources and effectively transfer pollen among plants. However, the potential for these sublethal stressor effects on pollinator–plant interactions at the individual level to scale up into changes to the dynamics of wild plant and pollinator populations at the system level remains unclear. We developed an empirically parameterized agent-based model of a bumblebee pollination system called SimBee to test for effects of stressor-induced decreases in the memory capacity and information processing speed of individual foragers on bee abundance (scenario 1), plant diversity (scenario 2), and bee–plant system stability (scenario 3) over 20 virtual seasons. Modeling of a simple pollination network of a bumblebee and four co-flowering bee-pollinated plant species indicated that bee decline and plant species extinction events could occur when only 25% of the forager population showed cognitive impairment. Higher percentages of impairment caused 50% bee loss in just five virtual seasons and system-wide extinction events in less than 20 virtual seasons under some conditions. Plant species extinctions occurred regardless of bee population size, indicating that stressor-induced changes to pollinator behavior alone could drive species loss from plant communities. These findings indicate that sublethal stressor effects on pollinator behavioral mechanisms, although seemingly insignificant at the level of individuals, have the cumulative potential in principle to degrade plant–pollinator species interactions at the system level. Our work highlights the importance of an agent-based modeling approach for the identification and mitigation of anthropogenic impacts on plant–pollinator systems.     

Uncertainty analysis of transient population dynamics

Two types of demographic analyses, perturbation analysis and uncertainty analysis, can be conducted to gain insights about matrix population models and guide population management. Perturbation analysis studies how the perturbation of demographic parameters (survival, growth, and reproduction parameters) may affect the population projection, while uncertainty analysis evaluates how much uncertainty there is in population dynamic predictions and where the uncertainty comes from. Previously, both perturbation analysis and uncertainty analysis were conducted on the long-term population growth rate. However, the population may not reach its equilibrium state, especially when there is management by harvesting or hunting. Recently, there has been an increased interest in short-term transient dynamics, which can differ from asymptotic long-term dynamics. There are currently techniques to conduct perturbation analyses of short-term transient dynamics, but no techniques have been proposed for uncertainty analysis of such dynamics. In this study, we introduced an uncertainty analysis technique, the general Fourier Amplitude Sensitivity Test (FAST), to study uncertainties in transient population dynamics. The general FAST is able to identify the amount of uncertainty in transient dynamics and contributions by different demographic parameters. We applied the general FAST to a mountain goat (Oreamnos americanus) matrix population model to give a clear illustration of how uncertainty analysis can be conducted for transient dynamics arising from matrix population models.     

Hierarchical spatial modeling for estimation of population size

Estimation of population size has traditionally been viewed from a finite population sampling perspective. Typically, the objective is to obtain an estimate of the total population count of individuals within some region. Often, some stratification scheme is used to estimate counts on subregions, whereby the total count is obtained by aggregation with weights, say, proportional to the areas of the subregions. We offer an alternative to the finite population sampling approach for estimating population size. The method does not require that the subregions on which counts are available form a complete partition of the region of interest. In fact, we envision counts coming from areal units that are small relative to the entire study region and that the total area sampled is a very small proportion of the total study area. In extrapolating to the entire region, we might benefit from assuming that there is spatial structure to the counts. We implement this by modeling the intensity surface as a realization from a spatially correlated random process. In the case of multiple population or species counts, we use the linear model of coregionalization to specify a multivariate process which provides associated intensity surfaces hence association between counts within and across areal units. We illustrate the method of population size estimation with simulated data and with tree counts from a Southwestern pinyon-juniper woodland data set.     

Integral projection models for finite populations in a stochastic environment

Continuous types of population structure occur when continuous variables such as body size or habitat quality affect the vital parameters of individuals. These structures can give rise to complex population dynamics and interact with environmental conditions. Here we present a model for continuously structured populations with finite size, including both demographic and environmental stochasticity in the dynamics. Using recent methods developed for discrete age-structured models we derive the demographic and environmental variance of the population growth as functions of a continuous state variable. These two parameters, together with the expected population growth rate, are used to define a one-dimensional diffusion approximation of the population dynamics. Thus, a substantial reduction in complexity is achieved as the dynamics of the complex structured model can be described by only three population parameters. We provide methods for numerical calculation of the model parameters and demonstrate the accuracy of the diffusion approximation by computer simulation of specific examples. The general modeling framework makes it possible to analyze and predict future dynamics and extinction risk of populations with various types of structure, and to explore consequences of changes in demography caused by, e.g., climate change or different management decisions. Our results are especially relevant for small populations that are often of conservation concern.     

Do resources or natural enemies drive bee population dynamics in fragmented habitats?

The relative importance of bottom-up or top-down forces has been mainly studied for herbivores but rarely for pollinators. Habitat fragmentation might change driving forces of population dynamics by reducing the area of resource-providing habitats, disrupting habitat connectivity, and affecting natural enemies more than their host species. We studied spatial and temporal population dynamics of the solitary bee Osmia rufa (Hymenoptera: Megachilidae) in 30 fragmented orchard meadows ranging in size from 0.08 to 5.8 ha in an agricultural landscape in central Germany. From 1998 to 2003, we monitored local bee population size, rate of parasitism, and rate of larval and pupal mortality in reed trap nests as an accessible and standardized nesting resource. Experimentally enhanced nest site availability resulted in a steady increase of mean local population size from 80 to 2740 brood cells between 1998 and 2002. Population size and species richness of natural enemies increased with habitat area, whereas rate of parasitism and mortality only varied among years. Inverse density-dependent parasitism in three study years with highest population size suggests rather destabilizing instead of regulating effects of top-down forces. Accordingly, an analysis of independent time series showed on average a negative impact of population size on population growth rates but provides no support for top-down regulation by natural enemies. We conclude that population dynamics of O. rufa are mainly driven by bottom-up forces, primarily nest site availability.     

Estimating Population Size in a Continuous-time Removal Experiment with a Known Sub-population Size Ratio

We study a continuous-time removal model for estimating the population size for a population in which a sub-population size ratio is known. The maximum likelihood estimate and the optimal martingale estimate of the population size are obtained; these are shown to be equivalent. A comparison between the proposed estimator and the maximum likelihood estimate which ignores the information on the known size ratio is made, using a simulation study. The asymptotic variances of these two estimators are also obtained, and a comparison between them is made. The sensitivity of mis-specification of the known size ratio is examined. We also apply the corresponding discrete-time model to the proposed continuous-time setting, and study the efficiency of the corresponding discrete-time type estimator relative to the proposed estimator.     

Generalized extreme value regression for ordinal response data

This paper introduces a flexible skewed link function for modeling ordinal response data with covariates based on the generalized extreme value (GEV) distribution. Commonly used probit, logit and complementary log-log links are prone to link misspecification because of their fixed skewness. The GEV link is flexible in fitting the skewness in the response curve with a free shape parameter. Using Bayesian methodology, it automatically detects the skewness in the response curve along with the model fitting. The flexibility of the proposed model is illustrated by its application to an ecological survey data about the coverage of Berberis thunbergii in New England. We employ the latent variable approach by Albert and Chib (J Am Stat Assoc 88:669–679, (1993) to develop computational schemes. For model selection, we employ the Deviance Information Criterion (DIC).     

Colony level and within colony level selection in honeybees

Summary Although honeybee workers are usually infertile, in queenless colonies some workers can develop ovaries and produce offspring. Therefore the classical Darwinian fitness of workers is not zero. Experimental studies in the Cape honey bee (Apis mellifera capensis) reveal a huge genetic variation for individual fitness of workers. The present study with a one locus, two allele model for reproductive dominance of workers shows that a balanced system between colony level and individual within colony selection plausibly explains the phenomenon of a high genetic variance of worker fitness. In particular, a frequent occurrence of queenless colonies in the population leads to stable polymorphic equilibria. Also the multiple mating system of the honey bee queen supports the propagation of alleles causing reproductive dominance of workers.