A Mathematical Model of Forager Loss in Honeybee Colonies Infested with <Emphasis Type="Italic">Varroa destructor</Emphasis> and the Acute Bee Paralysis Virus

We incorporate a mathematical model of Varroa destructor and the Acute Bee Paralysis Virus with an existing model for a honeybee colony, in which the bee population is divided into hive bees and forager bees based on tasks performed in the colony. The model is a system of five ordinary differential equations with dependent variables: uninfected hive bees, uninfected forager bees, infected hive bees, virus-free mites and virus-carrying mites. The interplay between forager loss and disease infestation is studied. We study the stability of the disease-free equilibrium of the bee-mite-virus model and observe that the disease cannot be fought off in the absence of varroacide treatment. However, the disease-free equilibrium can be stable if the treatment is strong enough and also if the virus-carrying mites become virus-free at a rate faster than the mite birth rate. The critical forager loss due to homing failure, above which the colony fails, is calculated using simulation experiments for disease-free, treated and untreated mite-infested, and treated virus-infested colonies. A virus-infested colony without varroacide treatment fails regardless of the forager mortality rate.     

A new multi-population artificial bee algorithm based on global and local optima for numerical optimization

Artificial Bee Colony (ABC) algorithm is a nature-inspired algorithm that showed its efficiency for optimizations. However, the ABC algorithm showed some imbalances between exploration and exploitation. In order to improve the exploitation and enhance the convergence speed, a multi-population ABC algorithm based on global and local optimum (namely MPGABC) is proposed in this paper. First, in MPGABC, the initial population is generated using both chaotic systems and opposition-based learning methods. The colony in MPGABC is divided into several sub-populations to increase diversity. Moreover, the solution search mechanism is modified by introducing global and local optima in the solution search equations of both employed and onlookers. The scout bees in the proposed algorithm are generated similarly to the initial population. Finally, the proposed algorithm is compared with several state-of-art ABC algorithm variants on a set of 13 classical benchmark functions. The experimental results show that MPGABC competes and outperforms other ABC algorithm variants.

     

Demand for Task Performance and Workforce Replacement: Undertakers in Honeybee, Apis mellifera, Colonies

Undertakers are a specialized task group of honey bees that remove dead bees from the colony. The mean adult age of undertakers is 12.5 days; this is similar to that of other specialized task groups, such as guards. The mean number of undertakers in colonies was 544. However, because the number of bees expressing this behavior is dependent on the demand for task performance, undertaker estimates vary depending on the experimental technique. Increasing the demand for undertaking resulted in more bees engaging in the task. Depleting the number of undertakers by removal of bees carrying corpses resulted in new bees assuming undertaking duties. These results support a response-threshold model for engagement of worker bees in task performance.     

Is acetylcholinesterase a pertinent biomarker to detect exposure of pyrethroids? A study case with deltamethrin

The possibility to use acetylcholinesterase as biomarker of exposure to deltamethrin insecticide in the honeybee, Apis mellifera were considered. Joined actions of deltamethrin and pirimicarb (carbamate), alone or in association (dual treatment), were investigated on AChE activity in surviving and dead honeybees in order to test its reliability as biomarker. All treatments induced a reduction in tissue AChE activity in dead bees. In surviving bees, deltamethrin treatment induced an important increase of AChE activity that is not abolished by pirimicarb treatment. The analysis of AChE forms revealed an increase in the soluble form in surviving and dead bees and an increase of the membrane form in surviving bees. No direct effect of deltamethrin on soluble and membrane AChE was observed in vitro. The important increase in AChE activity in response to deltamethrin, not altered by pirimicarb treatment, suggests that AChE activity could represent a robust biomarker specific to deltamethrin exposure in living bees.     

Effects of body size and sociality on the anti‐predator behaviour of foraging bees

Pollinators, like most other animals, often face a tradeoff between increasing food uptake and minimising predation. An earlier model suggests that social bees should be more likely than solitary bees to adopt riskier foraging strategies in order to increase food uptake. In this paper, we extend this model by studying the effect of body size, in addition to sociality, on the predation–intake rate tradeoff. When, following standard practice, we express the foraging strategies in terms of mortality probability and net food uptake, we find that body size should have no effect on the foraging strategies of solitary bees. Social bees, on the other hand, should change their foraging preferences according to their size. Small social bees should tend to maximise food uptake, and large social bees to minimise mortality rate. Mortality, however, is the product of two terms: the probability of suffering an attack and the probability of succumbing to it. Noting that larger bees are less susceptible to succumb to a predation attempt than smaller bees, model predictions change when foraging strategies are expressed in terms of exposure to predators. Following this second approach, exposure to predators should increase monotonically with body size in solitary bees. In social bees it should reach a minimum for medium‐sized bees. We conclude that both bee body size and sociality should be considered when studying the effect of predators on resource use.     

The repellent effect of two pyrethroid insecticides on the honey bee*

ABSTRACT. . An improved model for the repellent effect of pyrethroid insecticides on insects was developed using small colonies of honey bees, Apis mellifera L., in flight cages. Conditioning to scented feeders allowed the separation of foraging bees from a single colony into paired treatment and control groups. The repellent response was characterized as a sublethal toxic effect resulting in transitory inhibition of activity. Permethrin and cypermethrin were shown to be contact repellents to honey bees; exposure was primarily to the tarsi and abdominal venter. Repellency was fully reversible within 24 h. No permanent effects on either memory function or foraging efficiency were observed following acute exposure.     

Remote perception of floral nectar by bumblebees

Summary On both artificial flowers in the laboratory and certain plant species in the field, bumblebees often closely approached flowers and then departed without probing for nectar. In laboratory experiments where nectar rewards were associated with subtle visual or olfactory cues, bumblebees approached and avoided non-rewarding flowers. Flowers that bees entered and probed for nectar contained rewards much more frequently than predicted by chance alone. When there were no external cues associated with nectar content, bees visited rewarding flowers by chance alone, provided rewarding flowers were not spatially clumped. In the field, bumblebees approached and rejected a large proportion of dogbane flowers and red clover inflorescences. On both species, flowers or inflorescences probed by bees contained more nectar than those rejected by bees or those that I chose at random. On fireweed and monkshood, bees rarely or never approached and rejected healthy-looking flowers. Predictions generated by an optimal foraging model were tested on data from four bumblebee species foraging on red clover. The model was highly successful in qualitatively predicting the relationship between handling time and proportion of inflorescences rejected by individual bees, and the relationship between threshold nectar content for acceptance by bees and average resource availability. Thus, bees appeared to use remotely perceived cues to maximize their rates of nectar intake.     

Effect of age,behaviour and social environment on honey bee brain plasticity

We examined the effects of behaviour, age and social environment on mushroom body volume in adult bees. The mushroom bodies are regions of the central brain important for sensory integration and learning. Their volume was influenced by behaviour throughout life: always larger in forager bees than age-matched nurse bees, even in old bees up to 93 days of age as adults. Mushroom body development was influenced by the social environment in the first 8 days of adult life, with different environments having markedly different effects on mushroom body size. Compared to hive-reared bees, isolation slowed mushroom body growth, but bees reared in isolation confined with a single dead bee showed a dramatic increase in mushroom body volume comparable to that seen in active foragers. Despite their precocious mushroom body development, these bees did not show improved performance in an olfactory learning test. Since simple environmental manipulations can both accelerate and delay mushroom body growth in young bees, and since mushroom body volume is sensitive to behaviour throughout life, the honey bee has great potential as a model for exploring the interactions between environment, behaviour and brain structure.     

A Simple Iterative Model Accurately Captures Complex Trapline Formation by Bumblebees Across Spatial Scales and Flower Arrangements

Pollinating bees develop foraging circuits (traplines) to visit multiple flowers in a manner that minimizes overall travel distance, a task analogous to the travelling salesman problem. We report on an in-depth exploration of an iterative improvement heuristic model of bumblebee traplining previously found to accurately replicate the establishment of stable routes by bees between flowers distributed over several hectares. The critical test for a model is its predictive power for empirical data for which the model has not been specifically developed, and here the model is shown to be consistent with observations from different research groups made at several spatial scales and using multiple configurations of flowers. We refine the model to account for the spatial search strategy of bees exploring their environment, and test several previously unexplored predictions. We find that the model predicts accurately 1) the increasing propensity of bees to optimize their foraging routes with increasing spatial scale; 2) that bees cannot establish stable optimal traplines for all spatial configurations of rewarding flowers; 3) the observed trade-off between travel distance and prioritization of high-reward sites (with a slight modification of the model); 4) the temporal pattern with which bees acquire approximate solutions to travelling salesman-like problems over several dozen foraging bouts; 5) the instability of visitation schedules in some spatial configurations of flowers; 6) the observation that in some flower arrays, bees'' visitation schedules are highly individually different; 7) the searching behaviour that leads to efficient location of flowers and routes between them. Our model constitutes a robust theoretical platform to generate novel hypotheses and refine our understanding about how small-brained insects develop a representation of space and use it to navigate in complex and dynamic environments.     

Some techniques in building and validating stochastic models of human reproduction

Stochastic models of human reproduction are beginning to play significant roles in the evaluation of family planning programs. A class of stochastic processes called absorbing, agedependent, semi-Markov processes frequently arises in the construction of such models. The paper begins with a discussion of some technicalities regarding absorbing, age-dependent, semi-Markov processes. Then, an algorithm due to Littman, which makes possible the computerization of this class of stochastic processes, is presented. Briefly, Littman’s algorithm provides an efficient method for numerically solving systems of renewal type integral equations, provided the system does not contain a large number of equations. After setting down a concrete model for a large clinical trial of intrauterine devices conducted in Taiwan, the paper concludes with a discussion of a method for validating the model based on the data collected in the clinical trial. Presented at the Society for Mathematical Biology Meeting, University of Pennsylvania, Philadelphia, August 19–21, 1976.     

Varroa-Virus Interaction in Collapsing Honey Bee Colonies

Varroa mites and viruses are the currently the high-profile suspects in collapsing bee colonies. Therefore, seasonal variation in varroa load and viruses (Acute-Kashmir-Israeli complex (AKI) and Deformed Wing Virus (DWV)) were monitored in a year-long study. We investigated the viral titres in honey bees and varroa mites from 23 colonies (15 apiaries) under three treatment conditions: Organic acids (11 colonies), pyrethroid (9 colonies) and untreated (3 colonies). Approximately 200 bees were sampled every month from April 2011 to October 2011, and April 2012. The 200 bees were split to 10 subsamples of 20 bees and analysed separately, which allows us to determine the prevalence of virus-infected bees. The treatment efficacy was often low for both treatments. In colonies where varroa treatment reduced the mite load, colonies overwintered successfully, allowing the mites and viruses to be carried over with the bees into the next season. In general, AKI and DWV titres did not show any notable response to the treatment and steadily increased over the season from April to October. In the untreated control group, titres increased most dramatically. Viral copies were correlated to number of varroa mites. Most colonies that collapsed over the winter had significantly higher AKI and DWV titres in October compared to survivors. Only treated colonies survived the winter. We discuss our results in relation to the varroa-virus model developed by Stephen Martin.     

Dispersed versus gregarious nesting strategies in the mason bee Chalicodoma siculum

Chalicodoma siculum (Rossi) is a mason bee that usually nests in dispersed sites, constructing spherical mud nests on twigs or hemispherical nests on hard surfaces. Under favourable conditions it may nest in aggregations of several hundred bees. At the nesting aggregation, nest usurpation often occurs, either by the laying of eggs in finished but unsealed cells, by opening a sealed cell and replacing its egg, or by taking over an unfinished cell. Mutual construction and provisioning of a single cell by several females was also often observed. Because participant bees display extreme aggression in prolonged disputes over cell ownership, these interactions can be regarded as competitive rather than cooperative. Moreover, since the total investment in such cells is not different from that in cells located in dispersed sites, the female that actually manages to lay an egg gains by participating in a cell under construction.
We discuss the advantages of nesting in aggregations vs. the risks of being usurped, as selective forces underlying nesting behaviour of bees.     

Field-Level Sublethal Effects of Approved Bee Hive Chemicals on Honey Bees (Apis mellifera L)

In a study replicated across two states and two years, we tested the sublethal effects on honey bees of the miticides Apistan (tau fluvalinate) and Check Mite+ (coumaphos) and the wood preservative copper naphthenate applied at label rates in field conditions. A continuous covariate, a colony Varroa mite index, helped us disambiguate the effects of the chemicals on bees while adjusting for a presumed benefit of controlling mites. Mite levels in colonies treated with Apistan or Check Mite+ were not different from levels in non-treated controls. Experimental chemicals significantly decreased 3-day brood survivorship and increased construction of queen supercedure cells compared to non-treated controls. Bees exposed to Check Mite+ as immatures had higher legacy mortality as adults relative to non-treated controls, whereas bees exposed to Apistan had improved legacy mortality relative to non-treated controls. Relative to non-treated controls, Check Mite+ increased adult emergence weight. Although there was a treatment effect on a test of associative learning, it was not possible to statistically separate the treatment means, but bees treated with Apistan performed comparatively well. And finally, there were no detected effects of bee hive chemical on colony bee population, amount of brood, amount of honey, foraging rate, time required for marked released bees to return to their nest, percentage of released bees that return to the nest, and colony Nosema spore loads. To our knowledge, this is the first study to examine sublethal effects of bee hive chemicals applied at label rates under field conditions while disambiguating the results from mite control benefits realized from the chemicals. Given the poor performance of the miticides at reducing mites and their inconsistent effects on the host, these results defend the use of bee health management practices that minimize use of exotic hive chemicals.     

Population growth of Varroa destructor (Acari: Varroidae) in commercial honey bee colonies treated with beta plant acids

Varroa (Varroa destuctor Anderson and Trueman) populations in honey bee (Apis mellifera L.) colonies might be kept at low levels by well-timed miticide applications. HopGuard^® (HG) that contains beta plant acids as the active ingredient was used to reduce mite populations. Schedules for applications of the miticide that could maintain low mite levels were tested in hives started from either package bees or splits of larger colonies. The schedules were developed based on defined parameters for efficacy of the miticide and predictions of varroa population growth generated from a mathematical model of honey bee colony–varroa population dynamics. Colonies started from package bees and treated with HG in the package only or with subsequent HG treatments in the summer had 1.2–2.1 mites per 100 bees in August. Untreated controls averaged significantly more mites than treated colonies (3.3 mites per 100 bees). By October, mite populations ranged from 6.3 to 15.0 mites per 100 bees with the lowest mite numbers in colonies treated with HG in August. HG applications in colonies started from splits in April reduced mite populations to 0.12 mites per 100 bees. In September, the treated colonies had significantly fewer mites than the untreated controls. Subsequent HG applications in September that lasted for 3 weeks reduced mite populations to levels in November that were significantly lower than in colonies that were untreated or had an HG treatment that lasted for 1 week. The model accurately predicted colony population growth and varroa levels until the fall when varroa populations measured in colonies established from package bees or splits were much greater than predicted. Possible explanations for the differences between actual and predicted mite populations are discussed.     

The Allometry of Bee Proboscis Length and Its Uses in Ecology

Allometric relationships among morphological traits underlie important patterns in ecology. These relationships are often phylogenetically shared; thus quantifying allometric relationships may allow for estimating difficult-to-measure traits across species. One such trait, proboscis length in bees, is assumed to be important in structuring bee communities and plant-pollinator networks. However, it is difficult to measure and thus rarely included in ecological analyses. We measured intertegular distance (as a measure of body size) and proboscis length (glossa and prementum, both individually and combined) of 786 individual bees of 100 species across 5 of the 7 extant bee families (Hymenoptera: Apoidea: Anthophila). Using linear models and model selection, we determined which parameters provided the best estimate of proboscis length. We then used coefficients to estimate the relationship between intertegular distance and proboscis length, while also considering family. Using allometric equations with an estimation for a scaling coefficient between intertegular distance and proboscis length and coefficients for each family, we explain 91% of the variance in species-level means for bee proboscis length among bee species. However, within species, individual-level intertegular distance was a poor predictor of individual proboscis length. To make our findings easy to use, we created an R package that allows estimation of proboscis length for individual bee species by inputting only family and intertegular distance. The R package also calculates foraging distance and body mass based on previously published equations. Thus by considering both taxonomy and intertegular distance we enable accurate estimation of an ecologically and evolutionarily important trait.     

From continuum Fokker-Planck models to discrete kinetic models

Two theoretical formalisms are widely used in modeling mechanochemical systems such as protein motors: continuum Fokker-Planck models and discrete kinetic models. Both have advantages and disadvantages. Here we present a "finite volume" procedure to solve Fokker-Planck equations. The procedure relates the continuum equations to a discrete mechanochemical kinetic model while retaining many of the features of the continuum formulation. The resulting numerical algorithm is a generalization of the algorithm developed previously by Fricks, Wang, and Elston through relaxing the local linearization approximation of the potential functions, and a more accurate treatment of chemical transitions. The new algorithm dramatically reduces the number of numerical cells required for a prescribed accuracy. The kinetic models constructed in this fashion retain some features of the continuum potentials, so that the algorithm provides a systematic and consistent treatment of mechanical-chemical responses such as load-velocity relations, which are difficult to capture with a priori kinetic models. Several numerical examples are given to illustrate the performance of the method.     

The role of trophallaxis in the distribution of Perizin in a honeybee colony with regard to the control of the Varroa mite

It is claimed that Perizin, a pesticide to control the mite Varroa jacobsoni, acts systemically and is distributed by trophallaxis of the bees. We studied the role of trophallactic interactions in the distribution of coumaphos, the active ingredient, among the colony members and whether coumaphos can reach all mites by systemic activity. Colonies were divided into three compartments by a screen, one receiving a Perizin treatment by sprinkling, the others receiving no Perizin. In this way it was possible to trace the amount of coumaphos transferred between bees through the screen from the treated part to the untreated one by trophallaxis. After different periods of time the number of fallen mites was counted and the amount of coumaphos in bees was determined for all hive compartments. We found that trophallactic interactions are of minor importance in the distribution of Perizin between the two compartments. The recommended method of sprinkling Perizin over the bees was shown to be very inefficient; only 24% of the applied amount reaches the alimentary canal of the bees; the rest must therefore remain at other places: on the outside of the bees, in the combs and on the hive-parts.     

Sub-lethal effects of pesticide residues in brood comb on worker honey bee (Apis mellifera) development and longevity

Background

Numerous surveys reveal high levels of pesticide residue contamination in honey bee comb. We conducted studies to examine possible direct and indirect effects of pesticide exposure from contaminated brood comb on developing worker bees and adult worker lifespan.

Methodology/Principal Findings

Worker bees were reared in brood comb containing high levels of known pesticide residues (treatment) or in relatively uncontaminated brood comb (control). Delayed development was observed in bees reared in treatment combs containing high levels of pesticides particularly in the early stages (day 4 and 8) of worker bee development. Adult longevity was reduced by 4 days in bees exposed to pesticide residues in contaminated brood comb during development. Pesticide residue migration from comb containing high pesticide residues caused contamination of control comb after multiple brood cycles and provided insight on how quickly residues move through wax. Higher brood mortality and delayed adult emergence occurred after multiple brood cycles in contaminated control combs. In contrast, survivability increased in bees reared in treatment comb after multiple brood cycles when pesticide residues had been reduced in treatment combs due to residue migration into uncontaminated control combs, supporting comb replacement efforts. Chemical analysis after the experiment confirmed the migration of pesticide residues from treatment combs into previously uncontaminated control comb.

Conclusions/Significance

This study is the first to demonstrate sub-lethal effects on worker honey bees from pesticide residue exposure from contaminated brood comb. Sub-lethal effects, including delayed larval development and adult emergence or shortened adult longevity, can have indirect effects on the colony such as premature shifts in hive roles and foraging activity. In addition, longer development time for bees may provide a reproductive advantage for parasitic Varroa destructor mites. The impact of delayed development in bees on Varroa mite fecundity should be examined further.     

Juvenile hormone paces behavioral development in the adult worker honey bee

Behavioral development in the adult worker honey bee (Apis mellifera), from performing tasks inside the hive to foraging, is associated with an increase in the blood titer of juvenile hormone III (JH), and hormone treatment results in precocious foraging. To study behavioral development in the absence of JH we removed its glandular source, the corpora allata, in 1-day-old adult bees. The age at onset of foraging for allatectomized bees in typical colonies was significantly older compared with that of sham-operated bees in 3 out of 4 colonies; this delay was eliminated by hormone replacement in 3 out of 3 colonies. To determine the effects of corpora allata removal on sensitivity to changes in conditions that influence the rate of behavioral development, we used "single-cohort" colonies (composed of only young bees) in which some colony members initiate foraging precociously. The age at onset of foraging for allatectomized bees was significantly older compared with that of sham-operated bees in 2 out of 3 colonies, and this delay was eliminated by hormone replacement. Allatectomized bees initiated foraging at significantly younger ages in single-cohort colonies than in typical colonies. These results demonstrate that JH influences the pace of behavioral development in honey bees, but is not essential for either foraging or altering behavioral development in response to changes in conditions.     

Tree resin composition, collection behavior and selective filters shape chemical profiles of tropical bees (Apidae: Meliponini)

The diversity of species is striking, but can be far exceeded by the chemical diversity of compounds collected, produced or used by them. Here, we relate the specificity of plant-consumer interactions to chemical diversity applying a comparative network analysis to both levels. Chemical diversity was explored for interactions between tropical stingless bees and plant resins, which bees collect for nest construction and to deter predators and microbes. Resins also function as an environmental source for terpenes that serve as appeasement allomones and protection against predators when accumulated on the bees' body surfaces. To unravel the origin of the bees' complex chemical profiles, we investigated resin collection and the processing of resin-derived terpenes. We therefore analyzed chemical networks of tree resins, foraging networks of resin collecting bees, and their acquired chemical networks. We revealed that 113 terpenes in nests of six bee species and 83 on their body surfaces comprised a subset of the 1,117 compounds found in resins from seven tree species. Sesquiterpenes were the most variable class of terpenes. Albeit widely present in tree resins, they were only found on the body surface of some species, but entirely lacking in others. Moreover, whereas the nest profile of Tetragonula melanocephala contained sesquiterpenes, its surface profile did not. Stingless bees showed a generalized collecting behavior among resin sources, and only a hitherto undescribed species-specific "filtering" of resin-derived terpenes can explain the variation in chemical profiles of nests and body surfaces from different species. The tight relationship between bees and tree resins of a large variety of species elucidates why the bees' surfaces contain a much higher chemodiversity than other hymenopterans.