Mary R. Myerscough

A quantitative model of honey bee colony population dynamics.

Since 2006 the rate of honey bee colony failure has increased significantly. As an aid to testing hypotheses for the causes of colony failure we have developed a compartment model of honey bee colony population dynamics to explore the impact of different death rates of forager bees on colony growth and development. The model predicts a critical threshold forager death rate beneath which colonies regulate a stable population size. If death rates are sustained higher than this threshold rapid population decline is predicted and colony failure is inevitable. The model also predicts that high forager death rates draw hive bees into the foraging population at much younger ages than normal, which acts to accelerate colony failure. The model suggests that colony failure can be understood in terms of observed principles of honey bee population dynamics, and provides a theoretical framework for experimental investigation of the problem.

Rapid behavioral maturation accelerates failure of stressed honey bee colonies

Significance Honey bee colony death rates are unsustainably high. While many stressors have been identified that contribute to this problem, we do not know why colonies transition so rapidly from a state of apparent health to failure. It is well known that individual bees react to nutritional and pathogen stresses by foraging precociously: our study explains how colony failure arises from the social responses of individual bees to stress. We used radio tracking to monitor performance of bees and found that workers who begin foraging prematurely perform very poorly. This compounds the stresses on the colony and accelerates failure. We suggest how colonies at risk can be identified early, and the most effective interventions to prevent failure. Many complex factors have been linked to the recent marked increase in honey bee colony failure, including pests and pathogens, agrochemicals, and nutritional stressors. It remains unclear, however, why colonies frequently react to stressors by losing almost their entire adult bee population in a short time, resulting in a colony population collapse. Here we examine the social dynamics underlying such dramatic colony failure. Bees respond to many stressors by foraging earlier in life. We manipulated the demography of experimental colonies to induce precocious foraging in bees and used radio tag tracking to examine the consequences of precocious foraging for their performance. Precocious foragers completed far fewer foraging trips in their life, and had a higher risk of death in their first flights. We constructed a demographic model to explore how this individual reaction of bees to stress might impact colony performance. In the model, when forager death rates were chronically elevated, an increasingly younger forager force caused a positive feedback that dramatically accelerated terminal population decline in the colony. This resulted in a breakdown in division of labor and loss of the adult population, leaving only brood, food, and few adults in the hive. This study explains the social processes that drive rapid depopulation of a colony, and we explore possible strategies to prevent colony failure. Understanding the process of colony failure helps identify the most effective strategies to improve colony resilience.

Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation

We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989, J. exp. Zool. 251, 186-202). We determine finite-amplitude, steady-state, spatially heterogeneous solutions and study the effect of domain growth on the resulting patterns. We also investigate in-depth bifurcating solutions as the chemotactic parameter varies. This numerical study shows that this deceptively simple-chemotaxis model can produce a surprisingly rich spectrum of complex spatial patterns.

Pigmentation pattern formation on snakes

We consider a cell-chemotaxis model mechanism for generating some of the common, simple and complex, patterns found on the skin of snakes. By investigating the pattern generation potential of the model we show that many of the more complex patterns might result from growth of the integument during the pattern formation process. We suggest that many of the diverse elaborate patterns on snakes, and other species, can be generated by a single mechanism if the time scale of the pattern process is commensurate with the time scale associated with significant embryonic growth.

An analysis of an ordinary differential equation model for a two-species predator-prey system with harvesting and stocking

An analysis is presented for a model of a two-species predator-prey system where each species can be harvested or stocked. Using methods from bifurcation theory the qualitative nature of the steady-state solutions is examined. The effect of harvesting and stocking rates and the prey carrying capacity is examined in detail.

Modelling food and population dynamics in honey bee colonies.

Honey bees (Apis mellifera) are increasingly in demand as pollinators for various key agricultural food crops, but globally honey bee populations are in decline, and honey bee colony failure rates have increased. This scenario highlights a need to understand the conditions in which colonies flourish and in which colonies fail. To aid this investigation we present a compartment model of bee population dynamics to explore how food availability and bee death rates interact to determine colony growth and development. Our model uses simple differential equations to represent the transitions of eggs laid by the queen to brood, then hive bees and finally forager bees, and the process of social inhibition that regulates the rate at which hive bees begin to forage. We assume that food availability can influence both the number of brood successfully reared to adulthood and the rate at which bees transition from hive duties to foraging. The model predicts complex interactions between food availability and forager death rates in shaping colony fate. Low death rates and high food availability results in stable bee populations at equilibrium (with population size strongly determined by forager death rate) but consistently increasing food reserves. At higher death rates food stores in a colony settle at a finite equilibrium reflecting the balance of food collection and food use. When forager death rates exceed a critical threshold the colony fails but residual food remains. Our model presents a simple mathematical framework for exploring the interactions of food and forager mortality on colony fate, and provides the mathematical basis for more involved simulation models of hive performance.

Simulation models of the role of genetic variability in social insect task allocation

SummaryA feature of some species of eusocial Hymenoptera is a high level of intra-colonial genetic diversity, and correlated diversity in the level of the stimulus required for individuals to initiate work. Here we explore the effects of intracolonial variability on the responsiveness of colonies to changing needs in task allocation using computer simulation. Our simulations show that colonies comprised of individuals of uniform task threshold are poor at adapting to changing colony needs – that is, they did not allocate the appropriate numbers of workers to tasks. On the other hand, colonies comprised of many groups of differing task threshold adapt quickly and more appropriately to changes in task need. Our simulations suggest that intracolonial genetic variability may be an important component of an efficient task allocation system for some species of social Hymenoptera. We speculate that the benefits of an improved task allocation system may have contributed to the high levels of polyandry and polygyny seen in some of these insects.

A flexible model of foraging by a honey bee colony: the effects of individual behaviour on foraging success.

This paper develops and explores a model of foraging in honey bee colonies. The model may be applied to forage sources with various properties, and to colonies with different foraging-related parameters. In particular, we examine the effect of five foraging-related parameters on the foraging response and consequent nectar intake of a homogeneous colony. The parameters investigated affect different quantities critical to the foraging cycle--visit rate (affected by g), probability of dancing (mpd and bpd), duration of dancing (mcirc), or probability of abandonment (A). We show that one parameter, A, affects nectar intake in a nonlinear way. Further, we show that colonies with a midrange value of any foraging parameter perform better than the average of colonies with high- and low-range values, when profitable sources are available. Together these observations suggest that a heterogeneous colony, in which a range of parameter values are present, may perform better than a homogeneous colony. We modify the model to represent heterogeneous colonies and use it to show that the most important effect of heterogeneous foraging behaviour within the colony is to reduce the variance in the average quantity of nectar collected by heterogeneous colonies.

Clonal diversity in carcinomas: its implications for tumour progression and the contribution made to it by epithelial- mesenchymal transitions

The progression of tumours to malignancy is commonly considered to arise through lineal evolution, a process in which mutations conferring pro-oncogenic cellular phenotypes are acquired by a succession of ever-more dominant clones. However, this model is at odds with the persistent polyclonality observed in many cancers. We propose that an alternative mechanism for tumour progression, called interclonal cooperativity, is likely to play a role at stages of tumour progression when mutations cause microenvironmental changes, such as occur with epithelial-mesenchymal transitions (EMTs). Interclonal cooperativity occurs when cancer cell–cancer cell interactions produce an emergent malignant phenotype from individually non-malignant clones. In interclonal cooperativity, the oncogenic mutations occur in different clones within the tumour that complement each other and cooperate in order to drive progression. This reconciles the accepted genetic and evolutionary basis of cancers with the observed polyclonality in tumours. Here, we provide a conceptual basis for examining the importance of cancer cell–cancer cell interactions to the behaviour of tumours and propose specific mechanisms by which clonal diversity in tumours, including that provided by EMTs, can drive the progression of tumours to malignancy.

Modelling the role of intracolonial genetic diversity on regulation of brood temperature in honey bee (Apis mellifera L.) colonies

Abstract.In polyandrous social insects such as honey bees, a worker’s affinity for a particular task may be genetically infl uenced and so some patrilines may have lower stimulus thresholds for commencing a task than others. We used simulation models to investigate the effects of intracolonial diversity in the task thresholds that stimulate workers to engage in heating and cooling during nest thermoregulation. First, we simulated colonies comprised of one or 15 patrilines that were engaged in heating the brood nest, and observed that single patriline colonies maintained, on average, less stable brood nest temperatures than multiple patriline colonies. Second we simulated colonies with five patrilines that were engaged in cooling their nest, recording the proportions of bees of different patrilines that engaged in nest cooling in response to changing temperatures. Both of our simulations show remarkably similar qualitative patterns to those that we have previously observed empirically. This provides further support for the hypothesis that geneticallybased variability in task thresholds among patrilines within honey bee colonies is an important contributor to the ability of colonies to precisely thermoregulate their nests, and we suggest that diversity is important for optimal expression of a range of other colony-level phenotypes.