James Sneyd

Collective decision-making in honey bees: how colonies choose among nectar sources

SummaryA honey bee colony can skillfully choose among nectar sources. It will selectively exploit the most profitable source in an array and will rapidly shift its foraging efforts following changes in the array. How does this colony-level ability emerge from the behavior of individual bees? The answer lies in understanding how bees modulate their colonys rates of recruitment and abandonment for nectar sources in accordance with the profitability of each source. A forager modulates its behavior in relation to nectar source profitability: as profitability increases, the tempo of foraging increases, the intensity of dancing increases, and the probability of abandoning the source decreases. How does a forager assess the profitability of its nectar source? Bees accomplish this without making comparisons among nectar sources. Neither do the foragers compare different nectar sources to determine the relative profitability of any one source, nor do the food storers compare different nectar loads and indicate the relative profitability of each load to the foragers. Instead, each forager knows only about its particular nectar source and independently calculates the absolute profitability of its source. Even though each of a colonys foragers operates with extremely limited information about the colonys food sources, together they will generate a coherent colonylevel response to different food sources in which better ones are heavily exploited and poorer ones are abandoned. This is shown by a computer simulation of nectar-source selection by a colony in which foragers behave as described above. Nectar-source selection by honey bee colonies is a process of natural selection among alternative nectar sources as foragers from more profitable sources “survive” (continue visiting their source) longer and “reproduce” (recruit other foragers) better than do foragers from less profitable sources. Hence this colonial decision-making is based on decentralized control. We suggest that honey bee colonies possess decentralized decision-making because it combines effectiveness with simplicity of communication and computation within a colony.

A single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis oocyte

We construct a minimal model of cytosolic free Ca2+ oscillations based on Ca2+ release via the inositol 1,4,5-trisphosphate (IP3) receptor/Ca2+ channel (IP3R) of a single intracellular Ca2+ pool. The model relies on experimental evidence that the cytosolic free calcium concentration ([Ca2+]c) modulates the IP3R in a biphasic manner, with Ca2+ release inhibited by low and high [Ca2+]c and facilitated by intermediate [Ca2+]c, and that channel inactivation occurs on a slower time scale than activation. The model produces [Ca2+]c oscillations at constant [IP3] and reproduces a number of crucial experiments. The two-dimensional spatial model with IP3 dynamics, cytosolic diffusion of IP3 (Dp = 300 microns 2 s-1), and cytosolic diffusion of Ca2+ (Dc = 20 microns 2 s-1) produces circular, planar, and spiral waves of Ca2+ with speeds of 7-15 microns.s-1, which annihilate upon collision. Increasing extracellular [Ca2+] influx increases wave speed and baseline [Ca2+]c. A [Ca2+]c-dependent Ca2+ diffusion coefficient does not alter the qualitative behavior of the model. An important model prediction is that channel inactivation must occur on a slower time scale than activation in order for waves to propagate. The model serves to capture the essential macroscopic mechanisms that are involved in the production of intracellular Ca2+ oscillations and traveling waves in the Xenopus laevis oocyte.

A model of collective nectar source selection by honey bees: Self-organization through simple rules

The honey bee colony chooses among different nectar sources available in the field, selectively foraging from those which are most profitable. We present a model that describes the colonys decision-making process. The model consists of a system of non-linear differential equations describing the activity of the foraging bees. Parameter estimates are based on previously published data. Numerical solutions of the equations agree closely with experimental observations. Selective exploitation of the most profitable nectar sources occurs through an autocatalytic, self-organizing process.

A mathematical model of self-organized pattern formation on the combs of honeybee colonies.

We present a mathematical model that generates the characteristic concentric pattern of brood, pollen and honey which develops on the combs of a honeybee colony. Parameter estimates are derived from experimental observations and previously published data. Numerical solutions of the model equations exhibit patterns similar to those observed in honeybee colonies. Our model demonstrates how a colony-level pattern arises from the dynamic interactions of many bees using simple behavioral rules based on local cues. Through a self-organizing process, a consistent, global pattern emerges on an initially homogeneous comb.

Calcium wave propagation by calcium-induced calcium release: an unusual excitable system

We discuss in detail the behaviour of a model, proposed by Goldbeter et al. (1990. Proc. natn. Acad. Sci. 87, 1461-1465), for intracellular calcium wave propagation by calcium-induced calcium release, focusing our attention on excitability and the propagation of waves in one spatial dimension. The model with no diffusion behaves like a generic excitable system, and threshold behaviour, excitability and oscillations can be understood within this general framework. However, when diffusion is included, the model no longer behaves like a generic excitable system; the fast and slow variables are not distinct and previous results on excitable systems do not necessarily apply. We consider a piecewise linear simplification of the model, and construct travelling pulse and periodic plane wave solutions to the simplified model. The analogous behaviour in the full model is studied numerically. Goldbeters model for calcium-induced calcium release is an excitable system of a type not previously studied in detail.

Curvature dependence of a model for calcium wave propagation

Abstract The propagation of a two-dimensional wave front in an excitable medium is dependent on the curvature of the front; current theories of excitable reaction-diffusion models predict that, when reaction is much faster than diffusion, the normal wave speed (N) is approximately related to the curvature of the wave front (κ), the plane wave speed (c), and the diffusion coefficient of the propagator variable (D), by the “eikonal” equation, N = c - Dκ. We show that a simple model for intracellular calcium (Ca2+) wave propagation does not obey the eikonal equation, and postulate an alternative curvature equation that is dependent on the parameter values used in the model. This new curvature relation is confirmed by numerical simulations. We raise the possibility that different models for Ca2+ wave propagation will have qualitatively different spiral wave patterns, providing a new way of distinguishing between proposed models. The theory developed here also necessitates a reconsideration of methods previously used to measure the intracellular diffusion coefficient of Ca2+.

On a simplified model for pattern formation in honey bee colonies

We present a simplified version of a previously presented model (Camazine et al. (1990)) that generates the characteristic pattern of honey, pollen and brood which develops on combs in honey bee colonies. We demonstrate that the formation of a band of pollen surrounding the brood area is dependent on the assumed form of the honey and pollen removal terms, and that a significant pollen band arises as the parameter controlling the rate of pollen input passes through a bifurcation value. The persistence of the pollen band after a temporary increase in pollen input can be predicted from the model. We also determine conditions on the parameters which ensure the accumulation of honey in the periphery and demonstrate that, although there is an important qualitative difference between the simplified and complete models, an analysis of the simplified version helps us understand many biological aspects of the more complex complete model.