A game theoretical model of the evolution of food hoarding: applications to the Paridae

A game against the field is proposed that models the evolution of food-hoarding behavior in a group-living species, like many members of the family Paridae (Aves, Passeriformes). The model predicts that no special retrieval mechanisms (e.g., memory) are necessary for food-hoarding individuals to invade a population of nonhoarders, as long as the winters are very severe. Once food hoarding is established in a population, having smaller groups and separating foraging niches between group members prevent cheaters from benefiting from other individuals' caches. A scenario is proposed for the evolution of hoarding in the Paridae.     

The hippocampus, spatial memory and food hoarding: a puzzle revisited

Behavioural ecology assumes that cognitive traits and their underlying neural substrates are shaped by natural selection in much the same way as morphological traits are, resulting in adaptation to the natural environment of the species concerned. Recently, however, the 'neuroecology' approach of attempting to gain insight into brain structure and function by testing predictions about variation in brain structure based on knowledge of the lifestyle of the animal has been criticized on the grounds that such an adaptationist view cannot provide insight into the underlying mechanisms. Furthermore, the criticism has focussed on attempts to use variation in demand for spatial memory and in hippocampal size as a basis for predicting variation in cognitive abilities. Here, we revisit this critique against the field of so-called 'neuroecology' and argue that using knowledge of the natural history of animals has lead to a better understanding of the interspecific variation in spatial abilities and hippocampal size, and to the generation of novel hypotheses and predictions.     

A game theoretical model of kleptoparasitism with incomplete information

Kleptoparasitism, the stealing of food from one animal by another, is a common natural phenomenon that has been modelled mathematically in a number of ways. The handling process of food items can take some time and the value of such items can vary depending upon how much handling an item has received. Furthermore this information may be known to the handler but not the potential challenger, so there is an asymmetry between the information possessed by the two competitors. We use game-theoretic methods to investigate the consequences of this asymmetry for continuously consumed food items, depending upon various natural parameters. A variety of solutions are found, and there are complex situations where three possible solutions can occur for the same set of parameters. It is also possible to have situations which involve members of the population exhibiting different behaviours from each other. We find that the asymmetry of information often appears to favour the challenger, despite the fact that it possesses less information than the challenged individual. The research was supported by EPSRC grant EP/E043402/1 and NSF 0634182.     

A game theoretical model of deforestation in human-environment relationships

We studied a two-person game regarding deforestation in human-environment relationships. Each landowner manages a single land parcel where the state of land-use is forested, agricultural, or abandoned. The landowner has two strategies available: forest conservation and deforestation. The choice of deforestation provides a high return to the landowner, but it degrades the forest ecosystem services produced on a neighboring land parcel managed by a different landowner. Given spatial interactions between the two landowners, each landowner decides which strategy to choose by comparing the expected discounted utility of each strategy. Expected discounted utility is determined by taking into account the current and future utilities to be received, according to the state transition on the two land parcels. The state transition is described by a Markov chain that incorporates a landowner's choice about whether to deforest and the dynamics of agricultural abandonment and forest regeneration. By considering a stationary distribution of the Markov chain for land-use transitions, we derive explicit conditions for Nash equilibrium. We found that a slow regeneration of forests favors mutual cooperation (forest conservation). As the forest regenerates faster, mutual cooperation transforms to double Nash equilibria (mutual cooperation and mutual defection), and finally mutual defection (deforestation) leads to a unique Nash equilibrium. Two different types of social dilemma emerge in our deforestation game. The stag-hunt dilemma is most likely to occur under an unsustainable resource supply, where forest regenerates extremely slowly but agricultural abandonment happens quite rapidly. In contrast, the prisoner's dilemma is likely under a persistent or circulating supply of resources, where forest regenerates rapidly and agricultural abandonment occurs slowly or rapidly. These results show how humans and the environment mutually shape the dilemma structure in forest management, implying that solutions to dilemmas depend on environmental properties.     

Modelling dominance hierarchy formation as a multi-player game

Animals who live in groups need to divide available resources amongst themselves. This is often achieved by means of a dominance hierarchy, where dominant individuals obtain a larger share of the resources than subordinate individuals. This paper introduces a model of dominance hierarchy formation using a multi-player extension of the classical Hawk-Dove game. Animals play non-independent pairwise games in a Swiss tournament which pairs opponents against those which have performed equally well in the conflict so far, for a fixed number of rounds. Resources are divided according to the number of contests won. The model, and its emergent properties, are discussed in the context of experimental observations.     

Long-term hoarding in the Paridae: a dynamic model

Using stochastic dynamic programming we modeled the hoardingand foraging behavior of tits and chickadees, Pandas, that areresident in the boreal forest at high latitudes. Here autumnshave a rich supply of seeds and temperatures are relativelymild, while winters are cold with short days and a low foodsupply. We assumed that parids have a memory of limited durationand that forgotten seeds accumulate in a bank that adds to thegeneral food supply in the hoarder's territory. Our model predictsthat birds should start "high-intensity" hoarding in early autumn,but not before that. Because of mass-dependent costs the birdswill keep their fat levels low during the autumn. When winterarrives they will carry more body fat, both for the long winternights and to hedge against the large effects of weather variationsin winter. After increasing the fat level at the start of winter,fat should gradually increase even more, to compensate for thediminishing food supply. Most hoarding occurs in autumn as away of building up the supply of long-term stores. Remembered,or short-term caches, may hedge against stochastic events inthe environment. Even though conditions are not beneficial forhoarding in winter, the birds still stored in winter to maintainlarger short and long-term hoards if environmental variationincreased. Almost all time in winter that not was spent foragingwas spent perching, mainly to avoid predation     

The effects of dominance on leadership and energetic gain: a dynamic game between pairs of social foragers

Although social behaviour can bring many benefits to an individual, there are also costs that may be incurred whenever the members of a social group interact. The formation of dominance hierarchies could offer a means of reducing some of the costs of social interaction, but individuals within the hierarchy may end up paying differing costs dependent upon their position within the hierarchy. These differing interaction costs may therefore influence the behaviour of the group, as subordinate individuals may experience very different benefits and costs to dominants when the group is conducting a given behaviour. Here, a state-dependent dynamic game is described which considers a pair of social foragers where there is a set dominance relationship within the pair. The model considers the case where the subordinate member of the pair pays an interference cost when it and the dominant individual conduct specific pairs of behaviours together. The model demonstrates that if the subordinate individual pays these energetic costs when it interacts with the dominant individual, this has effects upon the behaviour of both subordinate and the dominant individuals. Including interaction costs increases the amount of foraging behaviour both individuals conduct, with the behaviour of the pair being driven by the subordinate individual. The subordinate will tend to be the lighter individual for longer periods of time when interaction costs are imposed. This supports earlier suggestions that lighter individuals should act as the decision-maker within the pair, giving leadership-like behaviours that are based upon energetic state. Pre-existing properties of individuals such as their dominance will be less important for determining which individual makes the decisions for the pair. This suggests that, even with strict behavioural hierarchies, identifying which individual is the dominant one is not sufficient for identifying which one is the leader.     

Neural and hormonal control of food hoarding

Many animals hoard food, including humans, but despite its pervasiveness, little is known about the physiological mechanisms underlying this appetitive behavior. We summarize studies of food hoarding in humans and rodents with an emphasis on mechanistic laboratory studies of species where this behavior importantly impacts their energy balance (hamsters), but include laboratory rat studies although their wild counterparts do not hoard food. The photoperiod and cold can affect food hoarding, but food availability is the most significant environmental factor affecting food hoarding. Food-deprived/restricted hamsters and humans exhibit large increases in food hoarding compared with their fed counterparts, both doing so without overeating. Some of the peripheral and central peptides involved in food intake also affect food hoarding, although many have not been tested. Ad libitum-fed hamsters given systemic injections of ghrelin, the peripheral orexigenic hormone that increases with fasting, mimics food deprivation-induced increases in food hoarding. Neuropeptide Y or agouti-related protein, brain peptides stimulated by ghrelin, given centrally to ad libitum-fed hamsters, duplicates the early and prolonged postfood deprivation increases in food hoarding, whereas central melanocortin receptor agonism tends to inhibit food deprivation and ghrelin stimulation of hoarding. Central or peripheral leptin injection or peripheral cholecystokinin-33, known satiety peptides, inhibit food hoarding. Food hoarding markedly increases with pregnancy and lactation. Because fasted and/or obese humans hoard more food in general, and more high-density/high-fat foods specifically, than nonfasted and/or nonobese humans, understanding the mechanisms underlying food hoarding could provide another target for behavioral/pharmacological approaches to curb obesity.     

A theoretical model of the effect of continuum damage on a bone adaptation model

Throughout life, bone is continuously turning over by the well-regulated processes of bone formation and resorption. Everyday activities damage bone, and this damage is normally repaired in a continuous remodelling process. When an imbalance in this remodelling process occurs, bones may become more susceptible to fracture. This paper is devoted to a theoretical modelling of the competition between damage and internal remodelling in bones. The general theory of adaptive damaged-elastic materials proposed here as a model for the physiological process of damaged-bone remodelling follows the general framework of continuum thermodynamics where new damaged-bone remodelling law and associated thermodynamical restrictions are stated, and specialized to the case of small strain in isothermal processes. An attempt is also made to derive: (a) the damage force (adaptive damage energy release rate ) which controls the microcracks propagation and arrest, and (b) the damage rule by introducing damage thresholds and loading/unloading conditions.     

Fat pad-specific effects of lipectomy on foraging, food hoarding, and food intake

Unlike most species, after food deprivation, Siberian hamsters increase foraging and food hoarding, two appetitive ingestive behaviors, but not food intake, a consummatory ingestive behavior. We previously demonstrated (Wood AD, Bartness TJ, Am J Physiol Regul Integr Comp Physiol 272: R783-R792, 1997) that increases in food hoarding are triggered by directly decreasing body fat levels through partial surgical lipectomy; however, we did not test if lipectomy affected foraging, nor if the magnitude of the lipid deficit affected food hoard size. Therefore, we tested whether varying the size of the lipectomy-induced lipid deficit and/or foraging effort affected foraging, food hoarding, or food intake. This was accomplished by housing adult male Siberian hamsters in a foraging/hoarding system and removing (x) both epididymal white adipose tissue (EWATx) pads, both inguinal white adipose tissue (IWATx) pads, or both EWAT and IWAT pads (EWATx + IWATx) and measuring foraging, food hoarding, and food intake for 12 wk. The lipectomy-induced lipid deficit triggered different patterns of white adipose tissue mass compensation that varied with foraging effort. Foraging for food (10 wheel revolutions to earn a food pellet) abolished the EWATx-induced compensation in IWAT pad mass. The magnitude of the lipid deficit did not engender a proportional change in any of the appetitive or consummatory ingestive behaviors. EWATx caused the greatest increase in food hoarding compared with IWATx or EWATx + IWATx, when animals were required to forage for their food. Collectively, it appears that the magnitude of a lipid deficit does not affect appetitive or consummatory behaviors; rather, when energy (foraging) demands are increased, loss of specific (gonadal) fat pads can preferentially stimulate increases in food hoarding.     

Asynchronous snowdrift game with synergistic effect as a model of cooperation

The snowdrift (or chicken) game emerges as a new paradigm inthe study of nonkin cooperation in animals. Many situations,for example, cooperative hunting, group foraging, territorialdefense, predator watching, or parental care, can be adequatelydescribed as a snowdrift game. In this paper, we investigatethe asynchronous version of the game in which, contrary to therather unrealistic assumption of simultaneous moves, one ofthe players acts first and the other responds by knowing itsdecision. Players are assigned to be first or second moversrandomly and with the same probability. We found that both asynergistic effect of cooperation (i.e., cooperative effortis better than the sum of the individual efforts) and populationstructure (low dispersal, spatial confinement, or group formation)are crucial for mutual cooperation to emerge. Otherwise, onlyone of the players will carry the burden of cooperation.     

Mating strategies in primates: a game theoretical approach to infanticide

Infanticide by newly immigrated or newly dominant males is reported among a variety of taxa, such as birds, rodents, carnivores and primates. Here we present a game theoretical model to explain the presence and prevalence of infanticide in primate groups. We have formulated a three-player game involving two males and one female and show that the strategies of infanticide on the males' part and polyandrous mating on the females' part emerge as Nash equilibria that are stable under certain conditions. Moreover, we have identified all the Nash equilibria of the game and arranged them in a novel hierarchical scheme. Only in the subspace spanned by the males are the Nash equilibria found to be strict, and hence evolutionarily stable. We have therefore proposed a selection mechanism informed by adaptive dynamics to permit the females to transition to, and remain in, optimal equilibria after successive generations. Our model concludes that polyandrous mating by females is an optimal strategy for the females that minimizes infanticide and that infanticide confers advantage to the males only in certain regions of parameter space. We have shown that infanticide occurs during turbulent changes accompanying male immigration into the group. For changes in the dominance hierarchy within the group, we have shown that infanticide occurs only in primate groups where the chance for the killer to sire the next infant is high. These conclusions are confirmed by observations in the wild. This model thus has enabled us to pinpoint the fundamental processes behind the reproductive decisions of the players involved, which was not possible using earlier theoretical studies.     

Dissociating ocular dominance column development and ocular dominance plasticity: a neurotrophic model

 Recent experimental data indicate that both neurotrophic factors (NTFs) and intracortical inhibitory circuitry are implicated in the development and plasticity of ocular dominance columns. We extend a neurotrophic model of developmental synaptic plasticity, which previously failed to account correctly for the differences between monocular deprivation and binocular deprivation, and show that the inclusion of lateral cortical inhibition is indeed necessary in understanding the effects of visual deprivation in the model. In particular, we argue that monocular deprivation causes a differential shift in the balance between inhibition and excitation in cortical columns, down-regulating NTFs in deprived-eye columns and up-regulating NTFs in undeprived-eye columns; during binocular deprivation, however, no such shift occurs. We thus postulate that the response to visual deprivation is at the level of the cortical circuit, while the mechanisms of afferent segregation are at the molecular or cellular level. Such a dissociation is supported by recent experimental work challenging the assumption that columnar organisation develops in an activity-dependent, competitive fashion. Our extended model also questions recent attempts to distinguish between heterosynaptic and homosynaptic models of synaptic plasticity. Received: 17 April 2001 / Accepted in revised form: 7 November 2001     

Fighting for food: a dynamic version of the Hawk-Dove game

Summary The Hawk-Dove game (Maynard Smith, 1982) has been used to analyse conflicts over resources such as food. At the evolutionarily stable strategy (ESS), either a proportionp* of animals always play Hawk, or each animal has a probabilityp* of playing Hawk. We modify the standard Hawk-Dove game to include a state variable,x, that represents the animal's level of energy reserves. A strategy is now a rule for choosing an action as a function ofx and time of day. We consider a non-reproductive period and adopt the criterion of minimizing mortality over this period. We find the ESS, which has the form play Hawk if reserves are belowc* (t) at timet, otherwise play Dove. This ESS is very different from the ESS in the standard Hawk-Dove game. It is a pure ESS that depends on the animal's state and on time. Furthermore, it is characterized by the strong condition that any single mutant that does not adopt the ESS suffers a reduction in fitness. The standard Hawk-Dove game assumes pay-offs that are related to fitness; our approach starts from a definition of fitness and derives the pay-offs in the process of finding the ESS. When the environment becomes worse (e.g. food becomes less reliable or energy expenditure increases) the ESS changes in such a way as to increase the proportion of animals that will play Hawk.     

The effect of leaf-level spatial variability in photosynthetic capacity on biochemical parameter estimates using the Farquhar model: a theoretical analysis

Application of the widely used Farquhar model of photosynthesis in interpretation of gas exchange data assumes that photosynthetic properties are homogeneous throughout the leaf. Previous studies showed that heterogeneity in stomatal conductance (g_s) across a leaf could affect the shape of the measured leaf photosynthetic CO₂ uptake rate (A) versus intercellular CO₂ concentration (C_i) response curve and, in turn, estimation of the critical biochemical parameters of this model. These are the maximum rates of carboxylation (V_c,max), whole-chain electron transport (J_max), and triose-P utilization (V_TPU). The effects of spatial variation in V_c,max, J_max, and V_TPU on estimation of leaf averages of these parameters from A-C_i curves measured on a whole leaf have not been investigated. A mathematical model incorporating defined degrees of spatial variability in V_c,max and J_max was constructed. One hundred and ten theoretical leaves were simulated, each with the same average V_c,max and J_max, but different coefficients of variation of the mean (CV_VJ) and varying correlation between V_c,max and J_max (Ω). Additionally, the interaction of variation in V_c,max and J_max with heterogeneity in V_TPU, g_s, and light gradients within the leaf was also investigated. Transition from V_c,max- to J_max-limited photosynthesis in the A-C_i curve was smooth in the most heterogeneous leaves, in contrast to a distinct inflection in the absence of heterogeneity. Spatial variability had little effect on the accuracy of estimation of V_c,max and J_max from A-C_i curves when the two varied in concert (Ω = 1.0), but resulted in underestimation of both parameters when they varied independently (up to 12.5% in V_c,max and 17.7% in J_max at CV_VJ = 50%; Ω = 0.3). Heterogeneity in V_TPU also significantly affected parameter estimates, but effects of heterogeneity in g_s or light gradients were comparatively small. If V_c,max and J_max derived from such heterogeneous leaves are used in models to project leaf photosynthesis, actual A is overestimated by up to 12% at the transition between V_c,max- and J_max-limited photosynthesis. This could have implications for both crop production and Earth system models, including projections of the effects of atmospheric change.     

Topography and ocular dominance: a model exploring positive correlations

The map from eye to brain in vertebrates is topographic, i.e. neighbouring points in the eye map to neighbouring points in the brain. In addition, when two eyes innervate the same target structure, the two sets of fibres segregate to form ocular dominance stripes. Experimental evidence from the frog and goldfish suggests that these two phenomena may be subserved by the same mechanisms. We present a computational model that addresses the formation of both topography and ocular dominance. The model is based on a form of competitive learning with subtractive enforcement of a weight normalization rule. Inputs to the model are distributed patterns of activity presented simultaneously in both eyes. An important aspect of this model is that ocular dominance segregation can occur when the two eyes are positively correlated, whereas previous models have tended to assume zero or negative correlations between the eyes. This allows investigation of the dependence of the pattern of stripes on the degree of correlation between the eyes: we find that increasing correlation leads to narrower stripes. Experiments are suggested to test this prediction.     

Effects of foraging effort on body fat and food hoarding in Siberian hamsters

Food hoard size varies inversely with body fat levels in Siberian hamsters. If food hoarding only increases when body fat decreases, then hamsters foraging for their food should only increase food hoarding when foraging efforts decrease body fat (lipostatic hypothesis); however, if food hoarding increases whenever there is an energy flux away from fat storage, then it should increase regardless of significant body fat decreases (metabolic hypothesis). Female Siberian hamsters (Phodopus sungorus) earned food pellets after completion of a programmed number of wheel revolutions (Immobilized Wheel [free access to food], Free Wheel [wheel active, free food], and 10, 50, 100, and 200 revolutions/pellet). Hamsters were killed after 19 days and inguinal, retroperitoneal, and parametrial white adipose tissue (WAT) pads (IWAT, RWAT, and PWAT, respectively) were harvested and carcass composition determined. Food hoard size increased fourfold with the availability of running wheels alone (Free Wheel), increased threefold with low foraging levels (10 and 50 revolutions/pellet), but was nearly abolished at the highest foraging level (200 revolutions/pellet). Surplus food (earned, not eaten or hoarded) was significantly greatest at the lowest level of foraging. As foraging effort increased, PWAT mass decreased the most (<10 revolutions/pellet), while RWAT and IWAT mass only were decreased at the highest foraging effort. Carcass lipid content only was significantly decreased at the highest foraging effort, yet food hoarding was nearly abolished at that level. Collectively, these results demonstrate that body fat levels and food hoarding can be uncoupled with increases in foraging effort. J. Exp. Zool. 289:162-171, 2001.