Patch leaving strategies and superparasitism: an asymmetric generalized war of attrition

When several competitors deplete a patch, it can be advantageous for each of them to stay provided that others leave, whereas, on the other hand, staying longer decreases the expected payoff for everyone. This situation can be considered as a generalized war of attrition. Previous studies have shown that optimal patch leaving strategies become stochastic and the expected leaving time is much larger than predicted by the marginal value theorem when competitors interfere. The possibility of superparasitism, as occurs for example in parasitoids, induces such interference. In addition, it gives several complications. First, the payoff of females that have left the patch is affected by the ovipositions of the remaining individuals. Second, differences in the arrival time of females cause payoff-relevant asymmetries, since females that arrived early on have parasitized more hosts in a patch at the moment superparasitism starts than those that arrived later. We show that this can be modelled as an asymmetric generalized war of attrition, and derive global characteristics of the ESS for simultaneous decisions on when to start superparasitism and when to leave a patch.     

The asymmetric war of attrition

The paper, which has an informal discussion at the end, provides a game theoretical analysis of the asymmetric “war of attrition” with incomplete information. This is a contest where animals adopt different roles like “owner” and “intruder” in a territorial conflict, and where the winner is the individual prepared to persist longer. The term incomplete information refers to mistakes in the identification of roles. The idea by Parker & Rubenstein (1981) is mathematically worked out and confirmed that there exists only a single evolutionarily stable strategy (ESS) for the model with a continuum of possible levels of persistence and no discontinuities in the increase of cost during attrition. The ESS prescribes to settle the conflict according to “who has more to gain or less to pay for persistence”. The only evolutionarily stable convention is thus to give the player access to the resource who has the role which is favoured with respect to payoffs. By contrast, it was shown earlier (Hammerstein, 1981) for various asymmetric versions of the “Hawks-Doves” model that an ESS can exist which appears paradoxical with respect to payoffs. The nature of this contrast is further analyzed by introducing elements of discreteness in the asymmetric war of attrition. It turns out that some conditions must be satisfied in order to have the possibility of an alternative ESS which is not of the above simple commonsense type. First, a decision to persist (or escalate) further in a contest must typically commit a contestant to go on fighting for a full “round”, before he can give up without danger. Second, such a “discontinuity” must occur at a level of persistence where the contest is still cheap, and, finally, errors in the identification of roles must be rare.     

The ESS in an asymmetric generalized war of attrition with mistakes in role perception

We derive the ESS for the generalized asymmetric war of attrition, where payoffs to contestants may vary in time and may depend on some characteristic, called the "role" of an individual. We use the same approach as Hammerstein & Parker (1982), who examined an asymmetric war of attrition. We consider two roles, A and B. Role A is assumed to be favoured with respect to payoffs. It is assumed that there is always a true asymmetry, so in each contest one individual has role A and the other has role B. It is assumed that roles are assigned to contestants at random and that they can make mistakes in role perception. It is shown that, under certain assumptions about shapes of payoff functions and probabilities of making mistakes, there is an ESS which can be characterized by two probability distributions with non-overlapping support. Individuals who perceive their role as A should choose larger persistence times. This ESS structure is similar to that in the asymmetric war of attrition. In that model, the resource values and the cost rates are constant. We consider situations where all these values may change in time and where rewards and costs may be equal after some finite time. Such shapes of payoff functions arise naturally in competitive patch depletion (Sjerps & Haccou, 1994a,b). As a result, the probability density functions that specify the conditional strategies are no longer necessarily negative exponentials (as in the war of attrition), but may have very different shapes. Furthermore, under some conditions there is a maximum persistence time, at which there can be an atom of probability. We give explicit expressions as well as numerical approximations for the ESS.     

The war of attrition with random rewards

This paper describes a type of fitness indicating trait which is particularly likely to be exaggerated because of sexual selection on fitness-faking modifier genes, describes the selection process which tends to exaggerate such traits, and indicates by citing examples from different taxa the wide range of traits which can be explained as resulting from this type of selection.     

Evolution of kleptoparasitism as a war of attrition

Previous models of kleptoparasitism (resource stealing) assume that contests over resource items are of fixed duration. Here we suggest that such contests will often be well represented as a war of attrition, with the winner being the individual who is prepared to contest for the longer time. Given that time spent in contests cannot be used to search for other resource items, we provide an analytical expression for the evolutionarily stable distribution of contest times. This can be used to investigate the circumstances under which we would expect kleptoparasitism to evolve. In particular, we focus on situations where searching for conspecifics to kleptoparasitize can only be achieved at a cost of reduced resource discovery by other means; under such circumstances we show that kleptoparasitism is not evolutionarily stable.     

Strong evolutionary equilibrium and the war of attrition

In developing the concept of an evolutionarily stable strategy, Maynard Smith proposed formal conditions for stability. These conditions have since been shown to be neither necessary nor sufficient for evolutionary stability in finite populations. This paper provides a strong stability condition which is sensitive to the population size. It is then demonstrated that in the war of attrition with uncertain rewards there is a unique “strong evolutionary equilibrium” strategy. As the population becomes large this is shown to approach the solution strategy proposed by Bishop, Cannings and Maynard Smith.The analysis is then extended to wars of attrition between different populations. It is concluded that for such contests there is a whole family of potential strong evolutionary equilibria.     

Neighbours,strangers, and the asymmetric war of attrition

The literature showing that territorial residents generally respond more intensely to an intrusion by a stranger than by a known neighbour is reviewed. The functional basis of this discrimination has not been seriously considered in this extensive literature, and it is shown here how the asymmetric war of attrition can explain why neighbours settle with relatively little aggression. In the asymmetric war-of-attrition model the degree of escalation observed in a territorial contest depends on the familiarity of the contestants with each other. Predictions of this model about neighbour-stranger contests are supported by data in the literature.     

On the war of attrition and other games among kin

Evolutionarily stable strategies or ESSs of games among kin have been calculated in the literature by both personal-fitness and inclusive-fitness methods. These methods were compared by Hines and Maynard Smith (1979) for games with bilinear payoffs. Although Hines and Maynard Smith regarded the first method as correct, they regarded the second method as useful because the inclusive-fitness conditions for an ESS gave necessary conditions for a personal-fitness ESS in the class of games they considered. In general, however, satisfying the inclusive-fitness conditions is neither necessary nor sufficient for satisfying the personal-fitness conditions, although the two methods may often yield identical ESSs. This result is established by reformulating the classic war-of-attrition model to allow variation in energy reserves, assumed to have a Gamma distribution. For this game, the two methods may disagree for intermediate values of relatedness. By the correct method, if the coefficient of variation in energy reserves is sufficiently high, then the game has a unique ESS in pure strategies at which populations with higher coefficients of variation or relatedness display for shorter times. Unrelated contestants are prepared to expend at least half of their reserves. For populations with lower variation coefficients, the ESS exists only if the cost of displaying per unit time is low compared to the rate at which remaining reserves translate into expected future reproductive success for the victor. The critical variation coefficient, below which the ESS exists regardless of cost, decreases from 0.52 to 0 as the coefficient of relatedness increases from 0 to 1. Although there is no assessment, contests are always won by the animal with greater energy reserves in a population at the ESS.     

Diffusion with attrition

This article treats the problem of the sharp front observed when a diffusing substance interacts irreversibly with binding sites within the medium. The model consists of two simultaneous partial differential equations that are nonlinear and cannot be solved in closed form. The parameters are the diffusion coefficient D in the direction under consideration (x), the interaction constant k, the binding-site concentration μ and the boundary concentration of the diffusing ion c ₀. Our aim is to develop methods to enable the estimation of these parameters from the experimental data. An analytical solution for the case k → ∞, as found by others, is given first and then a finite element analysis package is used to obtain numerical solutions for the general case. Graphs are presented to illustrate the effects of the various parameters. Simple graphical procedures are described to compute μ and c ₀. The position of the advancing front ξ then provides, together with μ, a way to estimate D. A mathematical identity relating D and x and a second one involving D, k and t help to reduce the complexity of the problem. A new, measurable quantity S(t) is defined as where f is the total concentration (free + bound) of the diffusing ion at time t, and detailed plots are furnished that permit the computation of k directly from S(t), μ and D. The accuracy with which such methods can be expected to determine the various parameters of the model is considered at some length. Finally, in a concluding section, we simulate typical experimental data, examine the validity of our methods, and see how their accuracy is affected by controlled amounts of various kinds of noise.     

Lignocellulose pretreatment: A comparison of wet and dry ball attrition

Summary A comparison of wet and dry ball attrition of various lignocellulosic substrates indicates that terminal crystallinity index following enzymatic hydrolysis usually decreases after wet attrition and increases after dry attrition. Particle size was reduced to a greater extent in dry attrition in accordance with increased friability. Conversions favored neither wet nor dry pretreatment, indicating substrate specific requirements.     

Telomere attrition due to infection

Background

Telomeres–the terminal caps of chromosomes–become shorter as individuals age, and there is much interest in determining what causes telomere attrition since this process may play a role in biological aging. The leading hypothesis is that telomere attrition is due to inflammation, exposure to infectious agents, and other types of oxidative stress, which damage telomeres and impair their repair mechanisms. Several lines of evidence support this hypothesis, including observational findings that people exposed to infectious diseases have shorter telomeres. Experimental tests are still needed, however, to distinguish whether infectious diseases actually cause telomere attrition or whether telomere attrition increases susceptibility to infection. Experiments are also needed to determine whether telomere erosion reduces longevity.

Methodology/Principal Findings

We experimentally tested whether repeated exposure to an infectious agent, Salmonella enterica, causes telomere attrition in wild-derived house mice (Mus musculus musculus). We repeatedly infected mice with a genetically diverse cocktail of five different S. enterica strains over seven months, and compared changes in telomere length with sham-infected sibling controls. We measured changes in telomere length of white blood cells (WBC) after five infections using a real-time PCR method. Our results show that repeated Salmonella infections cause telomere attrition in WBCs, and particularly for males, which appeared less disease resistant than females. Interestingly, we also found that individuals having long WBC telomeres at early age were relatively disease resistant during later life. Finally, we found evidence that more rapid telomere attrition increases mortality risk, although this trend was not significant.

Conclusions/Significance

Our results indicate that infectious diseases can cause telomere attrition, and support the idea that telomere length could provide a molecular biomarker for assessing exposure and ability to cope with infectious diseases.     

A generalized taxon concept

A generalized taxon concept (GTC) is proposed with a method for revealing and ranking difficult taxa at any level in the taxonomic hierarchy. The method is based on cluster quality, denned jointly by die compactness of a cluster's contents and its isolation from its informational neighbours. The cluster contents are individuals in die case of species and at higher levels, taxa from the rank below. A standard, quality threshold value is obtained from clustering accepted taxa in the informational region. If the quality value of a problem cluster lies at or above the threshold it is accepted as a taxon and ranked with others at the current level. If it lies below, and is likely to be informationally useful, it may be accepted as a sub-taxon such as a subgenus or subfamily. Provision is made for coarsely scored data. The clustering is mainly based on homogeneity, where possible with a rapid, fuzzily cladistic de-weighting of symplesiomorphies by self-graded factors. The strengms of inter-item reactions such as breeding and DNA-DNA hybridization may also be used. The method is agglomerative so that it can rapidly reveal polythetic groups which may be riddled with exceptional property states caused by long exposure to natural selective forces. All this fits the evolutionary oudook of the GTC, which sees taxa as fuzzy clusters of populations and lineages sharing much of a genetic memory, moulded by a unique history of evolution and extinction. Practical problems of memods based on mis and other taxon concepts are briefly compared. The GTC's approach offers important refinements that could be valuable in helping to speed up urgent surveys of biodiversity, especially in the moist tropics.     

A generalized sense of number

Much evidence has accumulated to suggest that many animals, including young human infants, possess an abstract sense of approximate quantity, a number sense. Most research has concentrated on apparent numerosity of spatial arrays of dots or other objects, but a truly abstract sense of number should be capable of encoding the numerosity of any set of discrete elements, however displayed and in whatever sensory modality. Here, we use the psychophysical technique of adaptation to study the sense of number for serially presented items. We show that numerosity of both auditory and visual sequences is greatly affected by prior adaptation to slow or rapid sequences of events. The adaptation to visual stimuli was spatially selective (in external, not retinal coordinates), pointing to a sensory rather than cognitive process. However, adaptation generalized across modalities, from auditory to visual and vice versa. Adaptation also generalized across formats: adapting to sequential streams of flashes affected the perceived numerosity of spatial arrays. All these results point to a perceptual system that transcends vision and audition to encode an abstract sense of number in space and in time.