Comparing alternative models to empirical data: cognitive models of western scrub-jay foraging behavior

Animals often select one item from a set of candidates, as when choosing a foraging site or mate, and are expected to possess accurate and efficient rules for acquiring information and making decisions. Little is known, however, about the decision rules animals use. We compare patterns of information sampling by western scrub-jays (Aphelocoma californica) when choosing a nut with three decision rules: best of n (BN), flexible threshold (FT), and comparative Bayes (CB). First, we use a null hypothesis testing approach and find that the CB decision rule, in which individuals use past experiences to make nonrandom assessment and choice decisions, produces patterns of behavior that more closely correspond to observed patterns of nut sampling in scrub-jays than the other two rules. This approach does not allow us to quantify how much better CB is at predicting scrub-jay behavior than the other decision rules. Second, we use a model selection approach that uses Akaike Information Criteria to quantify how well alternative models approximate observed data. We find that the CB rule is much more likely to produce the observed patterns of scrub-jay behavior than the other rules. This result provides some of the best empirical evidence of the use of Bayesian information updating by a nonhuman animal.     

A Comparative Bayes tactic for mate assessment and choice

Models of mate choice tactics have assumed that females randomlyencounter males when collecting information and the informationis perfect. Empirical observations of four bird species showthat females selectively visit males and repeat visits to malesbefore mating. This suggests that the assumptions of previousmodels have been too restrictive. An alternative model of informationgathering and mate choice, which relaxes the assumptions ofrandom encounters and perfect information, is presented. Inthis Comparative Bayes model, the decision of when and fromwhom to collect information is made using Bayesian estimatesof each male's quality. Predictions from the model are that:(1) the occurrence of mate assessment will increase as initialuncertainty about the quality of males increases, as the costof gathering information decreases, and as the signal perceivedby the female becomes a better representation of males' actualqualities; (2) the occurrence of repeat visits to males willbe highest when signals from males are of medium reliability;and (3) the decision of which male to assess will depend onthe estimated qualities of males, prior certainty about eachmale's quality, the reliability of each male's signal, and thecosts of assessment. Simulations compare the fitness outcomesof the Comparative Bayes tactic to other mate choice tactics.The fitness from the Comparative Bayes tactic is significantlyhigher than from the fixed threshold tactic and than from thebest-of-n tactic when the cost of assessment is low. [BehavEcol 7: 451–460 (1996)]     

Sequential search and the influence of male quality on female mating decisions

 The patterns of phenotypic association between mated males and females depend on the decision rules that individuals employ during search for a mate. We generalize the sequential search rule and examine how the shape of the function that relates a male character to the benefit of a mating decision influences the threshold value of the male trait that induces females to terminate search. If the fitness function is linear the optimal threshold value of a male character increases with the slope of the function. The phenotypic threshold criterion declines, all else being equal, if the fitness function is made more concave (or less convex) by an increase of the risk of the function. The expression of the trait in females has no effect on the optimal threshold value of a male character if the fitness function is linear and phenotypic values combine additively to influence the benefit of a mating decision; the phenotypic threshold criterion is ubiquitous among females. A convex fitness function induces females with high trait values to adopt a relatively high phenotypic threshold criterion, whereas a concave fitness function induces such females to adopt a low threshold value for the male trait. Thus, linear, convex and concave fitness functions effect random, assortative and disassortative combinations of phenotypes among mated individuals, respectively. Changes of female search behavior induced by changes of the distribution of a male character similarly depend on the shape of the fitness function. A variance-preserving increase of male trait values produces a relatively small increase of the threshold criterion for the male character if the fitness function is concave, relative to conditions in which the fitness function is either linear or convex. Our results suggest that a sequential search rule can in principle induce the kinds of mating patterns observed in nature and that the phenotypic association between mated individuals is likely to depend on how a male character translates into fitness, the distribution of the trait among males and attributes of searching females. Received: 20 September 1997 / Revised version: 13 August 1998     

Threshold assessment,categorical perception,and the evolution of reliable signaling

Animals often use assessment signals to communicate information about their quality to a variety of receivers, including potential mates, competitors, and predators. But what maintains reliable signaling and prevents signalers from signaling a better quality than they actually have? Previous work has shown that reliable signaling can be maintained if signalers pay fitness costs for signaling at different intensities and these costs are greater for lower quality individuals than higher quality ones. Models supporting this idea typically assume that continuous variation in signal intensity is perceived as such by receivers. In many organisms, however, receivers have threshold responses to signals, in which they respond to a signal if it is above a threshold value and do not respond if the signal is below the threshold value. Here, we use both analytical and individual-based models to investigate how such threshold responses affect the reliability of assessment signals. We show that reliable signaling systems can break down when receivers have an invariant threshold response, but reliable signaling can be rescued if there is variation among receivers in the location of their threshold boundary. Our models provide an important step toward understanding signal evolution when receivers have threshold responses to continuous signal variation.     

Choosing goals, not rules: deciding among rule-based action plans

In natural situations, movements are often directed toward locations different from that of the evoking sensory stimulus. Movement goals must then be inferred from the sensory cue based on rules. When there is uncertainty about the rule that applies for a given cue, planning a movement involves both choosing the relevant rule and computing the movement goal based on that rule. Under these conditions, it is not clear whether primates compute multiple movement goals based on all possible rules before choosing an action, or whether they first choose a rule and then only represent the movement goal associated with that rule. Supporting the former hypothesis, we show that neurons in the frontoparietal reach areas of monkeys simultaneously represent two different rule-based movement goals, which are biased by the monkeys' choice preferences. Apparently, primates choose between multiple behavioral options by weighing against each other the movement goals associated with each option.     

A rule is not a rule if it changes from case to case (a reply to Marshall's comment)

This is a reply to “Queller's rule ok: Comment on van Veelen ‘when inclusive fitness is right and when it can be wrong’ ” by James Marshall in the Journal of Theoretical Biology, in this issue.In order to circumvent the disagreement about the Price equation and focus on the issue of the predictive power of inclusive fitness for group selection models, I derive Queller's and Marshall's rule without the Price equation. Both rules however need a translation step in order to be able to link them to the group selection model in van Veelen (2009). Queller's rule applies to games with 2 players and 2 strategies, and is general. Marshall's rule on the other hand applies only to a small subset of 3-player games. His rule is correct, but for other, similarly small subsets we would get other rules. This implies that if we want a rule that applies to all symmetric games with 3 players and 2 strategies, it will have to use a vector of dimension 2 that represents population structure. More in general: for group selection models with groups of size n, a correct and general prediction will need to use a vector of dimension n−1 that represents population structure.     

Irrational decision-making in an amoeboid organism: transitivity and context-dependent preferences

Most models of animal foraging and consumer choice assume that individuals make choices based on the absolute value of items and are therefore ‘economically rational’. However, frequent violations of rationality by animals, including humans, suggest that animals use comparative valuation rules. Are comparative valuation strategies a consequence of the way brains process information, or are they an intrinsic feature of biological decision-making? Here, we examine the principles of rationality in an organism with radically different information-processing mechanisms: the brainless, unicellular, slime mould Physarum polycephalum. We offered P. polycephalum amoebas a choice between food options that varied in food quality and light exposure (P. polycephalum is photophobic). The use of an absolute valuation rule will lead to two properties: transitivity and independence of irrelevant alternatives (IIA). Transitivity is satisfied if preferences have a consistent, linear ordering, while IIA states that a decision maker''s preference for an item should not change if the choice set is expanded. A violation of either of these principles suggests the use of comparative rather than absolute valuation rules. Physarum polycephalum satisfied transitivity by having linear preference rankings. However, P. polycephalum''s preference for a focal alternative increased when a third, inferior quality option was added to the choice set, thus violating IIA and suggesting the use of a comparative valuation process. The discovery of comparative valuation rules in a unicellular organism suggests that comparative valuation rules are ubiquitous, if not universal, among biological decision makers.     

Mate choice when males are in patches: optimal strategies and good rules of thumb

In standard mate-choice models, females encounter males sequentially and decide whether to inspect the quality of another male or to accept a male already inspected. What changes when males are clumped in patches and there is a significant cost to travel between patches? We use stochastic dynamic programming to derive optimum strategies under various assumptions. With zero costs to returning to a male in the current patch, the optimal strategy accepts males above a quality threshold which is constant whenever one or more males in the patch remain uninspected; this threshold drops when inspecting the last male in the patch, so returns may occur only then and are never to a male in a previously inspected patch. With non-zero within-patch return costs, such a two-threshold rule still performs extremely well, but a more gradual decline in acceptance threshold is optimal. Inability to return at all need not decrease performance by much. The acceptance threshold should also decline if it gets harder to discover the last males in a patch. Optimal strategies become more complex when mean male quality varies systematically between patches or years, and females estimate this in a Bayesian manner through inspecting male qualities. It can then be optimal to switch patch before inspecting all males on a patch, or, exceptionally, to return to an earlier patch. We compare performance of various rules of thumb in these environments and in ones without a patch structure. A two-threshold rule performs excellently, as do various simplifications of it. The best-of-N rule outperforms threshold rules only in non-patchy environments with between-year quality variation. The cutoff rule performs poorly.     

Effects of host plant and genetic background on the fitness costs of resistance to Bacillus thuringiensis

Novel resistance to pathogens and pesticides is commonly associated with a fitness cost. However, measurements of the fitness costs of insecticide resistance have used diverse methods to control for genetic background and rarely assess the effects of environmental variation. Here, we explored how genetic background interacts with resource quality to affect the expression of the fitness costs associated with resistance. We used a serially backcrossed line of the diamondback moth, Plutella xylostella, resistant to the biopesticide Bacillus thuringiensis, to estimate the costs of resistance for insects feeding on two Brassica species. We found that fitness costs increased on the better-defended Brassica oleracea cultivars. These data were included in two meta-analyses of fitness cost experiments that used standardized protocols (and a common resistant insect stock) but which varied in the methodology used to control for the effects of genetic background. The meta-analysis confirmed that fitness costs were higher on the low-quality host (B. oleracea); and experimental methodology did not influence estimates of fitness costs on that plant species. In contrast, fitness costs were heterogeneous in the Brassica pekinensis studies: fitness costs in genetically homogenized lines were significantly higher than in studies using revertant insects. We hypothesize that fitness modifiers can moderate fitness costs on high-quality plants but may not affect fitness when resource quality is low.     

The empirical question of thresholds and mechanisms of mate choice

Summary Theoretical discussions concerning how animals might best sample and select mates have suggested that individuals could base decisions either on a sample of mates (sampled-based decisions) or on a threshold of comparison (threshold-based decisions). Recent theoretical work demonstrates that threshold-based mating decisions generate higher expected fitness than sample-based mating decisions when search costs exist. Empirical results from most unmanipulated systems, however, either conclude that females make sample-based decisions or are inconclusive. A few experimental studies designed to detect mating thresholds purport to demonstrate threshold-based choice but an examination of these studies indicates such conclusions were premature. We believe that few examples of threshold-based choice exist because protocols designed to identify mating thresholds were often inconsistent with models of threshold choice. We suggest that future empirical work strive not to document mating thresholdsper se. Rather, future work might best reveal decision rules by manipulating the distribution of quality among potential mates; such manipulations predict uniquely how females using sample-based and threshold-based decision rules should behave.     

Mate choice and optimal search behavior: Fitness returns under the fixed sample and sequential search strategies

The behavior of a female in search of a mate determines the likelihood that she encounters a high-quality male in the search process. The fixed sample (best-of-n) search strategy and the sequential search (fixed threshold) strategy are two prominent models of search behavior. The sequential search strategy dominates the former strategy—yields an equal or higher expected net fitness return to searchers—when search costs are nontrivial and the distribution of quality among prospective mates is uniform or truncated normal. In this paper our objective is to determine whether there are any search costs or distributions of male quality for which the sequential search strategy is inferior to the fixed sample search strategy. The two search strategies are derived under general conditions in which females evaluate encountered males by inspection of an indicator character that has some functional relationship to male quality. The solutions are identical to the original models when the inspected male attribute is itself male quality. The sequential search strategy is shown to dominate the fixed sample search strategy for all search costs and distributions of male quality. Low search costs have been implicated to explain empirical observations that are consistent with the use of a fixed sample search strategy, but under conditions in which the original models were derived there is no search cost or distribution of male quality that favors the fixed sample search strategy. Plausible alternative explanations for the apparent use of this search strategy are discussed.     

Genetic relatedness and group size in an aggregation economy

Summary We use Hamilton's Rule to investigate effects of genetic relatedness on the predicted size of social groups. We assume an aggregation economy; individual fitness initially increases with group size, but in sufficiently large groups each member's individual fitness declines with further increments in the size of the group. We model two processes of group formation, designated free entry and group-controlled entry. The first model assumes that solitary individuals decide to join groups or remain alone; group size equilibrates when solitaries no longer choose to join. The second model allows group members to regulate the size of the group, so that the predicted group size results from members' decisions to repel or accept intruding solitaries. Both the Nash equilibrium group size and any change in the equilibrium caused by varying the level of relatedness depend on the particular entry rule assumed. The largest equilibrium group size occurs when solitaries choose between joining or not joining and individuals are unrelated. Increasing genetic relatedness may reduce and can never increase, equilibrium group size when this entry rule applies. The smallest equilibrium group size occurs when group members choose between repelling or accepting intruders and individuals are unrelated. Under this entry rule, increasing genetic relatedness can increase and can never decrease, equilibrium group size. We extend the models' predictions to suggest when individuals should prefer kin vs non-kin as members of the same group.     

Body postures and patterns as amplifiers of physical condition

The question of why receivers accept a selfish signaller's message as reliable or 'honest' has fuelled ample controversy in discussions of communication. The handicap mechanism is now widely accepted as a potent constraint on cheating. Handicap signals are deemed reliable by their costs: signallers must choose between investing in the signal or in other aspects of fitness. Accordingly, resources allocated to the signal come to reflect the signaller's fitness budget and, on average, cheating is uneconomic. However, that signals may also be deemed reliable by their design, regardless of costs, is not widely appreciated. Here we briefly describe indices and amplifiers, reliable signals that may be essentially cost free. Indices are reliable because they bear a direct association with the signalled quality rather than costs. Amplifiers do not directly provide information about signaller quality, but they facilitate assessment by increasing the apparency of pre-existing cues and signals that are associated with quality. We present results of experiments involving a jumping spider (Plexippus paykulli) to illustrate how amplifiers can facilitate assessment of cues associated with physical condition without invoking the costs required for handicap signalling.     

Fitness cost from fluctuating ultraviolet radiation in Daphnia magna

Solar ultraviolet radiation (UVR) is an important environmental threat for organisms in aquatic systems, but its temporally variable nature makes the understanding of its effects ambiguous. The aim of our study was to assess potential fitness costs associated with fluctuating UVR in the aquatic zooplankter Daphnia magna. We investigated individual survival, reproduction and behaviour when exposed to different UVR treatments. Individuals exposed to fluctuating UVR, resembling natural variations in cloud cover, had the lowest fitness (measured as the number of offspring produced during their lifespan). By contrast, individuals exposed to the same, but constant UVR dose had similar fitness to control individuals (not exposed to UVR), but they showed a significant reduction in daily movement. The re-occurring threat response to the fluctuating UVR treatment thus had strong fitness costs for D. magna, and we found no evidence for plastic behavioural responses when continually being exposed to UVR, despite the regular, predictable exposure schedule. In a broader context, our results imply that depending on how variable a stressor is in nature, populations may respond with alternative strategies, a framework that could promote rapid population differentiation and local adaptation.     

Starlings uphold principles of economic rationality for delay and probability of reward

Rationality principles are the bedrock of normative theories of decision-making in biology and microeconomics, but whereas in microeconomics, consistent choice underlies the notion of utility; in biology, the assumption of consistent selective pressures justifies modelling decision mechanisms as if they were designed to maximize fitness. In either case, violations of consistency contradict expectations and attract theoretical interest. Reported violations of rationality in non-humans include intransitivity (i.e. circular preferences) and lack of independence of irrelevant alternatives (changes in relative preference between options when embedded in different choice sets), but the extent to which these observations truly represent breaches of rationality is debatable. We tested both principles with starlings (Sturnus vulgaris), training subjects either with five options differing in food delay (exp. 1) or with six options differing in reward probability (exp. 2), before letting them choose repeatedly one option out of several binary and trinary sets of options. The starlings conformed to economic rationality on both tests, showing strong stochastic transitivity and no violation of the independence principle. These results endorse the rational choice and optimality approaches used in behavioural ecology, and highlight the need for functional and mechanistic enquiring when apparent violations of such principles are observed.     

Rationality in collective decision-making by ant colonies

Economic models of animal behaviour assume that decision-makers are rational, meaning that they assess options according to intrinsic fitness value and not by comparison with available alternatives. This expectation is frequently violated, but the significance of irrational behaviour remains controversial. One possibility is that irrationality arises from cognitive constraints that necessitate short cuts like comparative evaluation. If so, the study of whether and when irrationality occurs can illuminate cognitive mechanisms. We applied this logic in a novel setting: the collective decisions of insect societies. We tested for irrationality in colonies of Temnothorax ants choosing between two nest sites that varied in multiple attributes, such that neither site was clearly superior. In similar situations, individual animals show irrational changes in preference when a third relatively unattractive option is introduced. In contrast, we found no such effect in colonies. We suggest that immunity to irrationality in this case may result from the ants’ decentralized decision mechanism. A colony''s choice does not depend on site comparison by individuals, but instead self-organizes from the interactions of multiple ants, most of which are aware of only a single site. This strategy may filter out comparative effects, preventing systematic errors that would otherwise arise from the cognitive limitations of individuals.     

Mutual assessment via visual status signals in Polistes dominulus wasps

Many animals use signals to assess the fighting ability of rivals and reduce the cost of aggressive competition. However, little is known about how an individual''s own quality influences their signal assessment decisions. Polistes dominulus wasps have visual signals of fighting ability that provide a good model for testing the dynamics of rival choice. We found that rival assessment behaviour was influenced by the advertised quality of the individual, their rivals, and the interaction between individual and rival quality. Individuals of high advertised quality were more likely to challenge rivals and individuals of low advertised quality were more likely to be challenged. However, when choosing among two rivals with different advertised quality, individuals did not simply choose the lower quality rival. Instead, they only preferred the lower quality rival when there was a small difference between their own advertised quality and that of their rivals. Individuals were not choosy when both rivals advertised relatively high or relatively low quality. Therefore, although P. dominulus facial patterns function as conventional signals of fighting ability that provide valuable information about their bearer''s behavioural strategy, there is substantial variation in signal responses based on the relative intensity of the senders'' and receivers'' signals.     

Prospecting and dispersal: their eco-evolutionary dynamics and implications for population patterns

Dispersal is not a blind process, and evidence is accumulating that individual dispersal strategies are informed in most, if not all, organisms. The acquisition and use of information are traits that may evolve across space and time as a function of the balance between costs and benefits of informed dispersal. If information is available, individuals can potentially use it in making better decisions, thereby increasing their fitness. However, prospecting for and using information probably entail costs that may constrain the evolution of informed dispersal, potentially with population-level consequences. By using individual-based, spatially explicit simulations, we detected clear coevolutionary dynamics between prospecting and dispersal movement strategies that differed in sign and magnitude depending on their respective costs. More specifically, we found that informed dispersal strategies evolve when the costs of information acquisition during prospecting are low but only if there are mortality costs associated with dispersal movements. That is, selection favours informed dispersal strategies when the acquisition and use processes themselves were not too expensive. When non-informed dispersal strategies evolve, they do so jointly with the evolution of long dispersal distance because this maximizes the sampling area. In some cases, selection produces dispersal rules different from those that would be ‘optimal’ (i.e. the best possible population performance—in our context quantitatively measured as population density and patch occupancy—among all possible individual movement rules) for the population. That is, on the one hand, informed dispersal strategies led to population performance below its highest possible level. On the other hand, un- and poorly informed individuals nearly optimized population performance, both in terms of density and patch occupancy.     

Hamilton's rule confronts ideal free habitat selection

If individuals occupy habitats in a way that maximizes their fitness, if they are free to occupy the habitats they choose and if fitness declines with population density, then their abundance across habitats should follow an ideal free distribution. But, if individuals are genetically related, this simple fitness-maximization mechanism breaks down. Habitat occupation should obey Hamilton's rule (natural selection favours traits causing a loss in individual fitness as long as they result in an equal or greater gain in inclusive fitness) and depends more on inclusive fitness than it does on individual fitness. We demonstrate that the resulting inclusive-fitness distribution inflates the population density in habitats of poorer inherent quality, creating pronounced source sink dynamics. We also show that density-dependent habitat selection among relatives reinforces behaviours such as group defence and interspecific territoriality, and that it explains many anomalies in dispersal and foraging.     

Why Wasp Foundresses Change Nests: Relatedness,Dominance, and Nest Quality

The costs and benefits of different social options are best understood when individuals can be followed as they make different choices, something that can be difficult in social insects. In this detailed study, we follow overwintered females of the social wasp Polistes carolina through different nesting strategies in a stratified habitat where nest site quality varies with proximity to a foraging area, and genetic relatedness among females is known. Females may initiate nests, join nests temporarily or permanently, or abandon nests. Females can become helpers or egglayers, effectively workers or queens. What they actually do can be predicted by a combination of ecological and relatedness factors. Advantages through increased lifetime success of individuals and nests drives foundresses of the social wasp Polistes from solitary to social nest founding. We studied reproductive options of spring foundresses of P. carolina by monitoring individually-marked wasps and assessing reproductive success of each foundress by using DNA microsatellites. We examined what behavioral decisions foundresses make after relaxing a strong ecological constraint, shortage of nesting sites. We also look at the reproductive consequences of different behaviors. As in other Polistes, the most successful strategy for a foundress was to initiate a nest as early as possible and then accept others as subordinates. A common feature for many P. carolina foundresses was, however, that they reassessed their reproductive options by actively monitoring other nests at the field site and sometimes moving permanently to new nests should that offer better (inclusive) fitness prospects compared to their original nests. A clear motivation for moving to new nests was high genetic relatedness; by the end of the foundress period all females were on nests with full sisters.