On the optimality of coarse behavior rules

Animal behavior can be characterized by the degree of responsiveness it has to variations in the environment. Some behavior rules lead to fine-tuned responses that carefully adjust to environmental cues, while other rules fail to discriminate as carefully, and lead to more inflexible responses. In this paper we seek to explain such inflexible behavior. We show that coarse behavior, behavior which appears to be rule-bound and inflexible, and which fails to adapt to predictable changes in the environment, is an optimal response to a particular type of uncertainty we call extended uncertainty. We show that the very variability and unpredictability that arises from extended uncertainty will lead to more rigid and possibly more predictable behavior. We relate coarse behavior to the failures to meet optimality conditions in animal behavior, most notably in foraging behavior, and also address the implications of extended uncertainty and coarse behavior rules for some results in experimental versus naturalistic approaches to ethology.     

Evolutionary design on a budget: robustness and optimality of bacteriophage T7

Exploring how biological systems have been 'designed' by evolution to achieve robust behaviours is now a subject of increasing research effort. Yet, it still remains unclear how environmental factors may contribute to this process. This issue is addressed by employing a detailed computer model for the intracellular growth of phage T7. More than 150 000 in silico T7 mutants were generated and the rates and efficiencies of their growth in two host environments, namely, a realistic environment that offered finite host resources for the synthesis of phage functions and a hypothetical environment where the phage was supplied infinite host resources, were evaluated. Results revealed two key properties of phage T7. First, T7 growth was overall robust with respect to perturbations in its parameters, but fragile with respect to changes in the ordering of its genetic elements. Secondly, the wild-type T7 had close to optimal fitness in the finite environment. Furthermore, a strong correlation was found between fitness and growth efficiency in the finite environment. The results underscore the potential importance of the environment in shaping robust design of a biological system. In particular, the strong correlation between fitness and growth efficiency suggests that T7 may have evolved to maximise its growth rate by minimising waste of finite resources.     

Assessing the robustness of randomization tests: examples from behavioural studies

Behavioural studies are commonly plagued with data that violate the assumptions of parametric statistics. Consequently, classic nonparametric methods (e.g. rank tests) and novel distribution-free methods (e.g. randomization tests) have been used to a great extent by behaviourists. However, the robustness of such methods in terms of statistical power and type I error have seldom been evaluated. This probably reflects the fact that empirical methods, such as Monte Carlo approaches, are required to assess these concerns. In this study we show that analytical methods cannot always be used to evaluate the robustness of statistical tests, but rather Monte Carlo approaches must be employed. We detail empirical protocols for estimating power and type I error rates for parametric, nonparametric and randomization methods, and demonstrate their application for an analysis of variance and a regression/correlation analysis design. Together, this study provides a framework from which behaviourists can compare the reliability of different methods for data analysis, serving as a basis for selecting the most appropriate statistical test given the characteristics of data at hand. Copyright 2001 The Association for the Study of Animal Behaviour.     

Conservation rules, their breakdown, and optimality in Caenorhabditis sinusoidal locomotion

Undulatory locomotion is common to nematodes as well as to limbless vertebrates, but its control is not understood in spite of the identification of hundred of genes involved in Caenorhabditis elegans locomotion. To reveal the mechanisms of nematode undulatory locomotion, we quantitatively analysed the movement of C. elegans with genetic perturbations to neurons, muscles, and skeleton (cuticle). We also compared locomotion of different Caenorhabditis species. We constructed a theoretical model that combines mechanics and biophysics, and that is constrained by the observations of propulsion and muscular velocities, as well as wavelength and amplitude of undulations. We find that normalized wavelength is a conserved quantity among wild-type C. elegans individuals, across mutants, and across different species. The velocity of forward propulsion scales linearly with the velocity of the muscular wave and the corresponding slope is also a conserved quantity and almost optimal; the exceptions are in some mutants affecting cuticle structure. In theoretical terms, the optimality of the slope is equivalent to the exact balance between muscular and visco-elastic body reaction bending moments. We find that the amplitude and frequency of undulations are inversely correlated and provide a theoretical explanation for this fact. These experimental results are valid both for young adults and for all larval stages of wild-type C. elegans. In particular, during development, the amplitude scales linearly with the wavelength, consistent with our theory. We also investigated the influence of substrate firmness on motion parameters, and found that it does not affect the above invariants. In general, our biomechanical model can explain the observed robustness of the mechanisms controlling nematode undulatory locomotion.     

Development of a decision support system for the introduction of alternative methods into local irritancy/corrosivity testing strategies. Creation of fundamental rules for a decision support system

The notification procedure of the European Union (EU) for new chemicals requires the application of protocols on physicochemical and toxicological tests for the evaluation of physicochemical properties and probable toxic effects of each notified substance. A computerised database was developed from data sets and toxicological test protocols relating to substance properties responsible for skin and eye irritation/corrosion. To develop specific structure-activity relationship (SAR) models and to find rules for a decision support system (DSS) to predict local irritation/corrosion, physical property data, chemical structure data and toxicological data for approximately 1300 chemicals, each having a purity of 95% or more, were evaluated. The evaluation demonstrated that the lipid solubility and aqueous solubility of a chemical are relevant to, or - in some cases - responsible for, the observed local effects of a substance on the skins and eyes of rabbits. The octanol/water partition coefficient and the measured value of the surface tension of a saturated aqueous solution of the substance give additional information that permits the definition of detailed SAR algorithms that use measured solubility values. Data on melting points and vapour pressure can be used to assess the intensity and duration of local contact with a chemical. Considerations relating to the reactivity of a pure chemical can be based on molecular weight and the nature of the heteroatoms present. With respect to local lesions produced following contact with the skin and eyes of rabbits, the data evaluation revealed that no general "local irritation/corrosion potential" of a chemical can be defined. A variety of mechanisms are responsible for the formation of local lesions on the skin or in the eyes: serious lesions are produced by mechanisms different from those that cause moderate irritation in these organs. In order to develop a DSS that uses the information extracted from the database, chemical main groups were categorised on the basis of their empirical formulae, and rules were defined of the type IF (physicochemical property) A, THEN not (toxic) effect B, based on correlations between specific local effects and measured physicochemical values. Other rules of the type IF substructure A, THEN effect B were developed based on correlations between specific local effects and the submitted structural formulae. Reactive chemical substructures relevant to the formation of local lesions and rules for the prediction of the absence of any skin irritation potential were identified. Proposals are made relating to the development of alternatives to eye irritation testing with rabbits.     

Assessing predation risk: optimal behaviour and rules of thumb

We look at a simple model in which an animal makes behavioural decisions over time in an environment in which all parameters are known to the animal except predation risk. In the model there is a trade-off between gaining information about predation risk and anti-predator behaviour. All predator attacks lead to death for the prey, so that the prey learns about predation risk by virtue of the fact that it is still alive. We show that it is not usually optimal to behave as if the current unbiased estimate of the predation risk is its true value. We consider two different ways to model reproduction; in the first scenario the animal reproduces throughout its life until it dies, and in the second scenario expected reproductive success depends on the level of energy reserves the animal has gained by some point in time. For both of these scenarios we find results on the form of the optimal strategy and give numerical examples which compare optimal behaviour with behaviour under simple rules of thumb. The numerical examples suggest that the value of the optimal strategy over the rules of thumb is greatest when there is little current information about predation risk, learning is not too costly in terms of predation, and it is energetically advantageous to learn about predation. We find that for the model and parameters investigated, a very simple rule of thumb such as 'use the best constant control' performs well.     

Complexity of environment and parsimony of decision rules in insect societies

This paper shows how colonies of social insects process information and solve problems in a complex environment, while keeping some parsimony at the level of the individuals' decision rules. Two studies on ant foraging reveal the diversity of adaptive colony-level patterns that can be generated through self-organization, based on the same individual-level recruitment rules. Regarding prey scavenging, the "ability to retrieve the prey" rule accounts for changes in foraging patterns, with increasing prey size, that show all stages intermediate between an individual and a mass exploitation of food resources. Regarding liquid food foraging, the "ability to ingest a desired volume" rule enables a colony to adjust the number of tending ants to the honeydew production of aphids. In both cases, decision rules are based on intelligent criteria that intrinsically integrate information on multiple variables that are relevant to the ants. Furthermore, the environment can contribute directly to the emergence of collective patterns, independently of any individual behavioral changes. Each environmental factor, including abiotic ones, that alters the dynamics of information transfer in group-living animals should be reconsidered not simply as a constraint but also as a part of the decision-making process and as a agent that shapes the collective pattern.     

Self-shading, carbon gain and leaf dynamics: a test of alternative optimality models

A simple model of shoot-level carbon gain is presented addressing the optimal number and life span of leaves in relation to alternative optimality criteria: (1) maximizing carbon export from the shoot, or (2) maximizing the rate of leaf production at the shoot tip. Additionally, the processes that cause declining assimilation with leaf age are considered in relation to (1) leaf position on the shoot (e.g., self-shading) versus (2) leaf age per se. Using these alternative scenarios, only a model based on position-dependent assimilation and maximization of leaf production rates resulted in quantitative predictions for all aspects of leaf dynamics on the shoot (i.e., leaf number, life span, and birth rate), while other approaches predicted that one or more parameters would be infinite. This formulation of the model also predicted that leaves should be maintained on the shoot until the diurnal carbon balance declines to zero, in contrast with other scenarios which predict that leaves should be shed while maintaining a positive carbon balance. Predictions of the model were supported by the results of a field study of carbon gain and leaf dynamics in saplings of three species of tropical pioneer trees (Carica papaya, Cecropia obtusifolia, and Hampea nutricia) which differ in the number of leaves per shoot. The results illustrate that in these fast-growing plants, leaf production and height growth may be more appropriate measures of performance than net carbon export from the shoot, and suggest that leaf senescence is primarily a function of the position of a leaf within the canopy, rather than its chronological age. Received: 13 October 1998 / Accepted: 27 January 1999     

Assessing the effect of varying sequence length on DNA barcoding of fungi

DNA barcoding shows enormous promise for the rapid identification of organisms at the species level. There has been much recent debate, however, about the need for longer barcode sequences, especially when these sequences are used to construct molecular phylogenies. Here, we have analysed a set of fungal mitochondrial sequences - of various lengths - and we have monitored the effect of reducing sequence length on the utility of the data for both species identification and phylogenetic reconstruction. Our results demonstrate that reducing sequence length has a profound effect on the accuracy of resulting phylogenetic trees, but surprisingly short sequences still yield accurate species identifications. We conclude that the standard short barcode sequences ( approximately 600 bp) are not suitable for inferring accurate phylogenetic relationships, but they are sufficient for species identification among the fungi.     

Reaction times in discriminations of varying difficulty: decision modulated by arousal

Pigeons discriminated the hue of a spot of light that appeared in discrete trials. A green spot always signaled food ("green S+") and so did a red spot of constant hue ("red S+"), but on most trials a different red hue appeared and no food was given for pecks ("red S-"). The hue of red S- stayed the same during blocks of up to twelve sessions, but it changed from block to block. During a final group of sessions red S- was omitted and the percent reinforcement to the two S+ stimuli was varied. Major findings were that (1) percent response (Pct(R)) to S- varied with S+/S- similarity, describing a typical ogival psychometric function; (2) Reaction times (RTs) to both red and green S+s were minimal when the red discrimination was impossible (that is, when red S+ and S- were identical); (3) RTs to red S+ were greatest during discriminations of intermediate difficulty; (4) as Pct(R) declined during the learning of a difficult discrimination, RTs increased to red S+ as well as red S-. Most aspects of the data were reproduced by simulations with a quantitative model that incorporated reinforcement-based decision and arousal processes.     

Equitable and reasonable freshwater allocation based on a multi-criteria decision making approach with hydrologically constrained bankruptcy rules

Effective water allocation among multiple jurisdictions is a key instrument to improve water use efficiency within the basin scale. To achieve equitable and reasonable water allocation, natural, socio-economic, and ecological conditions within a specific basin need to be systematically considered. Based on the main principles of equitable and reasonable water allocation that were defined by UN Watercourses Convention, an integrated multi-criteria decision making (MCDM) with bankruptcy rules (IMCDM-BR) under multiple hydrological constraints were proposed to allocate trans-jurisdiction water resources in Guanting reservoir basin (GRB), a shared basin between Zhangjiakou and Beijing in China. Projection pursuit (PP), as one of an effective MCDM approach, was employed to synthesize values of the related principles, which were ranked as weights for the corresponding water claims by relevant agents. Then, the weighted bankruptcy rules (BR) with multiple hydrological constraints were applied to allocate water among the related agents of the studying basin. The results of ordinary bankruptcy rules, bankruptcy rules with regular and hydrological constraints, and the proposed methods were compared and discussed. Among them, the proposed IMCDM-BR was recommended as an effective tool to support practical water allocation. Moreover, factors of equitable and reasonable water allocation were comprehensively considered. The results can thus be used for facilitating negotiation in trans-jurisdiction water allocation among agents within basins.     

Testing game theory models: fighting ability and decision rules in chameleon contests

Game theory models of animal contests make many non-mutually exclusive predictions, complicating empirical tests. These predictions regard the relationship between contest parameters and fighting ability, for which body size is usually used as a proxy. However, in many systems, body size may be a limited proxy since multiple traits and contextual factors such as experience influence fighting ability. Using contests between male Cape dwarf chameleons, Bradypodion pumilum, I test alternative game theory models of extended contests. I show how the most likely candidate model can be identified through a process of elimination, based on tests of key predictions. In addition, I present a measure of fighting ability based on multiple traits that allows ability to change as experience changes. In dwarf chameleons, persistence is based on loser thresholds rather than assessment of relative ability, ruling out the sequential assessment model. Winners and losers do not match behaviours in early parts of the contest, arguing against all types of war of attrition models. Although the cumulative assessment model remained as the most likely candidate model, not all specific predictions of this model were upheld.     

An alternative approach to asymptotic results on genetic composition when the population size is varying

This paper is concerned with methodology for studying the long-term genetic composition of a population of haploid individuals in the case where the population size is varying. A general approach requiring a minimum of assumptions is described based on constructing martingales out of expressions for the means of the numbers of allelic types, conditional on the past. Earlier investigations were based on studying the asymptotic behaviour of the proportion of alleles of a certain type in the population. Several applications demonstrate that the approach suggested in the paper provides results which usefully complement ones obtained previously.