The evolution of decision rules in complex environments
Authors: Tim W. Fawcett, Benja Fallenstein, Andrew D. Higginson, Alasdair I. Houston, Dave E.W. Mallpress, Pete C. Trimmer, John M. McNamara
Journal: Trends in Cognitive Sciences (2014)

•In natural environments, conditions are often heterogeneous and autocorrelated.•Decision rules will have evolved to exploit this statistical structure.•In simplified environments, such rules can lead to apparently irrational behaviour.•This may explain intransitivity, contrast effects, pessimism, and other biases.•Models and experiments on decision-making should consider richer environments. Models and experiments on adaptive decision-making typically consider highly simplified environments that bear little resemblance to the complex, heterogeneous world in which animals (including humans) have evolved. These studies reveal an array of so-called cognitive biases and puzzling features of behaviour that seem irrational in the specific situation presented to the decision-maker. Here we review an emerging body of work that highlights spatiotemporal heterogeneity and autocorrelation as key properties of most real-world environments that may help us understand why these biases evolved. Ecologically rational decision rules adapted to such environments can lead to apparently maladaptive behaviour in artificial experimental settings. We encourage researchers to consider environments with greater complexity to understand better how evolution has shaped our cognitive systems.Abandon the urge to simplify everything, to look for formulas and easy answers, and begin to think multidimensionally … appreciate the fact that life is complex (M. Scott Peck [1Peck M.S. Further Along the Road Less Travelled: Wisdom For the Journey Towards Spiritual Growth. Simon & Schuster, 1993Google Scholar]) Models and experiments on adaptive decision-making typically consider highly simplified environments that bear little resemblance to the complex, heterogeneous world in which animals (including humans) have evolved. These studies reveal an array of so-called cognitive biases and puzzling features of behaviour that seem irrational in the specific situation presented to the decision-maker. Here we review an emerging body of work that highlights spatiotemporal heterogeneity and autocorrelation as key properties of most real-world environments that may help us understand why these biases evolved. Ecologically rational decision rules adapted to such environments can lead to apparently maladaptive behaviour in artificial experimental settings. We encourage researchers to consider environments with greater complexity to understand better how evolution has shaped our cognitive systems.Abandon the urge to simplify everything, to look for formulas and easy answers, and begin to think multidimensionally … appreciate the fact that life is complex (M. Scott Peck [1Peck M.S. Further Along the Road Less Travelled: Wisdom For the Journey Towards Spiritual Growth. Simon & Schuster, 1993Google Scholar]) Patterns of decision-making in humans reveal some striking deviations from economically rational expectations [2Gilovich T. Heuristics and Biases: The Psychology of Intuitive Judgment. 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Evol. 2013; 28: 469-473Abstract Full Text Full Text PDF PubMed Scopus (53) Google Scholar]) because we make no assumptions about the underlying psychological or physiological mechanisms. Mounting evidence suggests that analogous biases exist in other organisms. For example, slime moulds violate regularity [13Latty T. Beekman M. Irrational decision-making in an amoeboid organism: transitivity and context-dependent preferences.Proc. R. Soc. B. 2011; 278: 307-312Crossref PubMed Scopus (104) Google Scholar], domestic dogs show negative contrast effects [14Bentosela M. et al.Incentive contrast in domestic dogs (Canis familiaris).J. Comp. Psychol. 2009; 123: 125-130Crossref PubMed Scopus (58) Google Scholar], and honeybees behave pessimistically when agitated [15Bateson M. et al.Agitated honeybees exhibit pessimistic cognitive biases.Curr. Biol. 2011; 21: 1070-1073Abstract Full Text Full Text PDF PubMed Scopus (212) Google Scholar]. Far from being uniquely human quirks, our biases appear to have deep evolutionary roots. This observation seems difficult to reconcile with the fundamental biological concept of natural selection as an optimising process. Why would evolution produce such apparently irrational behaviour? One possible answer is that in many situations the costs of deviating from the optimal, fitness-maximising decision are negligible, and/or that constraints in the mechanisms underlying decision-making prevent natural selection from reaching this optimum. Studies on noisy information processing [16Hilbert M. Toward a synthesis of cognitive biases: how noisy information processing can bias human decision making.Psychol. Bull. 2012; 138: 211-237Crossref PubMed Scopus (206) Google Scholar] and polygenic mutation–selection balance [17Keller M.C. Miller G. Resolving the paradox of common, harmful, heritable mental disorders: which evolutionary genetic models work best?.Behav. Brain Sci. 2006; 29: 385-404Crossref PubMed Scopus (326) Google Scholar] have argued for the importance of constraints. Here we summarise an emerging line of research that suggests an alternative explanation: that many surprising features of behaviour, which may at first appear irrational, can in fact be understood as the result of ecologically rational decision rules adapted to exploit environments that vary in space and time. The approach we describe is an extension of standard techniques [18Houston A.I. McNamara J.M. Models of Adaptive Behaviour: An Approach Based on State. Cambridge University Press, 1999Google Scholar] used in behavioural and evolutionary ecology to investigate the adaptive significance of animal behaviour. This approach does not assume that all behaviour is adaptive or that constraints are unimportant, but instead seeks to identify how natural selection shapes the decision rules underlying behaviour [19McNamara J.M. Houston A.I. Integrating function and mechanism.Trends Ecol. Evol. 2009; 24: 670-675Abstract Full Text Full Text PDF PubMed Scopus (223) Google Scholar, 20Fawcett T.W. et al.Exposing the behavioral gambit: the evolution of learning and decision rules.Behav. Ecol. 2013; 24: 2-11Crossref Scopus (146) Google Scholar]. The implications of this work for understanding cognitive systems have been largely overlooked, because theoretical models and laboratory experiments alike have traditionally focused on highly simplified situations that fail to capture some of the important complexities of the environments in which organisms have evolved. Simple mathematical models are of great value in behavioural and evolutionary ecology, where the techniques of game theory and optimisation are used to predict the endpoints of natural selection [21McNamara J.M. Weissing F.J. Evolutionary game theory.in: Székely T. Social Behaviour: Genes, Ecology and Evolution. Cambridge University Press, 2010: 88-106Crossref Scopus (34) Google Scholar]. This approach has revealed some important general principles of how organisms (including humans) should choose between different options, from food items to potential mates to the age at first reproduction. Most evolutionary models of decision-making consider a highly simplified environment in which the availability of different options is known to the organism and does not change over time. This is of course an unrealistic assumption. In most natural environments, the availability of different options fluctuates in time and space, and the fluctuations are often unpredictable. That mathematical models simplify and abstract the phenomena they aim to represent is not in itself a problem; indeed, this is precisely what models are designed to do, because a model that was as complex as the real world would be of little use. But there is a danger of over-simplification [22Evans M.R. et al.Do simple models lead to generality in ecology?.Trends Ecol. Evol. 2013; 28: 578-583Abstract Full Text Full Text PDF PubMed Scopus (187) Google Scholar] ('Einstein's razor' [23Evans M.R. et al.Predictive ecology: systems approaches.Phil. Trans. R. Soc. B. 2012; 367: 163-169Crossref PubMed Scopus (82) Google Scholar]): if we simplify things too much, we may fail to capture crucial features of natural environments that are needed to understand the behaviour. Similarly, laboratory experiments place individuals in artificial situations that are far simpler than most situations encountered in the natural world. In many of the standard laboratory protocols routinely used in behavioural ecology and experimental psychology, subjects are trained and tested using a small number of behavioural options, with straightforward relationships between the available stimuli, the actions of the subject and the resulting consequences [24Kagel J.H. et al.Economic Choice Theory: an Experimental Analysis of Animal Behavior. Cambridge University Press, 1995Crossref Google Scholar, 25Wasserman E.A. Zentall T.R. Comparative Cognition: Experimental Explorations of Animal Intelligence. Oxford University Press, 2006Google Scholar, 26Shettleworth S.J. Cognition, Evolution, and Behavior.2nd edn. Oxford University Press, 2010Google Scholar, 27Davies N.B. et al.An Introduction to Behavioural Ecology.4th edn. Wiley-Blackwell, 2012Google Scholar]. In these artificial situations the experimenter has created a deliberately simplified version of the types of problems the animal might encounter in its natural environment; the aim is to isolate the key variables needed to understand the behaviour. As with the simplified models discussed earlier, there is a risk that such laboratory settings may not reflect the statistical structure of the environment to which the animal is adapted, making it seem as though the animal is making errors [4Haselton M.G. et al.Adaptive rationality: an evolutionary perspective on cognitive bias.Soc. Cogn. 2009; 27: 733-763Crossref Scopus (107) Google Scholar]. However, if we recognise this problem, then deviations from rational behaviour in simplified laboratory set-ups can be illuminating because they may reveal unexpected biases that arise from rules adapted to the natural environment. Natural selection will tend to produce decision rules which, although not optimal, perform well in the types of situations the individual normally encounters [19McNamara J.M. Houston A.I. Integrating function and mechanism.Trends Ecol. Evol. 2009; 24: 670-675Abstract Full Text Full Text PDF PubMed Scopus (223) Google Scholar, 20Fawcett T.W. et al.Exposing the behavioral gambit: the evolution of learning and decision rules.Behav. Ecol. 2013; 24: 2-11Crossref Scopus (146) Google Scholar, 28Todd P.M. Gigerenzer G. Environments that make us smart: ecological rationality.Curr. Dir. Psychol. Sci. 2007; 16: 167-171Crossref Scopus (212) Google Scholar, 29Hutchinson J.M.C. Gigerenzer G. Simple heuristics and rules of thumb: where psychologists and behavioural biologists might meet.Behav. Processes. 2005; 69: 97-124Crossref PubMed Scopus (242) Google Scholar]; that is, they should be ecologically rational [30Todd P.M. et al.Ecological Rationality: Intelligence in the World. Oxford University Press, 2012Crossref Google Scholar]. The statistical properties of environments, including the distribution of resources and how that changes over time, favour particular decision rules. For example, noisy miners (a type of bird) change their foraging strategy depending on the resource they are exploiting: they use movement-based rules when searching for invertebrates, which are cryptic and highly mobile, but switch to using spatial memory when searching for nectar, which is found only in fixed, conspicuous locations (flowers) and is quickly depleted [31Sulikowski D. Burke D. Movement and memory: different cognitive strategies are used to search for resources with different natural distributions.Behav. Ecol. Sociobiol. 2010; 65: 621-631Crossref Scopus (14) Google Scholar]. The ecological and evolutionary context is crucial; animals follow decision rules that are adapted to the statistical properties of the resource types commonly encountered during their evolutionary history. In novel experimental contexts lacking this structure, such ecologically rational rules may lead to biased or irrational behaviour. When seeking to understand how natural selection has shaped decision rules, it can be instructive to use a form of reverse engineering. This process starts with the identification of some bias that is not accounted for by current theory. The next step is to consider which particular aspects of environmental complexity need to be included in the models to predict that bias. The aim is to identify the minimal amount of real-world complexity that is sufficient to account for the observed behaviour, thereby forming a basis for novel predictions that can be used to test the proposed explanation. Models developed in the past few years illustrate the power of this approach and highlight spatiotemporal heterogeneity and autocorrelation as two important factors affecting the psychology of humans and other animals (Figure 1). Incorporating these factors into standard models can explain several biases, listed in Table 1, that appear irrational in more simplified environments.Table 1Biases that seem irrational in a simplified worldBiasDescriptionWhy does it seem irrational?The placebo effect 5Meissner K. et al.The placebo effect: advances from different methodological approaches.J. Neurosci. 2011; 31: 16117-16124Crossref PubMed Scopus (130) Google ScholarMedicinally inert substances or fake treatment procedures enhance recoveryIndividual who is capable of recovery without external help should do so immediatelyOptimism 40Brydges N.M. et al.Environmental enrichment induces optimistic cognitive bias in rats.Anim. Behav. 2011; 81: 169-175Crossref Scopus (129) Google Scholar and pessimism 42Mendl M.T. et al.Dogs showing separation-related behaviour exhibit a 'pessimistic' cognitive bias.Curr. Biol. 2010; 20: R839-R840Abstract Full Text Full Text PDF PubMed Scopus (173) Google ScholarIndividual behaves as though conditions are better (optimism) or worse (pessimism) than they actually areRational decision-maker should base behaviour on an unbiased (Bayesian) estimate of current conditionsThe 'hot-hand' fallacy 6Avugos S. et al.The 'hot hand' reconsidered: a meta-analytic approach.Psychol. Sport Exerc. 2013; 14: 21-27Crossref Scopus (52) Google ScholarMisinterpretation of a statistically independent sequence of successes as a run of good formIn a sequence of trials known to be independent (e.g., roulette), estimated chance of success should not be influenced by outcome of previous trialIntransitive choice 63Shafir S. Intransitivity of preferences in honey bees: support for 'comparative' evaluation of foraging options.Anim. Behav. 1994; 48: 55-67Crossref Scopus (131) Google ScholarIndividual prefers option A over option B, and option B over option C, but prefers C over AInconsistent with absolute valuation of options, which would imply that if A > B, and B > C, then A > B > CViolation of regularity 61Shafir S. et al.Context-dependent violations of rational choice in honeybees (Apis mellifera) and gray jays (Perisoreus canadensis).Behav. Ecol. Sociobiol. 2002; 51: 180-187Crossref Scopus (202) Google ScholarPreference for one option over another is reversed by presence of a third optionInconsistent with absolute valuation of options, which would imply that ranking of two options is unaffected by alternative optionsState-dependent valuation learning 69Aw J. et al.State-dependent valuation learning in fish: banded tetras prefer stimuli associated with greater past deprivation.Behav. Processes. 2009; 81: 333-336Crossref PubMed Scopus (35) Google ScholarIndividual prefers options they previously found to be rewarding when in a state of needRational decision-maker should choose whichever option gives greatest benefit, irrespective of past statesSuccessive contrast effects 72Mitchell E.N. et al.Evaluation of an operant successive negative contrast task as a method to study affective state in rodents.Behav. Brain Res. 2012; 234: 155-160Crossref PubMed Scopus (18) Google ScholarResponse to current conditions depends on whether conditions in the past were better or worseRational decisions should depend only on current situation; how the decision-maker got there is irrelevant Open table in a new tab Conditions in most natural environments are not uniform but vary over time and space. For highly mobile organisms, these two forms of heterogeneity will typically be closely linked; an individual moving through a spatially heterogeneous environment will encounter temporal heterogeneity too. Spatiotemporal heterogeneity has important consequences for behaviour because in a heterogeneous world the optimal response of an individual to current conditions depends on the conditions it expects to encounter in the (near) future [32McNamara J.M. et al.Foraging routines of small birds in winter: a theoretical investigation.J. Avian Biol. 1994; 25: 287-302Crossref Scopus (184) Google Scholar, 33Lima S.L. Bednekoff P.A. Temporal variation in danger drives antipredator behavior: the predation risk allocation hypothesis.Am. Nat. 1999; 153: 649-659Crossref Scopus (1047) Google Scholar, 34Beauchamp G. Ruxton G.D. A reassessment of the predation risk allocation hypothesis: a comment on Lima and Bednekoff.Am. Nat. 2011; 177: 143-146Crossref PubMed Scopus (23) Google Scholar, 35Bednekoff P.A. Lima S.L. Risk allocation is a general phenomenon: a reply to Beauchamp and Ruxton.Am. Nat. 2011; 177: 147-151Crossref Scopus (19) Google Scholar]. The most basic form of heterogeneity we can consider is where the conditions at any one time or place are independent of those at any other time or place (Box 1). This is only a crude representation of the heterogeneity in most natural environments (see next section), but it can already account for some interesting biases:Box 1Modelling environmental heterogeneity and autocorrelationIncorporating environmental heterogeneity into models of adaptive behaviour requires the inclusion of an environmental state variable. Often we can capture sufficient complexity with only two environmental states A and B, such as high and low food availability, or safe and dangerous. Next, we characterise stochastic transitions between the environmental states. The simplest case is where the probability of transition (per unit time) between states depends only on the current state (Figure Ia ), because then we can write the transition probabilities as single values cA and cB (the subscripts indicating the current state), with cA + cB < 1 representing positive temporal autocorrelation. The length of time the environment stays in state i then follows a geometric distribution with mean ti = 1/ci. We assume that the individual 'knows' (i.e., is adapted to) these probabilities and can directly perceive the current conditions. We then investigate how environmental heterogeneity affects responses to current conditions, such as predation risk [49Higginson A.D. et al.Generalized optimal risk allocation: foraging and antipredator behavior in a fluctuating environment.Am. Nat. 2012; 180: 589-603Crossref PubMed Scopus (46) Google Scholar]. For a finer gradation of states, this approach can be extended to any number of states n, with an n × n matrix of transition probabilities. For some systems, such as gradual changes in the food supply, we set all the probabilities of moving between non-adjacent states to zero.Individuals will often be uncertain about the transition probabilities, and we may be interested in how they should respond to this uncertainty. A simple representation considers two possible transition matrices (e.g., fast- or slow-changing conditions). The individual may 'know' the transition probabilities of each matrix, but not which matrix currently applies (Figure Ib). If the environment is temporally autocorrelated, then the recent past is informative of the future, and therefore the individual should adjust its behaviour in response to its previous experience of the pattern of change. An optimal decision-maker would learn from past experience using Bayesian updating [93Trimmer P.C. et al.Decision-making under uncertainty: biases and Bayesians.Anim. Cogn. 2011; 14: 465-476Crossref PubMed Scopus (71) Google Scholar]. We can model this by including a state variable to represent the probability that one particular matrix applies, which can help to explain apparently irrational behaviour such as contrast effects [73McNamara J.M. et al.An adaptive response to uncertainty generates positive and negative contrast effects.Science. 2013; 340: 1084-1086Crossref PubMed Scopus (49) Google Scholar].The above assumes that the individual can accurately perceive whether the environmental state is currently A or B. To explore a situation where the individual knows neither the current conditions nor the transition probabilities with certainty, we can use an additional variable to represent the probability of a given situation. However, note that learning two interdependent probabilities requires three state variables and a very fine grid size; computational limitations may constrain our approach.We have described the simplest scenario for modelling temporal autocorrelation in a heterogeneous world. Real environments may show more complex patterns of change, but this is a mathematically convenient way to capture some of the statistical structure that could be important for understanding cognitive adaptations. Incorporating environmental heterogeneity into models of adaptive behaviour requires the inclusion of an environmental state variable. Often we can capture sufficient complexity with only two environmental states A and B, such as high and low food availability, or safe and dangerous. Next, we characterise stochastic transitions between the environmental states. The simplest case is where the probability of transition (per unit time) between states depends only on the current state (Figure Ia ), because then we can write the transition probabilities as single values cA and cB (the subscripts indicating the current state), with cA + cB < 1 representing positive temporal autocorrelation. The length of time the environment stays in state i then follows a geometric distribution with mean ti = 1/ci. We assume that the individual 'knows' (i.e., is adapted to) these probabilities and can directly perceive the current conditions. We then investigate how environmental heterogeneity affects responses to current conditions, such as predation risk [49Higginson A.D. et al.Generalized optimal risk allocation: foraging and antipredator behavior in a fluctuating environment.Am. Nat. 2012; 180: 589-603Crossref PubMed Scopus (46) Google Scholar]. For a finer gradation of states, this approach can be extended to any number of states n, with an n × n matrix of transition probabilities. For some systems, such as gradual changes in the food supply, we set all the probabilities of moving between non-adjacent states to zero. Individuals will often be uncertain about the transition probabilities, and we may be interested in how they should respond to this uncertainty. A simple representation considers two possible transition matrices (e.g., fast- or slow-changing conditions). The individual may 'know' the transition probabilities of each matrix, but not which matrix currently applies (Figure Ib). If the environment is temporally autocorrelated, then the recent past is informative of the future, and therefore the individual should adjust its behaviour in response to its previous experience of the pattern of change. An optimal decision-maker would learn from past experience using Bayesian updating [93Trimmer P.C. et al.Decision-making under uncertainty: biases and Bayesians.Anim. Cogn. 2011; 14: 465-476Crossref PubMed Scopus (71) Google Scholar]. We can model this by including a state variable to represent the probability that one particular matrix applies, which can help to explain apparently irrational behaviour such as contrast effects [73McNamara J.M. et al.An adaptive response to uncertainty generates positive and negative contrast effects.Science. 2013; 340: 1084-1086Crossref PubMed Scopus (49) Google Scholar]. The above assumes that the individual can accurately perceive whether the environmental state is currently A or B. To explore a situation where the individual knows neither the current conditions nor the transition probabilities with certainty, we can use an additional variable to represent the probability of a given situation. However, note that learning two interdependent probabilities requires three state variables and a very fine grid size; computational limitations may constrain our approach. We have described the simplest scenario for modelling temporal autocorrelation in a heterogeneous world. Real environments may show more complex patterns of change, but this is a mathematically convenient way to capture some of the statistical structure that could be important for understanding cognitive adaptations. It is a widely reported (though controversial [36Hróbjartsson A. Gøtzsche P.C. Is the placebo powerless? Update of a systematic review with 52 new randomized trials comparing placebo with no treatment.J. Intern. Med. 2004; 256: 91-100Crossref PubMed Scopus (292) Google Scholar, 37Wechsler M.D. et al.Active albuterol or placebo, sham acupuncture, or no intervention in asthma.N. Engl. J. Med. 2011; 365: 119-126Crossref PubMed Scopus (240) Google Scholar]) finding that fake treatments such as sugar pills or sham surgery, known as placebos, can lead to improvement in a patient's health [38Benedetti F. et al.How placebos change the patient's brain.Neuropsychopharmacology. 2011; 36: 339-354Crossref PubMed Scopus (273) Google Scholar]. Although health improvement is of course beneficial to the patient, if they are capable of recovering without help it would seem rational to do so immediately, rather than waiting for an external, inert cue. In an environment where conditions change over time, however, a delayed response may be adaptive. If an individual falls sick when conditions are harsh, it may be worth waiting until the environment is perceived to be less challenging, when it will be less costly to mount an immune response. Recent theory [39Trimmer P.C. et al.Understanding the placebo effect from an evolutionary perspective.Evol. Hum. Behav. 2013; 34: 8-15Abstract Full Text Full Text PDF Scopus (16) Google Scholar] has shown that the optimal strategy for recovery depends on the beliefs of the patient about current and future conditions, which affect the relative benefits of investing in recovery now rather than later. From this viewpoint, placebos falsely alter the expectations of the patient regarding the costs and benefits of putting effort into recovery, in some cases triggering an immediate response (i.e., a placebo effect). The placebo effect itself is not adaptive, but a generalised response to external cues may be favoured by natural selection if, on average, those cues reliably indicate a change in environmental conditions. Natural selection should, in general, produce behaviour that is appropriate for the environmental conditions, giving the impression that individuals 'know' what those conditions are even if they cannot perceive them directly. Sometimes, however, humans and other animals consistently behave in a way that does not maximise their short-term gains, but would maximise their short-term gains if conditions were better than they actually are (an 'optimistic' bias) [40Brydges N.M. et al.Environmental enrichment induces optimistic cognitive bias in rats.Anim. Behav. 2011; 81: 169-175Crossref Scopus (129) Google Scholar, 41Sharot T. et al.How dopamine enhances an optimism bias in humans.Curr. Biol. 2012; 22: 1477-1481Abstract Full Text Full Text PDF PubMed Scopus (120) Google Scholar] or worse than they actually are (a 'pessimis