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Optimality and Behavioural Strategies
Behavioural strategies are the fundamental vehicles for interaction between a phenotype and its environment. The success or failure of these strategies determine the fitness of an individual and hence the distribution of the genotypes in the population. Essentially, genotypes are the depository of behavioural strategies, and in the long run, behavioural strategies determine the genotype (not vice versa!).
A fundamental observation is that not every conceivable behaviour is generated by an organism. Behaviours are not purely random movements but are organised. They depend on the current (or anticipated) context the organism finds itself in, and the they tend to be stereotyped for a given context. That is, for a given context, one observes similar behaviours from the same individual or from different individuals. There are variations from one instance to the next, and there are individual differences, but overall there can be no doubt that some behavioural strategies are preferred over others. Indeed, this preference can be so strong that any large deviation from the norm may indicate pathological behaviour. The distal question is why are there such preferences, rather than how are they implemented?
Behaviour and Behavioural Strategies
Before we go any further we need to make a distinction between the observed behaviour and the behavioural strategy that is adopted for a given context. Behaviour is the continuous flow in time of the physical state of the organism. For us that means the observed position, velocity, acceleration, etc. of each body part at every instant in time. Behaviour is real-time action that the organism emits and for the most part (we assume) it is the product of a behavioural strategy.
A behavioural strategy is the intended or expected behaviour generated by the nervous system for a given context (eg. task). A behavioural strategy may be a simple movement (such as a withdrawal reflex, a saccadic eye movement, or a reaching movement) or a complex sequence of movements (such as dressing, brushing your teeth, or washing sweet potatoes). The strategy may be planned far ahead in time or an immediate response to a threat or opportunity. Planning and decision-making may also require considerable information processing (cognitive processes).
The selection of a behavioural strategy may be explicit. When you reach for a cup of coffee there are many ways in which you could move your arm and grasp the cup. Most people use a similar strategy of smoothly rotating all the joints (torso, shoulder, elbow, wrist, fingers) at the same time, but they could for example rotate each joint sequentially. (This is surprisingly difficult to do, unless you are Michael Jackson.) The point is that there is a range of strategies available for the phenotype to choose from.
Selection can also be implicit. Certain choices are physically impossible and therefore unavailable to the phenotype. For example there is a limit to how far a human can rotate the head and eyes when looking at an object behind. Owls also have frontal eyes but much more freedom of head movement. Many predator species have laterally placed eyes and have near panoramic vision. Here evolution has effectively selected a strategy by virtue of the phenotypes morphology. One could reasonably argue that morphology has evolved to support the behavioural strategy. Although implicit strategies are fascinating, we will focus mostly on explicit strategies. Contexts
Natural behaviour occurs against a background of different situations or contexts. By context we mean the current task, the current external environment, and the current state of the organism (the internal environment). A strategy that is suitable (ie. fit) for one context may be totally unsuitable in another. Eating grass is not a good idea for a gazelle when a lion is about to pounce (external threat), but running around all the time would rapidly deplete energy stores (internal threat). It is not hard to think of any number of examples of inappropriate human behaviour!
In an individual' s lifetime, contexts may repeat themselves many times, such as being hungry, sleeping, mating, and moving. Each context may evoke the same behavioural strategy. Consider how many times a chicken pecks for food on the ground, or how often a bird flaps its wings, or how often we humans make an eye movement? These are prolific stereotyped behavious. On the other hand, contexts may also occur infrequently in any individual's lifetime (but may occur often across a large population). The number of times a specific gazelle is chased by a cheetah in its lifetime is probably quite low. Clearly, contexts have different frequencies of occurrence.
Contexts also expose individuals to different severities of threat, or potential fitness reductions, which we call costs. Failure to escape a predator is catastrophic for the individual. In contrast, there seems to be little if any consequence if a pigeon makes an inaccurate peck for food. However, we should not think of contexts and strategies as always being dramatic life vs. death scenarios, but rather that strategies can give an edge to long-term performance (and hence fitness). A small increase in accuracy over many hundreds of thousands of pecks may become an important advantage when in competition with other pigeons. Multiply this advantage across millions of pigeons over many generations, and an apparently infinitesimal advantage becomes hugely significant. This is a simplification, but the point is that we should not underestimate the asymptotic nature of natural selection, especially in high-frequency contexts.
There are many interesting issues about contexts, such as what constitutes a new context for a given organism (or species), how well a context is recognised, why does a strategy occur, how is it learnt, and how well can the organism switch from one strategy to another. There are also serious issues about how we, as experimentalists, can fully know the current context of an organism. This is especially difficult when observing natural behaviour, as the relevant stimuli are only partly known, or guessed. Often we resort to laboratory experiments to define the context, but whether lab conditions are a substitute for a natural context (ecological validity) is always open to debate. We shall leave these important issues aside (for the moment) and proceed with our main argument. The Assumption of Optimality
Let us assume that the organism is in a known context (ie. recognised by the organism). There are potentially many different explicit strategies that could, in principle, be adopted. However not every behaviour that we can imagine could occur. There are limitations on which behaviours are biologically feasible. Muscles cannot contract instantaneously or generate infinite force. These are internal constraints (internal to the organism), and they may vary according to the state of the organism (eg. energy reserves). Thus we need to consider the context in which the behaviour is occurring (task, external environment). When an organism enacts a behavioural strategy, s, it selects it from a set of feasible strategies, S, depending on the Context.
Different feasible strategies have different degrees of fitness. That is, for a given context the organism has a better probability of survival and producing viable progeny by adopting one strategy over another. With Natural Selection, over many occurrences of a given Context, and over many individuals over many generations, a fitter strategy will become more prevalent in the population than a less fit strategy. The key point is that the feasible strategy with the greatest fitness will become the most prevalent strategy in the population for a given Context. We call this the Assumption of Optimality.
Let us be careful about what we mean by this. We do not mean that organisms are Panglossian ideals (S J Gould's criticism of adaptationism). First, only optimal strategies among feasible strategies can be adopted (not simply anything that you could imagine). Second, Natural Selection only takes small steps so it is possible that only a local optimum may be found, and the true optimum never reached (more about this elsewhere). It is even possible that individual(s) may adopt more than one locally-optimal strategy at any given instance.
It is also possible, if not likely, that locally-optimal strategies may not be the only strategies adopted by all individuals. Instead there may be a distribution of strategies whose fitnesses are close to a local optimum. These distributions will depend in a very complicated way on genotypic variations, phenotypic variations (per genotype), evolutionary dynamics, and context variations. We are saying that the most prevalent strategy will be a locally-optimal among those available for the given context. It is important to note that strategies with similar costs may look completely different to the casual observer. Genes and Behavioural Strategies
Before we lose our thread, let us remind ourselves that genes and behavioural strategies are inexorably linked. If behavioural strategies were independent of the genotype then Natural Selection simply could not wield its influence. Genetic variations must lead to different behaviour! And different behavioural strategies must be deposited in the genes. There is no other way for Darwinian evolution to work. But how genes and behavioural strategies are linked is not so clear, and certainly not consistent. Some behaviours, even quite complex ones, can be innate. Just look at a newborn calf plopping to earth and struggling to its feet and walking in seconds (if somewhat incoordinated), and there are many other examples. Here genes seem to code behaviour directly. On the other hand, other behavioural strategies must be learnt and require the appropriate environment for teaching, which can also occur in a myriad of ways including the environment switching genes! Here genes provide the means for learning and also (as we will propose later) the learning objectives, without specifying the specific behavioural strategy per se. This is a crucial point, and the astute reader will undoubtedly realise that we are stepping up to our armpits into the nature vs. nurture morass, but as Matt Ridley beautifully describes, it is really Nature via Nurture more later! Cost
Instead of talking about fitness of a strategy, we prefer to use the term cost or expected cost. One reason for this preference is borne out of the pessimistic view that life is always finite and that behavioural strategies can, at best, stave off the inevitable. There is no loss of generality, since minimising cost always maximises fitness. There is another more subtle reason however. Fitness usually refers to the ability to survive to produce viable progeny. This is the ultimate measure of the worth of behaviour, but it is doubtful that we could ever measure it in humans. We will always deal with surrogate measures of fitness, such as energy reserves, speed, accuracy etc., and combinations thereof. We need to attribute some value to these measures, so we use the word cost and will always denote it by the symbol J (as common in most texts on optimality). Our premise therefore is that an actual behaviour (or absence of a behaviour) will incur a cost to the owner, and that different behaviours generally incur different costs for a given context.
The distinction between behaviour and behavioural strategy now becomes important. The organism may adopt the same strategy, but the actual behaviour may vary from one instance to the next. There are uncontrollable factors such as fluctuations in the neural and muscular systems, and also subtle variations in the context (both internal and external) that may not be recognised by the organism. Such variations in outcome will appear as noise in the system and will lead to variations in cost even though the same strategy was adopted. For example, every time you press a light switch your finger will end up in a slightly different position, and occasionally you might miss the switch altogether. These variations are well-known and normal natural uncontrollable fluctuations in the human neuromuscular system (and will figure largely in subsequent discussions). Provided the fluctuations in costs from one event to the next are statistically independent, then the cost to the organism per event can be determined from the average or expected cost. The expected cost can then be attributed to the behavioural strategy.
In summary, the cost of a behavioural strategy is the expected cost of the actual behaviours generated by the strategy. [It is crucial to realise that the expected cost is NOT the cost of the average behaviour, but the average of the costs of the behaviours!] Composite Costs & Trade-offs
We must now deal with a common misunderstanding, namely the misconception that nature does as well as it needs to, or the just good enough hypothesis. At one level, this just good enough hypothesis implies that evolution knows not only when to stop but also how to fall short of an optimum. This is impossible and quite teleological. Evolution is a trial and error process and will continue making random variations forever, which may improve fitness or may not. There is no way it can know when an optimum has been reached, or has not been reached.
However, the just good enough hypothesis is sometimes used in a different way. For example, one might argue that the gazelle only runs as fast as it needs to escape the cheetah, not any faster, and therefore just good enough. Otherwise, gazelles would continue to evolve to become ever faster. The answer is that making faster gazelles is expensive as they need more energy and need to eat more (there may be other problems to deal with such as changing metabolism, muscle size, skeletal morphology etc., but we will ignore these). Thus improving fitness by increasing speed has a downside of reducing fitness in terms of energy production. On the other hand, trying to improve fitness by reducing energy production will reduce fitness dramatically by slowing the gazelle until it becomes eaten. There is no simple solution (the phrase "there is no such thing as a free lunch" comes to mind). The evolution of gazelles must make a trade-off by being as slow as possible without being caught (on average). This is an optimal trade-off, rather than being just good enough.
We can handle this trade-off by incorporating composite costs. One simple and intuitive way is to assume that there is a cost to the organism that increases as speed decreases and another cost that increases with energy production, and total cost is the sum of these:
Total Cost = Cost(slowness) + Cost(energy production)
as shown in this diagram on the right. As the gazelle goes faster the probability of being caught decreases, and the expected cost therefore also decreases (red line). However, going faster consumes more energy (green line). The total cost (pink line) therefore will have some minimum, which is the optimal speed. This diagram is completely artificial (I just made it up) - real life is much more complex! But it illustrates some basic points.
The Forward vs. the Inverse Problem of Optimality
If we knew the cost functions that govern an organism's fitness, we could in principle find the optimal behavioural strategy. This is the classic forward problem that most human designers (ie. engineers) grapple with. It is not easy to solve, except for simple textbook cases. Often an engineer will choose a cost function that is both easy to manipulate mathematically and bears some resemblance to what appears to acceptably good performance, and then builds the machine to fulfil that chosen optimal performance.
We do not have this luxury - biology and physics determine the cost function, and they are unlikely to be convenient mathematical functions. Our problem is to find Nature's cost functions. This is the inverse problem. It is a bit like being shown a completed crossword puzzle and trying to work backwards to find the clues. It seems daunting if not impossible because, in principle, there are many cost functions that could give rise to observed optima. In mathematics we call this an ill-posed problem a problem that at the outset does not have a single or even a finite number of solutions.
But before we put our hands up in despair, let us remember that this kind of ill-posed problem is exactly the kind of problem faced by physicists in the dawn of enlightenment and thereafter. Sure, apples fall from trees they always have done but why (not how)? By making models that fit observations, the physicist sees what predictions the model makes and then perform experiments to test them. The model is strengthened if predictions are well fit by the data, but weakened or discarded if the fit is poor. Often the new observations give clues to a new or modified model, which is then tested with its new predictions, and so on. This is, of course, the standard scientific method. This is exactly how we should proceed to solve the inverse optimality problems:
Ultimately we will arrive at a plausible explanation for an observed behavioural strategy. Unfortunately, success has been rather patchy so far, with most examples drawn from studies of foraging behaviour. The main reason for this that so much of biology, and particularly neurophysiology, is still firmly entrenched in the proximal school -- an obsession with dissecting rather than watching Newton's apple!
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