While it seems apparent that animals (including humans) do have the ability to respond in accordance with different rates of return, some questions do arise. Specifically, how can we use knowledge of rates to predict behaviour and how is this information represented in the brain? In this section, I will address these two questions by presenting different levels of models.
How is knowledge of rate used to predict behaviour?
According to Church (1984), there are three distinct levels of models: the formal or computational model, the psychological model and the physiological model. The first level of a model is the formal or computational model. At this level, the model proposes the specific computations that must be made for a certain behaviour to occur. Myerson & Miezin (1980) developed a compuational model for choice behaviour and representation of rate. However, before discussing their model, it is necessary to outline Herrnstein's (1961) Matching Law (on which Myerson & Miezin's theory is based) and Baum's (1974) generalized version of the matching law.
Herrnstein (1961) proposed that animals match the number of responses that they make on a specific choice to its rate of return through the following equation:
R1/(R1 + R2) = r1/(r1 + r2)
where Rs equal the responses made on each choice, and rs equal the rate of reinforcement for each choice. For example, imagine a rat with a choice between two levers: lever one (L1) that pays off on a VI 30 schedule, and lever two (L2) that pays off on a VI 60 schedule. Since L1 will ideally provide twice as many reinforcers as L2, the rat will make twice as many responses on L1 (as compared to L2).
What is especially useful about this computation is that it can be easily modified to account for differences in the amount and/or quality of the reinforcer. In the equation:
in which the qs account for the quality or desirability of each reinforcer and the as account for the amount of each reinforcer. In the simplest case, if the schedules on each lever are the same but L1 produces two reinforcers for every one on L2, the animal will make twice as many responses on L1. Similarly, if rate and amount of reinforcement are held constant but the quality of the reinforcer delivered from L1 is twice as good (or twice as desirable) as the reinforcer delivered from L2, the animal will again make twice as many responses on L1.
Herrnstein’s Matching Law has been largely successful in predicting response rates in concurrent VI schedules. However, his equation fails to account for the animals’ accuracy in representing the different rates of reinforcement. Baum (1974) modified Herrnstein’s equation to include the variable s, which stands for the sensitivity of the animals’ behaviour to the rate of reinforcement for each choice. In Baum’s equation (called the generalized form of the matching law):
R1/R2
= b(r1/r2)s
perfect matching occurs when s is equal to one. An advantage to Baum’s equation is that it can explain undermatching and overmatching simply by adjusting the value of s to a value less than or greater than one (respectively).
The b in Baum’s equation represents bias in choice behaviour. Bias can result from different amounts and qualities of the reinforcer, or from different mechanisms of choice (for example, a lever for one choice and a stepping plate as the other). An advantage to Herrnstein’s Matching Law is that it adds a degree of specificity to the equation. That is, using Herrnstein’s equation, one can determine how each variable affects the choice behaviour. Baum’s equation, on the other hand, lumps all the variables together under the label of ‘bias’.
Myerson & Miezin (1980) elaborated upon Herrnstein's matching law to provide more generalizability and predictability. Their computational model extends the Matching Law to include three types of choice schedules (VI-VI, VR-VR, and VI-VR). As well, the model includes equations that account for the animal switching between choices. (These equations will be discussed in more detail below). Myerson & Miezin presented their model as a purely compuational model; however, Gallistel (1990) reinterpreted it "as a model of the causative process in the brain of the animal" (Gallistel, p. 369). Thus, Gallistel's reinterpretation of the model transforms in into a psychological model by describing the functional components involved in implementing the computations.
How is this information represented in the brain?
As stated above, a psychological model goes a step beyond the formal model, and speculates about the components of a system that implement the computations (Church, 1984). The following psychological model discusses the computations proposed by Myerson & Miezin (1980) and Gallistel's (1990) reinterpretation of them. The model proposes four major components or assumptions.
1. Animals have a 'relative patch affinity' which is equal to the observed amount or prevalence of food in the choice of patches. Essentially, this is a form of Herrnstein's matching law (As represent the affinity for each patch and ps represent the observed prevalence of food):
A1 = p1/(p1 + p2) A2 = p2/(p1 + p2)
2. The second assumption states that "the greater the relative affinity for an alternative, the more likely the animal is to switch to it" (Gallistel, p. 369). Simply stated, an animal will be more likely to switch to a patch if the proportion of food in that patch is high. In this equation, x indicates the transition rate from each patch:
x1 = cA1 x2 = cA2
3. Thirdly, each animal will have its own constant tendency to switch patches. The constant c can be called the flightiness or switchiness constant. A high c value indicates a tendency to switch patches frequently:
c = x1 + x2
4. Finally, in the natural world, the prevalence of food is likely to change as a patch become depleted. Thus, the fourth assumption states that relative patch affinities will change more rapidly when the imbalance between prevalence of food in each patch is large:
dA1/dt = k(p1A2 - p2A1) dA2/dt = k(p2A1 - p1A2)
In combination, these four assumption
account for what causes an animal to enter or switch between foraging patches.
Questions/Concerns/Links not working? pls. contact egray@ualberta.ca
| main | theory | human examples | conclusion | references |