Figure 1

Adaptation can be represented by motion in phenotype space. This figure shows a hypothetical phenotype space for feeding rate and expression of digestive enzymes. (a) Point O is the optimal phenotype, and P is the animal's current phenotype. Now suppose that a mutation changes the phenotype. This can be thought of as a step from P to some other point. If the new point is closer to O than P was, that is, if it is within the black circle, then it is adaptive. For very small steps the probability of an adaptive step is close to 50%. The set of adaptive points for a step 1.2 times the distance from P to O is shown by the red arc; the probability of improved adaptation is 30%. This probability continues to decrease as step size increases, until it becomes 0 for steps of size 2 or greater. (b) Part (a) assumes no interaction between feeding rate and digestive enzyme expression. In reality, correlated changes are more likely to be adaptive than changes in which one increases while the other decreases. This can be represented by changing the target area to an ellipse. It is still the case that small changes are more likely to be adaptive than big changes. However, much larger adaptive changes are now possible, if they are along the axis of the ellipse. The figure shows a change of size 2.4, which would always be maladaptive for a circular target of equal area. Here the probability of improvement is 7%.