2 Climbing a phenotypic landscape
2.1 The phenotypic landscape
The Darwinian evolution may be seen as something climbing a phenotypic value landscape with very many peaks and hollows. That such a landscape exists may be understood from the fact that certain DNA-messages more probably multiply and survive due to a higher fitness or adaptation of the corresponding individual. This ability may in the metaphor represent a higher altitude, which should not be confused with the equal dignity of all human beings (cp. 3 Valuations, 3.1).
If the gene pool of a large population is situated on a slope of the landscape, then more offspring will be generated on the higher side, which - because the variability and number of individuals must always be limited – causes the gene pool to move upwards towards some peak(s) in the landscape. As a result the mean fitness (i. e. the mean value of individual fitness taken over the whole population) tends to increase in the population (six theorems in control of evolution).
2.2 An enormous complexity
Nobody knows how many peaks there might be in such a landscape, but many-dimensional landscapes, with an astronomical number of peaks, may be formed by very simple means. Assuming that the landscape is formed as a sum of 170 functions (not very many) of one parameter each, where each function has three peaks (not many), then the number of peaks in this 170-dimensional landscape will be roughly 1080, or about the estimated total number of atoms in the universe. We can neither survey such a landscape, nor can we see in what direction the highest peak may be found. Even the less difficult task of finding the nearest higher peak seems extremely difficult, and the real landscape is probably more complex than that, even within the range of our own species.
2.3 An ambition to find higher peaks
Despite this, evolution has the “ambition” to find the highest peak, even if there is no guarantee of success. The reason is that the increased mean fitness gives room for more phenotypic disorder and processes that repeatedly undergo random changes tend (according to the entropy law) to increase the disorder provided that the mutation rate is sufficiently high. So the method used by evolution is to increase, also, the phenotypic disorder in the gene pool. In fact it might happen that mean fitness is not increased but only the disorder. Besides, arms races between different species may even cause disorder to decrease, but the disorder will grow as much as possible with respect to the circumstances.
Unfortunately the concept of disorder has an unpleasant ring for most people. But observing that this concept is synonymous to mean value of information and biological diversity (See chapter 4, Disorder, information and biological diversity), the ring seems more pleasant. The disorder becomes even more pleasant when it turns out that – as we shall see – the probability of finding higher peaks increases. Thus, the disorder is of crucial importance to survival. This disorder also means diversity within the same species, and that individuals will differ more from each other. But unfortunately, not everyone is delighted with this diversity, which may also give rise to different forms of racism.
2.4 The distribution of parameter values in a large population
Since the development from fertilized egg to adult individual may be seen as a stepwise modified repetition of the evolution of a particular individual, parameters tend – according to the central limit theorem (Cramér) – to become normally distributed (the Gaussian bell curve). As examples of such parameters we may mention morphological parameters as for instance the length of a certain bone or the distance between the pupils. Mental parameters, as for instance IQ, may also be normally distributed. Thus, the normal distribution is a simple, good and credible basis for a model of evolution. In biological text books, such parameters are also called quantitative traits, i. e. traits that depend on many different genes. Traits that depend on a single or only a few genes will not be considered here.
2.5 How to climb a mountain
Mean fitness may be calculated provided that the distribution of parameters and the structure of the landscape is known. The real landscape is not known, but figure 2.1 below shows a fictitious profile (blue) of a landscape along a line (x) in a room spanned by such parameters. The red curve is the mean based on the red bell curve at the bottom of figure 2.1. It is obtained by letting the bell curve slide along the x-axis, calculating the mean at every location. As can be seen, small peaks and pits are smoothed out. Thus, if evolution is started at A with a relatively small variance (the red bell curve), then climbing will take place on the red curve. The process may get stuck for millions of years at B or C, as long as the hollows to the right of these points remain, and the mutation rate is too small.
Figure 2.1.
If the mutation rate is sufficiently high, the disorder or variance may increase and the parameter(s) may become distributed like the green bell curve. Then the climbing will take place on the green curve, which is even more smoothed out. Because the hollows to the right of B and C have now disappeared, the process may continue up to the peaks at D. But of course the landscape puts a limit on the disorder or variability. Besides - dependent on the landscape - the process may become very jerky, and if the ratio between the time spent by the process at a local peak and the time of transition to the next peak is very high, it may as well look like a punctuated equilibrium as suggested by Gould (see Ridley).