Adaptive Landscapes

Adaptive landscapes describe how populations adapt to their environment. Evolution is that process that converts genetic variation within populations to variation between populations. Wright (1930) first presented the concept of adaptive landscapes. On this webpage I discuss briefly this model as a prerequisite to using it as a model to talk about personal and spiritual growth and why these are important. Before reading this page and depending on your background, you may want to review the pages on basic genetics and evolutionary genetics. This discussion takes off from these two pages.

The basic model

Assume two alleles in a population: A and B. From Mendelian genetics, these two alleles yield three genotypes: AA, AB, BB. Let p be the frequency of the A allele in the population and q = the frequency of the B allele, such that p+q=1. Based on the Hardy-Weinberg equation, which is a binomial expansion, the frequencies of the three genotypes before selection will be (p+q)2=p2AA+2pqAB+q2BB. OK, we've got one other set of terms to define, namely, fitness.

Fitness

Fitness is a measure of how well a given genotype survives and reproduces. Technically it can be defined as the average number of offsprigs produced by a given genotype. Let wAA= fitness of the AA genotype, wAB fitness of the AB genotype, and wBB fitness of BB.

Let W=the average fitness of the population. W is the sum of the fitnesses of the various geneotypes weighted by their frequencies in the population. So,

W=p2wAA+2pqwAB+q2wBB

Then, in this simple case, an adaptive landscape would look as seen in Fig 1:

adaptive landscape

Fig 1. A simple adaptive landscape for 2 alleles where the Y axis is W, the average fitness of the population, and the X-axis is p, the frequency of the A allele. X1 is where the population is at time t. Selection (arrow) will act to move the population's average fitness to Xmax on the peak. Thus, the average fitness, W, is maximized.

What this simple model shows is that at the beginning of our story, the population is at x1, meaning the frequency of the p alleles is say about .25 and the population has a mean fitness of about 0.33, assuming fitness spans 0-1 in this example. Selection will act to maximize fitness at Xmax where p=.5, which will have W=1. Hence, the frequency of the A allele will increase. Now to a more complex model with a more complex adaptive landscape.

A More Complex Adaptive Landscape

In actuality adaptive landscapes are much more complex. Let us look at a more complex adaptive landscape, one with two adaptive peaks as in Fig 2:

Adaptive Landscape 2

X1 now is what is called a local maximum. A more global maximum exists at p=.75. If the population could get across the fitness valley, it could obtain an even higher average fitness (W) at Xmax. But selection can only act to increase W. This is where the other forces of evolution can help out. The other forces are migration, mutation, and random genetic drift (see evolutionary genetics for explanations).

Other considerations

Out it nature and real life, things are much more complicated. There are some estimated 30,000 genes (loci), many with multiple alleles. All of these genes interact together to yield a genotypes fitness--and these interactions can be non-linear, as in epistasis. Then their are how the other genotypes in the population affect each other's fitness, the other organism, the physical environment. In actuality, adaptive landscapes are very complex. Instead of smooth valleys and peak, the peaks can be rugged and sharp, so that a population can fall off a cliff like a bunch of stampeding lemmings or have to climb a sheer wall.

Self-Organization and Selection

Complex open systems self-organize: an incredibly important fundamental principle of nature we are just beginning to appreciate. Based in Chaos Theory, we are learning that in addition to natural selection in evolution, self-organization is a driving force that sometimes runs counter to selection. So another factor in moving populations to adaptive peaks, or getting them across fitness valleys, that comes into play, is the stability of such self-organized systems. For an in depth discussion of this important topic, see S. Kauffman's, The Origins of Order: Self-Organization and Selection in Evolution

Book Outline

Prologue
1 Coming Down the Mountain (free)
2 The Chamber
3 Turtle Rock

Day 1: Center and North (Wisdom)
4 Lajitas Lizard    
5 Center/God I: Warrior God
6 Center/God II: Process
7 Scripture
8 North/Christ (Teacher)

Day 2: Down/Below and South (Love)
9 Down/Below--Nature and Mother Earth
10 Turquoise Woman
11 South--Healer and Love

Day 3: Up/Above and West (Courage)
12 Warrior
13 Shadow Dance/Bandido
14 Turning Westward--Relationships

Day 4: East (Truth)
15 Visionary and Personal Archetypes
16 Spiritual Practice and Prayer
17 Dancin' Airport Blues