Conclusions and Discussion - Genetic Diversity in Establishing Plant Populations: Founder Number and Geometry - page 329

Suppose that one result of these founder spationumeric differences is that
the initially identical founding population allele frequencies come to differ
between the two derived populations as shown in Table 18.1.

Table 18.1 Populations X and Y are founded identically (including with founding population
allele frequencies for selected loci as shown), except for the geometry of the founders. Owing
to these differing geometries, after several generations, the X and Y populations derived
from the respective founding conditions have come to differ in the gene frequencies of those
alleles as shown.

Founding population Derived population

Y X Y X

Gamete allele frequencies

for allele:

Locus 1, allele 1d 0.28 0.28 0.25 0.3

Locus 2, allele 2g 0.78 0.78 0.75 0.8

Locus 3, allele 3c 0.03 0.03 0.05 0.01

Note that the changes in the frequencies of these alleles from the
founding to the derived populations are not large. In the derived X
population, the probability of a gamete having the alleles 1d, 2g, and 3c will
be 0.0094 (that is, 0.25 * 0.75 * 0.05, which is approximately 1 in 100), while
the probability of this multilocus combination occurring in the derived
Y population will be 0.0024 (approximately 1 in 400). Population X has a
probability that is approximately four times the probability of generating
such a gamete in population Y.
But can minor to moderate differences in founding geometry alone
bring about multilocus probability differences of the above magnitude
between two populations that were otherwise founded identically? In the
following arguments, we use change in heterozygosity to demonstrate
that spationumeric founding conditions can induce alterations in allele
frequencies to the degree shown in Table 18.1, and thus associated changes
in multilocus probabilities occur on a regular basis. Note that we calculated
expected heterozygosity as (Chapter 5):

m
∑

H = 1 − p i 2

1

where p i is the frequency of the i th of m alleles. Can shifts in allele frequencies
of the magnitude used in the three-locus example just above occur because of
the loss of copies of alleles at unique alleles of higher frequency in changing
populations of the type explored in this topic? If such shifts do occur, then
we should be able to detect corresponding shifts in expected heterozygosity
as calculated above by NEWGARDEN.
Consider just the allele called “Locus 2, allele 2g” in Table 18.1. This
allele has a frequency of 0.78 in both populations X and Y at founding.