Founder Number and Allelic Diversity - Genetic Diversity in Establishing Plant Populations: Founder Number and Geometry - page 86

number of unique alleles retained in the founding population when that
founding population includes only 100 or 200 individuals. At higher founder
numbers (300 or 400 individuals), there is little or no difference in the mean
number of unique alleles in the founding populations, with approximately
100% of the available alleles retained in both cases. Thus, it is not just the
one allele of lowest frequency, but also the number of low-frequency alleles
at a locus that ultimately affects unique allele retention. This outcome is
due to the multiplicative nature of the probabilities of drawing each allele
in calculating the total probability of retaining all alleles at a locus given a
certain number of founders (Lawrence et al. 1995).
This effect of higher numbers of low-frequency unique alleles acting
to lower the probabilities of capturing all unique alleles, although
seemingly small, may take on some relevance when considering entire
genomes. According to Lawrence et al. (1995), considering one locus with
two alleles with frequencies 0.95 versus 0.5 in a completely outcrossing
source population, drawing 86 founders from that population would
give a probability of capturing at least one copy of both alleles among the
founders of p = 0.9999 (their table 1, p. 91). They further argue (p. 95) that a
reasonable estimate of the number of polymorphic structural genes for the
typical plant is approximately 20,000 loci. If one is interested in calculating
the probability of capturing at least one copy of each allele for 20,000 such
loci with two alleles as described above (i.e., the least frequent allele having
frequency = 0.05), that probability can be estimated as p = (0.9999) 20,0000
= 0.135, or 13.5%. Using NEWGARDEN, we estimated that for a source
population with one locus with 20 different alleles, all at equal frequency =
0.05, the probability of capturing all unique alleles with a founding sample
of 86 individuals is 0.9973 (out of 10,000 replicate draws of 86 founders from
such a virtual source population, 27 draws were missing alleles). While this
does not seem like much of a difference, if estimated for 20,000 such loci,
the probability of capturing all unique alleles in a sample of 86 individuals
becomes 3.28 * 10 -22 . Increasing the number of low-frequency alleles at loci
does decrease the probability of capturing all unique alleles, especially with
lower numbers of founders.
The above simple examples concerning loci array differences were
not presented to demonstrate new population genetics principles. Rather,
they were presented to give examples of how NEWGARDEN can be used
to explore ways in which variations in loci array allelic composition can
infl uence founder effects, along with demonstrating the form of the actual
input. However, they do serve as reminders that in the reintroduction of a
species, or the founding of a population, or in the sampling of a population
for genetics analyses, the initial condition of the population genetics of
the source population can have profound effects on founding populations
relative to the size of the founding group, and further, as will be seen, on