514 Paul Thompson
Using theX^2 result and 1 degree of freedom allows a probability value to be
determined.
In this case, the relevant probability is 0.63. This is the probability that chance
alone could have produced the discrepancy between the H-D expected values and
the observed values. Since we are measuring the probability that chance alone
could have producedthe discrepancy(not to be confused withthe similaritybe-
tween the two^44 ), the higher the probability, the more robust one’s confidence
that there areno factors other than chancecausing the discrepancy and, hence,
that there is a good fit between the values expected based on the model and the
observed values^45 ; any discrepancy is a function of chance alone.
The elementary framework sketched above has been expanded to include the
Wright-Fisher model of Random Drift, mutations, inbreeding and other causes of
non-random breeding, migration speciation, multiple alleles at a locus, multi-loci
systems, phenotypic plasticity, etc. One important expansion relates to interdemic
selection.
The account so far describes intrademic selection. That is, selection of individ-
uals within an interbreeding population — a deme. However, the mathematical
model also permits the exploration of interdemic selection (selection between ge-
netically isolated populations) using adaptive landscapes. One outcome of such
explorations is a sophisticated account of why and how populations reach sub-
maximal, sub-optimal peaks of fitness. Richard Lewontin, building on concepts
set out by Sewell Wright, provided the first mathematical description of this phe-
nomenon.
Consider a population genetic system with two loci and two alleles (here for
simplicity I revert to upper and lower case letter for alleles and for dominance and
recessiveness). The possible combinations of alleles is:
AB Ab aB ab
AB AABB AABb AaBB AaBb
Ab AABb AAbb AaBb Aabb
aB AaBB AaBb aaBB aaBb
ab AabBb Aabb aaBb aabb(^44) If one were to determine the probability that thesimilaritywas due to chance alone, the
lower the probability the more robust the isomorphism. That is, the lower the probability that
chance alone has produced an agreement of the two domains, the higher the probability that the
agreement is due to the intrinsic features of the domains (e.g., the ontology and causal structure).
(^45) Determining at precisely what probability value one is justified in declaring discrepancies are
important (significant) is controversial. A convention has emerged that aP<.05 cutoff yields
statistical significance for the discrepancies. That is, if the probability that the discrepancy is
due to chance is less than .5 it is reasonable to reject a claim that there is a fit between the
model and the observed data — the discrepancy is significant and cannot be dismissed.