P. 10: One needs the to know (from calculus) that lim_{n->infty}
(1+x/n)^n = e^x, that is, this limit needs to hold for any x,
not just for x=1.
Eq. I-31: Missing prime on p_f
Eq. I-12, I-13: I would have changed p_i on the left hand side of
these equations to say, p_i^* as p_i is already defined as the
gene frequency at the haploid phase of the same generation.
Using the same symbol would imply that these quantities in
general are equal but this only follows when the assumption of
random mating is made in the last paragraph on p. 8.
P. 361 (References): Dempster et al. (1977) seems to be in volume 39,
pages 1-38, at least according to
http://links.jstor.org/sici?sici=0035-9246%281977%2939%3A1%3C1%3AMLFIDV%3E2.0.CO%3B2-Z
P. 19: It is not entirely true that one can compute all gamete
frequencies from gene frequencies if the population is in linkage
equilibrium (at least if LE is defined in a narrow sense) because
P_AB=p_A p_B, P_AC=p_A p_C, P_BC=p_B p_C don't really imply that
P_ABC = p_A p_B p_C etc...
P. 42, first paragraph: "...then the number of gametes coming
from AA, Aa, and aa parents will be (respectively) 1/2 N p^2
W_AA, ...." I don't think this is entirely correct. In general
the contributions will depend on who mates with who -- under
random mating there will be a common additional factor bar W in
each of the three expected numbers (so it is only true that "the
number of gametes" are proportional to "..."
Also, in the paragraph after eq. (I-31) it is perhaps worth
noting that Hardy-Weinberg proportions at this point only follow
if the product-rule mating-fertility assumption is made (in
addition to random-mating)
P. 30: Complement 1 and 6: These seem to be identical except for
the last sentences. Compl. 1: "gene" misspelled.
Mutational load: I started thinking about the fact that these
results are only true for infinite population size. Of course,
someone have looked at the expected mutational load in a finite
population which differs and is no longer independent of s:
http://www.daimi.au.dk/~tbata/tap/BataillonKirk.pdf
P. 54: Solution of the ressisive case: There is no need to
approximate sp^2(1-p)/(1+2sp^2) (eq. II-52) with sp^2(1-p). The
only approximation needed is to replace Delta p with dp/dt such
that
int (1 + 2sp^2)/(p^2(1-p)) dp = s int dt
int [1/p + 1/p^2 + (2s+1)/(1-p)] dp = st + C
which can be solved for t
t = [ ln p/(1-p)^(1+2s) - 1/p - ln p0/(1-p0)^(1+2s) + 1/p0 ] / s
P. 55. There seems to a sign error in equation II-97. The
expression on the right hand side seems to be equal to -t.
P. 74, second paragraph: There appear to be missing bars on w_3,
w_4, w_7 and w_8.
P. 128, eq. IV-3: m_{li} should be m_{1i}.
P. 128, eq. IV-5: Uppercase P here? (P_{AA})
P. 140, after eq. IV-29: "When m > s there is no equilibrium"
(not m < s here).
P. 159, 2. paragraph: "In some case (recessive advantageous gene)
a wave does not even exist". I'm not sure what is meant here. I
looked at this numerically and I was not able to find a set of
nontrivial initial conditions for which a stationary wave front
was not formed. I suppose the theoretical result that only "the
growth rate at low densities" (in this case d/dp p*(p) in p=0) is
important (Kot 1996 in Ecology) now breaks down (since this
quantity in fact now becomes zero and that the tail of the wave
front instead is more "pushed" forward by selection behind its
tail...)
P. 165, eq. V-3: a factor (1-f) is missing here.
P. 171, last paragraph: The reference should be to eq. V-16 and
not V-13.
P. 172, first paragraph: The reference here should be to V-15 and
not V-12.
P. 129, second last paragraph: The heterozygote frequencies are
_increased_ (not diminished) by 2 Cov(p,q) (but most covariances
are negative). This agrees with the special case of q=1-p (two
alleles) in which case 2 Cov(p,q) = 2 Cov(p,1-p) = - 2 Var(p)
(IV-8).
P. 159, Exerc. 1. "Find three set of gene frequencies": Perhaps
add something like "more heterozygotes of a particular type"
here. Otherwise, it is not clear if total heterozygosity (which
can not be in excess) is meant.
P. 208: Between eqs. (VI-47) and (VI-48): An additional
approximation is used here (not just rearrangement) valid for
small 1/N_i....
P. 210: Derivation of N_e=(4N-2)/(2+Vn): Instead of thinking of
n_1,n_2,...,n_N as constants it is perhaps better to think of
these quantities as random variables just as in the idealized
model. The probability P in eq. VI-54, the probability that
individuals I and J from which to genes in the next generations
descends from are identical, P=P(I=J), can then be thought of as
the conditional probabability
P(I=J | n_1,n_2,...n_N)
The unconditional probability of interest is then given by
P(I=J) = sum_{all n_1,...n_N} P(I=J | n_1,n_2,...n_N) P(n_1,...,n_N)
= E P(I=J | n_1,...,n_N)
= 1/(2N(2N-1)) E sum n_i(1-n_i) = ....
where the expectation is taken with respect to the distribution
of n_1,...n_N leading to equation VI-57. So there is need to
introduce the expectation E(1/N_t)...
Chap. VI, Ex. 10: I suppose N _is_ supposed to decline here?
P. 240, "the largest root is relevant. We can approximate it
by..." Actually the smallest root is being approximated here.....
P. 245, The branching process: p_0, p_1, p_2 (not p_l) here...
P. 320, delta_{ij} (not "delta_{i}j")
Ex. 1, Chap. IX: I suppose you need to say that the recombination
rate r=1/2 here since for example the mean fenotype in F2 depends
on r.