Supplementary Table S3
The probabilities that each of the 11 possible matings will give rise to offspring of each phenogenotype in the population-genetic model (Model
1) with oblique/horizontal cultural transmission of paternity beliefs. The rows r1-r11 show all permitted genotype matings. (Note that not all
combinations are possible given our assumptions, e.g. two m individuals cannot be monogamous. Only the permitted matings are shown in the
table.) Column c0 shows the frequency of each genotype mating under the assumption of random mating, where x1, x2, x3, x4 are the
frequencies of MBp, MBs, mBp and mBs in males and y1, y2, y3 and y4 the equivalent for females. Columns c1-c14 show the probabilities that the
offspring of each mating will adopt each phenogenotype, given haploid genetic inheritance and oblique/horizontal cultural transmission (where z
is the frequency of Bp in the previous generation, i.e. z=x1+y1+x3+y3 and 1-z is the frequency of Bs). The bias b1 promotes Bs in the offspring of M
matings, and the bias b2 promotes Bp in the offspring of m matings. See Methods for further details.
OFFSPRING
MATING
FREQ
Monogamy
Polygyny
Polyandry
Polygynandry
c0
c1
c2
c3
c4
c5
c6
c7
c8
c9
c10
c11
c12
c13
Male1 Female1 Male2 Female2
MBpp MBsp MBpp MBsp mBpp mBsp MBpp MBsp mBpp mBsp MBpp MBsp
mBpp
r1
M
M
(x1+x2) (y1+y2) z - b1 z 1-z+b1 z
r2
m
M
M (x3+x4)(y1+y2)
0.5 z 0.5 (1-z) 0.5 z 0.5 (1-z)
(y1+y2)
r3
M
m
M
(x1+x2) (y3+y4)
0.5 z 0.5 (1-z) 0.5 z 0.5 (1-z)
(x1+x2)
r4
M
m
m
M (x1+x2) (y3+y4)
3/8 z 3/8 (1-z)5/8 z
(x3+x4) (y1+y2)
r5
M
m
m
m (x1+x2) (y3+y4)
1/8 z 1/8 (1-z)7/8 z
(x3+x4) (y3+y4)
r6
m
M
M
m (x3+x4) (y1+y2)
3/8 z 3/8 (1-z)5/8 z
(x1+x2) (y3+y4)
r7
m
M
m
m (x3+x4) (y1+y2)
1/8 z 1/8 (1-z)7/8 z
(x3+x4) (y3+y4)
r8
m
m
M
M (x3+x4) (y3+y4)
0.5 z 0.5 (1-z) 0.5 z
(x1+x2) (y1+y2)
r9
m
m
M
m (x3+x4) (y3+y4)
1/8 z 1/8 (1-z)7/8 z
(x1+x2) (y3+y4)
r10
m
m
m
M (x3+x4) (y3+y4)
1/4 z 1/4 (1-z)3/4 z
(x3+x4) (y1+y2)
r11
m
m
m
m (x3+x4) (y3+y4)
z+b2(1-z)
(x3+x4) (y3+y4)
c14
mBsp
5/8 (1-z)
7/8 (1-z)
5/8 (1-z)
7/8 (1-z)
0.5 (1-z)
7/8 (1-z)
3/4 (1-z)
1-z-b2(1z)