Electronic Appendix. 1. Skew indices used in this study.
1
(1) B index (Nonacs 2000, 2003)
2
B index was calculated by following equation:
3
4 5
N = the total number of males
6
pi= the proportion of copulations gained by the i th male
7
ni = time that i th male spends in a group
8
K = the total number of copulation
9
10
11
, where nmax is the maximum time that a male could be present.
12
As is shown in the above equation, the B index incorporates the residency of each male in a group. This characteristic is
13
suitable for calculating mating skew for some samples in the primate literature, given that individual male residence times often vary.
14
Finally, the B index is accurate when the total amount of ‘group productivity’ (i.e., total number of copulations in this study) is low
15
(Nonacs 2003). Studies in which two or more males failed to copulate were excluded when calculating B index.
16
In analyses of phylogenetic signal that used the test for serial independence (TFSI; Abouheif 1999), the B index was not
17
significantly associated with phylogeny (P = 0.28). Abouheif (1999) recommended using 10% as an alpha level when the power of the
18
TFSI seems low. However, the P value of the B index is still larger than the 10%, suggesting that the lack of correlation of B index with
19
phylogeny is not a result of low power.
20
21
(2) Lambda index (‘Iterative skew index’: Kokko and Lindstrom 1997)
22
The lambda index was calculated as follow:
23
24
r = rank of male (note that rank does not mean the dominance rank; instead, it reflects rank based on copulation frequency)
25
N = number of males
26
E[pr] = expected proportion of mating by r males
27
28
The lambda index does not depend on the total level of ‘group productivity’ (i.e., the number of copulation). By using the lambda index,
29
we were able to quantify the mating skew of some studies that report only the relative frequency of mating by each male.
30
We used Skew Calculator software (http://www.obee.ucla.edu/Faculty/Nonacs/) to calculate the B and lambda indices. Values
31
were calculated on a per-group basis, and these were averaged when more than one estimate was available for a species. In some cases,
32
these estimates were for the same group over time (Bercovitch 1986; Curie-Cohen et al. 1983; Nishida 1983, 1997; Possamai et al.
33
2005; Strier 1992, 1994, 1997; Strier et al. 1993).
34
35
Electronic Appendix. 2. The expected probability of female receptive overlapping.
35
The expected probability was calculated from the length of breeding season, duration of estrus, and the number of females in a
36
group (k), following Dunbar (1988, 1999) and Nunn (1999a).
37
38
P(Y) = k! / {Y!*(k-Y)!} * pY * (1-p) k-Y
39
40
In this equation, P(Y) is the probability that Y females are mating simultaneously, k is the number of females in the group (rounded to
41
nearest integer), and p is the probability of mating during the breeding season. P was calculated as 2 * (duration of estrus) / (the length
42
of breeding season), thus assuming two cycles to conception. These parameters were used to calculate the probability of zero or one
43
female mating per day, which was subtracted from 1 to give the probability that two or more females mate on a given day (because
44
probabilities must sum to 1).
45
46
47
Electronic Appendix. 3. Studies used to calculate the mating skew
47
48
ID Species #
male
# female
B index
P value of B index
lambda the maximum proportion mating
Rank of the most successful male
#
Copulation observed
Male dispersal pattern
Breeding season duration (days = birth season)
Duration of estrus (days)
Observed estrous overlap
Expected estrous overlap
synchrony index
1 mantled howler monkey
Alouatta palliata
3 15 0.02 0.18 0.33 0.47 1 34 D 365 3 7.50 2.50 0.41
2 2 10 -0.31 0.72 0.39 0.62 1 8 1.10
3 red howler monkey
Alouatta seniculus
2 - - - 1 1 1 - D 365 3 2.50 - 0.13
4 2 - - - 1 1 1 -
5 muriqui Brachyteles arachnoides
5 18 0.01 0.01 0.16 0.26 - 227 P 153 2 14.90 7.90 0.53
6 7 8 0.06 0.001 0.34 0.39 - 39 1.70
7 8 8 0.16 0 0.50 0.50 - 18 1.70
8 19 25 0.01 0 0.09 0.10 - 215 13.80
9* brown capuchin
Cebus apella 5 6 - - 0.34 0.38 1 - D 92 5 9.50 13.20 0.44
10 white-faced capuchin
Cebus capucinus
4 6 -0.63 0.91 0.50 0.50 3 4 D 212 - 15.80 2.90 -
11 red-tailed monkey
Cercopithecus ascanius
9 10 - - 0.59 0.59 - 18 D 182 3 4.10 4.10 -
12 blue monkey Cercopithecus mitis
9 12 - - 0.24 0.29 1 - D 120 2 1.50 5.90 -0.61
13 19 18 - - 0.19 0.18 4 150 12.00
14 vervet Chlorocebus 2 3 0.48 0 1 1 1 26 D 92 33 92.90 80.60 -
monkey aethiops
15 3 4 0.60 0 1 1 1 10 92.90
16 redfronted lemur
Eulemur fulvus
4 2 - - - 0.77 1 - D - - - - -
17 6 3 - - - 0.41 1 -
18 2 3 0.38 0.12 1 1 1 4
19 2 3 0.25 0.49 1 1 1 2
20 patas monkey Erythrocebus patas
5 4 - - 0.41 0.36 1 31 D 62 2 47.70 2.30 0.56
21 mountain gorilla
Gorilla gorilla 2 7 0.21 0 0.8 0.83 1 48 D 365 2 0 0.20 -0.39
22 3 11 0.15 0.001 0.63 0.66 1 35 0.60
23 ringtailed lemur
Lemur catta 3 5 0.08 0.21 0.63 0.50 1 7 D 38 1 0 2.5 -0.61
24 3 5 -0.08 1 0.22 0.57 1 7 2.5
25 2 4 -0.08 1 0 0.43 1 and 2 6 1.5
26 gray-cheeked mangabey
Lophocebus albigena
5 7 0.18 0 0.55 0.53 1 53 D 212 4 1.90 2.60 -
27 stump-tailed macaque
Macaca arctoides
7 16 - - - 0.69 1 113 D - - - - -
28 long-tailed macaque
Macaca fascicularis
10 12 - - - 0.26 1 940 D 123 15 66.60 83.00 0.48
29* Japanese macaque
Macaca fuscata
5 6 - - 1 1 1 - D 46 11 56.50 86.90 0.27
30 8 - 0.03 0 0.21 0.25 1 204 -
31 9 - 0.01 0.002 0.11 0.19 1 276 -
32 7 - 0.08 0 0.34 0.34 3 204 -
33 11 18 - - - 0.30 1 - 96.80
34 rhesus macaque
Macaca mulatta
11 12 0.05 0 0.23 0.18 3 184 D 82 9 39.80 77.60 0.23
35 5 9 0.53 0 0.86 0.86 1 28 62.00
36 6 16 - - - 0.76 1 99 89.60
37 10 17 - - - 0.72 1 85 91.40
38 10 15 - - - 0.68 1 72 87.30
39 6 12 - - - 0.56 1 34 77.60
40 7 12 0.26 0 0.59 0.57 1 42 77.60
41 9 19 - - - 0.43 1 46 94.30
42 pig-tailed macaque
Macaca nemestrina
5 22 0.19 0 0.56 0.55 1 56 D 365 13 41.70 47.10 0.31
43 3 14 0.13 0 0.58 0.57 1 150 26.30
44 black macaque
Macaca nigra 6 30 0.08 0.002 0.41 0.42 2 26 D - - - - -
45 bonnet macaque
Macaca radiata
5 28 - - - 0.46 1 - D 92 5 - 82.40 -
46 6 29 - - - 0.31 1 83.90
47 Barbary macaque
Macaca sylvanus
5 28 0 0.21 0.16 0.27 1 97 D 76 14 35.90 100.00 0.08
48 9 32 0.11 0 0.36 0.38 1 325 100.00
49 7 9 0.05 0 0.28 0.24 4 179 90.00
50 mandrill Mandrillus sphinx
3 14 0.31 0 0.79 0.80 1 30 D - - - - -
51* bonobo Pan paniscus 8 15 - - 0.24 0.28 1 - P 365 15 - 35.30 -
52* 7 8 0.03 0.002 0.20 0.23 1 13.60
53 chimpanzee Pan troglodytes
4 19 - - 0.76 0.74 1 23 P 365 14 7.8 43.40 -0.49
54 4 19 0.33 0 0.76 0.77 1 29 43.40
55 4 19 0.12 0.04 0.50 0.48 1 13 43.40
56 4 19 - - 1.00 1 1 21 43.40
57 3 19 0.28 0.07 1.00 1 1 10 43.40
58 2 19 0.21 0.02 0.88 0.89 1 3 43.40
59 2 19 - - 1.00 1 1 5 43.40
60 3 19 - - 1.00 1 1 12 43.40
61 3 19 0.47 0 0.91 0.91 1 15 43.40
62 3 19 0.27 0 0.72 0.75 1 7 43.40
63 3 19 0.36 0 0.87 0.88 1 21 43.40
64 3 19 0.03 0.06 0.38 0.51 3? 42 43.40
65 3 19 0.42 0 0.89 0.90 1 34 43.40
66 3 19 0.28 0 0.70 0.71 1 37 43.40
67 5 17 0.01 0.24 0.19 0.28 4 42 37.90
68 9 29 - - 0.27 0.27 1 27 66.30
69 9 29 0.02 0.08 0.24 0.29 1 67 66.30
70 savanna baboon
Papio anubis 8 19 0.27 0 0.59 0.59 6 41 D 365 6 - 12.80 -
71 6 19 0.10 0 0.40 0.37 2 100 12.80
72 6 19 0.12 0 0.45 0.38 4 47 12.80
73 5 19 0.10 0 0.43 0.39 2 92 12.80
74 6 19 0.09 0 0.39 0.36 4 103 12.80
75 7 19 0.05 0 0.27 0.33 5 337 12.80
76 5 19 0.07 0 0.35 0.34 3 340 12.80
77 chacma baboon
Papio ursinus 3 31 0.04 0.04 0.41 0.51 2? 35 D 365 9 - 45.60 -
78 6 7 0.04 0.002 0.31 0.34 1 53 4.30
79 3 - 0.05 0 0.41 0.52 1 194 -
80* red colobus Pilicolobus badius
8 16 - - 0.29 0.31 - - P 244 5 75 13.80 -
81 olive colobus Procolobus verus
2 2 0.48 0 0.99 0.99 1 207 D 89 - 18.40 - -
82 Verreaux’s sifaka
Propithecus verreauxi
2 3 -0.08 1 0.33 0.60 1 5 D - - - - -
83 squirrel monkey
Saimiri oerstedii
3 16 0.18 0.002 0.67 0.70 - 27 P 59 2 11.90 29.60 -
84 common langur
Semnopithecus entellus
6 19 0.07 0 0.36 0.38 1 48 D 365 6 4.20 12.80 -0.49
*: calculated from the relative frequency
49
# male: the number of males; # females: the number of females
50
‘the rank of the most successful male’: the dominance rank of the male that copulated most frequently
51
‘Empirical overlapping of female receptivity’: data from Nunn (1999a)
52
‘Expected overlapping of female receptivity’: calculated from the reproductive data in Nunn (1999a) and the number of females in each
53
study
54
‘Synchrony index’: data from Nunn (1999a)
55
56
References -- 1, 2: Jones 1985; 3, 4: Pope 1990; 5: Strier 1997; 6: Strier 1994; Strier 1992; 7: Strier 1994; Strier et al. 1993; 8: Possamai
57
et al. 2005; 9: Janson 1984; 10: Perry 1997; 11: Cords 1984; 12: Tsingalia and Rowell 1984; 13: Cords et al. 1986; 14, 15: Struhsaker
58
1967; 16, 17: Ostner & Kappeler 1999; 18, 19: Gachot-Neveu et al 1999; 20: Ohsawa et al. 1993; 21, 22: Robbins 1999; 23: Taylor &
59
Sussman 1985; 24, 25: Sauther 1991, Sussman, 1992; 26: Wallis 1983; 27: Brereton 1994; 28: de Ruiter et al. 1994; 29: Matsubara
60
2003; 30-32: Takahata 1982; 33: Inoue et al. 1991; 34: Loy 1971; 35-41: Curie-Cohen et al. 1983; 42, 43: Oi 1996; 44: Reed et al. 1997;
61
45, 46: Samuel et al. 1984; 47, 48: Paul 1989; 49: Taub 1980; 50: Dixson et al. 1993; 51: Gerloff et al. 1999; 52: Kano 1996; 53-66:
62
Nishida 1983; 67: Boesch and Boesch-Achermann 2000; 68, 69: Nishida 1997; 70-76: Bercovitch 1986; 77: Saayman 1971; 78, 79: Hall
63
and de Vore 1965; 80: Struhsaker and Pope 1991; 81: Korstjens and Noe 2004; 82: Brockman & Whitten, 1996, Brockman et al 1998;
64
83: Boinski 1987; 84: Jay 1965
65
Notes -- 8: from Table 1, copulation with ejaculation; 10: when females were cycling; 11: copulation with ejaculation; 21, 22: from Fig.
66
1; copulation only during cycling; 27: From Fig. 2(a); 28: From Fig. 1; 34: R006 was excluded from the analysis because of
67
emigration; 67: Table 4.4; 72-76: cycle stage from cycle days ‘3’ to ‘0’; 77: copulation with ejaculation; 80: copulation with
68
ejaculation; 82: conception cycle (Brockman and Whitten 1996); Vavy Masiaka group was not included because of group
69
instability; 83: From Table 2, excluding copulation by juvenile males and females;.
70
71
72
Electronic Appendix. 4. Dataset of demography, male dispersal pattern, and three indices of mating skew (species averages).
72
Species Male
dispersal patterna
# males
# females
B index
Significantly skewed? b
<.05 .05 > .1 ~ .1
lambda the maximum
proportion mating
% cases that the alpha male or the resident male
copulated most frequently
dominance rank of the male that copulated most frequently other than the alpha male
mantled howler monkey
Alouatta palliata
D 2.50 12.50 -0.15 - - 2 0.36 54.50 100 (2/2)
red howler monkey
Alouatta seniculus
D 2.00 - - - - - 1.00 100 100 (2/2)
Muriqui Brachyteles arachnoides
P 9.75 14.80 0.06 4 - - 0.27 30.95 -
brown capuchin
Cebus apella D 5.00 6.00 - - - - 0.34 38.18 100 (1/1)
white-faced capuchin
Cebus capucinus
D 4.00 6.00 -0.63 - - 1 0.50 50.00 0 (0/1) 3rd
red-tailed monkey
Cercopithecus ascanius
D 9.00 10.00 - - - - 0.59 58.86 -
blue monkey Cercopithecus mitis
D 14.00 15.00 - - - - 0.22 23.13 50 (1/2)c 4th
vervet monkey Chlorocebus aethiops
D 2.50 3.50 0.54 2 - - 1.00 100 100 (2/2)
Redfronted lemur
Eulemur fulvus
D 3.50 2.80 0.31 - - 2 1 79.50 100 (4)
patas monkey Erythrocebus patas
D 5.00 4.00 - - - - 0.41 36.18 100 (1/1)c
Mountain gorilla
Gorilla beringei
D 2.50 9.00 0.18 2 - - 0.71 74.52 100 (2/2)
Ringtailed lemur
Lemur catta D 2.70 4.70 -0.03 - - 3 0.28 50.00 67 (2/3) c 2nd d
Gray-cheeked mangabey
Lophocebus albigena
D 5.00 7.00 0.18 1 - - 0.55 52.83 100 (1/1)
stump-tailed macaque
Macaca arctoides
D 7.00 16.00 - - - - - 69.03 100 (1/1)
long-tailed macaque
Macaca fascicularis
D 10.00 12.00 - - - - - 26.00 100 (1/1)
Japanese macaque
Macaca fuscata
D 8.00 12.00 0.04 3.00 - - 0.41 41.46 80 (4/5) 3rd
rhesus macaque
Macaca mulatta
D 8.00 14.00 0.28 3 - - 0.56 59.49 87.5 (7/8) 3rd
pig-tailed macaque
Macaca nemestrina
D 4.00 18.00 0.16 2 - - 0.57 56.35 100 (2/2)
black macaque Macaca nigra - 6.00 30.00 0.08 1 - - 0.41 42.31 0 (0/1) 2nd
bonnet macaque
Macaca radiata
D 5.50 28.50 - - - - - 38.50 100 (2/2)
Barbary macaque
Macaca sylvanus
D 7.00 23.00 0.06 2 - 1 0.27 29.37 66.7 (2/3) 4th
Mandrill Mandrillus sphinx
D 3.00 14.00 0.31 1 - - 0.79 80.00 100 (1/1)
Bonobo Pan paniscus P 7.50 11.50 0.025 1 - - 0.22 25.57 100 (2/2)
Chimpanzee Pan troglodytes
P 3.94 20.10 0.23 8 3 1 0.71 72.67 88.23 (15/17) 3rd?, 4th
savanna baboon
Papio anubis D 6.14 19.00 0.12 7 - - 0.41 39.50 0 (0/7) 2nd, 2nd, 3rd,
4th, 4th, 5th, 6th
chacma baboon
Papio ursinus D 4.00 19.00 0.05 2 - - 0.38 45.82 50 (1/2) 2nd?
red colobus Piliocolobus baduis
P 8.00 16.00 - - - - 0.29 30.81 -
olive colobus Procolobus verus
D 2.00 2.00 0.48 1 - - 0.99 99.03 100 (1/1)
Verreaux’s sifaka
Propithecus verreauxi
D 2.00 3.00 -0.08 - - 1 0.33 60.00 100 (1/1)
squirrel monkey
Saimiri oerstedii
P 3.00 16.00 0.18 1 - - 0.67 70.37 -
common langur
Semnopithecu s entellus
D 6.00 19.00 0.07 1 - - 0.36 37.50 100 (1/1)
total 43 3 11 76.1 (51/67)
a: D = dispersal; P = philopatric
73
b: the number of studies classified by the P value of the B-index
74
c: resident male
75
d: the mating frequencies of the alpha (central) male and beta male was same
76
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