Appendix
Appendix 1
Neolamprologus pulcher is a cooperatively breeding cichlid endemic to Lake Tanganyika, East Africa.
The fish live in breeding groups composed of a dominant pair and several subordinates of both sexes
and of varying size and age (Taborsky & Limberger, 1981; Taborsky, 1984; Balshine et al., 2001;
Duftner et al., 2007; Wong & Balshine, 2011). Sexual maturity is reached at a size of ~3.5cm in both
sexes (Taborsky 1985), and relatedness between dominants and subordinates decreases with increasing
subordinate size, due to breeder turnover (Taborsky & Limberger, 1981). Consequently, most large
helpers are virtually unrelated to their respective dominant breeders (Dierkes et al., 2005). This limits
the indirect fitness benefits individuals can gain from cooperation (Stiver at al., 2005; Zöttl et al.,
2013b). Breeding groups defend territories that provide them with shelter for refuge and breeding
(Balshine et al., 2001; Heg et al, 2004; Heg et al., 2008a). In order to be tolerated, subordinates help
raising the dominants’ broods by caring for offspring and maintaining and defending the territory
(Taborsky 1984). The adaptive value of reciprocal commodity trading between fellow group members
has been well established in this species, using field and laboratory experiments (Taborsky, 1985;
Balshine-Earn et al., 1998; Bergmüller & Taborsky, 2005; Bergmüller, Heg, & Taborsky, 2005; Zöttl
et al., 2013a,b; Fischer et al., 2014). Territories of N. pulcher are typically aggregated in colonies of a
few up to some hundred breeding groups located in close vicinity (Heg et al., 2005, 2008a; Stiver et al.,
2007). Despite higher predator densities within such colonies, individuals prefer territories inside a
colony over vacancies at the colony edge (Heg et al., 2008a). Fish frequently visit the territories of other
groups, which allows them to establish extended safe havens and social relations beyond their own
group (Bergmüller et al., 2005).
Appendix 2
In order to obtain fitness estimates for individually marked N. pulcher in our study colony over the
course of the study period, we combined previous information on (i) the effect of subordinates’ help on
dominants’ reproduction, (ii) the subordinates’ share in a group’s reproduction, and (iii) estimates of
within-group relatedness, with our estimates of (a) group reproductive output, (b) the number of large,
potentially sexually mature subordinates in a group, and (c) individual survival. We first established
equations defining direct and indirect fitness based on the above mentioned parameters for each of the
four different classes of individuals, i.e. dominant males, dominant females, subordinate males, and
subordinate females (equations 1-7). We then parameterised these equations with the estimates derived
from the literature (see below: 3) to 12)) and inserted our measures of the numbers of juveniles produced
in a group and the number of large helpers found in a group (see below: 1) and 2)). We used this as
estimates of direct and indirect fitness for individuals surveyed over the course of our study period. It
is important to note that these estimates do not reflect a specific individual’s actual reproductive output
or fitness. Rather, it allows for a comparison of the relative fitness effects derived from group
membership in groups of different size and structure. Further, it allows for a comparison of the relative
importance of direct and indirect fitness components for fish of different sex and status.
We assumed that across all territories, the effects of the subordinates´ helping on dominants´
reproduction, relatedness between individuals, and the reproductive share of subordinate helpers would
be similar.
For our estimates of direct, indirect, and inclusive fitness, we assumed the following values for
the required variables:
1) niJ : the number of juveniles in territory i
2) niLH : the number of potentially mature helpers (subordinates >3.5 cm standard length) in
territory i
3) τ: the assumed sex ratio of large helpers (0.5)
4) μm: the reproductive share of male helpers (0.045)
5) μf : the reproductive share of female helpers (0.145)
6) μmf : the reproductive share of a large helper of unknown sex (0.095)
7) rLH-DM : the relatedness estimate between large helpers and their respective dominant male
(0.05)
8) rLF-DF : the relatedness estimate to their respective dominant female (0.2)
9) rLH-DP : the relatedness between large helpers and their respective dominant pair (0.125)
10) rLH-LH : the relatedness between large helpers from the same group (0.2)
11) rO : the relatedness to own offspring (0.5)
12) β : the increase in a dominant pair’s production of juveniles due to the presence of each
large helper (0.18)
The estimates of the subordinates’ share in reproduction are based on a meta-analysis of
multiple studies on extra-pair reproduction in N. pulcher (Taborsky 2016). The estimates of relatedness
between group members are based on a study investigating within-group relatedness with help of DNAmicrosatellites in wild N. pulcher groups (Dierkes et al. 2005). The estimate of the increase in pair
reproduction due to the presence of a large helper (‘helping effect’) was obtained by an experimental
lab study (Taborsky 1984).
Consequently, we estimated for each marked individual its direct and indirect fitness based on
the number of juveniles and the number of large subordinates counted in the individual´s territory in a
given year, multiplied by the scaling factors ‘reproductive share’, ‘relatedness’ and ‘helping effect’. We
should like to mention that only group members from the onset of maturity were individually marked
to not compromise group composition, as catching smaller individuals may cause significant
disturbance and subsequent changes in group structure. Therefore, our fitness estimates are confined to
large group members (potentially mature helpers and dominant breeders). The sum of direct and indirect
fitness estimates of marked individuals was taken as the estimate of the individual´s inclusive fitness.
(i) The direct fitness estimate of dominants (equations 1 and 2) reflects the number of juveniles
in the territory that were the dominant individual´s own offspring, which it would have produced also
in the absence of subordinate helpers. Thus it was calculated as the number of juveniles in the territory
(nij), from which we subtracted the share of reproduction of sexually mature helpers of the same sex
(niLH x τ x μm or niLH x τ x μf) and the number of juveniles produced through the effects of subordinate
helpers (niJ x β x niLH). We multiplied this number, i.e. the number of juveniles a dominant would have
produced in the absence of helpers, by the relatedness between parents and offspring (rO).
Equation 1 (direct fitness of dominant males):
(niJ - niLH x τ x niJ x μm - niJ x β x niLH) x rO
Equation 2 (direct fitness of dominant females):
(niJ - niLH x τ x niJ x μf - niJ x β x niLH) x rO
(ii) The direct fitness estimate of subordinates (equations 3 and 4) reflects those juveniles in the
territory that were the subordinate individual´s own offspring. Thus it was calculated as the number of
juveniles (nij) from which we subtracted the share in reproduction of other subordinates of the same sex
[(niLH - 1) x τ x niJ x μm or (niLH - 1) x τ x niJ x μf]. We multiplied this by the subordinate´s share in
reproduction (μm or μf). This number, i.e. the number of juveniles that were the subordinate’s own
offspring, was then multiplied by the relatedness between parents and offspring (rO).
Equation 3 (direct fitness of subordinate males):
(niJ - (niLH - 1) x τ x niJ x μm) x μm x rO
Equation 4 (direct fitness of subordinate females):
(niJ - (niLH - 1) x τ x niJ x μf) x μf x rO
(iii) The indirect fitness estimate of dominants (equations 5 and 6) reflects the number of
juveniles that were offspring of related subordinates. Thus, it was calculated as the number of juveniles
(niJ) multiplied by the number of large helpers present in the territory (niLH) times the reproductive share
of a large subordinate of unknown sex (μmf). This, i.e. the number of offspring produced by all large
subordinates in the group, was then multiplied by the relatedness between the dominant and large
subordinates (rLH-DM or rLH-DF).
Equation 5 (indirect fitness of dominant males):
niJ x niLH x μmf x rLH-DM
Equation 6 (indirect fitness of dominant females):
niJ x niLH x μmf x rLH-DF
(iv) The indirect fitness estimate of subordinates (equation 7) reflects the boost in dominants´
reproduction resulting from the subordinate´s help, and the effects the latter had on the reproduction of
related subordinates in their territory. Thus it was calculated as the number of juveniles that were
offspring of the dominants that would have been produced also in the absence of the focal subordinate’s
help (niJ - (niLH - 1) x niJ x μmf) multiplied by the boost in dominants´ reproduction due to the focal
subordinate´s help (β) times the relatedness between the subordinate and the dominants (rLH-DP). To this
we added other subordinates’ share in reproduction [(niLH - 1) x niJ x μmf] multiplied by their relatedness
to the focal subordinate (rLH-LH).
Equation 7 (indirect fitness of subordinates):
(niJ - (niLH - 1) x niJ x μmf) x β x rLH-DP + (niLH - 1) x niJ x μmf x rLH-LH
Appendix 3
To estimate the relationship between group size and nearest neighbour distance, we fitted a linear mixed
effects model (LME) including group size as the response variable, nearest neighbour distance as the
explanatory variable, and the territory’s identity and year of sampling as random factors. Diagnostic
plots did not reveal any indication of a violation of the assumption of normally distributed error
structures (no systematic correlation between the estimated residuals and the fitted values, and a good
fit of the residuals in the Q-Q plot). The full model fitted the data significantly better than the respective
null model including only the intercept and the random factors (Table Appendix 3) and revealed a
negative correlation between nearest neighbour distance and group size (Figure Appendix 3).
Table Appendix 3: comparison between the full model and the respective null model as described in
Appendix 3.
Degrees
AIC
BIC
Log
Likelihood Δ
P-value
of
Likelihood
ratio test degrees
(based on
freedom
of
(𝜒 2 )
𝜒2)
freedom
null
4
1953
1969.3
-972.51
model
full
5
1943
1963.5
-966.52
11.979
1
0.0005
model
Figure Appendix 3: Each group’s size in relation to its nearest neighbour distance in a given year.
Data collected in year T=2011 are represented by circles and the dashed line. Data collected in year
T=2012 are represented by triangles and the dotted line. Data collected in year T=2013 are
represented by squares and the solid line. Trendlines are based on values predicted by the respective
linear models, and depict significant negative correlations between group size and nearest neighbour
distance in each year.
Appendix 4
To investigate whether nearest neighbour distance was a good proxy of actual local colony density
(measured as absolute number of territories within 2 metres distance), we fitted a GLM with logistic
link function (family: quasipoisson). This model included the number of territories within 2 metres
around a given territory (averaged across all years in which the territory was occupied) as response
variable and the respective territory’s nearest neighbour distance (averaged across all years in which
the territory was occupied) as explanatory variable. The model revealed a negative correlation between
the number of territories within a 2 metres perimeter and the territory’s nearest neighbour distance
(Table Appendix 4; Figure Appendix 4).
Table Appendix 4: comparison between the full model and the respective null model as described in
Appendix 4.
Estimate Standard t value
P-Value Δ
Deviance Scaled
P-Value
error
(based
degrees
deviance (based
on t)
of
on
freedom
𝜒2 )
intercept
2.946
0.099
29.562
<0.0001
444.92
nearest
-1.44
0.161
-8.945
<0.0001 1
737.18
108.53
<0.0001
neighbour
distance
Figure Appendix 4: For each territory (n=166) the average number of territories within 2 metres
(from centre to centre) and the average nearest neighbour distance (also from centre to centre) were
assessed (averaged across all years in which the territory was inhabited). Each circle represents a
unique territory and the trendline is based on the respective GLM revealing a significant negative
relationship between nearest neighbour distance and local colony density (measured as the number
of close territories).
Appendix 5
To test whether a group’s size in one year was correlated with its size in the subsequent year, we fitted
a GLMM with logarithmic link function to account for the assumed Poisson error structure (GLMM
log link; family: Poisson). This model included one response variable (‘group size in year T+1’), a
single explanatory variable (‘group size in year T’), and a group’s identity and the year of sampling as
random factors. The model’s dispersion was tested using the R package blmeco version 1.1 (KornerNievergelt et al. 2015), and it was marginally underdispersed (dispersion parameter = 0.832). The model
revealed a positive correlation between a group’s size in one year and its size in the subsequent year for
both sampling periods (Table Appendix 5; Figure Appendix 5).
Table Appendix 5: comparison between the full model and the respective null model for the analysis
of group size correlations between years as described in Appendix 5.
Estimate Standard z value P-Value Deviance
Δ
P-Value
𝜒2
error
(based
degrees
(based
on z)
of
on
freedom 𝜒 2 )
intercept 1.266
0.067
19.018 <0.0001 1320.8
group
0.069
0.009
7.643
<0.0001 1128.5
192.22 1
<0.0001
size in
year T
Figure Appendix 5: A group’s size in a given year as a function of its size in the previous year. Circles
represent groups observed between 2011 and 2012, triangles represent groups observed between
2012 and 2013. Trendlines are based on values predicted by the respective GLMs and represent
significant relationships. Points were jittered around their x- and y-values to increase visibility.
Appendix 6
To analyse the effects of group size and nearest neighbour distance on a group’s reproductive output
and its probability of successful reproduction in the next year, we fitted GLMMs with either logarithmic
link function to account for an assumed Poisson error structure (counts of juveniles; GLMM log link),
or with logistic link function to account for an assumed binomial error structure (probability of
reproduction in the subsequent year; GLMM logit link). These models included one response variable
(‘reproductive output’ or ‘reproduction in the subsequent year: yes/no’), two explanatory variables
(‘group size’ and ‘nearest neighbour distance’), the interaction between the explanatory variables, and
the territory’s identity and the year of sampling as random factors. The Poisson models’ dispersion was
tested using the R package blmeco version 1.1 (Korner-Nievergelt et al. 2015), and it was not
significantly overdispersed (dispersion parameter = 1.172). Both full models fitted the data significantly
better than the respective null models only including the intercept and the random factors (Tables
Appendix 6a and 6b), and both revealed an interactive effect of group size and nearest neighbour
distance on the respective response variable (Tables Appendix 6c and 6d; Figure 2).
Table Appendix 6a: comparison between the full model for the analysis of reproductive output and
the respective null model as described in Appendix 5.
Degrees AIC
BIC
Log
Deviance Likelihood Δ
Pof
Likelihood
ratio test degrees Value
freedom
of
(based
(𝜒 2 )
freedom on
𝜒2 )
null
3
1484.9 1497.1 -739.43
1478.9
model
full
6
1424.3 1448.8 -706.16
1412.3
66.539
3
<0.0001
model
Table Appendix 6b: comparison between the full model for the analysis of the chances of
reproduction in the subsequent year and the respective null model as described in Appendix 5.
Degrees AIC
BIC
Log
Deviance Likelihood Δ
Pof
Likelihood
ratio test degrees Value
freedom
of
(based
(𝜒 2 )
freedom on
𝜒2 )
null
3
370.74 382.03 -182.37
364.74
model
full
6
295.06 316.89 -141.53
283.06
81.674
3
<0.0001
model
Table Appendix 6c: output of the full model for the analysis of reproductive output
Estimate
Standard
z value
P-Value
Likelihood
error
(based on z) ratio
test
2
(𝜒 )
intercept
-0.078
0.536
-0.145
0.884
group size
0.007
0.038
0.174
0.862
nearest
-1.202
0.313
-3.841
0.0001
neighbour
distance
interaction
0.224
0.051
4.368
<0.0001
18.814
P-Value
(based on
𝜒2 )
<0.0001
Table Appendix 6d: output of the full model for the analysis of the chance of reproduction in the
subsequent year
Estimate
Standard
z value
P-Value
Likelihood P-Value
error
(based on z) ratio
test (based on
2
(𝜒 )
𝜒2 )
intercept
1.094
0.906
1.208
0.227
group size
0.007
0.136
0.051
0.96
nearest
-2.354
0.952
-2.471
0.135
neighbour
distance
interaction
0.433
0.181
2.397
0.017
6.468
0.011
Appendix 7
To compare the survival probabilities between the different classes of individuals, we fitted a GLMM
with logistic link function to account for an assumed binomial error structure (GLMM logit link). This
model included the response variable (‘survival: yes/no’) and the explanatory variable (‘class:
DM/DF/SM/SF’), as well as an individual’s size as covariate and its territory’s identity as random
factor. Subsequently, we performed Tukey tests for all pairwise comparisons between different classes.
The full model fitted the data better than the respective null model only including the intercept, the
covariate, and the random factor (Table Appendix 7a); and it revealed significant differences in survival
probabilities between different classes of individuals. The Tukey tests revealed that this was driven by
a difference between the survival probabilities of dominant males and dominant females (Table
Appendix 7b).
Table Appendix 7a: comparison between the full model for the analysis of survival differences
between different classes of individuals and the respective null model as described in Appendix 7
Degrees AIC
BIC
Log
Deviance Likelihood Δ
Pof
Likelihood
ratio test degrees Value
freedom
of
(based
(𝜒 2 )
freedom on
𝜒2 )
null
3
368.72
379.44
-181.36
362.72
model
full
6
361.02
382.45
-174.51
349.02
13.699
3
0.0033
model
Table Appendix 7b: pairwise comparisons of survival probabilities between different classes of
individuals (dominant males: DM; dominant females: DF; subordinate males: SM; subordinate
females: SF)
Estimate
Standard error
z value
P-Value (based
on z)
DM – DF
-1.525
0.5
-3.052
0.0112
SF – DF
-0.571
0.426
-1.343
0.5165
SM – DF
-0.76
0.383
-1.983
0.1823
SF – DM
0.954
0.675
1.413
0.4719
SM – DM
0.765
0.591
1.295
0.5471
SM – SF
-0.188
0.414
-0.456
0.9659
Appendix 8
To analyse whether group size or nearest neighbour distance differentially influence individual survival,
we fitted GLMMs with logistic link function to account for an assumed binomial error structure
(GLMM logit link). These models included the response variable (‘survival: yes/no’), one explanatory
variable (‘group size’ or ‘nearest neighbour distance’), a second explanatory variable (‘class:
DM/DF/SM/SF’), the interaction between both explanatory variables, the individual’s size as covariate,
and the territory’s identity as random factor. Likelihood ratio tests revealed that the included interaction
did not increase the model’s fit in either case (Table Appendix 8a and 8b). We consequently refitted the
models without the interaction and compared these to the respective null models only including the
intercept, the covariate, and the random factor (Table Appendix 8c and 8d). The refitted models fitted
the data better than the respective null models, but subsequent single term deletions using likelihood
ratio tests revealed no significant influence of either group size or nearest neighbour distance on
individual survival (Table Appendix 8e and 8 f), although there was a trend for survival to be lower in
larger groups (Table Appendix 8e; Figure Appendix 8).
Table Appendix 8a: Likelihood ratio test output for the influence of including the interaction between
individual class and group size in the full model described in Appendix 8
Degrees
of AIC
Likelihood ratio P-Value (based
freedom
on
test (𝜒 2 )
𝜒2 )
null model
363.56
model
with 1
364.88
3.324
0.0683
covariate
full model
3
359.48
1.918
0.5896
Table Appendix 8b: Likelihood ratio test output for the influence of including the interaction between
individual class and nearest neighbour distance in the full model described in Appendix 8
Degrees
of AIC
Likelihood ratio P-Value (based
freedom
on
test (𝜒 2 )
𝜒2 )
null model
365.18
model
with 1
365.34
2.157
0.142
covariate
full model
3
363.01
3.825
0.281
Table Appendix 8c: the comparison between the full model for the analysis of survival differences
between different classes of individuals and the influence of group size and the respective null model
as described in Appendix 8
Degrees AIC
BIC
Log
Deviance Likelihood Δ
Pof
Likelihood
ratio test degrees Value
freedom
of
(based
(𝜒 2 )
freedom on
𝜒2 )
null
3
368.72
379.44
-181.36
362.72
model
full
7
359.48
384.48
-172.74
345.48
17.245
4
0.0017
model
Table Appendix 8d: the comparison between the full model for the analysis of survival differences
between different classes of individuals and the influence of nearest neighbour distance and the
respective null model as described in Appendix 8
Degrees AIC
BIC
Log
Deviance Likelihood Δ
Pof
Likelihood
ratio test degrees Value
freedom
of
(based
(𝜒 2 )
freedom on
𝜒2 )
null
3
368.72
379.44
-181.36
362.72
model
full
7
363.01
388.01
-174.5
349.01
13.713
4
0.0083
model
Table Appendix 8e: Likelihood ratio test output for the influence of individual class and group size
on individual survival in the final model described in Appendix 8
Degrees
of AIC
Likelihood ratio P-Value (based
freedom
on
test (𝜒 2 )
𝜒2 )
null model
359.48
model with group 1
361.02
3.526
0.0598
size
model
with 3
366.92
13.447
0.0038
individual class
model
with 1
360.81
3.33
0.068
individual size
Table Appendix 8f: Likelihood ratio test output for the influence of individual class and nearest
neighbour distance on individual survival in the final model described in Appendix 8
Degrees
of AIC
Likelihood ratio P-Value (based
freedom
on
test (𝜒 2 )
𝜒2 )
null model
363.01
model
with 1
361.02
0.014
0.904
nearest neighbour
distance
model
with 3
370.47
13.46
0.0037
individual class
model
with 1
363.27
2.266
0.1323
individual size
Figure Appendix 8: Survival probabilities of marked individuals as a function of their respective
group’s size. Circles represent dominant females (“DF”; n=94), squares subordinate females (“SF”;
n=58), triangles subordinate males (“SM”; n=59), and diamonds dominant males (“DM”; n=52).
Overlapping points were jittered around their x-value to increase visibility. Squares, triangles, and
diamonds were off-set by a fixed value on the y-axis to increase visibility. This did not influence the
position or shape of the trendlines, which are still plotted according to the original values. Trendlines
are based on values predicted by the respective GLMs, and depict non-significant relationships.
Appendix 9
To test whether fitness estimates differed between individuals depending on their sex and whether they
had been initially classified as subordinates or were dominant throughout the study, we fitted GLMs
with logarithmic link function to account for the assumed Poisson error structure (GLM log link; family:
quasipoisson;). These models included one response variable (‘estimated inclusive fitness’ or ‘estimated
direct fitness’ or ‘estimated indirect fitness’) and one explanatory variable (‘class: DM/DF/SM/SF’).
All models fitted the data significantly better than the respective null models only including the intercept
(Table Appendix 9a, 9b, 9c), and subsequent Tukey tests revealed significant difference in estimated
fitness for certain pairwise comparisons (Table Appendix 9d, 9e, 9f).
Table Appendix 9a: Single term deletion output for the influence of individual class on inclusive
fitness estimates as described in Appendix 9
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
295.65
full model
3
338.6
30.583
<0.0001
Table Appendix 9b: Single term deletion output for the influence of individual class on direct fitness
estimates as described in Appendix 9
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
290.99
full model
3
335.7
31.392
<0.0001
Table Appendix 9c: Single term deletion output for the influence of individual class on indirect
fitness estimates as described in Appendix 9
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
23.192
full model
3
26.409
32.472
<0.0001
Table Appendix 9d: Pairwise comparisons of inclusive fitness estimates between different classes of
individuals (dominant males: DM; dominant females: DF; subordinate males: SM; subordinate
females: SF)
Estimate
Standard error
z value
P-Value (based
on z)
DM – DF
-0.265
0.191
-1.385
0.4994
SF – DF
-0.697
0.215
-3.236
0.0065
SM – DF
-1.186
0.26
-4.556
<0.001
SF – DM
-0.432
0.247
-1.745
0.2921
SM – DM
-0.921
0.287
-3.206
0.0067
SM – SF
-0.489
0.304
-1.611
0.3637
Table Appendix 9e: Pairwise comparisons of direct fitness estimates between different classes of
individuals (dominant males: DM; dominant females: DF; subordinate males: SM; subordinate
females: SF)
Estimate
Standard error
z value
P-Value (based
on z)
DM – DF
-0.221
0.195
-1.132
0.6614
SF – DF
-0.746
0.227
-3.279
0.0055
SM – DF
-1.247
0.277
-4.504
<0.001
SF – DM
-0.525
0.258
-2.036
0.1684
SM – DM
-1.026
0.302
-3.395
0.0038
SM – SF
-0.501
0.324
-1.547
0.3997
Table Appendix 9f: Pairwise comparisons of indirect fitness estimates between different classes of
individuals (dominant males: DM; dominant females: DF; subordinate males: SM; subordinate
females: SF)
Estimate
Standard error
z value
P-Value (based
on z)
DM – DF
-1.676
0.382
-4.389
<0.001
SF – DF
-0.106
0.196
-0.54
0.9462
SM – DF
-0.497
0.222
-2.232
0.1065
SF – DM
1.57
0.396
3.965
<0.001
SM – DM
1.179
0.41
2.878
0.0192
SM – SF
-0.391
0.246
-1.589
0.3689
Appendix 10
To test whether fitness estimates of different classes of individuals were differentially influenced by
group size or nearest neighbour distance, we fitted GLMs with logarithmic link function to account for
the assumed Poisson error structure (GLM log link; family: quasipoisson). These models included one
response variable (‘estimated inclusive fitness’ or ‘estimated direct fitness’ or ‘estimated indirect
fitness’), two explanatory variables (‘class: DM/DF/SM/SF’ and either ‘group size’ or ‘nearest
neighbour distance’), and the interaction between both explanatory variables. Single term deletions
revealed that the interaction between individual class and group size did not increase the model’s fit for
any fitness estimate (Table Appendix 10a, 10b, 10c). The same was true for models including the
interaction between individual class and nearest neighbour distance (Table Appendix 10d, 10e, 10f).
We thus removed these interactions and refitted all models in order to investigate whether either group
size or nearest neighbour distance influenced estimated fitness when controlling for individual class
(i.e. including it as a covariate). Group size did not influence inclusive fitness estimates or direct fitness
estimates (Table Appendix 10g and 10h), but indirect fitness estimates were higher in larger groups
(Table Appendix 10i). Nearest neighbour distance had no influence on any fitness estimate (Table
Appendix 10j, 10k, 10l).
Table Appendix 10a: Single term deletion output for the influence of the interaction between
individual class and group size on inclusive fitness estimates as described in Appendix 10
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
286.02
full model
3
295.63
6.941
0.0738
Table Appendix 10b Single term deletion output for the influence of the interaction between
individual class and group size on direct fitness estimates as described in Appendix 10
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
280.85
full model
3
290.93
7.215
0.0654
Table Appendix 10c: Single term deletion output for the influence of the interaction between
individual class and group size on indirect fitness estimates as described in Appendix 10
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
20.68
full model
3
21.08
4.686
0.1963
Table Appendix 10d: Single term deletion output for the influence of the interaction between
individual class and nearest neighbour distance on inclusive fitness estimates as described in
Appendix 10
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
295.16
full model
3
295.6
0.311
0.9579
Table Appendix 10e Single term deletion output for the influence of the interaction between
individual class and nearest neighbour distance on direct fitness estimates as described in Appendix
10
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
290.53
full model
3
290.95
0.2914
0.9616
Table Appendix 10f: Single term deletion output for the influence of the interaction between
individual class and nearest neighbour distance on indirect fitness estimates as described in Appendix
10
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
23.13
full model
3
23.19
0.6385
0.8876
Table Appendix 10g: Single term deletion output for the influence of group size on inclusive fitness
estimates (including individual class as covariate) as described in Appendix 10
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
295.63
model
with 3
338.25
30.227
<0.0001
covariate
model with group 1
295.65
0.014
0.9059
size
Table Appendix 10h: Single term deletion output for the influence of group size on direct fitness
estimates (including individual class as covariate) as described in Appendix 10
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
290.93
model
with 3
334.69
30.63
<0.0001
covariate
model with group 1
290.99
0.0466
0.8292
size
Table Appendix 10i: Single term deletion output for the influence of group size on indirect fitness
estimates (including individual class as covariate) as described in Appendix 10
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
21.084
model
with 3
24.246
36.278
<0.0001
covariate
model with group 1
23.192
24.186
<0.0001
size
Table Appendix 10j: Single term deletion output for the influence of nearest neighbour distance on
inclusive fitness estimates (including individual class as covariate) as described in Appendix 10
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
295.6
model
with 3
338
30.1165
<0.0001
covariate
model
with 1
295.65
0.0335
0.8548
nearest neighbour
distance
Table Appendix 10k: Single term deletion output for the influence of nearest neighbour distance on
direct fitness estimates (including individual class as covariate) as described in Appendix 10
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
290.95
model
with 3
335.16
30.972
<0.0001
covariate
model
with 1
290.99
0.033
0.8558
nearest neighbour
distance
Table Appendix 10l: Single term deletion output for the influence of nearest neighbour distance on
indirect fitness estimates (including individual class as covariate) as described in Appendix 10
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
23.192
model
with 3
26.341
31.687
<0.0001
covariate
model
with 1
23.192
0.007
0.9347
nearest neighbour
distance
Figure Appendix 10: The estimated inclusive fitness of each marked individual over the whole
observation period in relation to its average group size. Fish classified as dominant females in their
first year of marking are represented by circles, subordinate females by rectangles, subordinate males
by triangles, and dominant males by diamonds. Trendlines are based on the respective GLMs and
represent non-significant relationships.
Appendix 11
To test whether group size and nearest neighbour distance interactively influenced individual fitness,
we fitted GLMs with logarithmic link function to account for the assumed Poisson error structure (GLM
log link; family: quasipoisson). These models included one response variable (‘estimated inclusive
fitness’ or ‘estimated direct fitness’ or ‘estimated indirect fitness’), two explanatory variables (‘group
size’ and ‘nearest neighbour distance’), the interaction between the two explanatory variables, and a
covariate (‘class: DM/DF/SM/SF’). Single term deletions did not reveal any interactive influence of
group size and nearest neighbour distance on either fitness estimate (Table Appendix 11a, 11b, 11c).
Table Appendix 11a: Single term deletion output for the influence of the interaction between group
size and nearest neighbour distance on inclusive fitness estimates (including individual class as
covariate) as described in Appendix 11
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
294.07
model
with 3
335.61
29.5566
<0.0001
covariate
model
with 1
295.59
1.0851
0.2976
nearest neighbour
distance
Table Appendix 11b: Single term deletion output for the influence of the interaction between group
size and nearest neighbour distance on direct fitness estimates (including individual class as
covariate) as described in Appendix 11
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
289.24
model
with 3
331.88
29.9715
<0.0001
covariate
model
with 1
290.86
1.1327
0.2872
nearest neighbour
distance
Table Appendix 11c: Single term deletion output for the influence of the interaction between group
size and nearest neighbour distance on indirect fitness estimates (including individual class as
covariate) as described in Appendix 11
Degrees
of Deviance
Scaled deviance
P-Value (based
freedom
on
𝜒2 )
null model
21.018
model
with 3
24.234
36.591
<0.0001
covariate
model
with 1
21.027
0.112
0.7378
nearest neighbour
distance
Appendix 12
To test whether either the direct or the indirect component of inclusive fitness exceeded the other for
the different classes of individuals, we used Wilcoxon signed-ranks matched-pairs tests. For each class
of individual, we performed a separate test, resulting in four tests in total. Estimated direct fitness
significantly exceeded the indirect component of fitness for all classes of individuals (Figure 4;
Appendix 12).
Table Appendix 12: The estimated minimum, mean, and maximum direct and indirect fitness gains
of individually marked N. pulcher. Fish were classified according to their sex and social status in the
year they were marked as either dominant male, dominant female, subordinate male, or subordinate
female. All classes of individuals gained significantly more direct fitness than indirect fitness.
Significance estimates are based on Wilcoxon signed-ranks matched-pairs tests.
Class
Direct fitness component
Indirect fitness component
Significance
level
Min
Mean
Max
Min
Mean
Max
p value
Dominant
males
0
1.037
4.785
0
0.014
0.072
<0.001
Dominant
females
0
1.293
6.99
0
0.077
0.532
<0.001
Male
0
subordinates
0.372
4.18
0
0.047
0.272
0.002
Female
0
subordinates
0.614
4.485
0
0.069
0.45
<0.001
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