Independent fitness consequences of group size variation in Verreaux’s sifakas

Abstract

The costs and benefits of group living are also reflected in intraspecific variation in group size. Yet, little is known about general patterns of fitness consequences of this variation. We use demographic records collected over 25 years to determine how survival and reproductive success vary with group size in a Malagasy primate. We show that female reproductive rates of Verreaux’s sifakas (Propithecus verreauxi) are not affected by total group size, but that they are supressed by the number of co-resident females, whereas mortality rates are significantly higher in larger groups. Neither annual rainfall nor the adult sex ratio have significant effects on birth and death rates. Hence, these sifakas enjoy the greatest net fitness benefits at small, and not the predicted intermediate group sizes. Thus, independent fitness proxies can vary independently as a function of group size as well as other factors, leading to deviations from optimal intermediate group sizes.

Full text

communications biology Article
https://doi.org/10.1038/s42003-024-06484-z
Independent fitness consequences of
group size variation in Verreaux’s sifakas
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Peter M. Kappeler 1,2 & Claudia Fichtel 1
The costs and benefits of group living are also reflected in intraspecific variation in group size. Yet, little
is known about general patterns of fitness consequences of this variation. We use demographic
records collected over 25 years to determine how survival and reproductive success vary with group
size in a Malagasy primate. We show that female reproductive rates of Verreaux’s sifakas (Propithecus
verreauxi) are not affected by total group size, but that they are supressed by the number of co-resident
females, whereas mortality rates are significantly higher in larger groups. Neither annual rainfall nor the
adult sex ratio have significant effects on birth and death rates. Hence, these sifakas enjoy the greatest
net fitness benefits at small, and not the predicted intermediate group sizes. Thus, independent fitness
proxies can vary independently as a function of group size as well as other factors, leading to
deviations from optimal intermediate group sizes.
Life in permanent groups has evolved repeatedly throughout the history of
the animal kingdom, and the size, composition as wel as social structure of
animal societies today varies widely among and within species1. Similar
selection pressures are thought to govern both interspecificevolutionary
transitions in social organisation and intraspecific variation in group size,
which varies as a function of variation in rates of reproduction, survival,
immigration and emigration in different age and sex categories2–6.Onlya
comparative study across 8 species of dolphins and porpoises found no
general and consistent relation between group size and other variables
within and across species7. However, whereas the general factors favouring
the evolution of group living have been studied extensively during the early
years of behavioural ecology8–11,thedriversaswellastheactualdirectand
indirect fitness consequences of intraspecific variation in social phenotypes
remain less studied, even though they can be variable across species,
populations and groups within species, sexes, age and dominance categories,
years and environmental conditions12–15, among other things because
members of different categories vary in their abilities to control group size.
This variation in the links between sociality and fitness is dis-
tributed unevenly between two core components of social systems, i.e.,
social structure and social organisation16,First,asinhumans
17–19, studies
of several species of Old World monkeys, but also of ungulates, ceta-
ceans, hyraxes, rabbits and meerkats, revealed that various aspects of
social structure, such as social status and integration, are positively
associated with sur vival, benefitting individuals with stro ng social bonds
or better social network connections20–24. Only studies of yellow-bellied
marmots did not consistently find associations between social structure
and fitness measures25,26.
Second, variation in social organisation, and group size in particular, is
associated with a wide array of fitness measures, though the effects are
heterogeneous within and across species and rarely correspond with theo-
retical predictions about an optimal group size. For example, in one study of
African wild dogs, groups size had no effect on survival27, whereas adult
survival decreased with pack size in another study28.Inmeerkats,mortality
was higher in smaller groups29, and in spotted hyenas, the size of one clan
was positively associated with reproduction, but not with subsequent
recruitment30. In rodents, survival and net reproductive rates increased with
increasing group size, but decreased in the largest groups in yellow-bellied
marmots31, whereas in degus, adult female and offspring survival were not
influenced by group size32. In prairie voles, juveniles survived better in
groups of intermediate sizes, but adult survival was independent of group
size33. Across primate studies, there appears to be a more uniform pattern
characterised by fitness costs for individuals living in larger groups, as
indicated by longer inter-birth intervals, lower fertility, reduced juvenile
survival, or delayed sexual maturity34–38.
Another set of studies analysed group size variation while simulta-
neously considering additional variables, because fluctuations in resources
and other factors may contribute to the maintenance of the distributions of
groups sizes around a presumed intermediate optimum39,40. In superb
starlings, for example, group size was positively correlated with adult sur-
vival, but only for males in wet years41, implicating an interaction between
environmental conditions and sex modulating the group size-fitness link.
Similarly, individual reproductive success of anis was higher in large groups
than in small groups in wet years, whereas the opposite pattern was found in
dry years39, suggesting that fluctuating selection may maintain variation in
1Behavioral Ecology & Sociobiology Unit, German Primate Center, Leibniz Institute for Primate Research, Kellnerweg 4, 37077 Göttingen, Germany. 2Department of
Sociobiology/Anthropology, Johann-Friedrich-Blumenbach Institute of Zoology and Anthropology, University Göttingen, Kellnerweg 6, 37077
Göttingen, Germany. e-mail: pkappel@gwdg.de
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group size. In giraffes, in contrast, group size was much more important in
predicting survival than social network metrics or any environmental
factor42. Finally, a study of prairie voles33, as well a recent experimental study
in ostriches43 demonstrated that the divergent reproductive interests of the
sexes, as reflected by different adult sex ratios (ASR), can also promote
different optimal group sizes.
Thus, in order to optimise fitness costs and benefits associated with
different current group sizes, there should generally be stabilising selection
for intermediate-sized groups44–46, but the costs and benefits of small and
large group sizes may vary locally with environmental and social factors, so
that group size variation persists and the optimal group size does not
necessarily coincide with the central tendency of group sizes. In particular,
selection for different group sizes may well vary between members of dif-
ferent age, sex and dominance categories –as will their capacity to control it.
The general pattern of fitness consequences remains relatively poorly
understood, however, because differentco-variatesaswellasshort-and
long-term fitness measures have been used in different studies. Therefore,
explaining the extent, drivers and consequences of group size variation
remains a key problem in social evolution, and data from additional taxa
that explicitly consider additional social and environmental factors in
shaping fitness are required for further insights.
The general aim of this study was therefore to examine fitness
consequences of group size variation in a representative of an indepen-
dent primate radiation from Madagascar–Verreaux’s sifakas (Propithe-
cus verreauxi). To put group size effects into the broader context of other
recent studies, we also considered variation in ASR as well as interannual
variation in rainfall and food availability as potential drivers of fitness
variation. ASR variation, which is maxima l in small groups47, has recently
been shown to have pronounced effects on reproductive strategies48,49 as
well as group size43. Rainfall, which is correlated with food availability,
and, hence, ultimately condition, survival and reproduction, has been
shown in a study of sympatric mouse lemurs to have varied over the last
30 years50. To understand variation in group size it is also important to
understand the relative roles of reproduction, survival, immigration and
emigration—and the extent to which individuals control them. Because
both reproductive effort and mortality are known to be age-dependent51,
we therefore also controlled for the effects of age. Furthermore, because a
previous study suggested that female competition might impact repro-
ductive rates in sympatric redfronted lemurs52, which also live in small
groups with philopatric females, we also examined effects of variation in
the number of adult females. Moreover, this study also contributes much
needed comparative data on absolutely small group sizes, where per
capita cost and benefits of minor changes in group size, but also in ASR,
are more pronounced, compared to groups that are—say—three or four
times larger47. Because changes in the ASR of Verreaux’s sifakas may be
accompanied by fundamental changes in the mating system (single- vs.
multimale group) and because the magnitude of ASR variation at small
group sizes is uncorrelated with the number of adult females, these
factors may have independent effects on the optimal group size. Finally,
our study is of particular interest because a previous report on the same
population revealed that intergroup variation in several commonly used
fitness proxies, such as daily travel distance, home range size, foraging
rate, resting rate, faecal glucocorticoid metabolites concentration and
parasite richness were all uncorrelated with group size53. Her e, we use two
direct fitness measures—birth rates and survival—obtained during a 25-
year field study, and predicted either no effect of group size, if our earlier
used indirect fitness proxies are functionally linked to reproduction and
survival, or higher reproductive and survival rates in groups of inter-
mediate size, as predicted by the optimal group size hypothesis44–46.
Results
Group size variation
Group size varied between 2 and 10 individuals (mean: 6.26, SD = 1.96;
Fig.1). The average number of adult females, adult males and juveniles were
1.93 ± 0.80, 2.13 ± 0.86, and 2.20 ±1.34, respectively.
Reproductive success
The probability of giving birth was best predicted by the model including
linear terms (AIC: linear terms = 425.99, quadratic terms = 434.96). The
probability of giving birth was not significantly affected by the size of the
group a female lived in (likelihood ratio test full-null model comparison:
X2= 29.26, df = 3, p< 0.001; Fig. 2a; Table S1a). However, females in groups
with more adult females were less likely to give birth (Fig. 2b). Moreover,
female age had a significant effect on the probability of giving birth, with
older females exhibiting the lowest birth rates (Fig. 3). Year-to-year variation
in resource abundance, as indexed by cumulative rainfall in the year before
giving birth had no effect on the probability of giving birth. The model
including inter-group variation in ASR revealed similar effects, but ASR was
not significant (likelihood ratio test full-null model comparison: X2= 22.18,
df = 5, p< 0.001; Table S1b). Since AICs of the model including linear or
quadratic terms did not differ by much (AIC: linear terms = 441.01, quad-
ratic terms =440.17), we present here the more comprehensive model
including quadratic terms. Finally, birth rates were not impeded by dom-
inance status (Table S2c-f).
Survival
Annual survival was best predicted by the model including the quadratic
terms (AIC: linear terms = 818.68, quadratic terms = 764.28). Annual sur-
vival was positively affected by group size, with individuals in larger groups
experiencing a significantly higher mortality risk (likelihood ratio test full-
null model comparison: X2= 55.02, df = 5, p< 0.001; Fig. 4a; Table S1c). Age
predicted the probability of dying as well, with younger individuals exhi-
biting higher mortality (Fig. 4b). Neither ASR nor rainfall in the year pre-
ceding a death were significant predictors of mortality risk, however
(Table S1c). Models including only confirmeddeaths or confirmed deaths as
well as all disappeared females revealed similar effects (Table S3).
Discussion
There is apparently no intermediate optimal group size in Verreaux’s sifakas
at which both reproduction and survival are maximised because the cor-
responding costs and benefits of group size variation are distributed
asymmetrically. While sifakas enjoyed higher survival in smaller groups and
higher birth rates in groups with few other adult females, there are appar-
ently no net fitness benefits of living in large groups, creating overall selective
Group size
Frequency
24681012
0
20
40
60
80
Fig. 1 | Group size variation in Verreaux’s sifaka at Kirindy Forest between 1994
and 2020. Depicted is the frequency distribution of group sizes in April of each
year (N= 352).
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pressures favouring small groups. Our study also revealed that the different
fitness measures exhibit different relationships with overall group size,
indicating that lifetime reproductive success (of females) is probably not
described by a simple linear function of overall group size and presumably
more closely related to certain components of group size, e.g., the number of
females competing over reproductive opportunities. Hence, different fitness
components can vary independently across group sizes. Furthermore, our
previous study of multiple indirect fitness proxies53,whicharemorecom-
monly recorded in other studies as well, has presumably not missed any
major effects, but they may be individuallytooweaktopredictthesurvival
costs of large group sizes. Finally, despite living in a highly seasonal envir-
onment with pronounced year-to-year variation in the length and intensity
of the wet season, environmental variation did not have an effect on either
fitness proxy. We discuss these major findings in detail below.
First, overall group size had no effect on the probability that a female
sifaka will give birth. Like virtually all other lemur species, Verreaux’s sifakas
are seasonal breeders that give birth in the middle of the local ca. 8-month
dry season, so that infant weaning coincides with the season of greatest food
availability at the end of the wet season54. On average, not every female gives
birth every year, but this intra- and interindividual variation in female
reproductive success is not explained by group size. Furthermore, variation
in group composition, which we quantified as ASR, had no effect on birth
rates, suggesting that females do apparently not enjoy any of the potential
benefits in the context of reproduction that can accrue as a result of male
services in other primates55,56.
Instead, an aspect of group size defined by a subset of individuals—the
number of co-resident adult females—best predicts variation in birth rates.
This result indicates that female Verreaux’s sifakas are subject to subtle
forms of female competition over reproduction because the probability of
giving birth declined with increasing numbers of adult females. Female
Verreaux’s sifakas are for the most part philopatric57. Only a small pro-
portion of them were observed to transfer between groups; typically, if a
group had three or more adult females and a breeding vacancy in an
adjacent group appeared, e.g. after the death of the only breeding female58.
Thus, in the vast majority of cases, co-resident adult females are close
relatives. They exhibit clear dominance relationships59 , but dominants do
not appear to actively suppress reproduction in subordinates. Hence,
competition over reproduction affects all females, but we do not yet know
whether the underlying mechanism is based on behaviour and or physiol-
ogy. In sympatric redfronted lemurs and other members of the Lemuridae,
as well as in meerkats and banded mongooses, females target co-resident
femalesfortemporaryorpermanenteviction
52,60–62, induce abortions63 or
commit infanticide64. Thus, in comparison, Verreaux’s sifaka females
engage in relatively subtle forms of reproductive competition.
What do female Verreaux’s sifakas compete for? Generally accepted
benefits of small group size include a reduction in the intensity of within-
group feeding competition and reduced travel costs in smaller home ranges
(assuming homogeneity in habitat quality53), both of which should make
more energy available for reproduction. By compromising reproduction in
group mates, females may contribute to a limitation of group size in the near
future because juvenile sifakas develop and reach nutritional independence
much faster than other primates of their size65 and would compete for food
with adults already in their first year of life. Additional energy for repro-
duction cannot be used to increase fecundity because litter size is invariably
equal to one51. A future analysis should therefore examine whether age of
first reproduction occurs earlier, average inter-birth intervals are shorter and
infant survival is higher in smaller groups; a pattern previously described for
Phayre’sleafmonkeys,whereinfantsinlargergroupsdevelopedmore
slowly, were weaned later and inter-birth intervals were larger36.
The nature and intensity of food competition may also depend on
climatic variation and competition among neighbouring groups. However,
group size does only play a subordinate role in predicting success in inter-
group encounters66 because only proximity to the core area influenced the
probability of winning67. Inter-annual variation in rainfall in Western
Fig. 2 | Group size effects on fitness proxies in
Verreaux’s sifaka at Kirindy Forest between 1994
and 2020. a Probability of giving birth as a function
of group size and (b) female age (N= 352). Size of
circles represents number of events (a)
range = 3–81, (b) range=10-68. Dotted line: regres-
sion line; shaded area: 95% confidence intervals.
N adult females at birth
Probability of giving birth
1234
0
0.2
0.4
0.6
0.8
1
Fig. 3 | Reproductive inhibition among female Verreaux’s sifaka at Kirindy
Forest between 1994 and 2020. The number of co-resident adult females has a
significant negative effect on the probability of giving birth (N= 352). Size of circles
represents number of events. Dotted line: regression line; shaded area: 95% con-
fidence intervals.
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Madagascar is substantial in the onset, duration and total yield during the
3–4 months long wet season. Mating in sifakas takes place in February near
the end of the wet season, when better female condition in a much smaller
sample predicted the probability of giving birth 5 months later54,68.
Assuming that rainfall, which has decreased substantially over the last
decades50, is positively correlated with food availability and, ultimately,
female condition, we would have expected to find a positive effect on birth
rates as well. However, these energetic considerations are apparently much
less important than some intrinsic (age) and social (number of co-resident
females) factors.
It is finally also possible that group composition has a stronger effect on
reproductive success than group size. In contrast to other studies (e.g.
ref. 38), we therefore included males in our analyses of group size. While
variation in ASR had no effect on reproductive rates, there should be sexual
conflict over group composition with down-stream effects on group size.
Male Verreaux’s sifakas also exhibit clear dominance relations, including
phenotypic modification of the highest-ranking male69 and physiological
suppression of subordinates70. They exhibit one of the highest levels of
reproductive skew among mammals, with the highest-ranking male
acquiring on average >90% of paternities in a group71. Male monopolisation
of oestrous females is achieved by mate guarding and facilitated by oestrus
asynchrony72. Dominant males should therefore benefit reproductively
from an increase in the number of adult females73, revealing an apparent
sexual conflict with females over group composition. Similarly, the share of
paternities of subordinate males increases with the number of females74,75,
aligning the reproductive interests of dominant and subordinate males.
Thus, the groups of Verreaux’s sifakas with above-average size may reflect
the effects of male reproductive interests. However, because sifaka females,
as those of many other lemur species76, unconditionally dominate males77,
this sex difference in agonistic power may proximately explain why females
win this sexual conflict on average, and ultimately explain the—compared to
anthropoid primates—relatively small group sizes of this and other lemur
species78. However, reports of male infanticide79 suggestthatfemalesarenot
always able to prevent the immigration of males. In horses and zebras, there
may be a similar conflict of interest over the optimal group size among
females, subordinate males and dominant males that is resolved by female
dispersal80. Thus, the costs and benefits of a given group size appear to be
shaped by more factors than the number of individuals as well as by the
behavioural mechanisms available to different classes of individuals to
resolve the arising conflicts.
Furthermore, reproductive success was influenced by age, with young
and old females exhibiting the lowest birth rates. In a recent study on
reproductive senescence in several lemur species, including Verreaux’s
sifaka, we analysed variation in the probability of giving birth within and
acrossfemalesasafunctionoftheirage
51.Incontrasttothispreviousstudy,
the present analyses include an additional year of data, and, hence, more
births and mothers. Furthermore, in the present analyses, we included
femaleswithanageof4yearsandolderbecausethatistheyoungestageat
which females have ever been observed to give birth. In the previous ana-
lyses, we only included females after they had given birth for the first time.
This different classification should explain why we found an effect of age on
the probability of giving birth in the present analysis, but not in ref. 51.
Second, the probability of dying was best predicted by group siz e, but in
the opposite direction from what conventional wisdom holds. Focusing on
potential causes of extrinsic mortality, several simple mechanisms, like the
dilution or predator confusion effect1, are thought to generate survival
benefits for individual living in larger groups because of reduced predation
risk, which, in turn, should result in greater longevity. However, these
advantages were neither evident in comparative analyses across more than
250 species of mammals81, nor across more than 400 species of birds82.Itis
therefore possible that larger groups may be actually more conspicuous for
predators or that more eyes and ears cannot defend against certain types of
predators that hunt by immediate attacks or ambush83.Large group size may
affect survival also indirectly because individuals experience greater feeding
competition that may translate into greater variance in body condition84.
Moreover, intrinsic causes of mortality may exacerbate the costs of
living in large(r) groups and contribute to the observed effect in Verreaux’s
sifaka and perhaps more generally. In general, the risk of parasite trans-
mission among group mates indeed increased weakly with group size85,but
it can also be mitigated by social network metrics86 and properties87.
Moreover, physiological costs of living in larger groups, such as increased
energy expenditure and feeding competition, are not linearly elevated in
larger groups88. Various proxies of these costs were also not consistently
related to group size in Verreaux’s sifaka53, and higher group size provided
no advantages in intergroup competitioninaccesstoresources
66,67.Atother
long-term study sites of Verreaux’s sifakas to the south of Kirindy Forest,
where seasonality is more pronounced and annual rainfall reduced, and
where key predators like the fosa are less abundant or totally absent89,90,the
average group size is also at around 6 individuals (Berenty91;Hazafotsy
92;
Beza Mahafaly57,93), indicating that group size is rather resilient to massive
variation in key environmental factors.
In conclusion, patterns of fitness consequences of group size variation
in Verreaux’s sifakas do not follow theoretical predictions, indicating that
the optimal group size model may be oversimplistic. More specific aspects of
group size, such as the number of adult females in this study, may be
additionally important drivers of fitness consequences beyond group size
per se. Similarly, sexual conflict over group composition can also have
repercussions for group size that deserve more scrutiny. Also, survival and
reproductive success seem to vary more often than not independently of
each other as a function of group size; i.e., different fitness components are
evaluated independently. Hence, there is a need for additional, more
comprehensive and fine-grained studies to unravel the drivers of intra-
specific variation in group size in order to finally clarify one of the oldest
questions in behavioural ecology.
Fig. 4 | Age effects on fitness proxies in Verreaux’s
sifaka at Kirindy Forest between 1994 and 2020.
aProbability of dying as a function of group size and
(b) age (N= 1022). Size of circles represents number
of events (a) range = 21–354, (b) range = 7–371.
Dotted line: regression line; shaded area: 95% con-
fidence intervals.
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Methods
Study site and species
This study was conducted on a population of Verreaux’s sifakas at Kirindy
Forest, Western Madagascar. Kirindy Forest is a protected dry deciduous
forest and subject to pronounced seasonality, with a long, cool dry season
(April to October) and a hot wet season (November to March), harbouring a
full set of local sifaka predators, including fosas and Harrier hawks58.Ver-
reaux’s sifakas are diurnal and arboreal primates with a frugi-folivorous
diet94. They can live up to 25 years (median longevity: 12 years) and can
produce a single infant every year (mean interbirth interval: 1.25 years) from
theirfourthyearoflife(meanageoffirst reproduction: 5.6 years) onwards
without any sign of reproductive senescence51. Since 1994, all animals within
a ca. 60 ha study area have been individually marked with unique nylon or
radio collars, either when they were about 8 months old or when they
immigrated into one of the study groups53. Here, we include data from a total
of 279 Verreaux’s sifakas living in up to 10 adjacent groups.
Our analyses are based on demographic data collected during multiple
weekly censuses of all study groups. Between 1994 and 2021, we recorded a
total of 236 births that were distributed among 41 mothers. Female lifetime
reproductive success ranged from 1 to 16 infants (mean: 5.75 infants). We
classified a total of 105 individuals (18 females, 21 males, 66 of unknown sex)
as dead. An individual was pronounced dead when either a successful
predation event was observed, its remains were found or when the indivi-
dual was less than 8 months old at the time of disappearance, and, hence,
barely weaned65. An additional total of 162 individuals (66 females, 89 males,
7 of unknown sex) disappeared from their group. They were classified as
“unknown”, as we could not unequivocally establish whether they had
emigrated from the study area or died. Twenty individuals (7 females, 13
males) were alive at the time of data acquisition for this study.
Statistics and reproducibility
We constructed binomial General Linear Mixed Models with a logit link
function to estimate factors predicting the likelihood of both, giving birth to
an offspring or dying. We included group size (i.e., the number of all
members of a group, excluding dependent infants at the time of a birth or
death, respectively), the age of the female at the time of giving birth or of the
dead individual at the time of its death (in years), the ASR, (i.e., the pro-
portion of adult males among the adults of a group95, with individuals with
≥5 of age being counted as adult58), and the total amount of rainfall at the
study site in the 12 months prior to the birth season in July, using rainfall
estimates detailed in ref. 50. Because group size and age may have non-linear
effects51, we also tested the effects of quadratic group size and quadratic age.
The model on birth rates also included the number of co-resident adult
females and the quadratic term of it as a factor because preliminary analyses
indicated a potentially inhibitory effect58. We compared models including
the linear and quadratic effects by using Akaike information criterion (AIC)
and present the models with a delta AIC < 2 in the main text and all other
models in the Supplementary Information (Table S2) We did not include
higher order polynomials because we are not aware of any hypothesis that
the probability of giving birth or annual survival should follow a cubic or
higher order function. Because the number of adult females and ASR were
collinear, we estimated two models for birth rates; one including the number
of adult females and one including ASR.
For the birth rate model including the number of adult females, we set
the occurrence of whether a female gave birth (yes, no) as response and
included group size and quadratic group size, females age and quadratic age,
the number of adult females and quadratic number of adult females, as well
as annual rainfall as fixed factors. We included individual and group identity
as random factors, with random slopes of group size and quadratic group
size, females age and quadratic age, the number of adult females and
quadratic number of adult females, and rainfall within individual and group
identity, respectively. Originally, we also included correlations between
random slopes and intercepts, but as the models did not converge, we
excluded them again. For the birth rate model including ASR, we fitted the
same model but included ASR instead of the number of females.
In addition, to estimate the effect of dominance status on birth rates, we
fitted two more models on a reduced data sets comprising only groups that
contained at least two adult females (Table S2). In these models, we included
the same factors as above and dominance status, i.e., whether a female was
dominant or not.
To estimate annual survival, we fitted three models including different
death classifications: a) only confirmed dead individuals (N=105), b)
confirmed dead combined with “unknown”females because females only
leave their natal group in rare, exceptional circumstances (N= 173, 83
females, 21 males, 67 of unknown sex)58, and c) confirmed dead, “unknown”
femalesandmalesthatwere≤4 of age because the youngest recorded
emigrated male was 5 years old (N= 216, 83 females, 65 males, 67 of
unknown sex)58. We set the occurrence of whether an individual was clas-
sified as dead (yes, no) as response and included group size and quadratic
group size, individuals’age and quadratic age, ASR, and annual rainfall as
fixed factors. We included individual and group identity as random factors.
For model a) we originally included random slopes of group size and
quadratic group size, individuals’age and quadratic age, ASR, and annual
rainfall within groups without correlations between random slopes and
intercepts but removed the age terms as the model did not converge
(Table S1c). For model b) and c) we included all random slopes without
correlations between random slopes and intercepts. Since the results of
models a and b revealed similar effects, we present only model c), which is
based on the largest sample size, in the main text. Results of models a) and b)
are reported in the Supplementary Information (Table S3).
Model implementation
All analyses were conducted using R (version 4.3.2, R Core Team 2023). To
ease model convergence, we log-transformed age and rainfall, and centred all
predictors to a mean of zero and a standard deviation of one before including
them into the models. We included all theoretically identifiable random
slopes to avoid Type I errors96.Totestthesignificance of predictors as a whole,
we compared the fit of the full model with that of the null model comprising
only random factors97,98. We obtained confidence intervals for all models by
means of parametric bootstraps using the function “bootMer”of the package
“lme4”, applying 1000 parametric bootstraps. We checked for collinearity by
determining Variance Inflation Factors (VIF) for a standard linear model
without random effects using the package “car”(version 3.0.1199). To estimate
model stability, we proceeded by dropping levels of the random effect one at a
time from the data set and compared the obtained estimates to the estimates
obtained for the full data set. All models revealed good model stability.
Reporting summary
Further information on research design is available in the Nature Portfolio
Reporting Summary linked to this article.
Data availability
Data and code are provided at https://figshare.com/s/c4fc966c04e6b36de6ea
Received: 12 February 2024; Accepted: 21 June 2024;
Published online: 05 July 2024
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Acknowledgements
We thank the Malagasy Ministère de l’Environnement, the members of the
CAFF/CORE, the Mention Zoologie et Biodiversité Animale de l’Université
d’Antananarivo and the Centre National de Formation, d’Etudes et de
Recherche en Environnementet Foresterie de Morondava for authorising
and supporting our research in Kirindy Forest. We are grateful to Tiana
Andrianj anahary, Mamy Razafindrasamba and other field assistants for their
support in data collection. This work was supported by the German Science
Foundation, DFG [grant numbers Ka 1082/9-1&2,Ka 1082/29-2] awardedto
P.M.K. We are grateful to Severine Hex and an anonymous referee for
constructive comments on this paper.
Author contributions
P.K. and C.F. designed the study. C.F. analysed data. P.K. wrote the
manuscript and C.F. critically revised it.
Competing interests
The authors declare no competing interests.
Ethics
We adhered to the “Guidelines for the ethical treatment of nonhuman
animals in behavioural research and teaching”as published in Animal
Behavior(2023, 195, I-XI)and the laws of the countrywhere the researchwas
conducted. This study was approved by the Département de Biologie
Animale of the University of Antananarivo and the CAFF/CORE of the
Direction des Eaux and Forêts de Madagascar.
Additional information
Supplementary information The online version contains
supplementary material available at
https://doi.org/10.1038/s42003-024-06484-z.
Correspondence and requests for materials should be addressed to
Peter M. Kappeler.
Peer review information Communications Biology thanks Severine Hex
and the other, anonymous, reviewer(s) for their contribution to the peer
review ofthis work. PrimaryHandling Editors: Richard Hollandand Benjamin
Bessieres. A peer review file is available.
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