Methods
System
We systematically monitored a population of house sparrows Passer
domesticus on Lundy Island in the Bristol Channel, UK (51.11N, 4.40W),
since 2000 (see Nakagawa et al. 2007; Ockendon, Griffith, and Burke
2009; Schroeder et al. 2012; Dunning et al. 2023). The sparrows on Lundy
breed in nesting boxes, arranged into neighbourhoods broadly defined by
building infrastructure or linear features. Females are socially
monogamous, but genetically promiscuous (Schroeder et al. 2016), and, on
Lundy, most have 2-3 broods of 4-5 eggs per breeding season (Westneat et
al. 2014).
We collected tissue samples from nestlings at the natal site and from
recaptured birds post-fledging and used the DNA extracted from those to
allocate paternity with the help of >22 microsatellite loci
(Dawson et al. 2012). We then constructed a near-complete genetic
pedigree (see Schroeder et al. 2015), spanning 19 years, 2000 - 2019.
All sparrows are fitted with a unique sequence of three coloured leg
rings and a British Trust for Ornithology (BTO) coded metal ring (for
details see Simons et al. 2015), which allowed us to later identify
social pairs at the nest box. Dispersal to and from Lundy Island is
limited. This, and our systematic and thorough monitoring, allowed us to
determine the exact age of birds in years, and to know when they died,
either from the rings of birds found dead or, defined as when ringed
birds were not observed for more than two years (see Simmons et al
2015).
To measure female divorce, we first excluded females that only had a
single brood, and thus, no opportunity to divorce their social mate. We
also excluded 17 females that divorced mates following the death of
their social partner, where the death of a social male occurred during
the female breeding year. We removed offspring whose parents (either
social or genetic) were missing or uncertain. We defined a divorce event
where a female paired socially with a new male to that of her previous
social partner, between broods but within years. This resulted in 353
female breeding years. These female years represented 920 broods by 190
females, 205 social fathers and 309 genetic sires between 2004 and 2019.
We defined a chick as extra-pair where they survived to the point of
sampling on day two and the confirmed social- differed from the genetic
father (the sire) in our pedigree. We counted the number of extra-pair
offspring and the number of both social and extra-pair fathers within
females within years (female years).
Models and permutations
To empirically test if females that divorce more often were also more
likely to produce extra-pair offspring, as implied by intrasexual
antagonistic pleiotropy theory, we ran two GLMM models with Bayesian
Markov Monte-Carlo simulations, using MCMCglmm in R (Hadfield 2010; R
Core team 2023):
The association of divorce with extra-pair paternity - To
examine the link between female year divorce and extra-pair paternity,
and because MCMCglmm cannot easily deal with proportion data, we ran a
multinomial model with the number of extra-pair and social offspring
per female year as response variables (see Hadfield 2010). We fitted
female divorce, measured as the number of social partners within a
female year, the number of broods she initiated, to control for
increased opportunity for extra-pair offspring, and her age in years
since hatching, to compensate for the effect of age on reproductive
value (Hsu et al. 2017), as fixed effects. We also included Female ID
and breeding year as random effects on the intercept to account for
variation within those groups.
The effect of divorce on extra-pair male engagement - To
examine the link between female divorce and engagement of extra-pair
partners, we used a bivariate model structure, with the number of
extra-pair partners within a given female year as the response
variable. We again fitted female divorce, the number of broods
initiated and her age in years since hatching as fixed effects. Female
ID and breeding year were again modelled as random intercepts to
account for variation within those groups. We first ran models using a
Poisson distribution and logit link function, but those models failed
to converge. Instead, we used a Gaussian distribution and link
function and output estimates between the Poisson and Gaussian models
were equivalent.
For all models, we used the default priors of the MCMCglmm package, and
ran over 343,000 iterations, with a burn-in of 34,000 and a thinning
interval of 200. We checked the posterior trace plots to ensure that
autocorrelation was below 0.1 and that the effective sample sizes ranged
between 1,000 and 2,000. The fixed effects were considered statistically
significant when the 95% credible interval (CI) of its posterior
distribution did not span zero.
To test that our results were biologically meaningful, and not the
outcome of random chance, we ran a series of permutations. We removed
the link between female ID and reproductive traits by building random
matrices between males and females to re-run our models. First, we
simulated 1000 breeding events, by shuffling the number of offspring and
extra-pair offspring between females while maintaining age structure. We
then repeated these steps to simulate the number of extra-pair partners
for each female. For each permutation, we ran an identical GLMM model to
those described above. We dropped the bottom 2.5% of the lower credible
intervals, and the top 2.5% of the upper credible intervals, to leave
95% of the 1000 credible intervals. We then extracted the minimum lower
and maximum upper credible interval and the mean estimate. We
interpreted significance – that is, our results were unlikely to have
occurred by chance – where the observed posterior mean fell outside the
span of the permuted credible intervals.
Results
From 533 female breeding years, we identified 4963 offspring of known
social and genetic parentage including 932 extra-pair offspring, 1.7 per
female year (0 – 11, sd: 1.77), from 1403 broods (2.6 per female year,
sd: 0.68). Females who engaged in extra-pair behaviour had a mean of 2.5
extra-pair offspring per female year (1 – 11, sd: 1.6). Within female
breeding years, 120 females divorced their social partners on at least
one occasion (110 once, and 10 twice, 1.24 per social partners female
year: sd 0.47), where 413 remained faithful to a single social partner
over multiple broods within a female year.
Neither the number of social fathers nor the number of broods was
significantly linked with the proportion of extra-pair offspring that
hatched within a female year. However, the number of social fathers and
the number of broods per female year were positively linked to the
number of extra-pair partners she chose within a breeding year. The log
odds of having an extra-pair partner increased by 0.43, or 1.54
extra-pair partners, per social partner, and by 0.24, or 1.27 extra-pair
partners per brood respectively (Figure 1). Female age was not linked to
either the proportion of extra-pair offspring or the number of
extra-pair sires.
Neither the number of broods nor the number of social fathers was
associated with the number of extra-pair partners in our randomizations.
The observed estimates all fell outside of the simulated confidence
intervals (Figure 1). Observed posterior means fell outside of simulated
95% confidence intervals for both broods (0.27, -1.29 – 0.13) and
social fathers(0.81, -0.00 – 1.86), implying that our results are not
the result of chance. Our results support the hypothesis that females
who divorce social partners regularly also engage more extra-pair males
than those who maintain social monogamy.