Spatial patterns of extra-pair paternity: beyond paternity gains and losses
Summary
- Most studies on extra-pair paternity (EPP) focus either on a specific male's extra-pair gains or his extra-pair losses. For an individual bird however, mate choice or mate availability may underlie strong spatial restrictions. Disregarding this spatial aspect may underestimate or mask effects of parameters influencing observed EPP patterns.
- Here, we propose a spatially explicit model for investigating the probability of having extra-pair offspring (EPO) within local networks of breeding pairs. The data set includes all realized and unrealized potential extra-pair matings. This method is biologically meaningful because it allows (a) considering both members of an extra-pair mating and their social mates, and (b) direct modelling of the spatial context in which extra-pair behaviour occurs. The method has the advantage that it can provide inference about the relative contribution of spatial and non-spatial parameters, and about the relative importance of male and female neighbourhoods.
- We apply this method to parentage data from 1025 broods collected over 12 breeding seasons in two independent study populations of blue tits (Cyanistes caeruleus). We investigate a set of predictions based on the EPP literature, namely that EPP depends on male age and body size, breeding density and breeding synchrony. In all analyses, we control for breeding distance, a parameter that is expected to influence EPP even under random mating.
- The results show that older and larger males were more likely to sire EPO, but both effects decreased with increasing breeding distance. Local breeding density but not synchrony predicted whether a particular male–female combination had EPO, at least in one of the study areas. Apart from breeding distance, male age had the strongest effect on EPP, followed by a measure of breeding density. The method thus allows a comprehensive assessment of the relative importance of different types of spatial and non-spatial parameters to explain variation in the occurrence of EPP, while controlling for the fact that individuals that breed further apart are less likely to have EPO.
- The proposed approach is not limited to investigate EPP, but can be applied to other behavioural interactions between two individuals, such as dominance, competition and (social) mating.
Introduction
Sexual behaviour outside the social pair-bond occurs frequently in socially monogamous birds (reviewed by Griffith, Owens & Thuman 2002). In passerines, extra-pair paternity (EPP) has been reported in 86% of the studied species (Griffith, Owens & Thuman 2002). However, levels of EPP may vary dramatically between species, between populations of the same species and between individuals within populations (Petrie & Kempenaers 1998; Griffith, Owens & Thuman 2002; Westneat & Mays 2005).
Extra-pair mating patterns may be influenced by the behaviour of at least four parties: a potential extra-pair female and her social mate, and a potential extra-pair male and his mate (Petrie & Kempenaers 1998; Westneat & Stewart 2003; Canal, Jovani & Potti 2012). However, most studies investigating patterns of extra-pair mating focused on either male or female extra-pair behaviour. This fails to provide a ‘balanced perspective of the sexes’ (Westneat & Stewart 2003) and may not reflect the biological mechanisms underlying the observed extra-pair mating patterns. Similarly, most studies investigate male EPP gains and losses, and correlate these either with characteristics of the focal males (e.g. body size, Kempenaers, Verheyen & Dhondt 1997) or with ecological parameters (e.g. breeding density, Westneat & Sherman 1997). However, the spatial setting in which extra-pair behaviour occurs is rarely modelled explicitly (e.g. Westneat & Stewart 2003).
In blue tits Cyanistes caeruleus L. (Kempenaers et al. 1992; this study) and other species (e.g. Eudocimus albus (white ibis): Frederick 1987; Dolichonyx oryzivorus (bobolink): Bollinger & Gavin 1991; Tachycineta bicolor (tree swallows): Kempenaers et al. 1999; Acrocephalus sechellensis (Seychelles warbler): Komdeur 2001; Passerculus sandwichensis (savannah sparrows): Freeman-Gallant et al. 2005), the majority of extra-pair matings occur between individuals that breed nearby, and often they are direct neighbours (but see Agelaius phoeniceus (red-winged blackbird): Westneat & Mays 2005). Thus, disregarding the spatial component that limits extra-pair behaviour may underestimate or obscure the effect of parameters that influence extra-pair mate choice and mate competition. This is the case even in small populations, as long as the spatial scale at which extra-pair mating takes place is considerably smaller than the population itself. The conventional way of investigating patterns of extra-pair mating has another important drawback: it is generally not possible to model spatial parameters (e.g. breeding synchrony or breeding distance) and non-spatial parameters (e.g. age, body size or experience) within the same model.
Here, we propose a spatially explicit method for investigating the probability of having extra-pair offspring (EPO) within local networks of breeding pairs. The approach considers all male–female combinations that can potentially occur (except for the social pair) as potential extra-pair partners. Instead of investigating which parameters influence the probability that an individual bird has EPO, we examine which parameters influence the likelihood that a particular male–female ‘extra-pair’ has produced EPO taking into account characteristics of all potential male–female combinations that breed at the same distance (same neighbourhood). This method follows more closely the biological arena in which extra-pair matings take place, and it allows considering both members involved in an extra-pair mating as well as their social mates. Additionally, the method allows to explicitly include information about those male–female combinations that did not have EPO with each other. Moreover, it allows direct modelling of the spatial context in which extra-pair behaviour occurs and provides inference about the relative contribution of spatial and non-spatial parameters. The aim of this study is to describe the general approach and illustrate it with a case study.
General approach
EPP has two basic behavioural requirements which usually remain unobserved (Figs 1 and 2). (a) A male and a female that do not form a social pair have to meet. Whether they meet depends on the overlap of the individuals’ spatio-temporal movement patterns. (b) The male and the female have to copulate. Males are generally assumed to utilize any mating opportunity, whereas females may be choosy and may mate selectively with some males but not with others.
Thus, the male and the female behaviour, interactions with their environment, their social mates and potential competitors, and post-copulatory processes determine which male and which female in a population have EPO with one another. Whether an individual has EPO may therefore strongly depend on the behaviour of the potential extra-pair partners (e.g. a low-quality male may be rejected by all females). Based on parentage data, we can now ask why specific male–female combinations have EPO, whereas others do not.
To make inferences about why specific pairs have EPO, we use a generalized linear mixed-effect model (GLMM), where we consider all potential ‘extra-pairs’ (i.e. all male–female combinations in the population apart from the social pair, including individuals without any EPO) as individual data points (Fig. 1, Box a). We then add information on which of these male–female combinations actually had EPO or not (Fig. 1, Box b), which is the response variable in the model. For every male–female combination, we can then add attributes which may influence the likelihood for this pair to have EPO. Such parameters may include traits of the focal individuals, the distance between the focal individuals’ territories, traits of their social mates or traits related to their local neighbourhood (Fig. 1, Box c). We defined the ‘neighbourhood’ as all individuals that breed at a fixed distance (in territories) from the focal individual. These attributes are the explanatory variables in the model. Which explanatory variables are included will depend on the available information, the specific hypotheses one wants to test and the sample size. Alternative models can be constructed and compared, for example those that consider male or female traits in absolute terms (population-wide comparison) with those that consider male or female traits relative to other males or females in the local neighbourhood (spatially explicit model).
Our approach shows similarities to ‘social network analysis’ (e.g. Aplin et al. 2013; McDonald 2013), but there are some key differences. Studies investigating social networks are based on interactions among individuals, whereby individuals are defined as ‘nodes’ and interactions as ‘edges’. Social network analyses generally focus on two aspects. (a) The ‘nodes’ of the network and their properties: individuals and their positioning within the network (e.g. centrality or connectedness) are investigated, often in relation to other traits of the individual (e.g. Aplin et al. 2013). (b) The grouping structure of ‘nodes’ in the network. This approach is used to investigate differences between groups of individuals that, for example, interact more often (e.g. Aplin et al. 2013), or to investigate attributes or behaviours of individuals given the group they live in (McDonald 2013). Network analysis thus generally asks questions about the properties or grouping structure of individuals in the network, but usually does not investigate what determines the strength of the association between two individuals. A few studies investigated correlations between strengths of different associations, for instance whether the number of social interactions of a pair of individuals predicts their future pairing status (e.g. McDonald 2009; Henry et al. 2013; Kurvers et al. 2013). These studies are limited, however, to correlations among two variables, as the statistical approaches only allow investigating the correlation between two interaction matrices. This constraint is lifted in our approach; analysing the relationship between dyadic combinations of focal individuals (here male–female combinations) as the response variable in a generalized linear mixed-effect model gives us the opportunity to investigate correlations with multiple variables (adjusted to their spatial scale) and their interactions.
Why should one use this approach and focus on all possible male–female combinations (all potential extra-pair partners), instead of using conventional methods of analysis? The advantage of our approach is that it allows testing hypotheses about mating decisions of a pair of individuals based on the specific social and ecological environment of each of the individuals, explicitly including traits of all other available potential extra-pair mates (independent of their extra-pair success). This can give us a better understanding of the causalities underlying EPP and about potential mate choice decisions. A simple example illustrates the issue. A researcher may want to investigate whether males that father EPO with neighbouring females differ from males that father EPO at larger distances. The researcher may find that extra-pair sires that have a territory far away, but not neighbouring extra-pair sires, are less related to the focal female (in absolute terms or compared to her social mate). Assuming by default a population with a spatially homogeneous genetic structure, the researcher could conclude that while some females seem to perform extra-pair copulations with random neighbours (e.g. due to male harassment), other females actively roam around to seek extra-pair copulations with unrelated males to increase the heterozygosity of their offspring (indicating female choice). However, relatedness among neighbours may on average be higher than among non-neighbours (due to small-scale genetic population structure as reported for blue tits; Foerster et al. 2006), such that extra-pair mates that breed further apart will always be less related (see also Foerster et al. 2003). Thus, without information about local genetic structure, the alternative hypothesis that all females behave in the same passive manner (e.g. copulate with an extra-pair male to avoid further harassment) is equally plausible. The two hypotheses are difficult to disentangle with conventional methods, because males that do not have EPO cannot be taken into account. With the approach presented here, we can investigate whether females have EPO with less related males, given all males available within the same area as the successful extra-pair sire, and whether this effect differs depending on breeding distance (e.g. direct neighbours, second-rank neighbours …). This allows us to tease apart correlations that arise due to the underlying spatial structure of the data (e.g. genetic relatedness among individuals depends on distance) and correlations that arise through other mechanisms, such as active mate choice (e.g. for less related males). Because interactive behaviours (such as mating, aggression and cooperation) usually take place on a local scale, this approach may prove useful in a wide array of contexts (see Discussion).
Case study
We apply the proposed method to a data set obtained through parentage analyses of 1025 broods of blue tits from two populations breeding 400 km apart, encompassing a total of 12 seasons. This allows us to compare the results of these independent studies of the same species. We first control for the breeding distance among two individuals, because EPP mostly occurs between close neighbours (e.g. Kempenaers et al. 1992, 1999; Freeman-Gallant et al. 2005; Canal, Jovani & Potti 2012). This is expected even under random mating, as long as neighbouring individuals have a higher chance to meet. To avoid an over-parameterized model and to demonstrate the validity of this approach in comparison with previous approaches, we focus on a limited set of explanatory variables that are usually available in this type of studies and are known to affect EPP. These are male age and body size (e.g. Akçay & Roughgarden 2007 and references therein), breeding density (e.g. Westneat & Sherman 1997; Thusius et al. 2001; but see Stewart et al. 2006) and breeding synchrony (e.g. Yezerinac & Weatherhead 1997; Thusius et al. 2001; Canal, Jovani & Potti 2012; but see Kempenaers 1997; Stewart et al. 2006). Additionally, we explicitly included the interaction between breeding distance and male body size and age, because a previous study on blue tits suggested that different mechanisms may be driving EPP for close vs. distant individuals (Foerster et al. 2003). To clarify the hypotheses addressed in this study, we stated the underlying scientific questions for each explanatory variable in Table 1. The method can easily be extended to other parameters, such as characteristics of the female's social mate (e.g. body size: Yezerinac & Weatherhead 1997; Neto, Hansson & Hasselquist 2010; plumage colour: Delhey et al. 2003; or behaviour: Kempenaers, Verheyen & Dhondt 1997), or to characteristics of the focal male–female combination (e.g. relatedness: Akçay & Roughgarden 2007; Kempenaers 2007).
| Variable | Definition of raw variable | Female traits and surroundings | Male traits and surroundings | ||
|---|---|---|---|---|---|
| Mean used for centring | Scientific question | Mean used for centring | Scientific question | ||
| Breeding distance | Distance between two birds in number of territories; identical for focal ♂s and ♀s; defines the ‘neighbourhood’ of an individual at a specific breeding distance | Not centred | Allows controlling for the fact that EPO are more likely among close-by individuals. | Not centred | Allows controlling for the fact that EPO are more likely among close-by individuals. |
| ♂ age | Yearling (1st year, coded as ‘0’) or adult (older, ‘1’) | Mean at the respective breeding distance | Is the potential extra-pair ♂ older compared to the other ♂s at the same distance? | Not applicable (two-level factor) | Are adult ♂s in the population more likely to sire EPO than yearlings? |
| ♂ body size | Tarsus length of the focal ♂ in mm | Mean at the respective breeding distance | Is the potential extra-pair ♂ larger compared to the other ♂s at the same distance? | Population mean | Are large ♂s in the population more likely to sire EPO than smaller males? |
| Territory size | Estimated area of a territory in m2a | Population mean | Are ♀ living in large territories more/less likely to be involved in extra-pair behaviour? | Population mean | Are ♂s living in large territories more/less likely to be involved in extra-pair behaviour? |
| Number of neighbours | Number of neighbours at a specific distance class (e.g. number of direct or 1st order neighbours) | Mean for each breeding distance class within the population (e.g. mean number of 1st order neighbours of all birds in the population)b | Does the proportion of realized EPP events of a ♀ depend on the number of available mates (at the same distance class)? | Mean for each breeding distance class within the population (e.g. mean number of 1st order neighbours of all birds in the population)b | Does the proportion of realized EPP events of a ♂ depend on the number of available mates (at the same distance class)? |
| Relative breeding asynchrony | Difference in the start of laying between the focal ♀ and the female of a (neighbouring) ♂ in days | Mean at the respective breeding distance | Is a ♀ more/less likely to be involved in extra-pair behaviour with males paired to asynchronously breeding ♀s in her surroundings? | Mean at the respective breeding distance | Is a ♂ more/less likely to sire EPO with asynchronously breeding ♀s in his surroundings? |
- For each variable, we provide a definition, indicate how the mean used for centring was calculated and explain the specific question (hypothesis) that can be tested using this approach. Variables that were excluded from the model because of strong collinearities are marked in italic. Note that all means were calculated within year (breeding season).
- a The square root of the raw values was used to account for the two-dimensional nature of the variable.
- b Transformation at breeding distance class level is necessary to take into account that the mean number of neighbours intrinsically increases with increasing distance class.
Materials and methods
Terminology
Each data point consists of a focal male and a focal female which could potentially have EPO together (see below, Fig. 2). We call this the ‘focal male–female combination’. Because a focal male–female combination represents potential extra-pair partners, it by definition cannot be a social pair.
The study sites
We use data from two study areas which contained the same type of nest boxes (inside dimensions: 9 × 12 cm; entrance hole diameter: 26 mm; distance to nest box floor: 16 cm). The first area is a mixed-deciduous woodland close to Vienna, Austria (‘Kolbeterberg’; 48°13′N, 16°20′E, c. 50 ha, c. 3·5 boxes per ha), which was studied between 1998 and 2004. The second study area is in a mixed-deciduous oak forest close to Landsberg am Lech, Germany (‘Westerholz’, 48°08′N 10°53′E, c. 40 ha, 7 boxes per ha), which was studied between 2007 and 2011. For more details regarding the study areas and the general field procedures, see Foerster et al. 2003 and Delhey et al. 2003 (Kolbeterberg) and Schlicht et al. 2012 (Westerholz).
Data on extra-pair paternity
We took blood samples (c. 50 μl) for parentage analyses from all breeding adults (captured 8–11 days after the first egg hatched) and from all nestlings (when the oldest nestling in a brood reached the age of 14 days). We also collected dead nestlings and unhatched eggs and genotyped all if sufficient quality DNA could be extracted. Some nestlings disappeared from the nest box at an early age and were not sampled. These young are expected to be the less developed nestlings from a brood and were therefore presumably late in both hatching and laying order. Because EPO are more often found among the first laid eggs in blue tit clutches (Magrath et al. 2009), we expect that only few broods were erroneously assigned to the ‘no EPO’ category. Because parentage analysis was done using a panel of 8–11 highly informative microsatellite markers (on average 25 alleles per marker), and because the biological mother is usually known with certainty (no intraspecific brood parasitism), the probability of false exclusion of the social male and the probabilities of false inclusion of an extra-pair male are low (~3*10−7 and on average ~10−5, respectively). Moreover, we only assigned an offspring to an extra-pair male when this male was the only candidate assigned with high confidence and with 0–1 mismatches or when the same male had already sired at least one other offspring in the same brood with high confidence. For further details, see Foerster et al. 2003 and Delhey et al. 2007 (Kolbeterberg), and Schlicht et al. 2012 (Westerholz).
It is important to keep in mind that the patterns of EPP we detected are not identical to and may underestimate the actual extra-pair mating patterns in the population. Because the latter data cannot currently be obtained, we assume that the occurrence of EPO in a brood reflects the extra-pair copulation patterns, at least in the sense that a higher rate of extra-pair copulations increases the likelihood of an extra-pair fertilization (as proposed by Brommer et al. 2007).
Territory mapping
We estimated the spatial distribution of territories within each breeding season using Thiessen polygons (Valcu & Kempenaers 2010). This method partitions the space among the individuals by assigning each point within an area to the closest point of interest (in this case an occupied nest box). This approach reflects the positions of breeding territories at relatively high densities (as in our study), because territories form as individuals partition the available space among them (Schlicht, Valcu & Kempenaers 2014). The approach also allowed us to define territory size and neighbour identities for all individuals. The ‘neighbourhood’ generally refers to all individuals breeding at the same distance as the focal male–female combination (see below) and is either centred around the female or around the male of the focal male–female combination. This means that when the focal male–female combination consists of direct (second rank …) neighbours, we calculate variables in relation to all direct (second rank …) neighbours of the female (= ‘female neighbourhood’) or in relation to all direct (second rank, …) neighbours of the male (= ‘male neighbourhood’). This allows us to investigate why a specific male–female combination – given their breeding distance – had EPO with one another.
Breeding parameters
We defined ‘breeding distance’ as the distance – in number of territories – between the focal male and female. Direct neighbours thus have a breeding distance of ‘1’.
Local breeding density may be expressed as the number of breeding pairs per unit area, but it is also reflected by the number of neighbours (e.g. Gray 1996; Sundberg & Dixon 1996; Perreault, Lemon & Kuhnlein 1997; Chuang, Webster & Holmes 1999). If extra-pair mating depends on the availability of potential mates, then individuals with many neighbours should have EPO with more individuals. Conventionally, the null hypothesis is thus that an increasing number of neighbours does not increase the number of EPP events for an individual. At least at very low densities, one would expect this hypothesis to always be rejected, because EPP by definition can only occur when mates other than the social mate are available. By including each individual as many times as there are potential partners, we already correct the number of EPP events for the number of available mates. In this context, the null hypothesis is thus that the proportion of realized (vs. available) EPP events is constant with an increasing number of neighbours. This is equivalent to assuming that the number of available mates and the number of EPP events change proportionately. Three different scenarios arise from this null hypothesis (Fig. 3). (a) No effect of the number of neighbours on the proportion of realized EPP. This indicates that the null hypothesis cannot be rejected and suggests that the number of EPP events of an individual strongly depends on the availability of mates (e.g. Formica & Tuttle 2009; Dunn et al. 1994; Stewart et al. 2006). (b) A negative effect of the number of neighbours on the proportion of realized EPP, suggesting a decreasing proportion of realized EPP events with an increasing number of neighbours. This may indicate that the number of an individual's EP mates is limited or (as an extreme case) even fixed. Such a scenario may occur, for instance, if more neighbours are not directly linked to encounters with more individuals or if courtships and/or copulations are costly (e.g. Dunn et al. 1994; Komdeur 2001). (c) A positive effect of the number of neighbours on the proportion of realized EPP, suggesting an increasing proportion of realized EPP events with an increasing number of neighbours. This could occur, for instance, if an increase in the number of neighbours increases the chances that at least one of them is suitable for EPP (e.g. Shellman-Reeve & Reeve 2000; Johnsen & Lifjeld 2003).
As measures of breeding density, we estimated territory size and the number of neighbours for all individuals based on Thiessen polygons. Although the number of neighbours is calculated on a local scale (see below), we standardize the number of neighbours using population means. We are therefore investigating population-wide effects of breeding density. We used the square root of territory size to correct for the two-dimensional nature of the data. We assessed the number of neighbours at the breeding distance of the focal male–female combination. Thus, if the focal male and the focal female are direct (second rank or third rank) neighbours, their number of direct (second rank and third rank, respectively) neighbours are assessed. Since the number of neighbours intrinsically differs among different breeding distances (Fig. 4), we then subtracted the mean number of neighbours found at the respective breeding distance throughout the population (Table 1).
Breeding synchrony is often defined based on the overlap in fertile period of females breeding within a certain area in a given season (e.g. Kempenaers 1993; Johnsen & Lifjeld 2003; Westneat & Mays 2005; Stewart et al. 2006). To obtain a variable with a similar biological meaning for individual male–female combinations, we here define ‘breeding asynchrony’ as the absolute value of the difference in first egg date between the focal female and the focal male's mate (Fig. 5). In the model, we used only relative breeding asynchrony, calculated once from the focal male's perspective (by subtracting the mean breeding asynchrony with all other potential extra-pair females surrounding the male from the breeding asynchrony of the focal male–female combination; ‘male asynchrony’) and once from the focal female's perspective (by subtracting the mean breeding asynchrony with all other potential extra-pair males surrounding the female from the breeding asynchrony of the focal male–female combination; ‘female asynchrony’; Table 1).
We compared characteristics of the two study populations (Table S1, Supporting information). The two populations did not differ in the number of breeding pairs, in breeding asynchrony among potential extra-pair partners and in the percentage of adult (older) compared to yearling males (first year breeders). However, in the study area Kolbeterberg, territories were on average larger (i.e. lower breeding density), males were larger, and females started to lay significantly earlier, laid larger clutches, hatched more offspring and were more likely to have EPO than in Westerholz. In Westerholz, almost all extra-pair fathers were known breeding males, and therefore, paternity assignment was more complete than in Kolbeterberg.
Data selection
For both study sites, we included only cases where both the male and the female were known breeders (to be able to calculate breeding distance). This implies that we cannot make inferences about the non-breeding extra-pair sires, which may be floater males (true non-breeders), undetected failed breeders or males that bred in natural cavities or outside the study area. However, the occurrence of unknown extra-pair sires was spatially independent in both study areas (significant spatial autocorrelation in only 1 of 12 seasons, low assortment coefficients in all years, Table S2, Supporting information). This means that broods with young from unknown sires were spatially independent and not clumped within the population. Hence, it is unlikely that our results are biased due to co-variation between the distribution of unknown fathers and unmeasured environmental variables.
Statistical analyses
We used generalized linear mixed-effect models (GLMMs) with a binomial error structure and a logit-link function and included the random effects ‘male ID’, ‘female ID’ and ‘year’. The dependent variable ‘occurrence of EPP’ indicates for every male–female combination within a particular population and breeding season (except the social pair, by definition) whether they had EPO together (yes/no). We constructed models with one explanatory variable defined for the focal male–female combination (breeding distance). We included five explanatory variables for the males (‘male perspective’): male age (population-wide effect), male body size (population-wide effect), male territory size (population-wide effect), male number of neighbours (population-wide effect) and male asynchrony (relative synchrony of male–female pair at the respective breeding distance class; see above). Similarly, we included five explanatory variables for the females (‘female perspective’): male age (age relative to that of the surrounding males), male body size (size relative to that of the surrounding males), female territory size (population-wide effect), female number of neighbours (population-wide effect) and female asynchrony (relative synchrony of male–female pair at the respective breeding distance class; see above). We therefore had a set of eleven variables for analysis (Table 1). Please note that whether the male or the female neighbourhood is under focus will usually lead to different parameter values, because the male and the female that have EPP per definition do not breed on the same territory and therefore do not share their entire neighbourhood, and because EPP generally takes place on a local scale (see also Figs 1 and 2).
We first calculated correlation coefficients between all explanatory variables, because strong collinearities can bias the model output (Dormann et al. 2013 and references therein). Two pairs of parameters were strongly correlated (r > 0·5), namely ‘male age’ and ‘male age relative to other males in the focal female's neighbourhood’ as well as ‘male body size’ and ‘male body size relative to other males in the focal female's neighbourhood’ (Table S3, Supporting information). This indicates that in our specific setting, we do not gain additional information by investigating male age and body size in a local context. This may reflect that in our population, there is no spatial structure in male age and male body size, that is males are distributed randomly across the population with respect to tarsus length and age (data not shown). All other correlation coefficients were well below the threshold of r = 0·5–0·7 (Dormann et al. 2013), indicating that here, variation among potential EP mates was sufficient to investigate local male and female neighbourhood effects separately. We therefore included male age and male tarsus length on a population-wide scale as explanatory variables, while all other parameters were included as relative measures, that is relative to other individuals in the male and the female neighbourhood. We also assessed whether male age and body size relative to that of the respective female's social mate (difference or quotient between potential extra-pair male and social male) was a good predictor of EPP. However, this reduced our sample size by 10%, because not all social males had been caught. Because relative age and size were not better predictors of EPP than absolute values, we used the latter in the final model.
Of the original eleven potential explanatory variables, we therefore excluded two (‘male body size given female surroundings’ and ‘male age given female surroundings’) due to strong collinearities, leaving a subset of nine variables in the final model. All explanatory variables, except ‘distance class’, were centred (see Table 1), and all variables were scaled (‘standardized’) by dividing each value by two times the population-wide standard deviation. The latter allows direct comparison of effect sizes among all variables, including two-level factors, such as male age (Gelman 2008). Thus, in our models, an increase by one reflects an increase by two standard deviations of the original data.
We aimed to investigate the effects of all variables while controlling for the spatial limitations of EPP. The relationship between breeding distance and the occurrence of EPP may take different shapes, but in our data is best described by two linear relationships with different slopes (for breeding distance 1–3, and 4–11, respectively; Fig. S1, Supporting information). We reduced our data set such that it included only the first three breeding distance classes, because extra-pair sires rarely bred at larger distances (Fig. 4, final sample size N = 316 broods with EPO, 398 male–female combinations with EPO) and controlled for breeding distance as a linear parameter (effect sizes were similar when including all distance classes, details not shown). We did not centre the variable breeding distance, because most EPP occurred at the first distance class. This implies that the model intercept is calculated at the first neighbouring distance class.
We compared the full models with all models where one parameter was eliminated using AICc values (Hurvich 1989). Since the full model performed as good as the other models (Table S4, Supporting information), we present only the results of the full model. Considering male–female combinations instead of individuals strongly reduces the proportion, but not the number of ‘EPP events’ in the data set. However, this does not reduce the power of the tests (Table S5, Supporting information). Additionally, including every male and female numerous times into the same analysis in different male–female combinations did not inflate our type I error rates when male and female identity were taken into account as random effects (function ‘eppSimDat’ in r package ‘expp’, Valcu & Schlicht 2014).
All statistical analyses were performed using the free statistical software r 3.0.2 (R Development Core Team 2013). As supplementary material accompanying this study, we designed the r package ‘expp’ (Valcu & Schlicht 2014). This package provides a set of tools to perform the spatial data transformations required to obtain a data set as described in Fig. 1. It also provides several graphical methods facilitating data visualization. A data set and example scripts for clarifying data transformation and analysis are also contained in the expp package. For generalized linear mixed-effect models, we used the r package ‘lme4’ (Bates & Maechler 2010). AICc tables were calculated using the r package ‘AICcmodavg’ (Mazerolle 2013).
Results
The further individuals bred apart, the less likely they had EPO with one another (Fig. 6, Table 2). Most extra-pair events occurred at the first neighbouring distance class (‘direct neighbours’) with a sharp decrease at higher neighbouring distance classes (Fig. 4).
| Standard deviation of centred (not scaled) variable | Study areas combined | Kolbeterberg | Westerholz | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Main effect | Estimate ± SE | z | P | Estimate ± SE | z | P | ||||
| Estimate ± SE | z | P | ||||||||
| Intercept | −3·27 ± 0·12 | −26·46 | <0·001 | −3·37 ± 0·17 | −20·37 | <0·001 | −3·10 ± 0·18 | −17·30 | <0·001 | |
| Breeding distance | 0·76 | −2·24 ± 0·16 | −13·68 | <0·001 | −1·96 ± 0·19 | −10·15 | <0·001 | −2·67 ± 0·31 | −8·50 | <0·001 |
| Male age (1st year) | 0·59 | −1·46 ± 0·16 | −6·90 | <0·001 | −1·22 ± 0·25 | −4·95 | <0·001 | −1·87 ± 0·42 | −4·45 | <0·001 |
| *distance | 0·70 ± 0·30 | 2·33 | 0·02 | 0·19 ± 0·35 | 0·54 | 0·59 | 1·32 ± 0·60 | 2·20 | 0·03 | |
| Male body size | 0·52 | 0·53 ± 0·22 | 2·46 | 0·01 | 0·45 ± 0·27 | 1·64 | 0·10 | 0·55 ± 0·34 | 1·61 | 0·11 |
| *distance | −0·62 ± 0·28 | −2·25 | 0·02 | −0·84 ± 0·32 | −2·66 | 0·007 | 0·12 ± 0·58 | 0·20 | 0·84 | |
| Neighbour Number | ||||||||||
| ♂ | 3·64 | −0·96 ± 0·22 | −4·46 | <0·001 | −1·28 ± 0·26 | −4·85 | <0·001 | −0·41 ± 0·39 | −1·05 | 0·62 |
| ♀ | 3·64 | −0·10 ± 0·19 | −0·56 | 0·58 | −0·15 ± 0·22 | −0·68 | 0·50 | −0·18 ± 0·36 | −0·50 | 0·62 |
| Territory size | ||||||||||
| ♂ | 0·38 | 0·30 ± 0·16 | 1·93 | 0·05 | 0·47 ± 0·20 | 2·32 | 0·02 | −0·22 ± 0·26 | −0·85 | 0·40 |
| ♀ | 0·38 | −0·27 ± 0·15 | −1·85 | 0·06 | −0·34 ± 0·18 | −1·82 | 0·07 | −0·17 ± 0·24 | −0·69 | 0·49 |
| Asynchrony | ||||||||||
| ♂ | 6·04 | 0·17 ± 0·13 | 1·28 | 0·20 | 0·21 ± 0·15 | 1·44 | 0·15 | 0·13 ± 0·27 | 0·50 | 0·62 |
| ♀ | 6·04 | 0·07 ± 0·15 | 0·43 | 0·67 | −0·07 ± 0·18 | −0·37 | 0·71 | 0·24 ± 0·29 | 0·82 | 0·41 |
- Shown are the estimates, standard errors, and z- and P-values. Variables that differ for males and females are marked by symbols. Significant variables are in bold. Back-transformed estimates, which can be interpreted as probabilities, are presented in Fig. 6. ‘* distance’ indicates the effect of the interaction with breeding distance. See Methods for model details. Note that P-values were not corrected for multiple testing.
Older males were more likely to sire EPO in both populations. Larger males tended to be more likely to have EPO overall, but not when the populations were modelled separately. The effect of male age and tarsus length decreased with increasing breeding distance, overall and in one of the study populations (Fig. 6, Table 2).
Having many neighbours reduced a male's chance of siring EPO with a specific female in his neighbourhood (overall, and in one study site, Table 2), indicating that an increase in the number of neighbours did not lead to a proportionate increase in EPP events. Overall, females with larger territories tended to be less likely to have EPO and males with larger territories tended to be more likely to have EPO (Fig. 6, Table 2); both effects were mainly driven by one study area. Breeding asynchrony did not influence EPP.
Effect sizes were comparable between the two study areas (Table 2, Fig. S2, Supporting information), except for breeding distance (interaction with study site: −0·75 ± 0·38, z = −2·00, P = 0·05), male territory size (−0·69 ± 0·33, z = −2·09, P = 0·04) and the male number of neighbours (0·89 ± 0·48, z = 1·86, P = 0·06).
Of the variance explained by the random effects, less than 1% could be attributed to differences between seasons and study areas, whereas 74% and 26% was explained by male and female ID, respectively. This indicates that attributes of individual males were more important than attributes of individual females. Note that the effect of female identity cannot be separated from attributes of her social partner, unless his characteristics or identity are explicitly taken into account as explanatory variables or random factors.
Discussion
Including the spatial availability of mates into studies on EPP is important, especially when studying who mates with whom (e.g. Westneat & Stewart 2003; Westneat & Mays 2005). A consequent next step is therefore to change the focus from studying EPP of individuals towards studying the occurrence of EPP among all potential extra-pair partners. Here, we suggested a new modelling approach and illustrated it with a case study on blue tits. We investigated which of several variables – previously reported to explain patterns of EPP – influenced the probability that a given male–female combination within a breeding population has EPO together. We tested traits of individuals either at the population level, or relative to other individuals in the male and female neighbourhood. Using data from two independent populations, we discuss general and population-specific effects below.
General approach
Our approach, which focuses on pairs of birds instead of individuals, has several major advantages.
First, spatial effects (such as breeding distance) and effects that take place at a local scale (e.g. interactions among neighbours) can be modelled explicitly. For example, assume that one would like to test the hypothesis that larger males are more likely to sire EPO because they are more competitive or because they are preferred by females. Typically, the effect of male body size is modelled population-wide. However, if EPP is largely restricted to close neighbours, absolute size may be less important than size relative to the surrounding males. On the other hand, relative size is difficult to assess without defining a complex spatial framework as we describe it here. As long as the breeding location and size data of all individuals are known, such local effects can explicitly be included in the model.
Second, variables that focus on the males (e.g. breeding asynchrony with the surrounding females; ‘male EP gains’) and variables that focus on the females (e.g. breeding asynchrony with the mates of the surrounding males; ‘male EP losses’) can be included at the same time, and their relative importance can be assessed in the same model. This is not possible with conventional methods, which usually focus only on one individual of the extra-pair (males or females). For example, we may want to investigate whether asynchronous breeding enhances EPP under two hypotheses. (a) The effect of asynchrony arises because males court only the most asynchronously breeding females due to a trade-off with mate guarding. In this case, the relevant variable is the asynchrony of the focal female relative to that of the other females surrounding the male. (b) The effect of asynchrony arises because females are more likely to have access to males whose female is incubating, for example because of female–female aggression. In this case, the relevant variable is the asynchrony with the mate of the focal male, relative to that of the mates of the surrounding males. Thus, different behavioural mechanisms can lead to different outcomes and thus effect sizes when tested from the male vs. the female perspective, as illustrated in Fig. 5. With the approach presented here, we can robustly test such hypotheses.
Third, the joint modelling of different types of traits allows controlling for various confounding factors. For instance, we can assess the effect of male age, territory size or relatedness on EPP while controlling for breeding distance, which may be a confounding factor, for example if there is a strong spatial structure in male age, territory size or quality (e.g. older males may breed clustered in high-quality areas of the habitat, Morton & Derrickson 1990; related individuals may cluster together due to philopatry; Brouwer et al. 2011). Similarly, we can assess effects of local density on EPP while controlling for effects of local, pairwise asynchrony and vice versa. Because breeding distance is a parameter defined by a pair of individuals, controlling for breeding distance is generally not possible when focusing on traits of one sex only, unless the analysis is restricted to a comparison among individuals that had EPP at different distances (without taking into account non-realized potential extra-pair mates).
Fourth, the joint modelling of different types of traits allows a direct comparison of effect sizes. For example, both effects of male age and of breeding asynchrony on EPP appear in the literature, but their relative strength could not previously be investigated.
Finally, the approach may also be used to specifically test hypotheses that imply that a parameter's importance for EPP depends on the partner's breeding distance (see Case Study below).
Our approach also has practical and statistical limitations. (a) Obviously, only events can be included where the EP father can be assigned and his breeding location is known. This may restrict the usefulness in species and studies where many of the EPO are sired by males that do not breed inside the study area. (b) A general concern for this and other behavioural studies is that individuals – or in this case pairs of individuals – are treated as independent data points. This independency assumption is violated if an interaction among two individuals changes the future behaviour of these individuals, which is likely, at least to some degree. Generally, such ‘social dependence’ is neglected, because it is not trivial to take it into account. Our method at least partly addresses this issue, because attributes and behaviour of potential interaction partners can explicitly be included in the model. (c) Calculating R2-values, which are often used to assess the relative importance of variables, is not straightforward in models that include random effects or that follow a non-linear distribution (Nakagawa & Schielzeth 2013). We suggest instead to compare the importance of different variables by their relative effect size and significance, which should correspond to the ‘traditional’ R2-value (Nakagawa & Schielzeth 2013 and references therein). (d) Special care should be taken to model only biologically meaningful effects, because the complexity of this type of model makes unexpected results (and potential type I errors) even more difficult to interpret.
Case study
As expected, breeding distance had a large effect on the probability of having EPO. The probability that a potential pair had EPO decreased by 89% from direct neighbours to second-order neighbours (Table 2, Fig. 6), and few extra-pair sires bred further than two territories away (Fig. 4). Such a pattern is expected, because individuals have a higher chance to meet and interact with close-by individuals.
As shown in previous studies on blue tits and other species (e.g. Akçay & Roughgarden 2007 and references therein), male age was an important determinant of the observed EPP patterns. Older males were on average 4·1 times as likely to gain EPO than first year males, potentially reflecting male quality, female choice or male investment into EPP (for further discussion see Akçay & Roughgarden 2007). Similarly, larger birds were more likely to have EPO (Table 2 and Table S1, Fig. S2, Supporting information), as shown previously in blue tits (Kempenaers, Verheyen & Dhondt 1997) and other birds (e.g. Akçay & Roughgarden 2007 and references therein). A previous study on the Kolbeterberg population, spanning the first 4 years, found that in a pairwise comparison, extra-pair males were older and larger than the social males they cuckolded, but only if they were close neighbours (Foerster et al. 2003). Here, we show explicitly that the effect of male age and body size decreases with increasing breeding distance (Table 2; similar outcome if pairwise comparison of male body size used, see methods). Our analysis thus suggests that the mechanisms driving EPP may differ depending on the breeding distance among individuals.
We expected that individuals with larger territories would be less likely to be involved in an extra-pair event, because a large territory may limit the encounter rate of an individual with potential EP mates (e.g. Westneat & Sherman 1997; Thusius et al. 2001; Westneat & Mays 2005). For females, effect sizes were indeed negative, but non-significant. However, in one population, males with larger territories (population-wide) tended to be more likely to have EPO (Table 2, Fig. 6). Such an effect could arise, for instance, if highly competitive males were able to secure both large territories and more EPO. Overall, our results suggest that individuals are not constrained in their extra-pair behaviour by having larger territories, at least for the territory sizes recorded in this study.
For males, we found a negative relationship between the number of neighbours and the probability of siring EPO (Table 2, Fig. 6). This means that an individual male with more neighbours sired EPO with fewer extra-pair mates than expected if the chance of extra-pair success was proportional to the number of available mates (Fig. 3), independently of potentially confounding effects such as male territory size, age or body size. In previous studies that tested the relationship between number of neighbours and EPP, the slope is generally difficult to interpret (see Methods). In contrast, our results imply that the number of females with whom a male can sire EPO is limited by other factors than mate availability. This outcome can occur, for instance, if males are limited by the amount of courtship (or sperm) they can produce, and thus have a limited number of successful extra-pair copulations they can achieve, or if the number of successful encounters with potential EP mates does not increase proportionately with the number of neighbours. The effect of the female's number of neighbours had the same sign, but was non-significant. Because the effect sizes are similar, speculations about different mechanisms acting on males and females seem unwarranted.
Breeding synchrony has been hypothesized to influence extra-pair mating patterns in two ways. First, a certain synchrony between breeding pairs may be necessary for extra-pair matings to occur, as it insures that sexually active potential mates are available (e.g. Chuang, Webster & Holmes 1999). Second, synchrony may reduce the opportunities for extra-pair matings in species that exhibit mate-guarding behaviour (such as the blue tit, Kempenaers, Verheyen & Dhondt 1995), because of a trade-off between investing in mate guarding and in extra-pair behaviour or courtship during the fertile period of the social female (e.g. Emlen & Oring 1977; Yezerinac & Weatherhead 1997; Chuang, Webster & Holmes 1999; Thusius et al. 2001; Canal, Jovani & Potti 2012; but see Kempenaers 1997). If this argument holds in blue tits, a larger asynchrony should facilitate the occurrence of EPO for any male–female combination. Since this reasoning is based on a trade-off for males, males are expected to be more strongly influenced by breeding asynchrony than females. However, our analysis shows that asynchrony was not linked to the likelihood of EPP in either study area, confirming an earlier study (Kempenaers 1997). This may indicate that there is no strong trade-off between mate-guarding and extra-pair behaviour in this population, as expected if EPP results from active female behaviour (Kempenaers et al. 1992; Kempenaers 1997).
Conclusions and outlook
In this study, we suggested a novel method that allows investigating which parameters influence the extra-pair mating patterns we observe and that helps to formalize and test hypotheses about the potential mechanisms underlying such effects. The novelty of the approach is that it takes into account all potential male–female combinations that could have EPO and investigates which of these potential ‘extra-pairs’ are realized based on the respective male and female characteristics and the characteristics of their neighbourhoods. Moreover, this approach is useful when considering behaviours or traits that show spatial clustering. Results of a case study on blue tits, where we corrected for the breeding distance between individuals, indicated that from those variables we tested, the most important factor driving EPP was male age (population-wide effect). Larger males were overall also more likely to sire EPO. Both effects decreased with breeding distance, indicating that different mechanisms may drive EPP between close neighbours and between individuals breeding further apart. Whereas breeding asynchrony did not influence EPP, one measure of breeding density (number of neighbours) did, but only for males. Our study therefore suggests that traits may have a different impact on EPP when considered relative to the focal male's or female's neighbourhoods.
We tested well-established hypotheses about EPP to illustrate a new approach to analyse interactions between individuals (here: whether a pair had EPO together). The method can be applied more widely to address a variety of questions and is particularly useful (a) to test whether and how processes differ at different spatial scales, and (b) to test how traits of individuals, of the potentially interacting pairs and of their neighbourhoods influence the outcome of these interactions. Traits of the interacting pairs can include behavioural observations. For example, our approach allows investigating whether pairs (excluding social mates) that interact more often in a different (e.g. foraging) context are more likely to have EPO with each other, given other known effects on the occurrence of EPP (e.g. male age, breeding distance).
Similar analyses can be conducted with other interactions than EPP as the response variable. For example, one could investigate parameters predicting which individuals form a social pair-bond, which individuals behave more (or less) aggressively towards each other, which individuals are more likely to forage together, etc. Furthermore, the same approach can be used to investigate underlying factors that can explain changes in the ‘value’ of a pair over time or to calculate the repeatability of this pair ‘value’. For example, if multiple measurements on reproductive parameters (e.g. clutch size) or pair behaviour (e.g. relative amount of male care, proportion of paternity lost) are available, one can test whether the change in pair ‘value’ can be explained by changes in aspects of the local neighbourhood (e.g. number of competitors). Thus, the approach we describe here can easily be extended to a wide range of questions in many behavioural systems.
Acknowledgements
We are grateful to many people involved in both field and laboratory work over the years in both study areas, and to Sylvia Kuhn and Alexander Girg for genotyping. We thank Raphael-Thomas Klumpp and Alfred Fojt from the institute of Silviculture, Vienna, and Hans Winkler from the Konrad Lorenz Institute for Comparative Ethology, Vienna, for logistic support at our Austrian study site, and the Bavarian regional office for forestry (LWF) for permission to work on our German study site. We are grateful to Ben Sheldon, the associate editor, and two anonymous referees for detailed and constructive feedback on the manuscript. This work was funded by the Max Planck Society. LS is a PhD student in the International Max Planck Research School for Organismal Biology.
Data accessibility
All data are supplied with the R package ‘expp’ (Valcu & Schlicht 2014; URL: http://CRAN.R-project.org/package=expp).
