Abstract
In a monogamous species two partners contribute to the breeding process. We study pair formation as well as the effect of pair bond length and age on breeding performance, incorporating individual heterogeneity, based on a high-quality dataset of a long-lived seabird, the common tern (Sterna hirundo). To handle missing information and model the complicated processes driving reproduction, we use a hierarchical Bayesian model of the steps that lead to the number of fledglings, including processes at the individual and the pair level. The results show that the age of both partners is important for reproductive performance, with similar patterns for both sexes and individual heterogeneity in reproductive performance, but pair bond length is not. The terns are more likely to choose a former partner independent of the previous breeding outcome with that partner, which suggests a tendency to retain the partner chosen at the beginning of the breeding career.
1. Introduction
Many bird species are monogamous and consequently two partners are involved in the breeding process [1]. Pair bonds in birds are often thought to influence breeding performance, especially in long-lived species with biparental care. Two main lines of thought have emerged that explain the implications of partner choice; on the one hand, some hypotheses explain why it might be advantageous to remain with the same partner (e.g. [2,3]), while others give reasons why it might be more beneficial to divorce and choose a new partner (e.g. [4,5]). Although many studies have been carried out to answer these questions, a large proportion of them have important limitations [6]. To understand the implications of partner choice and fidelity from an ecological and evolutionary perspective, it is fundamental to develop methods that incorporate the cumulative effect of pair bond on breeding output, while accounting for age effects of both sexes on survival and fertility, and for individual heterogeneity in breeding performance.
Divorce can be an adaptive strategy as long as the expected benefits of changing the mate outweigh the potential costs [7]. Individual heterogeneity plays a role here; if all birds have the same breeding capacity the expected gain of changing the mate will be low and might not pay off [8]. It has been suggested that divorce may arise when partners are not well coordinated [4], or more generally as a consequence of a previous wrong partner choice [5], the option of pairing with a higher-quality mate [8] or to avoid inbreeding [9]. By contrast, ‘non-adaptive’ explanations of divorce state that it arises as a side effect of asynchronous arrival of both partners in the breeding colony [10, 11], due to intraspecific competition [12] or as a consequence of external influences leading to temporary loss of the partner [13]. In these cases, the breeding performance does not necessarily increase after the divorce and divorced pairs frequently re-mate in following years [12,13].
Previously stated reasons for re-mating with the same partner are the lack of available alternative partners or territories [14], the exclusion of the risk of not having any partner [15] or the assurance of a partner of certain age or experience if these characteristics cannot be assessed but breeding performance increases with advancing age or experience [2]. It has also been suggested that repeated matings with the same partner might increase coordination of breeding behaviour within the pair, while reducing allocation of time and energy for partner search and courtship, as well as preventing the loss of already invested effort into the partnership [2,6]. Based on this ‘mate familiarity hypothesis’, pair formation early in life is of prime value and thus the long-term adjustment between partners is the process by which the pair increases its breeding performance [3].
Previous studies commonly evaluate only the immediate effect of partner change, comparing individuals pairing with new or retained mates (e.g. [16–18]). These approaches ignore the cumulative effect of pair bond duration and cannot test the ‘mate familiarity hypothesis’. There are only a few exceptions where the pair bond length is the focus of the study (e.g. [3,19–21]). Moreover, to our knowledge, there are no studies that consider all previous mates for the mating decision and thus analyse the overall partner choice mechanism rather than just the decision to split up with the previous partner.
In this study, we use a long-term, individual-based encounter–reencounter dataset of mostly aged and sexed common terns (Sterna hirundo), to examine the partner choice mechanism and the effect of pair-bond duration on breeding performance. More specifically, we test if a bird is more likely to choose a certain partner the more often it has bred with that partner in the past or the more fledglings that pair has produced. Furthermore, the influence of the number of times a pair has bred together in the past on the number of fledglings produced is analysed. Common terns are long-lived seabirds that nest in temperate and subarctic regions of the Northern Hemisphere. Since mate fidelity increases with longer adult life expectancy, pair bonds might be of importance especially in such long-lived species with biparental care [22]. In this species, mate retention is high, but divorces still occur [11,16]. There are contradictory results regarding breeding output after divorce; on the one hand, no advantage to changing mates was reported [11], while another study found higher breeding success for newly formed pairs after divorce in young breeders [17]. The latter gave some evidence that there might not be an advantage of re-mating with a previous partner by comparing the breeding success of the selected group of faithful second-time breeders to their first breeding attempt [17]. There are no studies for the common tern that analyse the effect of pair-bond length on partner choice and breeding performance.
We developed a hierarchical Bayesian model that reconstructs the yearly sequence of events that lead to choosing partners and subsequent fledging of chicks (figure 1). Despite the high quality of the dataset (electronic supplementary material), there are important sources of uncertainty and missing information that have prevented more in-depth analyses in the past, such as untagged partners, unknown dates of birth and death, unknown age, unknown sex or missing information before the start of the study for individuals that were already alive. Our Bayesian model accounts for these sources of uncertainty and allows us to test the long-term effect of partner choice as well as age on breeding performance, accounting for individual heterogeneity. Our model explicitly incorporates the conditional structure of the events that lead from surviving and choosing to breed, to choosing partners, to chick fledging and the decision to breed repeatedly within a given year. This structure is needed to handle the missing information. Moreover, it allows us to address further life-history issues, such as the form of the survival function, differences between sexes in reproductive performance and the probability of breeding repeatedly within a breeding season.
The structure of the model. It shows the hierarchical steps that lead to the number of fledglings: (i) survival analysis and the presence in the colony, (ii) partner choice, (iii) the number of fledglings per breeding attempt and (iv) additional breeding attempts. The parts of the model without a shaded background are processes at the single individual level. The striped background highlights the part of the model that depends on the decision of both partners. The grey shaded background represents parts that are modelled at the pair level.
2. Material and methods
(a) Study details
Our study was performed on a monospecific colony of common terns (
individually identified birds) nesting on six artificial islands in the Banter See in Wilhelmshaven (German North Sea coast, 53°27′ N, 08°07′ E), where the terns reproduce between early April and mid-August.
Over the breeding seasons between 1992 and 2009, all chicks born in the colony and few adults (
, with 
being of unknown age) were ringed and marked with subcutaneously implanted transponders (Trovan ID 100). All fledglings were sexed (electronic supplementary material). The use of transponders together with an efficient distribution of reading antennae ensured reencounter probabilities close to 1 [23] as well as an accurate identification of parents (electronic supplementary material) for the marked birds. There are partners at the colony that are not marked, which are typically immigrants [24], and some birds with incomplete breeding histories (e.g. birds transponder-tagged as adults and 13 birds ringed only). The electronic supplementary material gives details on how these individuals are treated in the model. The initial assignment of partner status is conducted using rules explained in the electronic supplementary material and displayed in the electronic supplementary material, figure S1.
(b) Model
The events we are modelling here are inherently hierarchical; from survival to producing fledglings, each process is conditioned on another process at a higher hierarchy (figure 1). Moreover, these processes occur at different levels: from survival to choosing to breed, the decisions are made by each individual, while pair formation and the production of fledglings is the result of pair-level processes. This bilevel hierarchical structure, along with the amount of missing information, is analysed in a Bayesian model that combines recent developments in survival analysis [25] with a mixture of generalized linear models, each of which corresponds to a different hierarchy. We divide the model into four main sections, which are all conditioned on the preceding section: (i) age-specific survival and the presence in the colony, (ii) choosing a partner, (iii) producing fledglings and (iv) additional breeding attempts. Below we explain each section in detail.
See the electronic supplementary material for an extended explanation of the algorithm, including the construction of the posterior distribution, prior details, as well as the sampling procedure and model choice. We wrote the model with the statistical software R v. 2.12.0 [26].
(i) Survival analysis and presence in the colony
The first level in our model is the analysis of survival patterns from one age to the next. We use a modelling framework for capture–recapture data based on Bayesian survival trajectory analysis (BaSTA) [27], which combines models for survival and recapture probability with imputation of unknown times of birth and death [25].
Let x represent age (in years) and X be the random variable for age at death. Our modelling approach requires the definition of a parametric model for mortality (hazard rate), noted as 
, where θ are parameters to be estimated. We use a Gompertz hazard [28] to describe the underlying mortality over age x as
2.1where 
are the baseline mortality and the rate parameters, respectively. Two additional relevant functions are calculated from 
, namely
2.2and
2.3where equations (2.2) and (2.3) are the survival probability and the probability density function of ages at death, respectively. Preliminary maximum-likelihood analyses with Gompertz, Gompertz–Makeham, Weibull and Siler functions using only aged individuals show that the Gompertz model adequately describes mortality patterns in this colony.
Although reencounter probabilities are essentially equal to 1 for marked individuals, detection is still conditioned on the bird being present in the colony. Since common terns are known to show high breeding site fidelity after the first breeding event [29], it is reasonable to assume that individuals not present at the colony in intermediate years are most probably skipping a breeding season. Thus, analogously to the typical recapture probability, we model the probability of an individual i being present at the colony at time t as a Bernoulli process where the indicator 
assigns 1 if the individual is present and 0 otherwise, with the random variable 
, such that
2.4where 
is the probability of being present at the colony. We represent an individual i's ‘presence history’ (analogous to the capture history) with the vector 
, while 
is the matrix for all histories in the dataset.
Inference on the posterior distribution of all unknowns, 
, follows a recent approach [25], where 
and 
are the subsets of unknown and of known ages at death, respectively (further details in the electronic supplementary material).
We conditioned our analysis on individuals that were at least 2 years old and assumed that breeding individuals of unknown age were at least 3 years old. Common terns usually start visiting the breeding colonies after spending their first 2 years in Africa. At that age, they are commonly prospectors and most terns do not start breeding before age three [23,30].
(ii) Partner choice
A bird i that has survived to year t and is present in the colony at that time (i.e. 
) has the choice to breed. Although a few young birds did not breed despite being present at the colony, most birds did attempt to breed. We do not model the probability of breeding explicitly, but all following steps are conditioned on breeding (i.e. 
) in the first breeding occasion 
within a season.
At this point, each breeding bird has to find a mate. We define 
and 
as the choice of partner that birds i and j make at time t. Assuming that each individual chooses independently (in common terns both partners are involved into the mating decision [31]), the joint probability of partner choice for birds i and j is
2.5This partner choice is a multinomial process between 
available individuals that include past mates that are still alive and all other birds of the opposite sex present in the colony at time t (i.e. potential new partners: number equals the difference between the number of nests and the number of previous partners that are still alive). We assumed that all birds choose partners at the same time and from the same pool of birds. This multinomial choice is informed by the bird's past history with previous partners. Thus, the probability that bird i chooses partner j is given by
2.6where 
are the link function parameters for the probability of choosing a certain partner, 
is the residuals of the linear regression between 
, the number of times partners i and j have been together before time t, and the total number of fledglings they have produced before year t, given by 
. Since both 
and 
can be correlated, we took the residuals to avoid inflation of the variances in the parameter estimates. Thus, the residuals 
would correspond to the number of fledglings produced beyond the expected number of fledglings given the time the partners have been together. This function is flexible and allows us to consider the process of deciding for a new partner separately from deciding for a former breeding mate based on past experience.
Here arises a complication when marked birds breed with unmarked ones. In that case, the model needs to treat the unmarked birds as potential partners and assign them an ID code. Thus, following a hidden Markov structure, our algorithm imputes these ID codes to all breeding unmarked birds as well as age and sex (for additional details on the imputation procedure, see the electronic supplementary material).
(iii) Number of fledglings per breeding attempt
After forming the pairs, the model moves to the nest level, which avoids drawing inference on duplicated breeding outputs. Both partners i and j are matched and assigned to a nest 
at time t, with a total number of nests M. Each time the same partners breed together, their nest has the same m assigned.
Within one breeding season, common terns can attempt to lay eggs on several consecutive occasions k with a maximum of 
. We define the random variable 
for the number of fledglings produced in nest m at time t and occasion k, where 
represents the number of fledglings produced. We assumed that 
; in other words, that it follows a Poisson distribution truncated at an upper value of three (i.e. maximum recorded number of chicks per attempt in the dataset), where 
is the expected number of fledglings for nest m at time t and occasion k. Since we did not detect overdispersion in the number of fledglings (i.e. coefficient of variation, 
), we assume that this Poisson model is adequate. The truncated Poisson distribution is calculated as
2.7where the denominator in the above equation is the Poisson cumulative density function (CDF), 
. The link function for the expected number of fledglings is given by
2.8with 
, and 
. Parameter 
determines the upper bound of 
, while 
relates the number of fledglings with the number of years both parents had nested together before year t, 
(equivalent to 
in equation (2.6)). The quadratic term in equation (2.8) allows us to test nonlinear effects on the number of fledglings as a function of the parents' ages for each sex s (
for males and 
for females); 
controls the steepness of the change in breeding performance with age, while 
controls the age at which the highest performance is reached.
Parameters 
are individual effects that facilitate testing for heterogeneity in breeding performance, where 
(
for good breeders and 
for poor breeders). If both parents are extremely poor breeders, the expected number of fledglings will be only 
of a nest with two extremely good breeders (electronic supplementary material, figure S2). This is very similar to the maximum difference in reproduction of 15.2% caused by individual heterogeneity in a study of the little penguin (Eudyptes minor [32]). In addition, by including these individual effects, we control for autocorrelation between repeated measurements from the same individuals.
We assume that partners remain together for the entire duration of the breeding season. Although individuals could potentially change their partner between breeding attempts within a season, we only recorded a negligible number of five cases [33].
(iv) Additional breeding attempts
The decision to breed at additional occasions in one breeding season is made at the pair and thus nest level. We define a random variable 
for the event that parents from nest m at time t attempt to breed on a second or third occasion, where 
is denoted as the event in which parents from nest m at time t attempt to breed on a second and third occasion (i.e. 
). The decision to breed an additional time is a Bernoulli process:
2.9We model the probability of breeding a second and third time in 1 year as being dependent on whether the pair bred successfully on the previous occasion within the same year 
, 
if 
and 
if 
. The link function is given by
2.10A summary of all variables and symbols in the model is given in the electronic supplementary material, table S2 and table S1 lists all parameters estimated.
3. Results
The model with the individual effects on reproductive output performs much better than the model without the individual effects (
; see the electronic supplementary material, tables S3 and S4 in for parameter values). Thus, we only report the results of the model with the individual effects unless stated otherwise.
The Gompertz baseline mortality (parameter α) for this colony of common terns is relatively high; of those individuals alive at age 2, almost 11% are expected to die before age 3. However, the rate parameter (β) shows that mortality changes slowly with age; 10% of those individuals being born in a given cohort and that initially survived to age 2 are expected to be still alive at age 15 (see the electronic supplementary material, figure S3 for the mortality and survival curves). The probability 
of showing up in the colony conditional on being seen once is very high.
The probability of choosing a certain partner increases with the number of times the pair has bred together in the past (figure 2). By contrast, the previous breeding outcome with a partner does not influence the partner choice (
parameter not different from 0; electronic supplementary material, table S3).
Function of the partner choice. In this example, the bird has a choice between two partners, partner A and partner B. The graphs show the probability of breeding with partner B dependent on the number of times the bird has bred with that partner in the past, given that it (a) has never bred with partner A or (b) has bred twice with partner A in the past. The grey area is the 95% predictive interval and the white line the predicted curve using the average estimated parameters.
Our results show that the number of fledglings per pair and year does not improve with the pair bond length (parameter 
not different from 0; electronic supplementary material, table S3). The age of both partners is instead important for the breeding outcome; there is a period of improvement followed by senescence in both sexes (figure 3). On average, males reach their maximum reproduction only slightly later than females (
): 11.2 and 10.5 years, respectively. However, if no individual effects are included, the maxima of the age curves for both sexes are at a later age; on average 1.9 years later for males and 1.6 years for females. The steepness of the change in breeding performance with age is very similar for both sexes (
).
A contour plot of the number of fledglings per pair and breeding attempt dependent on the age of the male and the female and their breeding potential for the model (a) with individual effects and (b) without. The breeding potential of the members of a pair is here defined in terms of the individual effect, where good is an individual effect of 0, medium of −0.5 and bad of −1.
The probability of breeding a second and third time in one breeding season is influenced by the breeding success on the previous occasion. Birds are much more likely to try to breed another time if the previous breeding occasion was unsuccessful (figure 4). The probability of breeding a second time after an unsuccessful first breeding attempt is 0.2043 (95% CRI: 0.1849–0.2250) and therefore not uncommon. By contrast, the probability of breeding a second time after a successful first breeding attempt is 0.0145 (95% CRI: 0.0077–0.0246), which is very low. Breeding a third time is unlikely, with a probability of 0.0260 (95% CRI: 0.0121–0.0495) after an unsuccessful and 0.0083 (95% CRI: 0.0008–0.0578) after a successful second breeding occasion.
The probability of breeding (a) a second and (b) a third time in one breeding season dependent on the breeding success on the previous occasion. The error bars represent 95% predictive intervals.
4. Discussion
Every year, the sequence of events that lead individual birds to breed and produce fledglings is complex and the events are strongly related. At the start of the breeding season, surviving individuals need to decide if they are to breed that year and, if so, they have to choose a partner. A number of hypotheses has been proposed to explain the mechanisms that lead either to divorce or to remaining with the same partner. Our results show that common terns from the Banter See colony are more likely to choose a partner that they know, regardless of their previous breeding outcome, even though the pair bond length does not influence the reproductive performance of the pair and thus confers no fitness advantage. The lack of an effect of pair bond duration on breeding success suggests that the ‘mate familiarity hypothesis’ [2] does not explain the mating pattern in our population. The variation in age at first breeding for the common tern is only a few years [23]. Especially in their first year of reproduction, common terns mate with a partner of their own age [34], which is not necessarily their preferred choice but a question of availability of partners that are willing to mate with them [35]. This explains the correlation of the ages of partners that are marked (
; see the electronic supplementary material, left-hand panel of figure S4), which was also found previously in other studies of the common tern (e.g. [11,35]). As reproductive performance first increases with age the ‘assured-age hypothesis’ [2] seems to be an explanation for the influence of pair bond duration on partner choice. In addition to the age, the breeding potential of partners is correlated within pairs (
; see the electronic supplementary material, right-hand panel of figure S4). This result suggests that birds choose their partner at the beginning of their reproductive career according to its reproductive quality and tend to stay with that partner.
A lack of improvement in breeding performance with pair duration has been found also in other species, such as in white-chinned petrels (Procellaria aequinoctialis [19]), common guillemots (Uria aalge [36]) and house sparrows (Passer domesticus [37]), as well as in the selected group of only second-time breeding common terns [17]. In the black-legged kittiwake (Rissa tridactyla), a positive effect of pair bond length on breeding success probability was only due to a selection effect [3], which highlights the importance of including the individual effects in our analyses. Contrary to our findings, there is evidence that, in some species, breeding performance improves with the duration of pair bond. This has been reported in northern fulmars (Fulmarus glacialis [38]), short-tailed shearwaters (Puffinus tenuirostris [39]), barnacle geese (Branta leucopsis [40], Cassin's auklets (Ptchoramphus aleuticus [41]), barn swallows (Hirundo rustica [21]) and little penguins [32].
In accordance with our findings, longer pair bonds made a mate change less likely in black-legged kittiwakes [3] and little penguins [32]. By contrast, pair bond length had no effect on divorce probability in white-chinned petrels [19] and in oystercatchers (Haematopus ostralegus [20]). The lack of an effect of previous breeding success for the mate decision is supported by studies on the common tern and other species, where breeding performance in the previous year did not influence the decision of divorce (e.g. [11,16,17,19]). However, several other studies on a number of bird species have shown that divorce probability is connected to a low breeding success or failure in the previous year (e.g. [3,4,10]).
The quadratic age pattern in breeding performance implies a directional preference [35], where it is best for a common tern to mate with a partner of intermediate age and of good reproductive potential. It was shown in previous studies that birds of high breeding potential were less likely to change their partner [32]. We found only small differences in the age pattern of reproductive performance for males and females, with a slightly later maximum for the males who also are older than females when breeding for the first time [30]. Extra-pair paternity is rare in common terns [42]. It was shown previously for monogamous bird and mammal species that the pattern of reproductive success is similar in both sexes [43]. Even though there are sex-specific differences in parental tasks, both males and females contribute to the incubation and chick provisioning in the common tern [44]. They are therefore likely to invest approximately equally in their young, which might explain the similar pattern for both sexes.
The comparison of the two nested models with and without the individual effects showed that there are differences in reproductive performance between individuals that cannot be neglected. The maxima of the age curves for males and females are shifted to higher ages when individual effects are not included. This is likely to be a sign for selective disappearance of individuals with lower reproductive success. However, the effect must be small since we found no correlation of age at death and the individual effect for birds marked with transponder (
; electronic supplementary material, figure S5). A previous study showed that there is some selective disappearance in the studied common tern population, even though it plays a minor role compared with average individual change [45].
A low general probability of additional breeding attempts, with a higher probability after an unsuccessful breeding attempt and a lower probability after a successful attempt, concurs with previous findings [46]. Very few pairs start a third breeding attempt. Having a successful previous breeding attempt probably does not give enough time within the constrained breeding season for another attempt. In the common tern, arrival time and onset of breeding within a season influence the re-nesting probability of individuals [46]. Furthermore, it might not be worth spending the additional effort after a successful breeding event given that the probability of a successful breeding decreases at the end of the season [47]. In all five cases of a third reproductive attempt it ended unsuccessfully. The birds that make more than one breeding attempt in a breeding season are probably of high reproductive quality [46].
(a) The model
Most studies that attempt to test the hypotheses connected to partner choice ignore the hierarchical structure that leads to choosing a partner and producing fledglings, in many cases due to data limitations. In this study, we developed a model that explicitly reconstructs the sequence of events involved in producing fledglings, testing how individuals choose partners as a function of their breeding history. Our approach is unusual because we simultaneously model multiple aspects of the breeding process, while making inferences about information missing from the data. Other models typically include only one level of the breeding process or consider the different processes separately (e.g. [3,11,20]). There are only a few models that take more than one level into account (e.g. [48,49]), but to our knowledge there are none that consider all the levels used in this study together. Moreover, males and females have only rarely been modelled simultaneously in other studies of divorce or mate retention before (e.g. [20,39,41]).
In ecology and evolutionary biology, differences between individuals are often modelled by random individual intercepts, which requires the assumption of a certain distribution of these effects. We instead included individual identity as a fixed effect in our model and did not assume a specific distribution. This is commonly used in panel data analyses in human demography.
The robustness of our findings is also supported by the consistency between the output of the different sections of our model and other studies on the demography of the common tern. For instance, our results stress that the probability of showing up in the colony conditional on being seen once is very high. This high breeding site fidelity has been previously reported for the common tern [29]. Also, the basic age pattern in breeding performance with improvement at early ages followed by senescence at old ages, with minor differences between sexes, has previously been reported [45,50]. Although we have shown that our results are biologically sensible and robust, several potential future extensions of the model remain (electronic supplementary material).
(b) Conclusion
Our novel model, which includes all steps leading to reproductive output and is the first that considers all previous mates for the partner decision, sheds light on various life-history characteristics. Our results show that age of both partners rather than pair bond length is the important component driving the reproductive pattern of the common tern. Nevertheless, individuals are more likely to choose a previous partner, regardless of the joint past breeding success, suggesting that they make a choice once at the beginning of their breeding career and then retain that partner.
Ethics
The long-term field study and marking of birds with transponders complied with the laws of Germany and were done under licences of the Bezirksregierung Weser-Ems, the city of Wilhelmshaven, and the Nds. Landesamt für Verbraucherschutz und Lebensmittelsicherheit, Oldenburg.
Data accessibility
All relevant data are available on Dryad: http://dx.doi.org/10.5061/dryad.ck5c0 [51].
Author's contributions
M.R. came up with the idea for this study and wrote the first draft of the manuscript, which was substantially improved by F.C. M.R. and F.C. developed and programmed the model, as well as creating the figures. P.H.B. collected and provided the data. All co-authors commented on the model and the manuscript.
Competing interests
The authors have no competing interests.
Funding
This research was supported by the Max Planck Society (F.C. specifically by the Research Group for Modelling the Evolution of Ageing). Since 1992, the data collection was supported by the Deutsche Forschungsgemeinschaft (BE 916/3 to 9).
Acknowledgements
We thank all fieldworkers and technical assistants who contributed to the large data set. We are grateful to T. Coulson for his guidance and discussion during the project development. We further thank J.-M. Gaillard and I. Owens for their discussion and suggestions during the PhD viva of the first author.
Footnotes
Electronic supplementary material is available online at https://dx.doi.org/10.6084/m9.figshare.c.3647819.
- Received June 23, 2016.
- Accepted October 10, 2016.
- © 2017 The Author(s)
Published by the Royal Society. All rights reserved.
References
Volume 284, issue 1846
Keywords
