Population dynamics of the pipistrelle bat: effects of sex, age and winter weather on seasonal survival


Thomas Sendor, Schaumburgstr. 20 b, 30419 Hannover, Germany (tel: +49 511 2281346, e-mail thomas_sendor@web.de).


  • 1Life-history theory assumes increased mortality at certain stages such as hibernation. However, seasonal variation of survival rates of hibernating mammals has rarely been estimated. In this study, apparent survival of pipistrelle bats (Pipistrellus pipistrellus) hibernating and performing summer swarming at a large hibernaculum (Marburg Castle, Hesse, Germany), was modelled using seasonal (summer/winter) capture–recapture data for the years 1996–2000. The spring survival interval includes the period of arousal at the end of hibernation and therefore validly measures survival associated with hibernation.
  • 2In five summers and four winters, 15 839 bats were captured and released (13 082 individuals) and 3403 recaptures recorded. Analysis was complicated by transience and trap-dependence. Recapture rates varied seasonally and by group. The autumnal survival estimates were negatively biased due to transience effects that could not be taken into account.
  • 3Survival could be modelled using two age-classes, with reduced first-year juvenile survival. The age effect persisted over the first autumn and spring. There was virtually no evidence for sex-specific survival rates; male and female survival were found to be almost equal. In the best-fitting models, survival rates varied over time and differed among sexes and age-classes by a constant amount. Between years, there was only a small variation in spring survival, which could not be explained by winter severity.
  • 4Adult spring survival was surprisingly high, averaging 0·892 (inline image= 0·028). No evidence for increased mortality during hibernation could be found. This contradicted the expectation of reduced over-winter survival due to depleted fat reserves at the end of hibernation. Thus, hibernation does apparently not entail a survival cost for the pipistrelle bat. Rough estimates of annual adult survival averaged 0·799 (inline image = 0·051), which considerably exceeds previous estimates; annual juvenile survival was estimated at 0·527 (inline image = 0·095). Hence, previous studies have substantially underestimated pipistrelle bat survival. Possible consequences of these findings for various aspects of life histories are discussed.


Understanding factors that influence patterns of population dynamics is of fundamental importance in animal ecology and conservation biology. Among life-history traits, the probability of survival, particularly adult survival, has the largest impact on population changes in long-lived species (Prévot-Juillard, Lebreton & Pradel 1998), as is the case with many mammal and bird species. Among mammalian species of comparable body size, bats are generally considered long-lived (Tuttle & Stevenson 1982; Altringham 1996). Also of importance is the first-year survival of juveniles, as this often determines recruitment to reproductive age. Therefore, knowledge of survival rates is of special interest in the study of bat population dynamics.

The pipistrelle bat (Pipistrellus pipistrellus Schreber, 1774), with a body mass of about 5·5 g, is probably the smallest hibernating mammal of the northern hemisphere (Geiser & Ruf 1995). It is widely distributed and one of the most common bat species in Europe (e.g. Barratt et al. 1997). So-called mass hibernacula of P. pipistrellus, comprising up to several thousand individuals, are known to occur (Dumitresco & Orghidan 1963; Lustrat & Julien 1997). Recent findings suggest that P. pipistrellus should be split into two sibling species (Jones & van Parijs 1993; Barratt et al. 1997). According to spectral characteristics of their echolocation calls, they are tentatively referred to as the 45- and 55-kHz phonic type, respectively. The 45-kHz type will retain the name Pipistrellus pipistrellus (Jones & Barratt 1999). The discovery of this ‘new’ species complicates the interpretation of previous studies and calls for further research.

For endothermic animals of the temperate zones, winter represents a serious energetic challenge. Animals respond to food shortage and low temperatures by either migration, by morphological or behavioural adaptation, or by reducing metabolism, i.e. hibernation (Speakman & Rowland 1999). The overwhelming majority of temperate zone bat species hibernate to bypass the energetic bottleneck (Webb, Speakman & Racey 1996). Hibernation is clearly a strategy to promote over-winter survival. Nevertheless, bat populations are suspected to suffer from increased mortality in the cold season (Davis & Hitchcock 1965; Speakman & Rowland 1999). The critical period is early spring: although emergence from hibernacula coincides with increased food availability (Speakman & Racey 1989; Park, Jones & Ransome 2000), arousal at the end of hibernation may entail increased mortality risks because it is energetically costly (Thomas, Dorais & Bergeron 1990) and fat reserves are depleted in early spring, which may lead to starvation, particularly of lighter bats (e.g. Johnson, Brack & Rolley 1998). Consequently, we suspected seasonal patterns in survival probabilities of temperate bats, with reduced over-winter survival compared to summer/autumn.

Survival rates often differ between sexes and age-classes (Lebreton et al. 1992) and are influenced by environmental variables like temperature (North & Morgan 1979). Hibernators like bats are likely to be less affected by winter temperatures than, e.g. non-hibernating birds because they select hibernacula that are buffered against fluctuations of ambient temperature. Nevertheless, there is some evidence that winter mortality of hibernators may be related to weather factors (Armitage & Downhower 1974). Pipistrelle bats are known to select cold sites for hibernation, which may even freeze (Nagel & Nagel 1991; Webb et al. 1996), and may thus be more susceptible to varying winter conditions than many other temperate bats.

Little is known on sex-specific survival in temperate bats, but various patterns are suspected depending on the mating system (Davis 1966; Greenwood 1980; Stevenson & Tuttle 1981). Gerell & Lundberg (1990) have explained low male survival rates in the pipistrelle bat with reference to its mating system, which is a resource defence polygyny (Clutton-Brock 1989). Juvenile survival in mammals and birds is generally assumed to be low during some period following fledging or weaning, and to approach stability after becoming adult (Loery et al. 1987). Studies that have investigated age-specific or seasonal survival are sparse (but see Ransome 1995 for life history tactics of the greater horseshoe bat, Rhinolophus ferrumequinum Schreber).

Population studies are usually confined to female bats, who form easily observable maternity colonies, whereas males roost solitarily during summer and are therefore difficult to sample (e.g. Speakman et al. 1991). At hibernacula, however, sexes are mixed and thus can be studied comparatively.

Survival processes are usually not directly observable in wild animals. This applies particularly to bats. Therefore, survival studies frequently employ mark–recapture methods. Recent advances in capture–recapture methodology have enabled researchers to address specific biological hypotheses concerning variation of population parameters (Lebreton et al. 1992). This sophisticated modelling approach has still not been applied to bat population dynamics, apart from a recent study by Hoyle, Pople & Toop (2001). However, some earlier studies using simpler approaches provided rough estimates of annual and sex-specific survival rates (e.g. Davis 1966; Keen & Hitchcock 1980; Hitchcock, Keen & Kurta 1984; Boyd & Stebbings 1989; Gerell & Lundberg 1990).

In this study, we present a survival analysis based on live-recapture data of Pipistrellus pipistrellus, 45-kHz phonic type, sampled at a mass hibernaculum where about 5000 pipistrelles hibernate (Sendor, Kugelschafter & Simon 2000). Summer swarming, defined simply as nocturnal flight activity at hibernacula (Fenton 1969; Sendor et al. 2000), is a regular phenomenon at this location. The bats arrive at and leave the site on the same night, without using it as a day roost. Due to the almost year-round presence of bats, hibernacula are ideal locations to study population dynamics, permitting a study design that allows an examination of seasonal patterns. The aims of our study were to examine variation in pipistrelle bat survival by addressing the following working hypotheses: (i) male survival probabilities are expected to be lower than females (Gerell & Lundberg 1990); (ii) first-year survival of juveniles is expected to be lower than adult survival; (iii) autumnal survival rates are expected to exceed spring survival; and (iv) cold winters should reduce, mild winters should enhance, spring survival probabilities.

We will discuss the results obtained in the context of mortality-related aspects of life-history theory (Stearns 1992) and their consequences for population dynamics.

Materials and methods

study site

We caught pipistrelle bats at a large bat hibernaculum, Marburg Castle, Hesse, Germany. The castle is situated on top of a hill at about 290 m a.s.l., in the centre of the city of Marburg, on the western side of the Lahn valley. The pipistrelle hibernaculum is located in a vaulted cellar of this building, partially situated at ground level. The cellar measures about 32·5 × 12·5 × 6 m (l × w × h). The bats roost in narrow crevices in the walls (3·5–4·5 m thick) and the ceiling. The inside of the cellar is accessible for the bats via an embrasure. The hibernaculum is almost exclusively used by pipistrelle bats. Occasionally, a few individuals of other species as the grey long-eared bat (Plecotus austriacus Fischer), the barbastelle (Barbastella barbastellus Gray), and the serotine bat (Eptesicus serotinus Schreber) may also be encountered, but these make up less than 1% of the observations. About 5000 pipistrelle bats use this location for hibernation (Sendor et al. 2000), and substantially larger numbers participate in summer swarming between June and September.

field methods and data sources

Bats were caught with a mist-net, usually placed close to the embrasure, so that capture was immediately after the bats had entered the hibernaculum. Alternatively, we sometimes placed a mist-net further inside the cellar, covering its entire cross-sectional area, likewise ensuring high success of capture. The capture sessions took place in the years 1996–2000. They covered the periods of summer swarming between mid-May and mid-September, and the hibernation periods between late November and early March. In the latter case the pipistrelles were mainly caught when they were immigrating for hibernation. Each primary capture period (season) consisted of approximately 20–30 individual nights. We attempted a capture frequency of two nights per week in summer. In winter, the timing of the capture nights was highly dependent on changes in ambient temperature between frosty and mild weather. Changing weather conditions caused substantial bat movements into and out of the hibernaculum (Sendor et al. 2000). Thus, bats were caught only when they were active (flying), to keep disturbance at a minimum.

The pipistrelles were marked with uniquely coded alloy bands of 2·4–2·9 mm diameter, attached to the forearm. The bats were released immediately after each capture session. Bat bands were provided by the Museum Alexander Koenig, Bonn. Individuals were sexed, and aged according to the degree of epiphyseal fusion (Racey 1974). Reproductive status was assessed according to the size of the testes and distension of the epididymis in the males, as well as size and hair covering of the nipples in the females (Racey 1974, 1988). Individuals with unfused epiphyses were classified as juveniles/immatures, those with fused epiphyses as adults (unknown age). During winter, age discrimination of newly captured young of the year was usually impossible due to the advanced ossification of the epiphyses. Male young of the year still could be distinguished by the black pigmentation of the tunica vaginalis, which covers the epididymis (Racey 1974). Apart from a few exceptions where the epiphyses were still unfused, we had no means to determine the age of unmarked females in winter and hence classified them all as adults, which introduced some heterogeneity to the data.

Capture, handling and marking of the bats was carried out under licence of the Regierungspraesidium Giessen (Upper Nature Conservation Authority).

Weather data were obtained from a weather station located within the municipal area of Marburg, about 4·5 km from the study site, that is operated by the Technical University of Darmstadt.

data analysis

The pipistrelle bat data were divided into four groups, according to sex and age: juvenile males, adult males, juvenile females and adult females. Data from within a summer or winter were pooled into one capture occasion, respectively. We constructed capture histories representing an alternating sequence of summer and winter samples, according to the seasonal design of our study. This resulted in a data set with nine capture occasions (five summers and four winters). The respective survival intervals are spring and autumn. Spring validly measures winter survival as it includes the critical period of arousal from hibernation (see Introduction).

We used capture–recapture models of the Cormack-Jolly Seber (CJS) type (Lebreton et al. 1992) to estimate apparent survival probabilities (φ). The fully time-dependent CJS-model makes some fundamental assumptions (Pollock et al. 1990): (1) the individuals of the ith sample have the same probability of recapture, (2) the individuals of the ith sample have the same probability of surviving to i+ 1, (3) marks are not lost or overlooked, and (4) samples are instantaneous and the individuals are released immediately after the sample. Unknown mark loss (assumption 3) was probably negligible: according to Keen (1988), forearm bands are more permanent than most other marking systems applied to vertebrates. Hestbeck & Malecki (1989) estimated neck band retention rate, which is often considered problematic, in a double-banding study on Canada geese at 99·3%. Furthermore, we got the impression that pipistrelle bats are not capable of removing the bands. For only 13 recaptured individuals was it necessary to revome the bands because of injuries. We treated them as losses on capture, as we did the 24 individuals reported as dead by the public. Assumption 4, however, was not well met: the sampling periods (see above) were long relative to the inter-sample intervals. This problem was less serious in summer, because individuals from a certain group (e.g. adult males) were predominantly caught during restricted periods of approximately 4–6 weeks. According to Smith & Anderson (1987), lengthy ringing periods have only a negligible effect on survival estimates if there is little variation in the pattern of the temporal distribution of ringing effort (TDR) and if survival within the periods is high. In our study, variation in TDR within the groups was low because the phenology of summer swarming was similar among years. Noteworthy mortality was unlikely to occur during the summer marking periods. This was probably also the case in the winter samples, because capture efficiency was highest in the first half of the winters, during the immigration period (c. 6 weeks). Accordingly, we expect only negligible bias resulting from the lengthy sampling periods.

Departures of the data from assumptions 1 and 2 were tested by a χ2 goodness-of-fit (GOF) test using a modified version of program release (Burnham et al. 1987; Pradel 1993). The release test consists of four test components, two of them being sensitive to violations of assumption 1, while the remaining ones are sensitive to departures from assumption 2. Common sources of violations of model assumptions may be (i) permanent emigration from the study area after first capture, also termed the transience effect (Pradel et al. 1997), (ii) positive or negative trap-response (Pollock et al. 1990), or (iii) additional heterogeneity in survival and recapture probabilities, which may include temporary emigration and individually varying recapture probabilities, etc. The GOF of models accounting for transience or trap-dependence, as well as a combination of both, were tested by using various subsets of the test components (for details we refer the reader to Pradel 1993; Viallefont, Cooke & Lebreton 1995; Pradel et al. 1997).

To allow modelling of possible trap-dependence, capture histories were split into histories including only capture and first recapture, and histories containing all further captures (for details see Pradel 1993), with the help of program u-care (available from ftp://ftp.cefe.cnrs-mop.fr/pub/biom/Soft-CR). The sources of additional heterogeneity are frequently not testable because of the required splitting of capture histories, leading to low cell probabilities in the contingency tables (few recaptures). This was also the case in the present study. If no adequate model fit can be achieved at this point, it is convenient to assume that the data are overdispersed, i.e. contain extra-binomial variation (Lebreton 1995). Overdispersed data frequently result in underestimated sampling variances and selection of an overparameterized model. We corrected for overdispersion – if detected – in variance estimation and model selection (see below) by the inclusion of a variance inflation factor c; its estimate, ĉ, was obtained by dividing the goodness-of-fit statistic (χ2) of the highest-dimensioned acceptable model by its degrees of freedom (Anderson & Burnham 1999a).

After identification of a satisfactory general model, we fitted progressively simpler models using the maximum likelihood methods of program mark (White & Burnham 1999). Modelling strategy and model notation generally followed the approach of Lebreton et al. (1992), introducing the flexibility and power of generalized linear models to capture–recapture analysis. We modelled the effects of sex, age class (initially expressed as ‘group’), and time on recapture and survival probabilities. Time was also expressed as a seasonal effect, i.e. parameters were allowed to differ between summer and winter, but were constrained to be constant among all summers or winters, respectively. In contrast to fully time-dependent models, all parameters are individually identifiable in seasonal models, because there are no final α-terms in the probability statements (Lebreton et al. 1992). We hypothesized an age effect with two age classes, persisting for two sampling periods (subscripted as a2′). This type of effect accounts for the seasonal study design, in contrast to the bats’ annual life cycle. Transience and trap-dependence were included if required according to the GOF test. The symbols used for model notation and their biological meaning are summarized in Table 1. Note that transience or trap-dependence are structurally equivalent to an age-effect and hence cannot be distinguished from the latter within a group. The problem of modelling an age-effect in the presence of transience can partly be bypassed by comparing adults and juveniles, but the confounding of both effects will still remain with such a construction. The logit link-function was preferred in the modelling process (Lebreton et al. 1992).

Table 1.  Subscripts used for model notation in CJS survival analysis
NotationMeaningApplies to
transTransience effectφ
a2Age effect (two age classes) lasting for one survival intervalφ (p)
a2′Age effect carrying over two survival intervalsφ (p)
sexSex-effectφ, p
gGroup effect(φ)
tTime effectφ, p
seasonParameters vary between, but are constant within summers and wintersφ, p
mTrap-effect lasting until the first recapture periodp
mTrap-effect lasting until the second recapture periodp
TwTemperature sum November – March (winter severity)φ
FDNumber of frost days November – March (winter length)φ
ECapture effort: number of capture hours within a capture periodp

We also hypothesized that the above effects could have affected autumnal and spring survival rates differentially. This requires separate model structures for autumn and spring survival; thus, deviating from the usual notation (e.g. φt, pt), we will denote such models as, e.g. (φA, φS, pt), following Prévot-Juillard et al. (1998). The superscripts denote autumnal (A) and spring (S) survival rates, respectively.

We also modelled the effect of capture effort (E) as an external covariate (North & Morgan 1979), measured as hours of sampling within a capture period, on recapture probabilities (p). We further hypothesized that winter conditions had an effect on subsequent spring survival: temperature sums, calculated from the daily mean temperatures between November and March, were used as a measure of winter severity; the number of days with a mean temperature below 0 °C (frost days) reflected winter length. These covariates were included to affect spring survival. The months November to March correspond to the period when pipistrelle bats are predominantly torpid. The covariates were rescaled to fit in the interval (0,1) and included into the models as linear or logarithmic functions. Predictions for these models were that a covariate effect changed at a constant rate (linear), or approached an asymptote (logarithmic).

Model selection (i.e. finding the most parsimonious model) was performed by minimizing AICc, the small-sample version of Akaike's information criterion (Anderson & Burnham 1999b). For model ranking we further report the difference in AICc between the best fitting and alternative models (ΔAICc) and the relative Akaike weights (Anderson & Burnham 1999a), computed for each candidate model as


where Δi=ΔAICc. The weight wi is considered as a measure of evidence for the plausibility of a model, given the data (Burnham & Anderson 1998).

If overdispersion was identified in the data, we accounted for it by employing quasi-likelihood methods (Burnham & Anderson 1998; Anderson & Burnham 1999b): inclusion of ĉ then leads to QAICc instead of AICc and inflated variances of the parameter estimates.


global model

Between summer 1996 and winter 1999/2000, 15 839 pipistrelle bats were captured and released (3311 juvenile males, 3263 adult males, 4408 juvenile females, 4857 adult females), comprising 13 082 individuals. In subsequent sampling periods, 3403 recaptures were recorded (750 juv. males, 648 ad. males, 883 juv. females, 1122 ad. females). The numbers of captures varied between summers and winters: we regularly caught approximately three times the number of bats in summer, compared to winter.

The CJS-model (φt, pt) clearly did not fit the data in either group (Table 2). In the juvenile females, the GOF test results indicated a transience effect, and the corresponding model was acceptable (Table 2). In all other groups, the GOF test indicated a combined impact of transience and trap-dependence. Generally, about every second release cohort was affected by severe departures from expectations, which corresponds to a seasonal pattern in the violations of model assumptions: the autumn intervals were affected by transience and the winter occasions by trap-dependence. However, additional model structure did not lead to satisfactory model fit: neither a transience effect, nor trap-dependence, nor a model combining both effects was acceptable (Table 2). Thus, we assumed that the remaining lack of fit was caused by individual heterogeneity in survival and recapture probabilities, which should be considered as overdispersion. Actually, when accepting transience for the juvenile females and a combination of transience and trap-dependence for the other groups, overdispersion was moderate (ĉ = 1.89; inline image = 279·2). Thus, an appropriate global model included group, time and transience as factors affecting survival; group, time and trap-dependence affected recapture (no trap-effect in the juvenile females). We specified trap-dependence and time as additive effects, because full trap-dependence models have still unexplored parameter identification problems (Pradel 1993). The resulting initial model is denoted as φtrans × g × t, p(m + t) × g.

Table 2.  Results of the goodness-of-fit tests of various models accounting for departures from the assumptions of the standard CJS model
Juvenile males
 CJS102·5532< 0·001
 Transience 83·9025< 0·001
 Trap-dependence 79·4326< 0·001
 Combined 89·2938< 0·001
Adult males
 CJS131·8939< 0·001
 Transience109·8232< 0·001
 Trap-dependence 73·9223< 0·001
 Combined 79·5638< 0·001
Juvenile females
 CJS102·0037< 0·001
 Transience 33·5930  0·298
 Trap-dependence 93·6131< 0·001
Adult females
 CJS106·7632< 0·001
 Transience 87·4825< 0·001
 Trap-dependence 82·7026< 0·001
 Combined 76·7442< 0·001

modelling recapture

Despite the obvious presence of transience and trap-dependence revealed by the GOF test, the data were apparently insufficient (too few recaptures) to support such a complex model structure: Only 62 out of 87 parameters were estimable in the global model. To simplify model structure, we decided to remove the transience effect for modelling recapture rates, leading to model φg × t, p(m + t) × g, and to reintroduce transience after the most parsimonious recapture model was determined; ĉ was left at 1·89.

A trap-effect lasting two capture periods (m′) turned out to describe the data better than a simple one (m) or a model ignoring it (Table 3). A seasonal effect (models 1–4) described recapture rates better than full time dependence. This is not surprising considering the consistent threefold difference between summer and winter captures. Simpler models, with either a sex-effect or p constrained to be the same in all groups were inadequate (ΔQAICc ≥ 68·28; not listed in Table 3). Models that restricted the trap-effect to the winter were not well supported, although this could have been plausible in view of the seasonal variation of numbers of bats captured. In the best-fitting recapture model, p varied by season and group, and was affected by a two-period trap-effect (φg × t, pm′ × season × g; no trap-effect in the juvenile females). Models with an age-specific trap-effect had severe problems with parameter identifiability and are therefore not reported. The attempts to model p as a function of capture effort (E) lead to poor model fit (ΔQAICc ≥ 73·59; details not reported). The reason for this was probably that groups were differentially affected by capture effort across years. Also these models had considerable problems with parameter identifiability.

Table 3.  Modelling recapture probabilities of Pipistrellus pipistrellus marked at Marburg Castle, as functions of trap-dependence (m and m′), time (t), season and group, starting from model φg × t, p(m + t) × g; QAICc = Akaike's information criterion, quasi-likelihood corrected; ΔQAICc = QAICc-based difference to the best model; wi= normalized Akaike weight of model i; np = number of estimated parameters. The best supported models are highlighted in bold
No.Model nameQAICcΔQAICcwinp
  1. Note that the trap-effect (m, m′) does not apply to the juvenile females; however, this is not separately specified, to avoid unnecessarily complicated model notation

Group-specific time dependence and trap effect
1φg × t, pm′ × season × g13569·54 0·000·99946
2φg × t, p(m′ + season) × g13586·4016·860·00034
3φg × t, pm × season × g13588·6319·090·00046
4φg × t, p(m + season) × g13596·3926·850·00043
5φg × t, p(m′ + t) × g13607·2837·740·00063
6φg × t, p(m + t) × g13611·9242·380·00063
7φg × t, pg × t13628·3658·810·00060
Trap-effect restricted to winter captures (m(W))
8φg × t, pm(W) × season × g13584·6715·130·00143

The magnitude of the trap-effect was very different among the four groups (Fig. 1); it was most pronounced in the juvenile males and least obvious in the adult females. Recapture probabilities were generally rather low (Fig. 1). While in both male age-classes there appeared to be a negative trap-effect after the first two capture periods, no consistent pattern was apparent in the adult females.

Figure 1.

Recapture probabilities of the pipistrelle bats marked at the mass hibernaculum Marburg Castle, estimated from model φg × t, pm′ × season × g; vertical bars represent 95% confidence intervals; (a) juvenile males, (b) adult males, (c) juvenile females, and (d) adult females; in the juvenile females, only two parameters were estimated because there was no indication for a trap-effect in this group.

modelling survival


We started a new QAICc-ranking for modelling survival (cf. Tables 3 and 4). Reintroduction of group-specific transience lead to poor model fit (Table 4), compared to the best recapture model. Restricting transience to autumn was more appropriate than global transience, but still less useful than simple time-dependence. This seems surprising, considering the GOF results, but may be caused by the partial confounding of an age-effect and transience. Furthermore, the failure to model transience indicates that a general one-period age-effect would be inappropriate to describe survival patterns.

Table 4.  Modelling survival probabilities of Pipistrellus pipistrellus marked at Marburg Castle, as functions of transience (trans), time (t), season, sex and age (a), and differentially affected autumn and spring survival intervals (φΑ, φ S); the recapture part (pm′ × season × g) is held constant across all models; QAICc = Akaike's information criterion, quasi-likelihood corrected; ΔQAICc = QAICc-based difference to the best model; wi= normalized Akaike weight of model i; np = number of estimated parameters. The best supported models are highlighted in boldface. Note that not all tested models are presented
No.Model nameQAICcΔQAICcwinp
Best recapture model
1φg × t, pm′ × season × g13563·6916·350·00046
Reintroduction of the transience effect
9φtrans × g × t13597·8650·530·00072
10inline image13580·6033·270·00057
11inline image13570·3823·040·00045
Sex- and time-specific survival
13φsex × t13573·2025·860·00030
14φsex + t13573·4126·070·00022
15φsex × season13596·9949·660·00018
Age-effect constrained to last over first spring
16inline image13547·33 0·000·27723
17inline image13547·75 0·420·22524
18inline image13549·94 2·610·07520
19inline image13550·44 3·110·05921
20inline image13567·5020·160·00046

Effects of sex, age, and time

Models including sex and time but not accounting for an age-effect described the data poorly (numbers 12 and 13, Table 4). Time formulated as a seasonal effect was not appropriate (number 15; further seasonal models are not presented: they fit even less well). We introduced a biologically realistic age-effect, where the juvenile/immature age class was constrained to end after first spring. This required the notation to be split between autumn and spring because the model structure incorporates an age-effect that lasts for two survival intervals (a2′) in autumn, while a simple one (a2) applies to spring. The full model (inline image) was ranked below the group-specific model, but formulating age, sex, and time as additive effects was clearly favoured (Table 4, models 16–19).

There was some evidence for approximately constant spring survival from the transience models 10 and 11. The age-structured models with constant spring survival (numbers 18 and 19, Table 4) were also highly ranked, but the fully time-dependent models still fit approx. 3·7 times better. Generally, the model selection results indicated little importance of sex differences.

The two top-ranked models (numbers 16 and 17, Table 4) were almost equally supported. As they differ by inclusion/exlusion of a sex-effect, there is considerable uncertainty about the importance of sex differences in survival. However, the model excluding a sex-effect should be preferred as it is favoured slightly more and has fewer parameters (Burnham & Anderson 1992).

effect of winter conditions

We attempted to explain the apparently relatively small residual variation of spring survival by winter conditions. Therefore, we modelled spring survival based on the so far top-ranked time-dependent model (inline image). We held the autumnal part constant and modelled residual variation of spring survival by replacing time by the weather covariates.

The winter of 1996/97 was rather harsh from a human viewpoint, with daily mean temperatures dropping to −17 °C (Fig. 2). The subsequent winters had higher minimum temperatures and were characterized by rather short-term fluctuations in temperature. Nonetheless, there were also marked periods of frost, e.g. in November/December 1998. The numbers of days with frost (FD) were, in chronological order, 60, 45, 78, and 40, and the winter temperature sums (Tw) were 145·1, 321·0, 5·5 and 353·5 °C, respectively.

Figure 2.

Course of daily mean winter temperatures in Marburg in the four successive winters of the study period.

The best weather-dependent models (Table 5) were slightly favoured over constant spring survival (inline image), but were ranked below the models with full time dependence (numbers 16 and 17). Neither Tw nor FD was clearly preferred as explanatory weather variable (Table 5). The slope estimates for the weather variables from these two models inline image = 0·0008, inline image= 0·0011 for Tw; inline image = −0·0031, inline image= 0·0054 for FD) also indicated at most a weak relationship between winter conditions and survival, that could not satisfactorily explain residual variation.

Table 5.  Modelling the effect of winter severity, expressed as functions of temperature sums from November to March (Tw) and number of frost days (FD) on spring survival probabilities of Pipistrellus pipistrellus marked at Marburg Castle; the recapture part () as well as the autumnal survival part were held constant across all models; QAICc = Akaike's information criterion, quasi-likelihood corrected; ΔQAICc = QAICc-based difference to the best model; np = number of estimated parameters
No.Model nameQAICcΔQAICcwinp
21inline image13549·882·540·07821
22inline image13550·132·790·06921
23inline image13550·202·870·06621
24inline image13550·383·050·06021

survival estimates

We present survival estimates derived from model inline image, pm′ × g × season to illustrate the magnitude of sex-specific differences. As expected according to the model selection results, differences in survival estimates between the sexes were small (Fig. 3). On the basis of the sex-specific model, the male survival estimates slightly exceeded the female ones. Juvenile survival was approximately 20–25% lower than adult survival. The additive model structure suggests constant differences (on a logit scale) between sexes and age classes.

Figure 3.

Estimates of seasonal survival probabilities of the pipistrelle bats marked at the mass hibernaculum at Marburg Castle, estimated from model inline image, pm′ × g × season; error bars represent 95% confidence intervals; ▪= adults, □= juveniles.

In contrast to our expectations, the autumnal survival estimates were consistently lower than in spring. However, this can be explained by the unaccounted for effect of transience in all groups: according to the GOF tests, transience predominantly affected the autumnal interval. Consequently, the respective parameter estimates are negatively biased, while the spring estimates are approximately unbiased. There was only little variation in spring survival, although constancy was not justified (see above). Average adult spring survival, conditional on model (inline image), was 0·892 (inline image = 0·028). Variation in apparent autumnal survival was considerably higher (Fig. 3).

mean life span

Annual survival probabilities and average life expectancy in the literature usually refer to adults of unknown age (Loery et al. 1987). Due to the biased autumnal estimates, we cannot simply calculate annual survival by multiplying spring and autumn estimates. For convenience, we will ignore the biased autumnal survival rates. Instead, we assume that they will be approximately as high as in spring, so that squared spring survival can be regarded as a rough approximation of annual survival. Averaging the squared adult spring survival probabilities obtained under the best-fitting model (inline image, pm′ × g × season , we get a mean annual survival rate of 0·799 (inline image = 0·051). This estimate results in an expected mean life span (MLS) for unknown-aged adults of


for both sexes (95% CI = 2·04–6·96 years). Under the same assumptions, mean first-year survival of juveniles is estimated at φ̂ = 0·527 (inline image = 0·095).


In the present study, we modelled seasonal survival of Pipistrellus pipistrellus as functions of various population characteristics and weather variables, based on capture–recapture data collected at a large hibernaculum. The results suggest that pipistrelle bat survival follows an age-structure with two age-classes and does not, or only marginally, differ between sexes. Variations in winter conditions had no significant effect on spring survival.

impact of transience and trap-dependence

The most serious problem in our study was the confounding of age effects with transience effects, which are structurally equivalent. For this technical reason we did not specify models with a simple (i.e. lasting only one survival interval) age effect, in which first-interval juvenile survival would have been completely confounded with transience (Pradel et al. 1997). Although transience was clearly detected by the GOF test, models incorporating group-specific transience were obviously too complex to be supported by the data of the given sample size. Unaccounted transience was always confounded with age-effects to some degree in our analysis. However, this problem is alleviated in the models with the ‘realistic’ age-effect: transience is, by definition, permanent emigration after first capture (Pradel et al. 1997), and is therefore only partly confounded with the autumnal two-period age-effect (a2′). Nevertheless, the unaccounted transience effect produced negative bias of unknown amount in the autumnal survival estimates.

The spring survival estimates, in contrast, should be approximately unbiased in adults as well as in juveniles because transience was largely restricted to autumn according to the GOF test. The autumnal bias explains the unexpected seasonal survival pattern with higher apparent spring survival. Regarding this, there is no substantial evidence for seasonally differing survival rates. Transience can be best explained by dispersal processes, predominantly taking place in autumn (Davis & Hitchcock 1965).

The combination of transience and trap-dependence can partly be viewed as an artifact due to the study design: between summer and winter temporary emigration takes place, as indicated by the consistent threefold discrepancy in the numbers of individuals that were catchable. Temporary emigration interacting with natural mortality may have caused a quasi-trap-response. Autumnal transience itself is a rather plausible effect (also see above). It is likely that a considerable fraction of the individuals that are catchable during summer swarming choose alternative sites for hibernation and for swarming in subsequent summers, which corresponds to permanent emigration. In contrast, individuals caught during winter might have an increased probability of returning to the hibernaculum and thus to be recaptured, because bats are faithful to a hibernaculum once selected (Keen 1988).

differences between sexes

The model selection results are equivocal with respect to sex-specific survival: we may or may not accept the existence of sex differences (Table 4). However, the differences between estimates from the best sex-specific model (inline image) are only marginal (Fig. 3), so that rejection of the hypothesis of sex-specific survival seems appropriate. This finding contrasts the results of Gerell & Lundberg (1990), who estimated consistently lower male survival probabilities in southern Sweden. They discuss this difference as a consequence of energetic constraints imposed on the males by the mating system, a resource defence polygyny. One should be aware of several issues in this respect:

  • 1Gerell & Lundberg (1990) probably investigated the 55-kHz phonic type, while our study refers to the 45-kHz pipistrelle.
  • 2The study site of Gerell & Lundberg (1990) was composed of mating roosts (bat boxes) defended by territorial males.
  • 3The sample size in the Swedish study was rather small (501 individuals marked in 7 years) and the authors estimated survival using a rather ad hoc approach.

We consider the first point to be of little importance when discussing sex-specific survival because both, the 45- and the 55-kHz pipistrelle, have the same mating system (Park, Altringham & Jones 1996). Thus, they should share general survival patterns. Absolute survival rates, however, may actually differ between species, and may vary by geographical area. Nevertheless, the parameter estimates are not directly comparable here because the data were collected under different conditions.

The two latter points, however, appear more relevant: Larger sample sizes improve statistical inference. Furthermore, proper modelling and selection of a parsimonious model is a prerequisite for insight in the biological process of interest (Burnham & Anderson 1992). Models accounting for transience or trap-dependence had not yet been developed when Gerell & Lundberg (1990) conducted their study. Their conclusion that sex-specific survival is caused by energetic constraints imposed on the males due to territorial defence and mate attraction is contradicted by our study. There may be mainly two reasons for the conflicting results:

  • 1Differential bias in survival estimates between the sexes: Gerell & Lundberg (1990) report high turnover of individuals (i.e. transience, and possibly also trap-dependence, as in our study), and thus their estimates are heavily biased. We suspect turnover of male individuals to be higher at mating grounds than at hibernacula due to competition for territories, causing a more severe transience effect in the males and hence differences in apparent survival estimates. Clearly, our estimates are also still negatively biased, as discussed above.
  • 2Geographic variation of energetic constraints due to climatic factors: the mating season in pipistrelle bats extends until November (Gerell & Lundberg 1985). This is also valid for Marburg, where hibernal immigration starts in late November (Sendor et al. 2000). Autumnal temperatures, however, are lower in southern Sweden than in Central Europe. Consequently, territorial males in Sweden could suffer from more severe energetic stress than Central European ones. This might explain geographically varying survival patterns.

In conclusion, a resource defence polygyny does not appear to generally induce reduced male survival in temperate bats, but this may be a result of the interaction of courtship behaviour with environmental factors, such as ambient temperature during the mating season.


Although partly confounded with transience, an age-effect constrained to last until the end of the first year of life described variation in the data appropriately. According to the best-fitting models, there was a constant difference between adult and first-year juvenile survival (additive effects on a logit scale). This corresponds to prior expectations about age-specific survival in long-lived species (e.g. Loery et al. 1987). The additive model structure further demonstrates that variation in juvenile survival is not greater than in adult survival. This conforms with the statement that species generally tend to have either high or low mortality throughout their lifetime (Promislov & Harvey 1990). The low variation in juvenile survival leads to the conclusion that pipistrelle bat life histories are shaped in order to maintain approximately constant recruitment rates across years. However, as data on pre-weaning survival are scarce (see below) the question of recruitment to reproductive age should be treated with caution. To our knowledge, this is the first study to demonstrate age-effects on the mortality regime of both sexes in temperate bats (but see Thompson 1987 for age-structured female pipistrelle populations, based on cohort life tables).

seasonal, annual, and weather-related survival

Life-history theory attempts to identify factors that shape aspects of life histories (e.g. mortality regimes, Stearns 1992). A usual assumption is that natural mortality risk varies in an animal's annual life cycle (Gauthier et al. 2001). Hibernation, like reproduction or migration, is a stage to which response of mortality risk should be expected. However, we found little evidence for seasonal variation of pipistrelle bat survival (note the autumnal bias). Furthermore, winter survival was unexpectedly high. Thus, it appears that hibernation does not entail an increased survival cost for pipistrelle bats.

Variability of over-winter survival was low but significant. Winter severity and winter length could not explain the residual variation. There were reasons to assume an effect of winter weather on survival beforehand. First, there is evidence for weather-related mortality from other mammals which also hibernate in thermally well-buffered shelters (Armitage & Downhower 1974). Second, the range of temperatures at which pipistrelle bats hibernate extends to values below 0 °C (Nagel & Nagel 1991; Webb et al. 1996). Furthermore, previous studies at Marburg Castle have demonstrated extensive hibernal roost switching (Sendor et al. 2000), i.e. pipistrelles use alternative, probably less buffered hibernacula during long periods. Thus, the bats frequently expose themselves to harsher conditions than the microclimate of the study site, where temperatures in roost crevices never fell below 4 °C (T. Sendor, unpublished). Therefore, the microclimate of hibernacula was expected to be less important than in other bats (e.g. Humphries, Thomas & Speakman 2002). The present results contradict the corresponding expectation that winter weather would have an effect on hibernal survival – even if a number of pipistrelle bats obviously froze to death in close proximity to the hibernaculum in the harsh winter 1996/97 (T. Sendor, personal observation).

The reported hibernal roost switching may be an important factor in the mortality regime. It can be regarded as a behavioural component of life history strategy in order to avoid the risks associated with a fluctuating environment. Hibernal roost switching is apparently a trade-off between the risk of freezing to death in less buffered roosts when frost occurs, and the risk of starving due to too high an energy demand in stable but warmer hibernacula. This strategy seems to be favoured by natural selection because pipistrelle bats, with their small body size, are supposedly not able to accumulate enough fat to survive the winter in a stable hibernaculum. Thus, habitat stability of hibernacula seems to play a crucial role in influencing the mortality regime (Humphries et al. 2002), but the behavioural component is equally important because it partly compensates for the particular disadvantages of stable vs. unstable habitats. Consequently, with the hibernal roost switching strategy, pipistrelle bats are apparently very successful in selecting hibernation sites that maximize survival.

Studies on non-hibernating birds have found markedly decreased survival after harsh winters (e.g. North & Morgan 1979; Lebreton et al. 1992). This underpins the importance of hibernation as a stage with advantageous effects on survival in an animal's annual life cycle. Nevertheless, there are conflicting results for over-winter survival of hibernating small mammals (e.g. Arnold 1990; Fleming 1979; Schaub & Vaterlaus-Schlegel 2001). Schaub & Vaterlaus-Schlegel (2001), in their study on garden dormice (Eliomys quercinus L.), argue that these animals are sufficiently well adapted to typical European winter conditions to survive the hibernal period with a high probability. Mammalian species with reduced winter survival, in contrast, were usually studied in extreme habitats with a prolonged winter and/or unpredictable environmental conditions. In a temperate environment, microclimates of bat hibernacula are apparently stable enough to bestow positive effects on hibernal survival probability. Bats found dead in hibernacula (Davis & Hitchcock 1965) are presumably young of the year, which have usually smaller fat reserves (Johnson et al. 1998). This is supported by the age-effect found in our study. Furthermore, we expect that over-winter survival should be generally high in temperate bats in order to counteract their low reproductive output of usually one young per female per year (Tuttle & Stevenson 1982). Otherwise lifetime reproductive success would be too low to maintain stable populations.

Variation in apparent autumnal survival, in contrast to the nearly constant spring estimates, could for instance be caused by varying impact of transience, but there are also biological explanations: avian predation on bats is probably an important cause for mortality (Speakman 1991). Predator pressure may vary across years and consequently affect bat survival (this might also explain residual variation in spring survival). Annually varying food supply, leading to varying length of foraging times, might also interact with predator pressure. The significance of higher autumnal body weight for predation risk, as found in some birds (Swaddle & Lockwood 1998) is unclear: Webb, Speakman & Racey (1992) have found that pipistrelle bats normally do not reach an upper weight limit beyond which wing loading would reduce flight performance. Thus, predation risk would not be affected.

The results of the present study indicate that pipistrelle bat survival has previously been considerably underestimated: estimates of 0·44 for males and 0·54 for females (Gerell & Lundberg 1990) or in the range of 0·60–0·64 (Thompson 1987; von Helversen et al. 1987) probably result from methodological drawbacks. The latter two estimates were obtained with simple regression or cohort life table methods and are therefore somewhat questionable as, unlike CJS-models, they do not estimate survival and recapture separately, and because the underlying models make unrealistic assumptions about age distribution and population stability, etc. (Anderson, Burnham & White 1985; Promislov & Harvey 1990). Potential difficulties of the Swedish estimates were already discussed above.

Information on other life-history traits of the pipistrelle bat is more uncertain, as only rough estimates are available. Reproductive age is assumed to be reached at the end of the first year, and an unknown and geographically variable fraction of the female pipistrelles give birth to twins (Tuttle & Stevenson 1982). We think that this information is insufficient to reliably assess the life histories of pipistrelle bats. Viewing P. pipistrellus as an r-selected species (Gaisler 1987) therefore seems somewhat questionable, not least because the rK concept has been generally rejected (Stearns 1977, 1992). Not even the stochastic life-history model (Stearns 1977) is very useful here: it assumes that either juvenile or adult mortality rates fluctuate, but according to our results both show only slight variation. Alternatively, the model assumes that birth rates or pre-weaning mortality fluctuate, as is seen in other bat species such as Myotis myotis Borkhausen (Güttinger et al. 2001); however corresponding data are not available for the pipistrelle.

Generally, too little is known about seasonal survival, the role of hibernacula, and consequently the factors that influence population dynamics and life histories in temperate bats. We suspect a variety of patterns depending on the species and the geographical region considered. For instance, winter conditions in Central Europe are usually much milder than in Canada, where Davis & Hitchcock (1965) conducted their study. Thus, their conclusion of reduced survival during winter and spring in Myotis lucifugus (LeConte) might be correct under the local conditions. Conversely, the climatic conditions in Marburg are quite representative of Central Europe as a whole. We therefore believe that the survival patterns found in the present study can be generalized for pipistrelle bats in large parts of Europe.


We are grateful to the many people who assisted us in catching bats, too numerous to be named. We also thank Markus Kaempf and Tilman Holfelder for providing weather data. This work is a part of T. Sendor's doctorate degree, supported by a grant of the ‘Hessische Graduiertenförderung’ and further assistance by an ‘E & E-Project’ by the German Federal Agency for Nature Conservation (Bundesamt für Naturschutz). Fruitful discussions with Janna Smit, Sandra Hüttenbügel and Roland Brandl, as well as the comments of an anonymous referee, helped to improve the manuscript.