Studying phenology by flexible modelling of seasonal detectability peaks

Authors


Summary

  1. Many animals and plant species have advanced spring phenology in response to climate warming. The majority of avian phenological studies are based on arrival dates. Consequently, knowledge on bird phenology is mainly based on migratory species. In addition, arrival dates of migratory birds may be substantially affected by en route climate conditions, thus failing to provide good indicators for spring phenology on the breeding grounds. Correlating arrival dates with other phenological data or with environmental covariates may be meaningless in these cases.
  2. We propose the date of highest singing activity, quantified by detection probability, as a powerful proxy for breeding phenology that is applicable to migratory and sedentary bird species alike. In contrast to arrival dates, breeding phenology is mainly (non-migrants) or at least partially (migrants) influenced by conditions experienced within the breeding area.
  3. We developed a new method for flexible estimation of peak detectability date in spring by combining multiseason site occupancy with semi-parametric regression modelling (thin-plate splines). We applied our approach to opportunistic observations of 27 bird species (mostly passerines) in Switzerland.
  4. We found substantial differences among species in the date of spring peak detectability: late February to mid-April in sedentary and short-distance migratory species and mid-April to late May in long-distance migrants. Among 10 species with data for >9 years, five showed a trend in detectability peaks towards an earlier spring phenology by nine to 17 days within 10 years. The mean shift over all species was c. 3·5 days per 10 years.
  5. Our approach is widely applicable, especially for temporally and spatially large-scale data from monitoring or citizen-science programmes. Besides using the detectability peak as measure of phenology, the estimated seasonal pattern in detectability can help designing monitoring programmes for improved efficiency. Our approach may be applied to any species with pronounced acoustic displays or other behavioural traits strongly influencing detectability during the breeding period. We believe that it can contribute substantially to unravelling how species and communities respond to environmental change.

Introduction

Phenology is the study of annually recurring life cycle events in animals and plants and of the factors influencing these events. Timing of phenology is influenced by abiotic and biotic factors integrated by organisms over time (Both et al. 2009) and – for mobile species – over space (Balbontin et al. 2009). Optimal adaptation of phenology to the environment is crucial for individual fitness and may have substantial repercussions on population dynamics; failure to adapt to changing conditions was found to be associated with substantial population declines in songbirds (Both et al. 2006). At the individual level, phenology may be governed by phenotypic plasticity and, at the population level, by evolutionary changes leading to adaptation to changed environmental conditions (Balbontin et al. 2009; Pulido & Berthold 2010). In biodiversity monitoring focusing on breeding individuals, knowledge of breeding phenology is crucial to avoid surveying before or after the main breeding season when a species is most conspicuous (Bezzel 2011). Ignoring shifts in the breeding phenology by failing to adapt the temporal schedule of a monitoring programme may lead to biased estimates of population trend unless detectability is accounted for.

In some cases, phenology has been recorded for many centuries (Pfister 1984; Aono & Kazui 2008). Correlations between phenology and environmental factors over long time periods have been used to study climate change (Rathcke & Lacey 1985). Plant flowering date (Bai, Ge & Dai 2011), arrival of migratory birds (DeLeon, DeLeon & Rising 2011) or appearance of butterflies (Roy & Sparks 2000) was found to be correlated with ambient temperature. Timing of migration was found to be correlated with the North Atlantic Oscillation index in migratory birds (Forchhammer, Post & Stenseth 2002), and climate measures associated with plant growth (growing degree days, see McMaster & Wilhelm 1997) were found to explain a significant proportion of the annual variation in phenological traits of red deer Cervus elaphus (Moyes et al. 2011). Thus, owing to the high correlation with climate factors like mean ambient temperature, phenology is often used for reconstructing climatic conditions in the past (Meier et al. 2007; Aono & Kazui 2008).

Much of what we know about animal phenology is based on studies of migratory bird species, either en route (Saino et al. 2011) or on the breeding grounds (Both 2010). The adequacy of this species group as an indicator for phenological changes in a given geographical area has long been debated, especially for trans-Sahara migrants (Tryjanowski, Kuzniak & Sparks 2002). Highly mobile species such as migratory birds may integrate environmental cues over very large areas. Accurately identifying factors that influence phenological events like spring arrival is then a challenge (Temple & Cary 1987). Identification of likely causal correlations of local environmental factors with changes in arrival dates due to phenotypic plasticity may become virtually impossible. In contrast to arrival dates, breeding phenology is mainly (in sedentary species) or at least partially (in migrants) influenced by conditions sensed directly in the breeding area (Slagsvold 1977). Accordingly, egg-laying date has often been used as a measure for breeding phenology in passerines (Both et al. 2009; Eeva et al. 2012). Recording accurate egg-laying dates over long temporal periods is costly or, for non-cavity-breeders, difficult to achieve. Thus, the date of peak singing activity has been suggested as a useful measure for breeding phenology (Slagsvold 1977; Keast 1994) that can be determined based on observational data (Hegelbach & Spaar 2000).

However, the date of peak singing activity must be estimated from the observational data. In this paper, detectability is used as a proxy for singing activity and defined in the sense of site-occupancy species distribution models as the probability that at least one individual of a present species is detected in a study plot during one survey (MacKenzie et al. 2002). Detectability in species distribution models depends on abundance, perceptibility and activity of the individuals, among other things. Thus, detection probability will be higher when more individuals are present (e.g. have established territories) and, especially, when the territory owners are vocally more active. Seasonal changes in detectability of bird species have been recorded in several studies (Selmi & Boulinier 2003; Kéry & Royle 2009; McClure et al. 2011; Niemuth, Estey & Reynolds 2012; Lehikoinen 2013). A primary reason for this pattern is that the song rate of many species changes within the season (Slagsvold 1977; Best & Petersen 1985). Daily variation of song rates is affected by environmental factors like temperature (Slagsvold 1977; Amrhein, Kunc & Naguib 2004), but the underlying seasonal pattern is based on the breeding cycle (Slagsvold 1977). Individual singing activity peaked about 2 weeks before egg laying started in the redwing Turdus iliacus (Lampe & Espmark 1987) and before settling down with a female in willow warblers Phylloscopus trochilus (Gil, Graves & Slater 1999). Dusk singing of male nightingales Luscinia megarhynchos ceased immediately after pairing (Roth et al. 2012). Accordingly, the peak of singing activity is an index for the date when most males are attempting to attract a partner most ardently. Clearly, the peak of singing activity is closely related to breeding cycle. Thus, we propose the use of the date of highest detectability in spring (termed detectability peak henceforward) as a generic phenological measure for studies in avian phenology.

We developed a flexible model for estimating the detectability peak from opportunistic observations based on the combination of occupancy models (MacKenzie et al. 2002) and semi-parametric regression (thin-plate splines, Ruppert, Wand & Carroll 2003; Crainiceanu, Ruppert & Wand 2005). Our method can also be used to study phenology of species other than birds that vary seasonally in detectability, especially when the seasonal pattern in detectability is due to a change in vocalization rates. Unlike methods based on first observation dates or on en route observations, our method is not limited to migratory species; it can equally well be applied to sedentary species. By focusing on a function of all observations of a species, we avoid the use of unreliable first observation dates (Moussus, Julliard & Jiguet 2010; Lindén 2011).

To illustrate our method, we use opportunistic bird records collected by volunteers in Switzerland from 1995 to 2012 and estimate detectability peaks for 27 species and changes in the date of peak detectability for 10 among the 27 species. Combining the resulting estimates of the 10 species in a Bayesian meta-analysis, we estimate a mean overall change in date of peak activity over the last decade.

Materials and methods

Monitoring data used in our study

Estimation of detectability requires replicated detection–non-detection observations (Kéry & Schaub 2012). We used data from the Swiss citizen-science bird recording scheme IS (Information Service; Schmid et al. 2001), which has been collecting bird observation data from a total of approximately 1800 skilled volunteers (as of September 2012) since 1985. Records are stored at 1-km2 resolution. We used data from two different programmes within the IS: records of a list of 120 mostly rare species and checklists where all observed species are recorded. In the former, non-detections were deduced according to the logic laid out in Kéry et al. (2010): the combination of the absence of a record of a study species and the presence of that of another species at the same site during the same day by the same observer was taken as a zero observation (non-detection) for the study species. We analysed as response in our models the number of times that a species was detected per spatiotemporal unit (1 km2 and 1 day) among the total number of surveys for that unit (which was equal to the numbers of observers submitting a record for the unit). For each species, we restricted analysis to those quadrats wherein the species was ever detected between February and July during 1995–2012.

Observations from the southern slope of the Alps (Canton Ticino) were ignored since climatic conditions are rather different in Ticino from the rest of Switzerland (Stauffer 2008). Avian spring phenology is strongly influenced by altitude (Glutz von Blotzheim 2001); hence, we restricted our analyses to data from the lowlands (<600 m a.s.l.) from where most data were available.

Data selection

Only a subset of all (c. 180) breeding species could be included in the analysis. For species that are mainly recorded visually, the signal of singing activity will be weak in patterns of detectability, and no pre-breeding detectability peak is found (there is no distinction between visual and acoustic records in the data). For very abundant species, detectability at the 1-km2 scale is always close to one and hence useless as a proxy for singing activity. Observation counts from several species that are rare breeders in Switzerland are particularly high during spring migration period; therefore, we excluded these species from analysis. In addition, several species were excluded because observers are only asked to record observations of these species systematically after the previously mentioned date limits to avoid records of individuals en route; consequently, the detectability peak might be truncated in the data. We then selected data according to the number of records: we kept only data from years with at least 20 species-specific records between February and July. Thus, most rarely observed, non-breeding species were excluded from analysis, and for very rare breeding species, only data from some years were kept. Species were completely excluded from analysis if their records exceeded 20 in fewer than 4 years. As a next step, we visualized within-season detectability patterns from February to mid-July by plotting a raw detectability index (the ratio of the number of records and the number of surveys stratified by 7-day periods; see Fig. 1). The pattern visualized by this index is not necessarily directly proportional to the true temporal pattern of detectability, but it is the closest such thing that can be observed in the data. Only species with a pattern similar to Fig. 1a were considered for further analysis. Key criterion was a discernible peak in detectability matching roughly what is known about the species' breeding phenology (Maumary, Vallotton & Knaus 2007). For most species, data are collected year-round, so we had to define the period for analysis. Based on the raw detectability index plots (see Fig. 1), we made a species-specific data selection according to date using the following rules: the period to analyse should cover the first, generally easily visible peak in detectability. It should not cover a potential second peak in detectability because we were interested in pre-breeding singing activity peak. A second peak in detectability due to elevated post-breeding singing activity is described by Hegelbach & Spaar (2000), but could also be due to begging or fledging of the juveniles in some species. For migrating and partially migrating species, the analysed period should start shortly after the first observations were made. For non-migrants, we tried to exclude the winter period where species are unlikely to be associated with their breeding territory (according to Maumary, Vallotton & Knaus 2007). Starting date and ending date were not changed between years.

Figure 1.

Raw seasonal detectability patterns for Robin Erithacus rubecula in 2008 (a), Collared Dove Streptopelia decaocto in 2009 (b) and Black Woodpecker Dryocopus martius in 2007 (c). Detectability index is calculated as the ratio of the number of records and the number of surveys stratified by 7-day periods. The x-axis denotes months starting with February (F) and ending with June (J). We note that this index is as close to the true underlying detectability as we can directly observe from the data. However, there is no guarantee of a direct proportionality with detectability.

These criteria left us with 27 species (see Table 1). Among them, six species were non-migrants and 12 species were short-distance migrants; both are denoted as non-migrants here. Nine species were trans-Sahara migrants. Annual shifts in the detectability peak were estimated if data with at least 20 annual records of the species spanned at least 10 years; this was the case for 10 species. Most species analysed were small to middle-sized passerines or woodpeckers. Species-specific sample sizes are given in Table S1, for example number of sites, mean number of observations per year within breeding season and number of years.

Table 1. Estimated dates of peak detectability
NameScientific nameDetectability peak (Julian date)aMigration typebFirst YearcLast Yeard
  1. a

    Mean of the annual estimates of the date of peak detectability.

  2. b

    Migration type: Non = non-migratory species, Short = short-distance migrant, Trans = trans-Sahara migrant.

  3. c

    First year with at least 20 observations during breeding season; first year considered for analysis.

  4. d

    Last year with at least 20 observations during breeding season; last year considered for analysis.

Mistle Thrush Turdus viscivorus February 21 (52)Short20092012
Greenfinch Carduelis chloris March 12 (71)Non20072012
Short-toed Treecreeper Certhia brachydactyla March 15 (74)Non20072012
Eurasian Nuthatch Sitta europea March 16 (75)Non20072012
Song Thrush Turdus philomelos March 17 (76)Short20072012
Eurasian Wren Troglodytes troglodytes March 19 (78)Short20072012
Eurasian Stonechat Saxicola torquatus March 21 (80)Short19982012
Fieldfare Turdus pilaris March 21 (80)Short20072012
European Green Woodpecker Picus viridis March 22 (81)Non20032012
Common Reed Bunting Emberiza schoeniclus March 25 (84)Short20072012
Robin Erithacus rubecula March 25 (84)Short20072012
Grey-headed Woodpecker Picus canus March 26 (85)Non20082012
Lesser Spotted Woodpecker Dendrocopos minor March 28 (87)Non20032012
Dunnock Prunella modularis April 4 (94)Short20072012
Black Redstart Phoenicurus ochruros April 5 (95)Short20062012
Common Chiffchaff Phylloscopus collybita April 5 (95)Short20062012
Firecrest Regulus ignicapilla April 6 (96)Short20072012
Common Linnet Carduelis cannabina April 13 (103)Short20072012
Eurasian Wryneck Jynx torquilla April 26 (116)Trans19992012
Savi's Warbler Locustella luscinioides May 1 (121)Trans19962012
Common Whitethroat Sylvia communis May 6 (126)Trans20042012
Common Grasshopper Warbler Locustella naevia May 7 (127)Trans19962012
Common Nightingale Luscinia megarhynchos May 8 (128)Trans20022012
Eurasian Golden Oriole Oriolus oriolus May 19 (139)Trans19952012
Common Cuckoo Cuculus canorus May 20 (140)Trans20022012
Great Reed Warbler Acrocephalus arundinaceus May 23 (143)Trans19952012
Garden Warbler Sylvia borin June 6 (157)Trans20062012

Occupancy model with thin-plate splines for flexible estimation of the date of peak detection probability

We used occupancy models (MacKenzie et al. 2002) to estimate jointly the proportion of quadrats occupied (i.e. a species' distribution, or the area where abundance Ni is greater than 0) and detection probability (the probability to detect at least one of the Ni individuals present at site i). We parameterized the model with annual occupancy probabilities rather than the dynamics parameters (colonization, extinction) underlying their change, that is, strictly, we did not fit a dynamic model, but a multiseason model (Royle and Kéry 2007).

The distribution submodel distinguishes the latent state of occurrence, that is, true presence or absence, zi,j, of a species in quadrat i = 1,…,R in year (breeding period) j = 1,…,T, such that zi,j = 0 denotes a quadrat where a species is absent during a year and zi,j = 1 where it is present. We assumed zi,j to be a Bernoulli random variable with the year-specific occupancy probability ψj as success parameter.

display math

To account for an observation process with imperfect detection and no false-positive errors, the number of surveys in quadrat i at day d and year j in which the target species was detected (yi,d,j) among the total number of surveys made in i, d and j (Ti,d,j) was modelled as binomial random variables with success parameter depending on the product of the state of occurrence, zi,j, and of detection probability, pd,j, for day d and year j. True occurrence state and detection probability are latent, that is, only partially observable parameters, because the occurrence state zi,j = 1 may be recorded as an observed ‘absence’.

display math

Detection probability may be modelled by explanatory variables that vary by quadrat, day and year. Specifically, we modelled it as a function of year and date.

To flexibly estimate the date of peak spring detectability, we modelled detectability as a semi-parametric, smooth function of date using penalized thin-plate splines according to Crainiceanu, Ruppert & Wand (2005). The general methodology of semi-parametric modelling using the equivalence between penalized splines and mixed models is presented in Ruppert, Wand & Carroll (2003). Accordingly, we used quadratic splines and set the number of knots k as min (35, J/4), with J being the number of days in a season as did Gimenez et al. (2006). This rule led to the selection of 13–25 knots, because the defined observation period never exceeded 100 days. Detectability was modelled separately for each year as a smooth, nonlinear function of date.

We used Jags to fit the model separately for each species using Bayesian inference (Plummer 2003). For all parameters, mutually independent, vague priors were used (see model code in Data S1). Based on the Gelman–Rubin diagnostic math formula (Brooks & Gelman 1998), convergence was reached after at most 10 000 iterations. To get an math formula estimate, we run two chains over 50 000 iterations; discarding the first 25 000 as a burn-in and thinning by 1 in 50, math formula for all parameters was <1·01. A worked example is provided in the Data S4 containing the model code, code to visualize the model estimates and data of one species. As an example, the estimated detectability pattern for cuckoo Cuculus canorus in 2006 is visualized in Fig. 2.

Figure 2.

Seasonal change in detectability of cuckoos in 2006. The black regression line indicates the posterior mean of the estimated detectability; the dotted line the 95% credible interval. Grey bars indicate the detectability index, that is, the average proportion of surveys with cuckoos recorded for the raw data binned in weekly periods.

The date of peak detectability over all years was calculated as the mean of the dates of peak detectability for all years and of all MCMC iterations. Shifts in the date of peak detectability were calculated as follows: from a single MCMC iteration, we obtained one draw from the posterior distribution and selected for each year the date where detectability was estimated to be highest. Based on these values, we conducted a linear regression and saved the slope. This was repeated for each MCMC iteration, thus obtaining the posterior distribution of the annual change of the date of peak detectability, from which we computed the mean and the 95% credible interval (see Data S4).

Estimates of the annual change in the date of peak detectability were correlated with the estimates of the mean date of peak detectability to test whether species with an earlier activity peak showed a greater temporal shift than species with a later activity peak. Finally, we combined the species-specific slope estimates to obtain an estimate of the overall mean slope. We used a Bayesian meta-analysis to weight the contribution of the species-specific estimates by its precision (McCarthy & Masters 2005).

Results

Substantial differences in the date of peak detectability were found among species (Fig. 3). For non-migrants, detectability peaked between mid-March and mid-April. For trans-Sahara migrants, detectability peaked between mid-April and late May (see Table 1). Starting dates of nest building and egg laying in Switzerland taken from the literature (Maumary, Vallotton & Knaus 2007) were highly correlated with the date of peak detectability (Fig. 4).

Figure 3.

Distribution of estimated dates of peak detectability among 27 species in the Swiss lowlands (dark grey: sedentary species and short-distance migrants; light grey: trans-Sahara migrants).

Figure 4.

Correlation between date of peak detectability and date of nesting start and egg laying from the literature (Maumary, Vallotton & Knaus 2007). The dashed lines indicate 1:1 relationship.

For 10 species, sufficient data spanning at least 10 years were available. For these, we estimated an annual trend in the date of peak detectability to investigate whether phenology, expressed as the date of peak singing activity, has shifted over one decade. It was negative for all but two species, though not ‘significantly’ so, that is, the 95% Bayesian credible interval included zero (see Fig. 5 and Data S2). Only for the green woodpecker Picus viridis, the found shift was ‘significant’. For the 10 species with sufficient data spanning at least 10 years, we provide a graphical overview of the results (including the ‘naïve’ detectability index, see subchapter ‘Data selection’ in methods) in Data S3. Note that the naïve detectability index is likely to be lower than detectability estimated by the site-occupancy model. This is because a site-occupancy model estimates the probability of observing a species on a site given that the species is present there, whereas the detectability index indicates the proportion of successful observations over all sites (including sites where the species is not present). Combining the species-specific estimates in a Bayesian meta-analysis (according to McCarthy & Masters 2005), the overall trend towards an earlier date of peak detectability was estimated at 3·6 days over 10 years (posterior mean; CRI −0·36 to +9·23). These findings suggest an advance in date of peak detectability over the last decade, however, not significantly different from zero. We found no correlation between the date of peak detectability and the annual shift of the date of peak detectability (Data S5).

Figure 5.

Posterior means and 95% credible intervals for annual trends in the date of peak detectability from 1995 to 2012 in the Swiss lowlands (<600 m). Species are ordered by increasing posterior mean trend. 1 = green woodpecker, 2 = lesser spotted woodpecker, 3 = cuckoo, 4 = wryneck, 5 = nightingale, 6 = Savi's warbler, 7 = golden oriole, 8 = great reed warbler, 9 = grasshopper warbler, 10 = stonechat.

Discussion

Phenology has been studied for centuries for a variety of motivations (Pfister 1984). For animal species, phenological studies were traditionally based on first observation dates. However, first observation dates are not reliable phenological measures when detection is not perfect. In most species, detectability is <1, and this greatly complicates the study of phenology based on observational data (Moussus, Julliard & Jiguet 2010; Lindén 2011). In addition, the extremes of a distribution, such as a distribution of arrival times, are very much affected by chance events and hence would be hard to estimate reliably even in the absence of detection error. Here, we propose to use the period of highest detectability during the breeding period as a phenological measure in bird species with strongly vocal territory displays. Many bird species are mainly detected acoustically; hence, detectability is likely to depend heavily on singing activity. In turn, singing activity depends on an individual's stage in the breeding cycle, and we suggest that the date of peak detectability in the spring is a biologically relevant and often well-defined metric for the study of avian breeding phenology. For many bird species, singing activity of territorial males peaked just before settling down of a female (Gil, Graves & Slater 1999). Several studies of avian spring phenology used nest box data (e.g. in Both et al. 2009), but this limits application to cavity-breeding species. Phenological studies of non-migratory bird species based on observational data are very rare in the literature, and our knowledge of bird phenology is likely to be seriously biased towards migratory species. Our approach thus allows to fill a substantial knowledge gap in the study of avian phenology. To estimate the date of peak detectability, we combined powerful occupancy models (MacKenzie et al. 2002) with flexible spline regression models (Crainiceanu, Ruppert & Wand 2005). Our model estimates seasonal detectability patterns and allows flexible tracking of variation in detectability patterns within seasons and among years. Being based on a smooth regression function, the estimates will be robust to noise like short-term fluctuations in singing activity or observer effort. However, some species groups could not be included in the analysis because they are detected mostly visually, for example waterfowl and raptors. For such species, increased vocal activity need not result in higher detectability, and variation in detectability is likely to be caused by variation in behaviour or by numerical increase in spring and summer due to fledging of juveniles. And even for species that are mainly recorded acoustically, singing activity is just one among several factors that may contribute to temporal patterns in detectability. Detectability was found to be a positive function of survey length (Kéry & Royle 2009). One assumption underlying our analyses is therefore that mean survey length does not change during season, and a strong increase in survey length within season, for example due to elevated temperature, making time spent in the outdoors more agreeable, could influence the results. Thus, if data on survey length are available, we recommend incorporating it as a covariate influencing detectability. In addition, detectability is likely to correlate with density (Royle 2006) if the size of the surveyed plots is larger than the mean territory size. Density can be assumed to be stable over the course of the breeding season. However, this assumption is not met for migrants during the arrival period or if migration and settling are not temporally separated; especially for rare breeders, detectability could peak when most migrating individuals are passing through the observed area and sing on stopover sites. In such cases, the date of highest detectability can be regarded as spring migration peak, another interesting phenological measure. For woodland species, detectability can be reduced due to leaf formation (Schieck 1997), which could partly confound the seasonal patterns found. Obviously, the patterns in detection probability will be partly affected by such factors, but arguably, for many species (and all of those analysed in this paper) singing activity is the dominant mechanism underlying seasonal patterns in detection probability. This notion is supported by the fact that the estimated dates of peak detectability were very highly correlated with the starting date of nest building and egg laying (Maumary, Vallotton & Knaus 2007).

Our analysis is based on citizen-science data that were not collected according to a sampling design, neither in time nor in space. Our analyses assume that the seasonal detectability pattern is not affected by temporally varying observation effort. However, there is a site-selection bias due to observer preference, and the findings are mainly based on data from places preferably visited by ornithologists. However, we did not find a reason to assume that seasonal detectability pattern differs strongly between preferred and less preferred sites (within the altitudinal zone considered); thus, the seasonal detectability patterns that we identified should not be influenced by site-selection bias. A gain of observer experience over the years is likely to affect first observation dates. However, we assume that a measure like peak detectability that is based on all the data would be little affected by observer effects.

Accordingly to the method presented by Gimenez et al. (2006), we set the number of knots as min (35, J/4), with J being the number of days within the defined breeding period, which led to 13–25 knots. Conducting the analysis with a reduced number of knots resulted in an increase in speed of the analysis. The flexibility of the regression function is reduced (i.e. the basically quadratic effect of time more rigid) when the number of knots is reduced to three or five only. However, using at least 10 knots, the shape of the regression line and the resulting estimates of peak detectability are very similar to the estimates we got using the number of knots suggested by Gimenez et al. (2006); a further augmentation of the number of knots did not lead to a noticeable change in the shape of the regression line and the resulting estimates (which is in accordance with Ruppert, Wand & Carroll 2003).

Knowledge of breeding phenology is crucial to design the timing of avian monitoring programmes or atlas projects. Surveys should target the time period when detection is highest. Classic approaches for defining the seasonal monitoring schedule are usually based on prior knowledge of the species ‘breeding periods’ (Hill 2005). Using our method, seasonal detectability patterns and its variation among years can be tracked easily and in a rigorous and objective way. The patterns we uncovered can provide guidance for designing the timing of a monitoring schedule. Several studies have found a negative correlation between population trend and the degree to which a species shifts its phenology over the years in response to climate change (Moller, Rubolini & Lehikoinen 2008; Jones & Cresswell 2010). However, the decline in population size could also be an artefact in studies where the date of peak detectability is shifting towards a date prior to the observation period (Lehikoinen 2013), if an analysis does not account for detectability. This might particularly affect studies based on well-designed monitoring schemes with a set start and end of the survey period. Our model could detect such artefacts and correct for them; in addition, it could provide guidance for adapting the monitoring schedule.

Bioacoustics approaches are increasingly used for monitoring various species, for example insects, frogs, toads, reptiles, bats and marine mammals (Pellet & Schmidt 2005; Obrist et al. 2010). Imperfect detection and variation in detectability within season is likely to occur (Pellet & Schmidt 2005). Our approach to study phenology could therefore be applied to such monitoring data from a wide variety of species to estimate the period of highest detectability. The estimates could be used for adjusting monitoring schedules to a species' phenology or as measures for phenological studies. In addition, our model could be used to improve the estimates of site-occupancy probability and population size due to the flexible modelling of key patterns in the observation process. Besides estimating the date of peak detectability, our model could easily be adapted for estimating the time of the day when detectability is highest. Furthermore, information like atlas codes (e.g. in Zbinden, Keller & Schmid 2005) that allow the observer to report the behaviour of the observed species could be used for modelling behavioural traits within season or day.

By estimating the date of peak display of a trait and using it as a phenological measure, we avoid the issues concerning first observation dates (van Strien et al. 2008) and provide estimates that are presumably more suitable for phenological studies. Phenological changes are often associated with environmental factors. Accurately identifying the factors that influence phenological events like spring arrival might be virtually impossible for mobile species that integrate environmental cues from a broad area. We used the date of peak spring detectability as a phenological measure. In contrast to spring arrival, this measure is mainly influenced by environmental cues sensed within the breeding area in non-migratory species (Slagsvold 1977). Even for migrants, the date of peak detectability is at least partly influenced by environmental cues sensed within the surveyed region. Thus, we consider it as a reliable measure for local phenology and assume that comparisons of the date of peak detectability with local environmental factors should lead to meaningful results. Our model allows analysing long-term and large-scale data sets, even produced by citizen-science programmes. Based on the model output, differences in detectability patterns over time can be tested for. Hence, we believe that our method can help greatly to understand how species and communities adapt their phenology to climatic and other environmental changes.

Acknowledgements

We thank Tobias Roth and Martin Grüebler for insightful discussions, two anonymous reviewers for their helpful comments and the volunteer observers participating in the Swiss Information System for providing an extensive data set.

Data accessibility

Worked example: uploaded as online Data S4. Observation data and species attribute data: Will be upload to Dryad at acceptance (DRYAD entry, doi: 10.5061/dryad.k20q2).

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