A demonstration of the value of recapture data for informing moult phenology models for avian species with imperfect moult data

The Underhill–Zucchini model has revolutionised the study of moult in the context of birds’ annual cycles, but, as for all statistical models, inferences are vulnerable to violations of model assumptions. In particular, the standard Underhill–Zucchini models for moult phenology are vulnerable to imperfect moult data arising, for example, from non-random sampling and/or the misclassification of non-moulting birds. Similarly, inference is challenging for species with dispersed moult periods (population-level moult extending beyond an annual cycle). Using ringing data from Cape Weavers Ploceus capensis and SAFRING data for Cape Sugarbirds Promerops cafer, we demonstrate how recent extensions to the Underhill–Zucchini framework can help the robust estimation of moult parameters in such situations, in particular when within-season recapture data is available.


Introduction
A demonstration of the value of recapture data for informing moult phenology models for avian species with imperfect moult data field, but it limits the inferences that can be drawn about physiological, environmental and behavioural drivers of the timing, extent and rate of moult, and ultimately about the drivers of birds' annual cycles (Marra et al. 2015).Based on simulation studies, Boersch-Supan et al. (2022) recently demonstrated how violations of the assumptions underlying Underhill-Zucchini models can bias inferences, but also presented extensions to the Underhill-Zucchini framework that can mitigate such biases and thereby facilitate robust parameter estimation from real-world moult data.
We here demonstrate the utility of these extensions by focusing on two particular features of moult processes and datasets: uncertainty in the assignment of nonmoulting individuals, and weak seasonality in the moult process.Because the Underhill-Zucchini framework conceptually relies on temporally ordered moult stages, concurrent observations of "all old plumage" and "all new plumage" birds outside of the active moult period can provide a challenge for estimating moult parameters.Such observations can reflect the ecological process of moult -that is, when a species' moult season is sufficiently dispersed that individuals with new and old plumage are present year-round (e.g.Craig et al. 2014), or under observation uncertainty.Observation uncertainty arises as a result of feather wear between successive moults, namely the gradual transition from "new" to "old" plumage.Because feather wear can be difficult to assess in the field, the assignment of non-moulting birds to pre-moult and post-moult categories can be ambiguous, but even small numbers of misclassified individuals can lead to pronounced parameter biases (Erni et al. 2013;Boersch-Supan et al. 2022).In principle, this issue can be sidestepped by ignoring the non-moulting individuals altogether and employing the type 3 Underhill-Zucchini model (Erni et al. 2013).This is, however, a sub-optimal solution, for the following reasons: the type 3 model is generally less precise than models making use of information from non-moulting individuals (Underhill and Zucchini 1988), its precision is worse for species with extended moult seasons (i.e.weak seasonality) (Supplementary Figure S1), and it is vulnerable to biased estimates when individuals are not equally catchable across the progress of moult (Boersch-Supan et al. 2022).
Both extended moult seasons and uncertainty in the assignment of non-moulting individuals are apparent in moult datasets for many species, including southern African passerines (e.g.Erni et al. 2013;Craig et al. 2014).Here we use observations of Cape Weavers Ploceus capensis and Cape Sugarbirds Promerops cafer (Figure 1) to demonstrate how extended Underhill-Zucchini models can improve inference about moult parameters from such imperfect datasets.

Moult datasets
Cape Weaver moult data were collected by HDO, Lee Silks and Margaret McCall.Records collected by HDO were mostly from January 2000 to October 2022 at ringing locations across the Western Cape Province, but with the majority of records from the greater Cape Town area.
Birds were captured in the early morning using mist nets and ringed with unique SAFRING metal rings.The dataset included 4 053 individual weaver birds, with 698 recapture records.Cape Weaver moult records were collected by Lee Silks and Margaret McCall from sites mostly around Tygerberg and Durbanville (near Cape Town).
Initial analyses of Cape Sugarbird data were based on moult records collected by ATKL at ringing locations in the Baviaanskloof region of the Western Cape.These records proved too sparse to apply the Underhill-Zucchini model to obtain estimates for the standard parameters for moult.Therefore, we obtained additional wing-moult data for the Cape Sugarbird from the South African Bird Ringing Unit (SAFRING) database (SAFRING 2023).

Statistical analyses
Primary moult scores were transformed into proportion of feather mass grown (PFMG) using species-specific feather measurements (Underhill and Joubert 1995).For Cape Weaver, individuals were grouped into sexes (female, male, unknown) and age classes (juvenile: age codes 2,5,6; immature: age codes 3,7 for males, 3 for females and unknown sex; adult: age codes 4,8 for males, and 4,7,8 for females and unknown sex).Direct estimates of moult durations were obtained from records of individuals recaptured at least twice during active moult in the same season by dividing the time difference between the first and last active moult record by the corresponding difference in observed PFMG.
Records from individuals with more than one active moult record within a season were filtered to remove recaptures that implied biologically implausible moult durations (i.e.negative and very short [<50 days] or long [>300 days]).PFMG was then modelled as a function of date for each full dataset using the standard type 2 (T2) and standard type 3 (T3) models of Underhill and Zucchini (1988), as well as the following extended Underhill-Zucchini models (Boersch-Supan et al. 2022): the type 3 recaptures model (T3R), the lumped type 2 model (T2L) and the lumped type 2 recaptures model (T2LR).These intercept-only models are referred to as null models hereafter.In addition to the null models, sex and age-specific moult parameters were estimated for the Cape Weaver dataset using the same five moult model types with the following linear predictor structure: A model set with a full sex*age interaction for start date SD was attempted but did not converge.
The extended moult models are fully described in Boersch-Supan et al. (2022), and the R package moultmcmc was used to estimate moult parameters in a Bayesian framework in all cases.Hence, parameter estimates are given as posterior means and their associated Bayesian credible intervals (CI).Briefly, the lumped model is an analogue of T2, which takes both moulting and non-moulting individuals into account but treats pre-moult and post-moult individuals as indistinguishable.
The recaptures models additionally make use of withinseason recaptures of birds that are observed at least once during active moult.Like the standard Underhill-Zucchini models, the recaptures models assume a homogeneous moult duration for all individuals but allow the estimation of individualspecific start dates for the recaptured individuals.Because the standard Underhill-Zucchini models estimate the distribution of moult start dates in a population, it is conceptually straightforward to accommodate individual-level moult start dates as random intercepts drawn from the population distribution of start dates; that is, the random effect SD and the population start date SD are the same parameter.Worked examples of fitting the extended moult models to example data are given in the Supplementary Material.

Recaptures
Recaptures were rare in both datasets, with <4% of encountered individuals being recaptured within a season (Table 1; Figure 2).The majority of recaptured individuals were encountered outside their active moult phase, which meant only ~1.5% of captured Cape Weavers and ~1.3% of captured Cape Sugarbirds were able to provide additional information for the recaptures models.Less than 0.5% of individuals were captured at least twice during active moult, the requirement for direct estimates of moult speed.Filtering the data from recaptured individuals to remove biologically implausible moult speeds further reduced the number of recaptures available for modelling and direct estimation, leaving 36 Cape Weavers and only 10 Cape Sugarbirds for which direct estimates of moult duration could be obtained.

Direct estimates of moult duration
Recaptures for Cape Weaver during active moult were on average 48 days apart (SD 28, range 2-106 days) and yielded an average direct estimate of moult duration of 111 days (SD 27,.Active moult recaptures for Cape Sugarbird were on average 27 days apart (SD 13, range 8-47 days) and yielded an average moult duration of 98 days (SD 37, range 58-189 days).In both species, direct estimates were right-skewed, with median moult durations being lower than the corresponding means at 107 days and 86 days for Cape Weaver and Cape Sugarbird, respectively.Top panels show 3-weekly aggregates of records by moult category.Both "old" and "new" plumage individuals were recorded throughout the year in both species.The moult period is reasonably well defined in the Cape Weaver, but spans almost the entire year for the Cape Sugarbird Moult models T2 gave obviously non-sensical estimates for both datasets, with the estimated 95% moult interval (i.e. the time interval in which 95% of the population are expected to be in active moult, defined as the polygon bounded by the mean moult trajectory ± 1.96 × Start date SD) (Figure 3) spanning over 500 days and the mean start date preceding most active moult records.The fit for T3 was biologically more realistic, but moult duration appears to be biased low in Cape Weaver, as evident from the 95% moult interval excluding a substantial number of late records of large PFMG values (8% of active moult records occurred later than the interval) (Figure 3a).The fits for T2L, T2LR and T3R all appear reasonable, with a relatively symmetrical position of the 95% moult interval relative to the observations.For Cape Weaver, all null models estimated moult durations that were in the range of direct duration estimates obtained from within-season recaptures of moulting individuals (Table 2; Figure 4a), although the T2 and T3 estimates were at the higher and lower ends of the  observed durations, respectively.The duration estimates for the extended moult models were similar at 101-104 days, and were close to the mean of the direct moult duration estimates.For Cape Sugarbird, the T2 duration estimate was at the upper bound of the prior for this parameter (365 days), whereas the T3 duration estimate (137 days, 95% Bayesian CI 47-232 days) fell into the range of the directly observed moult durations yet was highly uncertain.The Figure 3: Fits of the null models (no covariates) to the Cape Weaver Ploceus capensis and Cape Sugarbird Promerops cafer moult datasets.Solid lines show the estimated average moult trajectory; dotted lines show the expected 95% moult interval (i.e. the time interval in which 95% of the population are expected to be in active moult).Note the different x-axis scale in the T2 model panels.The standard type 2 model (T2) gives implausible estimates, with the estimated 95% moult interval spanning more than one calendar year, and the mean start date at the edge of observed active moult records.The fit for the standard type 3 model (T3) is biologically more realistic, but moult duration appears to be biased short in the case of (a) Cape Weaver, as evident from the 95% interval excluding a substantial number of late records of large PFMG values.Visual assessments of model fit for (b) Cape Sugarbird are difficult given the wide spread of active moult records duration estimates for the extended moult models ranged from 73 to 81 days, somewhat lower than the mean of the direct duration estimated (Table 2; Figure 4b).
For Cape Weaver, sex and age-specific estimates were derived from a more complex model, with a sex*age interaction in the linear predictor for each moult parameter (Figure 5; Table 3).As for the null models, T2 performed poorly in the presence of misclassified non-moulting individuals, but T3 appeared to give more reasonable results.Estimates from the extended moult models were generally closer to the mean of the direct estimates (Figure 5) than the estimates from the standard models.Graphical summaries for all model types are given in Supplementary Figures S2-S6.
Results from T2R showed that the average moult duration for adult Cape Weaver females was 104 days (95% CI 101-107 days), and this did not differ significantly among age classes for females (Table 3; Supplementary Figure S1), nor did it differ from the estimate for adult males (100 days, 95% CI 97-103 days).However, juvenile and immature males had significantly longer moult durations at 110 days (95% CI 104-116 days) and 119 days (95% CI 114-124 days), respectively.Duration estimates from T2LR generally corresponded closely to the mean of direct estimates, where available (Figure 5).In both sexes, adults started moult in November, about 1 week ahead of immature birds and 15-17 days ahead of juvenile birds (Supplementary Table S1).Males started moult 13-25 days earlier than the corresponding female age classes.Moult was more synchronous in adults (Start date SD 22 days, 95% CI 21-23 days) than in the juvenile and immature age classes (Start date SD 30 days, 95% CI 29-32 days; Start date SD 31 days, 95% CI 30-33 days, respectively).Parameter estimates for the unknown sex class were generally intermediate between estimates for males and females, but closer to the latter.

Discussion
Our estimates for Cape Weaver moult duration were within the range of previous estimates of 98.1-124.2days, which were derived using the standard type 2 model (T2) (see Table 4).Previous work demonstrated differences between regions (provinces of South Africa: Oschadleus 2005) and by sex (Bonnevie and Oschadleus 2010).We did not attempt to obtain spatially disaggregated estimates, and found significant sex differences in moult duration for the juvenile and immature age classes but not for adults.Oschadleus (2005) also showed how start of moult varied by up to 2 weeks in different years (data from 1993-2003) while keeping duration constant at 96.3 days for the dataset.This, together with the difference in duration estimates, may explain the 6-13-day difference between the later start dates obtained in this study and previous results.The general sex-and age-specific patterns found in this study-shorter and more synchronous moult in adults compared with in younger age classes-may reflect timing trade-offs between breeding and moult in adult birds (Hemborg et al. 1998), and trade-offs between somatic growth and feather growth in younger birds (Delhey et al. 2020).
To our knowledge, moult in Cape Sugarbirds has not been previously studied in detail and is not covered  in any monographs or reference works (Broekhuysen 1959;Skead 1967;Cheke et al. 2010), although both an extended breeding season (Winterbottom 1962) and moult season (Oschadleus and Fraser 1988) have been noted for populations in the Western Cape.Our estimates are therefore the first moult-parameter estimates for the species.In the congeneric Gurney's Sugarbird Promerops gurneyi, primary moult was recorded in the Mpumalanga Highveld in South Africa during a prolonged period from September to March, coinciding with the breeding season.Notably, records in this period were predominantly of individuals in early moult (standardised moult scores of <20), although near-complete moult was recorded in three individuals as early as in October (de Swardt 1992).No firm conclusions can be drawn about moult duration from these data, which seem to indicate poor catchability of moulting individuals and/or temporary emigration after the onset of moult, yet the data are not incongruous with a moult duration of 2-3 months.Our estimates of moult durations from the extended Underhill-Zucchini models were consistent with the direct estimates.At 73-81 days (Table 2), the moult duration is short when compared with estimated moult durations for the much smaller-bodied sunbirds (70-155 days) (Bonnevie and Oschadleus 2010;Bonnevie et al. 2023), although within the range of moult durations observed in other passerines of comparable body size (Ginn and Melville 1983).The cause for the large disagreement about moult start dates between the fitted models (29 Sep-14 Nov) is not immediately clear and may be a consequence of the dispersed moult season of this species, resulting from differential breeding and associated moult seasons because of spatial-temporal resource availability across the Western Cape.The species lives in a fire-driven ecosystem and is thought to disperse widely in response to such disturbance events (Fraser 1989).
Our validation of the extended moult models is entirely reliant on direct moult-duration estimates from recaptured individuals.It should be reasonable to assume that these direct estimates represent accurate results since they include direct information on moult progress in individuals.However, just like the standard Underhill-Zucchini models, the direct estimation (and by extension the recapture models) rely on the linearity assumption of moult progress.Using PFMG instead of numerical moult scores is generally thought to produce a linear measure of moult progress (Underhill and Joubert 1995;Dawson and Newton 2004), but given the scarcity of recaptures in most moult datasets species-specific validation of the linearity of PFMG are lacking.Furthermore, the representativeness of direct estimates may be limited when sample sizes of recaptured individuals are very low, as in the case of Cape Sugarbirds here.Information from additional recaptures would improve the ability to validate moult durations, as might direct estimates of feather growth rates from growth bands (Rohwer and Broms 2012).
When sampling can be assumed to be even across all stages of moult but there is a possibility of confusion of 'old' and 'new' plumage, the lumped type 2 model offers improved inferences over using the standard type 3 model at little computational cost, with Markov chain Monte Carlo (MCMC) runtimes in the order of seconds to minutes even for large datasets.When there is the potential of uneven sampling across non-moulting and moulting birds or within the actively moulting birds, even small amounts of recapture information can yield results that are in better agreement with direct estimates of moult duration than the standard models.However, the scarcity of within-season recaptures in many moult datasets means this approach is not a perfect solution for precise estimates of moult parameters across many species, unless high ringing effort is targeted during the moult phase for a specieswhich is challenging for species that are vagile outside their breeding season, such as the sugarbirds or mousebirds (Oschadleus and Fraser 1988;de Swardt 1992;Craig et al. 2014).Additionally, fitting the recapture models comes with substantial computational overheads, with MCMC runtimes in the order of several minutes to several hours for large datasets (thousands of records), although future computational improvements may decrease runtimes.
Nonetheless, we demonstrate here that uncertainty about the assignment of non-moulting birds can be mitigated by using the lumped type 2 model, and that even small numbers of recaptures (~1% of captured individuals) can sufficiently constrain moult models to improve parameter precision and mitigate against parameter biases caused by uneven sampling.We encourage ringers to record all life-history and biometric data for recaptured birds, as these repeatedly sampled birds provide invaluable data for a range of biological insights, including life-history strategies.

Figure 1 :
Figure 1: (a, b) Moult records for Cape Weaver Ploceus capensis (n = 10 633) and (c, d) Cape Sugarbird Promerops cafer (n = 4 687).Top panels show 3-weekly aggregates of records by moult category.Both "old" and "new" plumage individuals were recorded throughout the year in both species.The moult period is reasonably well defined in the Cape Weaver, but spans almost the entire year for the Cape Sugarbird

Figure 2 :
Figure 2: Distribution of Cape Weaver Ploceus capensis and Cape Sugarbird Promerops cafer moult records by age and sex.Open symbols indicate records from individuals without within-season recaptures; filled symbols indicate records from recaptured individuals; lines connect individuals with two recaptures during the active moult period

Figure 4 :
Figure 4: Comparison of direct estimates (n = 36 for Cape Weaver Ploceus capensis; n = 10 for Cape Sugarbird Promerops cafer) and null model-derived estimates of moult duration for both species and five different moult model types.Estimates from the extended moult models are generally closer to the mean of the direct estimates than the estimates from the standard models.Error bars represent 95% posterior credible intervals for model estimates, and 2 standard errors for the direct estimates

Figure 5 :
Figure 5: Comparison of direct (n = 36) and model-derived sex-and age-specific estimates of moult duration for the Cape Weaver Ploceus capensis.No direct estimates were available for immature and adult birds of the unknown sex category.Estimates from the extended moult models (i.e.T2L, T2LR, T3R) are closer to the mean of the direct estimates than the estimates from the standard models (i.e.T2, T3).Error bars represent 95% posterior credible intervals for model estimates, and 2 standard errors for the direct estimates

Table 1 :
Breakdown of individually ringed Cape Weavers Ploceus capensis (n = 10 257) and Cape Sugarbirds Promerops cafer (n = 4 361) by number of captures within a season, and numbers of active moult records from those captures.Fewer than 2% of individuals were recaptured at least once during active moult in both species (bold font)

Table 3 :
Parameter estimates for the age-and sex-specific lumped type 2 recaptures model (T2LR) fitted to the Cape Weaver Ploceus capensis dataset.SD = standard deviation; 95% CI = 95% Bayesian credible interval of the estimated parameter means

Table 4 :
Direct estimate and model estimates of moult duration for adult Cape Weaver Ploceus capensis.SE = standard error; T2 = type 2 Underhill-Zucchini model; T2LR = lumped type 2 recaptures model