Elsevier

Ecological Modelling

Volume 212, Issues 3–4, 10 April 2008, Pages 233-243
Ecological Modelling

Multilevel models reveal no cohort-level variation in time spent foraging to account for a collapse in kittiwake (Rissa tridactyla) breeding success

https://doi.org/10.1016/j.ecolmodel.2007.10.003Get rights and content

Abstract

As central-place foragers, colonial seabirds should be able to compensate, up to some threshold, for changing breeding conditions by remaining flexible in the amount of time allocated to foraging versus other activities. Black-legged kittiwake (Rissa tridactyla) colonies in Chiniak Bay, Kodiak Island, Alaska experienced high productivity from 2001 to 2003 and virtually no productivity from 2004 to 2005. In the absence of disease epidemics, increased human disturbance or predation, we applied multilevel, mixed, regression models to assess the hypothesis that the collapse from high to low breeding success was due primarily to changes in prey availability. Under this hypothesis, we predicted that longer foraging trips would be associated with reduced breeding performance in cohorts of kittiwakes—groups marked with radio-transmitters at the same colony in the same year. We separately modeled two response variables: foraging trip-durations made during the incubation and early chick stages. Multilevel mixed models revealed only weak variation at the cohort-level in either response variable; hatching success and fledging success accounted for none or less than 2% of the total variation in trip-durations made during the incubation and early chick stages, respectively. The majority of the variation in our response variables was at the observation (ca. 80–90%) and bird (or individual) levels (ca. 10–12%). Our results expose the unreliability of using indirect evidence to implicate prey availability as the primary cause of widespread breeding failures in colonial seabirds. In the ecological literature, two types of inferences seem particularly vulnerable to indirect evidence: inferences following studies on species that are accepted or strongly promoted as bioindicators of changes in marine productivity such as the black-legged kittiwake, and inferences that implicate a fisheries-induced reduction in prey availability to failed breeding. In light of these pitfalls, we recommend that long-term monitoring studies on kittiwakes and other seabirds carefully consider in their study designs and implementations multiple working hypotheses that might explain major changes in breeding success.

Introduction

During the breeding period, colonially nesting seabirds allocate their time between the colony, usually incubating and brooding, and the sea, mainly foraging. Flexibility in the amount of time allocated to these activities allows seabirds, as central-place foragers, to compensate for the spatial and temporal constraints associated with raising young. The idea that seabirds could compensate through flexible time budgets to dynamic food resources was discussed in a theoretical context by Cairns (1987). Since that time, several studies have shown that seabirds are able to mediate poor foraging conditions by increasing time spent foraging (Monaghan et al., 1989, Burger and Piatt, 1990, Hamer et al., 1991, Hamer et al., 1993, Wanless and Harris, 1992, Uttley et al., 1994, Suryan et al., 2002, Litzow and Piatt, 2003, Wanless et al., 2005).

Black-legged kittiwake (Rissa tridactyla; “kittiwake” hereafter) colonies in Chiniak Bay, Kodiak Island, Alaska experienced high productivity for the region (Hatch and Hatch, 1990, Roberts and Hatch, 1993, Gill and Hatch, 2002, Frederiksen et al., 2005) from 2001 to 2003 and virtually no productivity from 2004 to 2005 (Kildaw et al., 2005, Buck et al., 2007). Concurrently, intensive seabird monitoring efforts (Gulf Apex Predator–Prey Project, unpublished) did not detect evidence of disease epidemics (in any year) or an important change in human disturbance between the high and low productivity periods. And, although predation by bald eagle (Haliaeetus leucocephalus), peregrine falcon (Falco peregrinus), common raven (Corvus corax), glaucous-winged gull (Larus glaucescens) and northwestern crow (Corvus caurinus) on kittiwake adults, chicks, and/or eggs was observed or suspected in all years, non-systematic sampling did not detect an increase in predation after 2003. In the absence of disease epidemics, increased disturbance or predation, we applied multilevel, mixed, regression models to assess the hypothesis that the shift from high to low breeding success experienced by Chiniak Bay kittiwakes was due to a major reduction in prey availability. Under this hypothesis, we predicted that longer foraging trips would be associated with reduced breeding performance.

Multilevel, mixed, regression models ‘mix’ fixed and random effects in a single linear regression model (Singer, 1998, Singer and Willet, 2003). ‘Multilevel’ corresponds to nesting in the response variable into one or more levels such as repeated observations nested within birds that are further nested within colonies (three levels: observation, bird, colony). Fixed or population-specific effects estimate the average population response while random or subject-specific effects estimate the subject deviations from the average population response (Singer, 1998, Fitzmaurice et al., 2004). ‘Subjects’ might be observations, individuals, or groups depending on the level of the multilevel response variable. An important advantage of multilevel models is the ability to estimate random effects and their variance at each level in the response (σlevel2). Subsequently, these variance components can be used to estimate the percentage of variance in y accounted for by each level and, assuming the magnitude of level-i variation warrants further investigation, the percentage accounted for at level-i by a covariate.

In the simple regression model yi = γ0 + ri, γ0 is the average population response (fixed intercept), ri are the (assumed) random deviations from γ0 and their variance is σ2 (notation closely follows Singer, 1998). In the context of multilevel regression, this simple model assesses variation on only one level (i). The variance of the ri deviations σ2 represents the residual, observation or level-1 variance component (the only variance component in the model).

Model yij = γ00 + μ0j + rij is an extension to two levels where yij represents the ith observation from the jth group. As in the previous model, γ00 represents the average population response. To this model we add random group deviations from γ00 and represent these as μ0j; the variance of these group-level random effects is σgroup2. With the inclusion of μ0j in the model, the residuals take on a slightly different interpretation but their variance remains σ2: rather than measure random deviations around the grand mean (γ00), the rij's instead measure variation around the group means where γ00 + μ0j = mean response for group j. Reminiscent of the ANOVA model, level-1 (σ2) and level-2 (σgroup2) variance components describe variation within and among groups, respectively. Consider, as an extension to the previous model, a covariate (X) at the group level (j) in the form of a fixed γ01(Xj) and random slope μ1j(Xj): yij = γ00 + μ0j + γ01(Xj) + μ1j(Xj) + rij. By including the random slope, the model assumes that group slopes deviate from the fixed (or population-average) slope γ01(Xj) by μ1j(Xj). In this model, γ01(Xj) has been ‘unfixed’ (Singer, 1998). Additional details are available in Singer (1998), Singer and Willet (2003) and Smolkowski et al. (2006).

Variance components can be used to calculate the proportion of the variance in (e.g.) yij that is accounted for by the group or level-2 variance using the estimator σˆgroup2/i=1R=2σˆlevel-i2 where R is the number of levels in yij. Note that if σgroup2 represented only a small fraction of the variance in yij, then there would be no point to fitting a group-level covariate to yij. Alternatively, if σgroup2 represented an important part of the variance, then the estimator, σˆgroup,A2σˆgroup,B2/σˆgroup,A2, could be used to calculate the variation at level-i accounted for by a level-i covariate. Models in this equation (A, B) need to be identical except for the level-i covariate in model B (Singer, 1998, Singer and Willet, 2003).

We used mixed models with up to four levels to estimate variance components in the responses yijklincubation and yijklearlychick where yijklstage describes the duration (h) of the ith foraging trip (or observation; level-1) from the jth bird (or individual; level-2), kth cohort (level-3) and lth colony (level-4) measured during the incubation or the early chick stage. Cohorts are groups of breeding adults fitted with radio-transmitters at the same colony in the same year. Conditional on the assumption that foraging trip-duration is a reliable proxy of moderate to large changes in prey availability (Cairns, 1987, Monaghan et al., 1989, Burger and Piatt, 1990, Hamer et al., 1991, Hamer et al., 1993, Wanless and Harris, 1992, Uttley et al., 1994, Suryan et al., 2002, Litzow and Piatt, 2003, Wanless et al., 2005), we predicted that if food available to kittiwakes plummeted after 2003, then breeding success, as a proxy of prey abundance, would account for an important amount of the cohort-level variation in time spent foraging. In particular, we expected that foraging trip-durations made by cohorts marked in 2004 and 2005 (low productivity years) would be (on average) substantially longer than those marked from 2001 to 2003 (high productivity years). It is important to note that if estimates of prey abundance had been available, our analysis would have looked for a cause and effect relationship between prey availability and trip-duration. However, given that estimates of prey abundance were unavailable, we employed what is widely believed to be a proxy of prey availability, breeding success, and looked for a correlation (not cause and effect) between breeding success and foraging trip-duration.

Section snippets

Study area and species

Chiniak Bay, Kodiak Island, Alaska (57°40′N, 152°20′W) is ca. 400 km2 and contains 21 kittiwake colonies encompassing ca. 10,000 breeding pairs from about April to August (breeding period) each year (Kildaw et al., 2005). Colonies are on cliffs throughout the main bay and three secondary bays on numerous islands, sea stacks, and on Kodiak Island itself (see Fig. 1 in Kildaw et al., 2005). Data for our analyses were collected at five island colonies (Gull, Kalsin, Kulichkof, Mary, and Svitlak)

Sex

Of the 108 birds in our analyses, the sexes of 37 and 16 were discriminated using head-to-bill (HB) with flattened wing (FW) and HB alone, respectively (models 6 and 7 in Table 3, Jodice et al., 2000). Accuracy predictions for discriminant functions used were 92% (HB + FW) and 88% (HB; prediction-DEE birds in Table 4, Jodice et al., 2000). The remaining 55 birds were sexed using DNA. From these methods, 69 and 39 were identified as females and males, respectively (Table 1).

Plots of means and breeding success

Two broad patterns are

Discussion

We monitored six black-legged kittiwake colonies distributed across a ca. 400 km2 bay over a 5-year period. During this time, breeding success was initially high relative to the extremely poor 2004 and 2005 seasons when ca. 10,000 kittiwake pairs produced less than 1/10th of a chick pair−1. Given the extent of the breeding failure, and an absence of disease epidemics, increased human disturbance or predation, we suspected a substantial decline in prey availability to be the root cause. However,

Acknowledgements

This research was sponsored in part by NOAA/NMFS (NA16FX1270) to CLB. We thank L. Baroff, SD, J. Brewer, T. Cooper, R. Fridinger, J.B. Gamble, D. McIntosh, K. M. Murra, R. Orben, N. Rojek, S. Studebaker, M. Van Sooy, S. Van Sooy and C.T. Williams for assistance in the field. We thank T. Drevon for donating time and expertise in developing our Visual Basic programs, K. Allard, J. Brewer, S.E. Whidden and C.T. Williams for valuable insights and discussions related to the preparation of this

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