study site: st denis national wildlife area
The 361-ha St Denis National Wildlife Area (NWA; 52°12′ N, 106°5′ W) is located approximately 40 km east of Saskatoon, Saskatchewan, Canada, and has over 100 temporary and permanent wetlands, most of which are fringed by grasses, shrubs or trees. Approximately 50% of the previously cultivated land has been seeded to a mixture of bromegrass Bromus spp. and alfalfa Medicago sativa for nesting cover. Full details of the study site can be found in Clark & Shutler (1999).
nest fate and clutch initiation date
Nest searches at St Denis NWA were conducted from early May to mid-July of each year between 1980–1981 and 1983–2000, by flushing females off the nest as heavy ropes or cable-chain devices were pulled between two all-terrain vehicles (Clark & Shutler 1999), or on foot and beating cover. Three or four nest searches were performed each year. When a nest was found, species was identified by watching the female, or by species-typing the eggs and/or feather lining of the nest (Klett et al. 1986). Clutch initiation date was determined by counting eggs (assuming one egg was laid per day, and that no eggs were lost) and candling to assess the stage of embryo development (Weller 1956). Nest fate (hatched, depredated, abandoned) was determined in subsequent visits following criteria in Klett et al. (1986). Nests that were abandoned or destroyed due to human interference (researcher disturbance, farm machinery), or were located inside predator fences or on islands, or whose fate was unknown were excluded from the analyses. The species considered in this study were the five most common dabbling duck species found nesting in the area: mallard Anas platyrhynchos, northern pintail A. acuta, blue-winged teal A. discors, northern shoveler A. clypeata and gadwall A. strepera.
Environment Canada has operated a weather monitoring station at St Denis NWA since 1989, and we compared data collected by that station with weather data from the Saskatoon Airport (52°10′ N, 106°43′ W), the next nearest weather station. Weather data from the Saskatoon Airport covered the entire time period of the breeding duck data. Mean daily temperature at St Denis NWA was highly correlated with mean daily temperature at the Saskatoon airport (R2 = 0·987, n = 3048). Regression of mean daily temperature (MDT) between the two sites indicated a near 1 : 1 conversion (MDT(St Denis NWA) = −0·50 + 0·99 × MDT(SK Airport)), and so temperature data from the Saskatoon Airport were used in the analyses. Mean spring temperature was calculated as the mean daily temperature between 1 April and 30 June of each year, and mean previous winter temperature was calculated as mean daily temperature between 1 January and 28/29 February of each year.
Precipitation at St Denis NWA was not strongly correlated with precipitation at Saskatoon Airport [R2 = 0·432 for daily accumulation (n = 2920), and R2 = 0·517 for monthly accumulation (n = 109)]. We therefore used May wetland (pond) density as a measure of environmental conditions as estimated for Stratum 30 from the aerial waterfowl surveys (Smith 1995). This estimate of pond density correlated strongly with pond counts done locally for years 1982–2000 (R2 = 0·825, n = 19; RGC, unpublished data), provided data for more years than the local pond counts, and allowed us to look at effects of pond density from previous years (Drever et al. 2004). Each year of breeding duck data was then assigned an estimate of pond density in the year of study, and an estimate of the previous year's pond density.
Nesting occurs earlier in the year during warmer springs than during cooler springs (Hammond & Johnson 1984; Greenwood et al. 1995). To allow comparisons among years, clutch initiation date was converted to relative clutch initiation date. For the five duck species nesting at St Denis NWA, relative clutch initiation date was calculated as deviations from the yearly median clutch initiation date for each species (x − x50%), a measure that made our analyses comparable with other studies published from the same site (Dzus & Clark 1998; Dawson & Clark 2000). To test whether timing of egg-laying was associated with spring temperature, we regressed the median clutch initiation date in each breeding season for each species against mean spring temperature.
We used ‘Mayfield logistic regression’ to model daily survival rate of duck nests as a function of weather variables and relative clutch initiation date (Aebischer 1999; Hazler 2004). Each nest represents multiple trials of a binomial process (failure/success) where the number of trials is the number of days the nest was under observation (‘exposure days’). Because nests are found in different stages of the nesting cycle, nests that fail early are least likely be found, which can upwardly bias estimates of nest success (Mayfield 1961, 1975). The Mayfield logistic regression reduces this bias by including exposure days, and also allows the incorporation of individual covariates into the analysis (Hazler 2004). The fate of each nest was categorized as ‘success’ if 1 or more eggs hatched, or ‘failure’ if no eggs hatched, either due to nest predation or abandonment. Note that because of programming considerations, Mayfield logistic regression models nest failure rates, and thus signs of coefficients and intercepts must be reversed to interpret their effects on survival rate (Hazler 2004). We thus converted these mortality rates into daily survival rates (DSR) such that DSR = (1 − daily mortality rate).
We compared five logistic regression models using an information-theoretic approach that considered several alternatives of how nest success, measured as daily nest survival rate, might vary with climate variables, clutch initiation date, and their interactions (Burnham & Anderson 2002). These five models corresponded to five functional forms shown in Fig. 1. Model 1 contained only the weather variables (spring temperature, previous winter's temperature, pond density and previous year's pond density), and assumed no variation with relative clutch initiation date. The next four models included all four weather variables and allowed daily survival rate to vary with relative clutch initiation date, either as a simple linear relationship or as a quadratic relationship. Model 2 assumed a linear relationship between daily survival rate and relative clutch initiation date regardless of weather conditions. Model 3 included spring temperature, clutch initiation date, and an interaction term between spring temperature and relative clutch initiation date. By allowing the relationship between daily survival rate and relative clutch initiation date to vary with spring temperature, this model was a formulation of the mismatch hypothesis. In particular, the mismatch hypothesis predicts that nest success should decline with lay date at a faster rate during warm springs than during cold springs. Model 4 included a quadratic term of relative clutch initiation date and assumed that daily nest survival rate of nests would vary nonlinearly over the breeding season, e.g. daily nest survival could increase in the beginning of the nesting period to a midpoint and then decrease later in the nesting period. Model 5 allowed this quadratic relationship to vary with spring temperature by including terms for interactions between spring temperature and relative clutch initiation date and between spring temperature and the quadratic term for relative clutch initiation date. Because it included an interaction between spring temperature and relative clutch initiation date, this model could also be a formulation of the mismatch hypothesis. Thus, we interpreted support for either Model 3 or Model 5 as support of the mismatch hypothesis, although these two models may suggest different mechanisms.
All models were constructed using proc genmod (SAS Institute 1997). For four species (mallard, blue-winged teal, gadwall and northern shoveler), the most highly parameterized model (Model 5) showed evidence of mild overdispersion. Deviance/DF values (φ) ranged between 1·2 and 1·4, where such values should be close to 1·0 if no overdispersion exists (SAS Institute 1997). To correct for overdispersion, we adjusted the likelihood functions and standard errors of parameters for each model by setting the SCALE option to the square root of the observed value of φ from Model 5 (SAS Institute 1997). For northern pintail, the φ-value from Model 5 was 0·98, so the SCALE option was set to 1 (Burnham & Anderson 2002). For each model, we calculated Akaike's Information Criterion modified for small samples (AICc), the difference in AICc between each model and the model with the minimum AICc (ΔAICc), and the Akaike weight (w) (Burnham & Anderson 2002). Inference about the relationship between nest survival rates and weather variables was based on all five models by using model averaging, where parameter estimates and their variances are calculated as weighted averages over all models (Burnham & Anderson 2002). The Akaike weights, which provide the relative level of support for each model, were used as the weighting factors.
We could not use model averaging to incorporate model selection uncertainty into the effect of relative clutch initiation date. The use of model averaging for β parameters can be problematic as a way to formally include model uncertainty when linear and quadratic forms of the same variable are compared (Blums et al. 2005). Therefore, when considering the role of clutch initiation date on nest success, we relied more heavily on inferences available from model selection, rather than model-averaging. In addition, we used a graphical approach to aid in interpreting results. We calculated predicted values of daily nest survival rates for all species from the five models based on mean values for pond density, previous year's pond density, and winter temperature, and a range of observed values of mean spring temperature and relative clutch initiation date. These values were then averaged over the five models using the Akaike weights as weighting factors to calculate predicted values that accounted for model selection uncertainty. These model-averaged predicted values were then plotted against relative clutch initiation date.