57 3.3 Modeling nesting abundance 3.3.1 Nest tracks persistence over time Although nesting trends can be detected from nest counts, an understanding of what proportion of the true abundance these counts represent is key to more accurately assess demographic progressions (SWOT Scientific Advisory Board 2011). Without an estimate of detection probability, i.e. the proportion of nests recorded on a given survey event, a simple nest count is not as reliable an index of population status or trends (Royle and Dorazio 2008). In order to assess this parameter with high precision, we have developed an empiric protocol that allows us to determine the average duration for which a nest track remains detectable for an observer. It is based on the fact that the marks generated by females during nesting activities persist in the sand for a given period of time, which may vary according to weather conditions and to their wind, rain and wave exposure (Metcalfe et al. 2015). Nests were marked on the spot with wooden poles on the first detection, then systematically prospected in following survey events. A status of their detection state was set by the observers, from good (coded as 1) to poor (uncertain or no detection, coded as 0). These data have been analyzed with a generalized linear mixed model using Penalized QuasiLikelihood with a binomial distribution and a logit link using the function glmmPQL of the ‘MASS’ R package (Venables and Ripley 2002). Age of the track in days and season (centered to December) were included as fixed factors and ID of the track has been included as a random factor with an autocorrelation structure of order 1 to take into account that the detection state (1 or 0) at time t is dependent on the detection state at time t-∆t. If the track was not detectable at time t, there are more chance that it is still not detectable at time t-∆t, except for false negative or positive cases. Confidence interval is not available for GLMM-AR1 model and we used 9999 bootstraps to estimate the uncertainty of the predictions. 3.3.2 Model for nesting seasonality Collected data were processed in a multiple-step pipe. The aim is to convert partial fieldwork data into an estimate of total seasonal nesting intensity through the establishment of the nesting phenology parameters and aggregation over multiple seasons. Assuming that t is an ordinal date (October 1st is 1 and September 30th in the following year is 365 or 366) and that Nt is the observed number of nests for this date, the number of nests deposited per night is modeled using the following set of equation:
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