Stochastic modelling and analysis of wildfowl anatidae monitoring data from the wetland bird survey

British wetlands are used by many different resident and migratory wildfowl species for some or all of the winter months. The Wetland Bird Survey (WeBS) is a scheme set up with the objectives of assessing the size of waterbird populations, determining trends in numbers and distribution and assessing the importance of individual sites for waterbirds as part of the requirements of international conservation conventions and directives. Over three thousand sites around Britain are included in the survey, and volunteers have been undertaking counts of wildfowl species for over forty years. One of the key features of WeBS is that sites are surveyed at monthly intervals over the winter season. The analyses for the project used data for twenty-six wildfowl (sub-)species for winter seasons from 1966/67 to 2006/07. The limitations and bias of the sampling methods currently used in the Wetland Bird Survey, are examined. It is shown that post-selection of sites by the proportion of missing values, as is done currently, introduces an addi­tional bias that impacts on reported population trends. A new site selection criteria that minimises additional bias is proposed. WeBS wildfowl data comprise monthly counts of populations that change over each win­ter season due to short-term immigration and emigration. Ideas and methods from the held of Functional Data Analysis are used to explore phenological changes (spatiotem-poral variation in the seasonal patterns) due to changing species distributions and to select months where the seasonal patterns are most stable. The Underhill method, of imputing missing values using a site-year-month multiplicative model and the EM algorithm to generate an annual Underhill Index, is reviewed. It is shown that the model is a poor fit to most wildfowl WeBS data sets. Currently WeBS abundance indices are calculated using the Underhill Index, which treats each species’ seasonality as stationary, using the arithmetic mean over months and sites to derive a population index. Using ideas from economics, various alternative indexing approaches to constructing a single yearly index from the monthly counts are compared with simulated examples and WeBS data. The results have implications beyond the Wetland Bird Survey, to other wildlife moni­toring schemes; particularly those that monitor populations which show strong seasonal dynamics