Prediction Intervals in Nonlinear Regression

By treating the nonlinear model as if it were linear in the parameterization θ in the neighbourhood of the least squares estimate θ, we construct two-sided nominally-q-prediction intervals by applying the usual linear model theory. The derivation of the truncated series expansion of the expected coverage of the prediction intervals at a feasible value of the parameter vector is described. The quadratic approximation of the expected coverage is then obtained for a two-parameter nonlinear model. Finally we show how we may construct the prediction intervals when a certain type of nonlinear transformation of the parameter vector has been applied.     

Reciprocal Fitness Feedbacks Promote the Evolution of Mutualistic Cooperation

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Climate change in our backyards: the reshuffling of North America's winter bird communities

Much of the recent changes in North American climate have occurred during the winter months, and as result, overwintering birds represent important sentinels of anthropogenic climate change. While there is mounting evidence that bird populations are responding to a warming climate (e.g., poleward shifts) questions remain as to whether these species‐specific responses are resulting in community‐wide changes. Here, we test the hypothesis that a changing winter climate should favor the formation of winter bird communities dominated by warm‐adapted species. To do this, we quantified changes in community composition using a functional index – the Community Temperature Index (CTI) – which measures the balance between low‐ and high‐temperature dwelling species in a community. Using data from Project FeederWatch, an international citizen science program, we quantified spatiotemporal changes in winter bird communities (n = 38 bird species) across eastern North America and tested the influence of changes in winter minimum temperature over a 22‐year period. We implemented a jackknife analysis to identify those species most influential in driving changes at the community level and the population dynamics (e.g., extinction or colonization) responsible for these community changes. Since 1990, we found that the winter bird community structure has changed with communities increasingly composed of warm‐adapted species. This reshuffling of winter bird communities was strongest in southerly latitudes and driven primarily by local increases in abundance and regional patterns of colonization by southerly birds. CTI tracked patterns of changing winter temperature at different temporal scales ranging from 1 to 35 years. We conclude that a shifting winter climate has provided an opportunity for smaller, southerly distributed species to colonize new regions and promote the formation of unique winter bird assemblages throughout eastern North America.