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Well-established statistical methods exist to estimate variation in a number of key demographic rates from field data, including life-history transition probabilities and reproductive success per attempt. However, our understanding of the processes underlying population change remains incomplete without knowing the number of reproductive attempts individuals make annually; this is a key demographic rate for which we have no satisfactory method of estimating. Using census data to estimate this parameter from requires disaggregating the overlying temporal distributions of first and subsequent breeding attempts. We describe a Bayesian mixture method to estimate the annual number of reproductive attempts from field data to provide a new tool for demographic inference. We validate our method using comprehensive data on individually-marked song sparrows Melospiza melodia, and then apply it to more typical nest record data collected over 45 years on yellowhammers Emberiza citrinella. We illustrate the utility of our method by testing, and rejecting, the hypothesis that declines in UK yellowhammer populations have occurred concurrently with declines in annual breeding frequency.

This study investigates, for the first time (to our knowledge) for any animal group, the evolution of phylogenetic differences in fibre digestibility across a wide range of feeds that differ in potential fibre digestibility (fibre to lignin ratio) in ruminants. Data, collated from the literature, were analysed using a linear mixed model that allows for different sources of random variability, covariates and fixed effects, as well as controlling for phylogenetic relatedness. This approach overcomes the problem of defining boundaries to separate different ruminant feeding styles (browsers, mixed feeders and grazers) by using two covariates that describe the browser-grazer continuum (proportion of grass and proportion of browse in the natural diet of a species). The results indicate that closely related species are more likely to have similar values of fibre digestibility than species that are more distant in the phylogenetic tree. Body mass did not have any significant effect on fibre digestibility. Fibre digestibility is estimated to increase with the proportion of grass and to decrease with the proportion of browse in the natural diet that characterizes the species. We applied an evolutionary model to infer rates of evolution and ancestral states of fibre digestibility; the model indicates that the rate of evolution of fibre digestibility accelerated across time. We suggest that this could be caused by a combination of increasing competition among ruminant species and adaptation to diets rich in fibre, both related to climatically driven environmental changes in the past few million years.