Much of the data that BTO deals with involve counts of individuals. When analysing these data, it is necessary to account for uncertainty in them. Few counts are ever perfect (for example not all individuals are equally detectable), and the larger the count typically the more uncertain it is. It might be tempting to apply the same logic to counts of nest contents, however, the amount of uncertainty around measures of fecundity such as clutch and brood sizes often tends to be lower than that assumed for standard count data. This is due to evolutionary constraints which select against clutch and brood sizes which are either too large or too small, to maximise the number of young produced whilst minimising over-exertion of the adults, whether through rearing or egg production. 

This paper uses an alternative formulation of a count data model, (the Exponentially Weighted Poisson), which accounts for this smaller variability by ‘squeezing’ the uncertainty interval of our estimates. Furthermore, this model also allows for the interval to be squeezed by different amounts either side of our estimated value based upon the data. The extent to which this happens is likely to reflect the different trade-offs in having clutches that are smaller or larger than optimal. This allowed a comparison the size of evolutionary constraints against too low and too high clutch/brood sizes using Nest Record Scheme data for over 50 UK bird species. This showed that generally there was a greater constraint on birds having too many offspring than too few. A comparison was also made between different functional groups of birds, such as hole-nesting passerines, waders and waterfowl. 

For this paper, the authors also created an R package to allow others to more easily implement this modelling framework (ewp). This will also be used in future Nest Record Scheme analyses to produce more accurate uncertainty estimates, which will also help with the accuracy of population models that integrate these data alongside data from BTO’s other monitoring schemes.

Changes in productivity are primary mechanisms via which bird populations change and understanding how these processes operate is key to monitoring their populations in a changing environment. A major component of productivity is fecundity, the number of propagules produced, which for birds is the number of eggs laid (clutch size) and chicks that hatch from these (brood size). There are evolutionary constraints on the size of these fecundity measures and, therefore, variation tends to be smaller than other forms of count data. Using data on clutch and brood sizes for 55 and 52 UK bird species respectively we show these are consistently under-dispersed with respect to the standard Poisson model, which is often used to fit such data. A three-parameter exponentially weighted Poisson (EWP3) model fits substantively better than either a Poisson or under-dispersed variants. We provide an R package to enable easy fitting of such models. The EWP3 is characterized by two dispersion parameters, and , and we suggest that these can quantify evolutionary constraints on incubation. We show that is generally greater than , indicating a greater compression at the right hand end of the distribution. This suggests that the cost of having an extra egg or chick is higher than the cost of having one too few. Although we consider avian reproduction this method should be suitable for any species which has a small number of offspring in each reproductive event.