Blog written by Ben Swallow. Read the full paper here.
Birds (amongst other ecological taxa) are consistently subjected to a variety of external environmental factors. Some species are responding to those external pressures more successfully than others, with trajectories varying across species as well as across spatial and temporal scales. In order to understand which of these factors are the principal drivers of those changing population trajectories, and hence implement beneficial conservation measures, it is important to develop statistical models that are able to account for those varying factors across spatial and temporal hierarchies.
Our paper expands on the statistical methodology developed in Swallow et al. (2015), applying the approach to a range of 10 avian species commonly found in UK gardens and contrasting two slightly different model structures to data from the British Trust for Ornithology’s (BTO) Garden Bird Feeding Survey (GBFS). The GBFS counts maxima of each species feeding on provisioned food in each of 26 weeks over the winter period. The aim of the methodology is to link observed changes in each of 10 species of birds to a higher range of environmental variables than has previously been accomplished. Statistically speaking, we wish to test for impacts of as many potentially relevant variables as possible, with the caveat that only a subset of these would be expected to impact any given species.
The modelling framework is conducted in a hierarchical Bayesian framework, accounting for correlations between and within both sites and years in the statistical model. We utilise a relatively underused statistical distribution, the Tweedie distribution, which is able to account for the excessive exact zeros inherent in the data. The reversible jump algorithm deployed allows us to move between models with different subsets of covariates, spending a larger proportion of iterations in models with covariates and associated slope parameters that match the observed counts of birds at that site and year. Subsequently we get a quantitative measure of how much evidence we have to support an impact of a given variable on each species.
In addition, we wished to test the impact of a change in model formulation, namely whether conclusions were similar when we looked at the rate of change in environmental variables instead of the absolute value of those variables. Conclusions from both frameworks were largely similar but also highlighted some additional interesting hypotheses.
One particular recurring hypothesis associated with declines observed in some small songbirds has been a return of Eurasian sparrowhawks to regions they had been wiped out from due to pesticide use during the 1950s and 60s. We found a consistent negative impact on three species, namely house sparrow, blue tit and starling. Our results also suggested an association between the level of impact of sparrowhawks on a given prey species and the prevalence of that species in the sparrowhawk’s diet. It is important to note, however, that while a statistically important impact of sparrowhawks on house sparrow and blue tit was detected, the practical difference in terms of reduction in numbers of these species is far from enough to account for the observed declines. It is also difficult to determine in this case whether the associated impact is a causal reduction in overall numbers or relates to these two species avoiding feeding areas where higher densities of sparrowhawks were observed. Furthermore, even if the former is the true case, previous large-scale studies of breeding densities (e.g. Newson et al. (2010)) failed to find significant impact of sparrowhawks on their prey species. This may suggest that the observed impact on house sparrows and blue tits detected in our paper corresponds to those individuals that would not subsequently form part of the breeding population due to other limiting factors.
Our results highlight a variety of other potential drivers of population changes. Ground frost was consistently found as an important factor in numbers of birds visiting gardens. Higher amounts of ground frost were associated with higher numbers of birds visiting garden feeders, but this became a negative association when annual change in ground frost was used. This may suggest that whilst birds will be encouraged to visit garden feeders when weather is poor, very severe changes between years can cause negative population impacts.
Whilst this research adds to the understanding of wide-scale impacts of environmental factors on garden birds, further developments in this area are inevitably to involve the creation of joint multispecies models, where species that share the same environment niche are modelled simultaneously. Nature does not exist in isolation and hence ideally its components should not be modelled independently. Our previous work on these data published in the same journal (Swallow et al. 2016) introduced a formal multispecies extension to the model presented in this paper, whilst in Jones-Todd et al. (2018), we developed a joint spatio-temporal model for house sparrow, collared dove and sparrowhawk. One of the principal difficulties with these types of models is the increasing complexity they introduce, which from a statistical point of view equates to an increased computational demand. There are therefore two complimentary priorities for research in this area. Firstly, we must construct increasingly realistic models to infer the complex and high-dimensional interactions inherent in these communities, harnessing the increase in data that we have observed over the past decade. With this, we also need to develop increasingly efficient statistical methodologies and inferential frameworks that allow us to gain the necessary understandings of these ecosystems in realistic computational timeframes.
- Jones-Todd, C. M., Swallow, B., Illian, J. B. and Toms, M. P. (2018) ‘A spatio-temporal multi-species model of a semi-continuous response.’ (JRSS(C), 67(3), 705–722)
- Newson, S.E., Rexstad, E.A., Baillie, S.R., Buckland, S.T. & Aebischer, N.J. (2010) Population change of avian predators and grey squirrels in England: is there evidence for an impact on avian prey populations? (Journal of Applied Ecology, 47, 244–252).
- Swallow, B., King, R., Buckland, S. T. and Toms, M. P. (2016) ‘Identifying multi-species synchrony in response to environmental covariates.’ (Ecology and Evolution, 6(23), 8515–8525)
- Swallow, B., Buckland, S. T., King, R. and Toms, M. P. (2015) ‘Bayesian Hierarchical Modelling of Continuous Non-negative Longitudinal Data with a Spike at Zero: An Application to a Study of Birds Visiting Gardens in Winter.’ (Biometrical Journal Special Issue, 58(2), 357–371, Special)