We live in an increasingly uncertain world. Therefore, when we model environmental processes of interest, it is vital to account for the inherent uncertainties in our analyses and ensure that this information is communicated to relevant parties. Whilst the use of complex statistical models to estimate quantities of interest is becoming increasingly common in environmental sciences, one aspect of uncertainty that is frequently overlooked is that of model uncertainty. Much of the research I conduct considers this additional aspect of uncertainty quantification; that is not just uncertainty in the quantities of interest, but also in the models that we use to estimate them.
An example of this is in a paper recently published in Ecology and Evolution (Swallow et al., 2016), which looks at how different species of birds that we commonly see in our gardens respond to the same environmental factors (or covariates). Some of the species have declined rapidly over the past 40 years, whilst others have remained stable or even increased in number. Possible drivers of these changes that have been suggested include increases in predators, changes in climate and availability of natural food sources. Statistically speaking, we try to understand and quantify changes in observed numbers of birds by relating them to changes in measured environmental quantities that the birds will be subjected to, such as numbers of predators, weather variables, habitat quality etc. Most previous analyses have modelled each of the species observed at many different geographical locations (or monitoring sites) independently of each other, and estimated the quantities of interest completely separately, despite the fact that all these species share the same environment and are subject to the same external influences. So how do we go about accounting for the fact that similar species may share similar population drivers?
This essentially constitutes a model uncertainty problem – that is, which parameters should be shared across which species in our statistical model and which parameters should be distinct?
If we were to consider two different species and use two different environmental factors to explain changes in those species, say habitat type and average monthly temperature, there are four possible models to consider. That is,
This can easily be extended to a higher number of species and covariates.
There is also inevitably going to be some aspects of variability shown by some of the species that we cannot account for through the quantities we have measured. We account for this using site-specific random effects, which explain variability that is linked to a specific monitoring site, but which is not accounted for by the environmental covariates in the model. Again, we would usually assume this is a single quantity representing the discrepancy between what we have accounted for using our measured covariates and what is ‘left over’. Following on from work of previous authors (Lahoz-Monfort et al., 2011), we again split this unexplained variation into two – unexplained variation that is common to all species and unexplained variation that is specific to a single species. The ratio of these two quantities can give us a good idea of what measurements we may be missing. Is it additional environmental factors that are wide-ranging in their effects or is it something relating to the specific ecology of an individual species?
In the paper, we apply our method to a large dataset spanning nearly 40 years, collected as part of the British Trust for Ornithology’s Garden Bird Feeding Survey. We selected two groups of similar species commonly found in UK gardens during the winter. For ecological reasons, we would expect the species within the two groups to show similar traits, so they act as ideal study species for detecting synchrony in responses to environmental factors. Whilst most the results were consistent with those from single-species models (e.g. Swallow et al., 2015), studying the species at an ecosystem level also highlighted some additional relationships that it would be impossible to study under more simplistic models. The results highlight that there is unsurprisingly a large degree of synchrony across many of these species, and that they share many of the traits and drivers of population change. The synchronies observed in the results corresponded to both significant positive or negative relationships with covariates, as well as those species that collectively show no strong relationship with a given environmental factor. There is, however, more to the story and some of the species showed strong differences in how they respond to external factors. Highlighting these differences may offer important information on how best to halt or reverse population declines.
The results from our analyses showed the importance of considering model uncertainty in statistical analyses of this type, and that by incorporating relevant uncertainties, we can improve our understanding of the environmental processes of interest. Incorporating more data into the analysis will help in further constraining common or shared parameters and reduce uncertainties in them. It also allows us to guide and improve future data collection procedures if we can gain a better understanding of what is currently missing from our model.
Blog written by Dr Ben Swallow, a Postdoctoral Research Associate, studying Ecological and environmental statistics in the School of Chemistry.
References
Lahoz-Monfort, J. J., Morgan, B. J. T., Harris, M. P., Wanless, S., & Freeman, S. N. (2011). A capture-recapture model for exploring multi-species synchrony in survival. Methods in Ecology and Evolution, 2(1), 116–124.
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, 58(2), 357–371
Swallow, B., King, R., Buckland, S. T. and Toms, M. P. (2016). Identifying multispecies synchrony in response to environmental covariates. Ecology and Evolution, 6(23), 8515–8525
An example of this is in a paper recently published in Ecology and Evolution (Swallow et al., 2016), which looks at how different species of birds that we commonly see in our gardens respond to the same environmental factors (or covariates). Some of the species have declined rapidly over the past 40 years, whilst others have remained stable or even increased in number. Possible drivers of these changes that have been suggested include increases in predators, changes in climate and availability of natural food sources. Statistically speaking, we try to understand and quantify changes in observed numbers of birds by relating them to changes in measured environmental quantities that the birds will be subjected to, such as numbers of predators, weather variables, habitat quality etc. Most previous analyses have modelled each of the species observed at many different geographical locations (or monitoring sites) independently of each other, and estimated the quantities of interest completely separately, despite the fact that all these species share the same environment and are subject to the same external influences. So how do we go about accounting for the fact that similar species may share similar population drivers?
This essentially constitutes a model uncertainty problem – that is, which parameters should be shared across which species in our statistical model and which parameters should be distinct?
If we were to consider two different species and use two different environmental factors to explain changes in those species, say habitat type and average monthly temperature, there are four possible models to consider. That is,
|
Model
|
Habitat type
|
Temperature
|
No parameters
|
|
1
|
Shared
|
Shared
|
2
|
|
2
|
Distinct
|
Shared
|
3
|
|
3
|
Shared
|
Distinct
|
3
|
|
4
|
Distinct
|
Distinct
|
4
|
This can easily be extended to a higher number of species and covariates.
There is also inevitably going to be some aspects of variability shown by some of the species that we cannot account for through the quantities we have measured. We account for this using site-specific random effects, which explain variability that is linked to a specific monitoring site, but which is not accounted for by the environmental covariates in the model. Again, we would usually assume this is a single quantity representing the discrepancy between what we have accounted for using our measured covariates and what is ‘left over’. Following on from work of previous authors (Lahoz-Monfort et al., 2011), we again split this unexplained variation into two – unexplained variation that is common to all species and unexplained variation that is specific to a single species. The ratio of these two quantities can give us a good idea of what measurements we may be missing. Is it additional environmental factors that are wide-ranging in their effects or is it something relating to the specific ecology of an individual species?
In the paper, we apply our method to a large dataset spanning nearly 40 years, collected as part of the British Trust for Ornithology’s Garden Bird Feeding Survey. We selected two groups of similar species commonly found in UK gardens during the winter. For ecological reasons, we would expect the species within the two groups to show similar traits, so they act as ideal study species for detecting synchrony in responses to environmental factors. Whilst most the results were consistent with those from single-species models (e.g. Swallow et al., 2015), studying the species at an ecosystem level also highlighted some additional relationships that it would be impossible to study under more simplistic models. The results highlight that there is unsurprisingly a large degree of synchrony across many of these species, and that they share many of the traits and drivers of population change. The synchronies observed in the results corresponded to both significant positive or negative relationships with covariates, as well as those species that collectively show no strong relationship with a given environmental factor. There is, however, more to the story and some of the species showed strong differences in how they respond to external factors. Highlighting these differences may offer important information on how best to halt or reverse population declines.
The results from our analyses showed the importance of considering model uncertainty in statistical analyses of this type, and that by incorporating relevant uncertainties, we can improve our understanding of the environmental processes of interest. Incorporating more data into the analysis will help in further constraining common or shared parameters and reduce uncertainties in them. It also allows us to guide and improve future data collection procedures if we can gain a better understanding of what is currently missing from our model.
Blog written by Dr Ben Swallow, a Postdoctoral Research Associate, studying Ecological and environmental statistics in the School of Chemistry.References
Lahoz-Monfort, J. J., Morgan, B. J. T., Harris, M. P., Wanless, S., & Freeman, S. N. (2011). A capture-recapture model for exploring multi-species synchrony in survival. Methods in Ecology and Evolution, 2(1), 116–124.
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, 58(2), 357–371
Swallow, B., King, R., Buckland, S. T. and Toms, M. P. (2016). Identifying multispecies synchrony in response to environmental covariates. Ecology and Evolution, 6(23), 8515–8525
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| Figure 1. Blue tits show a highly synchronous response with great tits, and to a lesser degree coal tits, to their surrounding environment. |
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| Figure 2. Male house sparrow feeding on fat balls. Whilst they show some synchrony in their response to environmental factors, they appear to be subject to a differing ecology to the other two species they were compared with. |