Embedding Population Dynamics Models in Inference

Increasing pressures on the environment are generating an ever-increasing need to manage animal and plant populations sustainably, and to protect and rebuild endangered populations. Effective management requires reliable mathematical models, so that the effects of management action can be predicted, and the uncertainty in these predictions quantified. These models must be able to predict the response of populations to anthropogenic change, while handling the major sources of uncertainty. We describe a simple ``building block'' approach to formulating discrete-time models. We show how to estimate the parameters of such models from time series of data, and how to quantify uncertainty in those estimates and in numbers of individuals of different types in populations, using computer-intensive Bayesian methods. We also discuss advantages and pitfalls of the approach, and give an example using the British grey seal population.Comment: Published at http://dx.doi.org/10.1214/088342306000000673 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

An experiment of the impact of a neonicotinoid pesticide on honeybees : the value of a formal analysis of the data

This work received funding from the MASTS pooling initiative (The Marine Alliance for Science and Technology for Scotland) and their support is gratefully acknowledged. MASTS is funded by the Scottish Funding Council (Grant reference HR09011) and contributing institutions.Background: We assess the analysis of the data resulting from a field experiment conducted by Pilling et al. (2013) on the potential effects of thiamethoxam on honey bees. The experiment had low levels of replication, so Pilling et al. concluded that formal statistical analysis would be misleading. This would be true if such an analysis merely comprised tests of statistical significance and if the investigators concluded that lack of significance meant little or no effect. However, an analysis that includes estimation of the size of any effects—with confidence limits—allows one to reach conclusions that are not misleading and that produce useful insights. Main Body: For the data of Pilling et al. we use straightforward statistical analysis to show that the confidence limits are generally so wide that any effects of thiamethoxam could have been large without being statistically significant. Instead of formal analysis, Pilling et al. simply inspected the data and concluded that they provided no evidence of detrimental effects and from this that thiamethoxam poses a “low risk” to bees. Conclusions: Conclusions derived from inspection of the data were not just misleading in this case but are unacceptable in principle, for if data are inadequate for a formal analysis (or only good enough to provide estimates with wide confidence intervals) then they are bound to be inadequate as a basis for reaching any sound conclusions. Given that the data in this case are largely uninformative with respect to the treatment effect, any conclusions reached from such informal approaches can do little more than reflect the prior beliefs of those involved.Publisher PDFPeer reviewe

Using distance sampling with camera traps to estimate the density of group-living and solitary mountain ungulates

This work is part of a project initiated under the National Mission for Sustaining the Himalayan Ecosystem (NMSHE) Programme funded by the Department of Science and Technology, Government of India (grant no.: DST/SPLICE/CCP/NMSHE/TF-2/WII/2014[G]). The Miriam Rothschild Travel Bursary Programme provided funding for a 4-week internship for R. Pal with S.T. Buckland at St Andrews University, UK.Throughout the Himalaya, mountain ungulates are threatened by hunting for meat and body parts, habitat loss, and competition with livestock. Accurate population estimates are important for conservation management but most of the available methods to estimate ungulate densities are difficult to implement in mountainous terrain. Here, we tested the efficacy of the recent extension of the point transect method, using camera traps for estimating density of two mountain ungulates: the group-living Himalayan blue sheep or bharal Pseudois nayaur and the solitary Himalayan musk deer Moschus leucogaster. We deployed camera traps in 2017-2018 for the bharal (summer: 21 locations; winter: 25) in the trans-Himalayan region (3,000-5,000 m) and in 2018-2019 for the musk deer (summer: 30 locations; winter: 28) in subalpine habitats (2,500-3,500 m) in the Upper Bhagirathi basin, Uttarakhand, India. Using distance sampling with camera traps, we estimated the bharal population to be 0.51 ± SE 0.1 individuals/km2 (CV = 0.31) in summer and 0.64 ± SE 0.2 individuals/km2 (CV = 0.37) in winter. For musk deer, the estimated density was 0.4 ± SE 0.1 individuals/km2 (CV = 0.34) in summer and 0.1 ± SE 0.05 individuals/km2 (CV = 0.48) in winter. The high variability in these estimates is probably a result of the topography of the landscape and the biology of the species. We discuss the potential application of distance sampling with camera traps to estimate the density of mountain ungulates in remote and rugged terrain, and the limitations of this method.Publisher PDFPeer reviewe

Chronic exposure to neonicotinoids increases neuronal vulnerability to mitochondrial dysfunction in the bumblebee (Bombus terrestris)

This work was funded jointly by the Biotechnology and Biological Sciences Research Council, the Department for Environment, Food and Rural Affairs, the Natural Environment Research Council, the Scottish Government, and The Wellcome Trust, under the Insect Pollinators Initiative (United Kingdom) Grant BB/ 1000313/1 (to C.N.C.).The global decline in the abundance and diversity of insect pollinators could result from habitat loss, disease, and pesticide exposure. The contribution of the neonicotinoid insecticides (e.g., clothianidin and imidacloprid) to this decline is controversial, and key to understanding their risk is whether the astonishingly low levels found in the nectar and pollen of plants is sufficient to deliver neuroactive levels to their site of action: the bee brain. Here we show that bumblebees (Bombusterrestris audax) fed field levels [10 nM, 2.1 ppb (w/w)] of neonicotinoid accumulate between 4 and 10 nM in their brains within 3 days. Acute (minutes) exposure of cultured neurons to 10 nM clothianidin, but not imidacloprid, causes a nicotinic acetylcholine receptor-dependent rapid mitochondrial depolarization. However, a chronic (2 days) exposure to 1 nM imidacloprid leads to a receptor-dependent increased sensitivity to a normally innocuous level of acetylcholine, which now also causes rapid mitochondrial depolarization in neurons. Finally, colonies exposed to this level of imidacloprid show deficits in colony growth and nest condition compared with untreated colonies. These findings provide a mechanistic explanation for the poor navigation and foraging observed in neonicotinoid treated bumblebee colonies.Publisher PDFPeer reviewe

Using density surface models to estimate spatio-temporal changes in population densities and trend

Funding – Centre for Research into Ecological and Environmental Modelling, University of St Andrews and U.S. Geological Survey provided funding for this analysis through a studentship to RJC.Precise measures of population abundance and trend are needed for species conservation; these are most difficult to obtain for rare and rapidly changing populations. We compare uncertainty in densities estimated from spatio–temporal models with that from standard design‐based methods. Spatio–temporal models allow us to target priority areas where, and at times when, a population may most benefit. Generalised additive models were fitted to a 31‐year time series of point‐transect surveys of an endangered Hawaiian forest bird, the Hawai'i ‘ākepa Loxops coccineus. This allowed us to estimate bird densities over space and time. We used two methods to quantify uncertainty in density estimates from the spatio–temporal model: the delta method (which assumes independence between detection and distribution parameters) and a variance propagation method. With the delta method we observed a 52% decrease in the width of the design‐based 95% confidence interval (CI), while we observed a 37% decrease in CI width when propagating the variance. We mapped bird densities as they changed across space and time, allowing managers to evaluate management actions. Integrating detection function modelling with spatio–temporal modelling exploits survey data more efficiently by producing finer‐grained abundance estimates than are possible with design‐based methods as well as producing more precise abundance estimates. Model‐based approaches require switching from making assumptions about the survey design to assumptions about bird distribution. Such a switch warrants carefully considered. In this case the model‐based approach benefits conservation planning through improved management efficiency and reduced costs by taking into account both spatial shifts and temporal changes in population abundance and distribution.Publisher PDFPeer reviewe

Distribution and abundance of long-finned pilot whales in the North Atlantic, estimated from NASS-87 and NASS-89 data

During the summers of 1987 and 1989, large scale transect surveys were conducted throughout the North Atlantic by several national agencies in Denmark (off Greenland), Faroe Islands, Iceland, Norway and Spain (North Atlantic Sightings Surveys, NASS-87 and NASS-89). This paper analyses the pilot whale (Globicephala melas) survey data collected by three Icelandic and one Faroese survey vessel in 1987, and four Icelandic, one Faroese and one Spanish vessel in 1989. Norwegian survey vessels operated north and east of this area in both years, but only five groups (three primary sightings) were observed in 1989 and none in 1987. Furthermore, no sightings were made in the area north and northeast of Iceland, thus indicating that the joint surveys covered the northernmost areas of pilot whale distribution east of 42°W. The area further to the west was not covered in either survey. The coastal European waters between 42-52°N were covered by the Spanish vessel in 1989. Sightings made in 1989 by the Icelandic vessels tended to be at the southernmost boundaries of the survey area. The present data were examined with respect to several potential stratification factors, namely geographic block, Beaufort (i.e. wind speed), vessel and school size, but sample size precluded stratification by all these factors simultaneously. The encounter rate was generally lower in the 1987 survey than in 1989, but the difference was not statistically significant. The total estimate for the 1989 survey, covering a wider area and further to the south than in 1987, was 778,000 (CV=0.295). This is regarded as the best available estimate of the total stock of long-finned pilot whales in the northeastern North Atlantic Ocean, although small numbers occur outside the NASS survey areas. The paper discusses potential biases in the abundance estimates, and the problems of estimating pilot whale abundance from sightings data

Identifying multi-species synchrony in response to environmental covariates

BTS was part funded by EPSRC/NERC grant EP/10009171/1.The importance of multi-species models for understanding complex ecological processes and interactions is beginning to be realised. Recent developments, such as those by Lahoz-Monfort et al. (2011), have enabled synchrony in demographic parameters across multiple species to be explored. Species in a similar environment would be expected to be subject to similar exogenous factors, although their response to each of these factors may be quite different. The ability to group species together according to how they respond to a particular measured covariate may be of particular interest to ecologists. We fit a multi-species model to two sets of similar species of garden bird monitored under the British Trust for Ornithology’s Garden Bird Feeding Survey. Posterior model probabilities were estimated using the reversible jump algorithm to compare posterior support for competing models with different species sharing different subsets of regression coefficients.There was frequently good agreement between species with small asynchronous random effect components and those with posterior support for models with shared regression coefficients; however, this was not always the case. When groups of species were less correlated, greater uncertainty was found in whether regression coefficients should be shared or not.The methods outlined in this paper can test additional hypotheses about the similarities or synchrony across multiple species that share the same environment. Through the use of posterior model probabilities, estimated using the reversible jump algorithm, we can detect multi-species responses in relation to measured covariates across any combination of species and covariates under consideration. The method can account for synchrony across species in relation to measured covariates, as well as unexplained variation accounted for using random effects. For more flexible, multi-parameter distributions, the support for species-specific parameters can also be measured.Publisher PDFPeer reviewe

Point process models for spatio-temporal distance sampling data from a large-scale survey of blue whales

Distance sampling is a widely used method for estimating wildlife population abundance. The fact that conventional distance sampling methods are partly design-based constrains the spatial resolution at which animal density can be estimated using these methods. Estimates are usually obtained at survey stratum level. For an endangered species such as the blue whale, it is desirable to estimate density and abundance at a finer spatial scale than stratum. Temporal variation in the spatial structure is also important. We formulate the process generating distance sampling data as a thinned spatial point process and propose model-based inference using a spatial log-Gaussian Cox process. The method adopts a flexible stochastic partial differential equation (SPDE) approach to model spatial structure in density that is not accounted for by explanatory variables, and integrated nested Laplace approximation (INLA) for Bayesian inference. It allows simultaneous fitting of detection and density models and permits prediction of density at an arbitrarily fine scale. We estimate blue whale density in the Eastern Tropical Pacific Ocean from thirteen shipboard surveys conducted over 22 years. We find that higher blue whale density is associated with colder sea surface temperatures in space, and although there is some positive association between density and mean annual temperature, our estimates are consitent with no trend in density across years. Our analysis also indicates that there is substantial spatially structured variation in density that is not explained by available covariates.Comment: 33 pages 19 figure