Human influences shape the first spatially explicit national estimate of urban unowned cat abundance

A framework to estimate unowned cat abundance

In the following sections, we describe the application of an IAM, a hierarchical modelling approach, which estimates unowned cat abundance in discrete geographical units from spatially replicated citizen data, in combination with expert data obtained from 162 sites across five urban areas in England. In doing so, we explored key predictors of unowned cat abundance. We then estimated unowned cat abundance across urban areas in England and the UK with respect to the modelling results. We used WinBUGS⁵³ and R⁵⁴ for all data analysis via the R package R2Winbugs⁵⁵ and QGIS⁵⁶ for plotting maps.

Data collation and preparation

A database of unowned cat count data were compiled from citizen science data and expert data collected throughout a one-year period that began between 2016 and 2018 across five urban areas in the UK. Areas included Beeston, Bradford, Bulwell, Dunstable & Houghton Regis and Everton (Fig. 1). These data were collected as part of Cat Watch, a community partnership project set-up by Cats Protection, a UK feline welfare charity, to control cat numbers^39,57. Two distinct forms of citizen science data were collected: (1) the first consisted of an initial cross-sectional random-sample door-to-door survey carried out with approximately 10% of households. At that stage, residents were asked how many cats they know of locally and how many they think were owned in the form of a multiple-choice question with the following options; none, 1–2, 3–4, 5–9, 10 or more, from which the number of unowned cats were derived. When a range was selected the central value was taken; for ten or more we used 15 (the average from reports when 10 or more was specified was 14.7). Location data were available for 3101 survey responses, within which there were estimates of 4411 unowned cats; (2) throughout the project, residents were able to report unowned cats in their area directly via social media or through a mobile application. During the study period, 877 reports were received reporting on the locations of 2790 unowned cats. These data were collected according to the study protocol approved by University of Bristol Faculty of Health Science Research Ethics Committee approval number 38661. All methods were performed in accordance with the relevant guidelines and regulations. Informed consent was secured in advance of survey participation. Residents provided report data voluntarily, with no identifying information collected. No experimental protocols were used.

Expert data were obtained from an experienced community team (CT) that recorded when and where an unowned cat was found or confirmed the lack of presence of an unowned cat. The CT carried out extensive door-to-door surveillance across both reported hot spot and cold spot areas. These data are considered of higher quality, due to the ability of the CT to correctly identify an unowned cat and with no risk of double counting the same individual. Unowned cats can be either stray or feral. Protocols to accurately identify a stray cat included; scanning for a microchip, attaching a paper collar to notify potential owners, advertising online, door-to-door notifications, local posters and contacting other animal welfare organisations, including veterinary practices. If no owner was found during this process it was identified as unowned. Feral cats were more likely to be identified via behavioural means; as they have not been socialised to humans, they will be more fearful and will not approach humans⁴⁷. If they have already been neutered they may also have their left ear “tipped”. During the study period, there were 601 records from the CT, reporting on the location of 605 confirmed unowned cats. All three of these data sources provided detailed location data (postcodes and/or addresses) enabling geo-referencing of unowned cat location data.

To account for duplicate sightings, the citizen science data required clustering to account for neighbours in close-proximity reporting the same cats. There is limited understanding of urban unowned cats in the UK, however studies of urban unowned cats in other areas indicate home range sizes between 3.7 and 10.4 ha for urban areas^58,59. Studies on unowned cats in the UK indicate that home ranges vary between 10 and 15 hectares⁶⁰. We assume a maximum 20 ha home range, equivalent to a circular area with a diameter of 504 m. Consequently, we apply a 500 m cluster function in R that derives clusters of cat sightings that are within 500 m of each other. The individual records were maintained as replicate counts within each cluster. Clustering of 500 m has also been shown to provide reasonable estimates in an urban area with high expert coverage (91%), where you would not anticipate cat numbers to be significantly inflated above those observed by experts²⁵. In the absence of expert data, the effect of violating this assumption (i.e. reporting them as replicate sightings when they are not) would result in lower estimates of cats. However, where expert data is available, the effect of violating this assumption would result in bias in the observation parameters, not estimates of the cats themselves, which are also inferred from the expert data that do not contain duplicate sightings.

Data analysis

We applied an integrated abundance model (IAM) within a Bayesian framework that combines count data across sites from two forms of citizen science data and expert data²⁵. The hierarchical structure of the IAM enables it to borrow strength from the sites with expert data to inform detection biases of citizen science data, including detection probability of an unowned cat and false positives due to misidentification of an owned cat as unowned. The goal of the inference is to estimate the abundance of unowned cats within each site and explore covariates as predictors of population density.

Specifically, observed citizen science counts at each site i and during each replicate survey j are linked to true site-specific population sizes (N_i) via a detection probability (p) and the expected number of misidentifications (m). We apply a Poisson distribution to account for additional stochasticity in spatial replicates not accounted for in the systematic biases (m and p). Each type of citizen science data is modelled separately to account for the different biases in collection methods between the survey data (y) and report data (u):

Expert consensus (w_i) was available on the abundance of individuals for 104 sites and linked to true population sizes via a Poisson observation error.

We additionally assume that where expert counts are available they are accurate at the level of presence or absence.

whereby z_i is a binary measure of occurrence, with each of the i sites occupied or not, that is modelled as a Bernoulli random variable determined by occupancy probability (Ω). True site-specific population sizes (N_i) are therefore a function of whether a site is occupied or not and a site-specific mean λ_i. When expert data on occurrence can be inferred from expert consensus this was included in z_i.

We extend the original development of an IAM²⁵ described above to model the log the site specific mean (λ_i) as a linear function of covariates (x) using the following linear relationship:

where x_j, I are the values of the jth covariate across sites i, βs are the regression coefficients for each covariate and ɛ is the residual site-specific variation providing estimates of unexplained variance. We also fitted a model without covariate effects to gain an estimate of total site-specific variance. The proportional reduction in the residual site-specific variation component is a measure for the proportion of the site-specific variance in abundance explained by that covariate or covariates.

To assess the credibility of covariate effects we calculated the probability that their effects were positive [P(β > 0)] or negative [P(β < 0)].

We used priors for each parameter as follows: uniform distributions U(0,1) for detection probability and occupancy; uniform distributions (0,5) for misidentification parameter; normal distribution N(0,100) for mu, uniform distribution (0,3) for standard deviation of the random effect. Preliminary simulations were assessed for convergence of the chains by visually checking mixing of the chains and more formally using the Brooks–Gelman–Rubin criterion (( overset{lower0.5emhbox{$smash{scriptscriptstylefrown}$}}{r} )⁶¹). Following the initial trials for each simulation we ran three chains of 20 000 with a burn‐in of 10,000 for each analysis, yielding a sample size of 30,000 iterations, from which full posteriors were stored. The IAM that included quintiles as a covariate took longer to converge, necessitating a longer model run of 100,000, a burn-in of 60,000 and retained every 4th value to yield a similar sample of 30,000 iterations.

Validation of IAM model

To check the validity of our inference with specific focus on our regression coefficients that are subsequently used to predict population sizes we used six approaches to model diagnostics.

First, we simulated datasets structured according to the raw data and parameterised using the model estimates to check model performance under similar scenarios and with the presence of covariates. We explore performance in terms of accuracy (proportion of simulations that capture the true value in their credible intervals) and bias (tendency for posterior distributions to lie above or below true values).

Second, we performed general Bayesian model-checking procedures including convergence of MCMC chains, which were assessed using the Gelman–Rubin statistic and values less than 1.1 were interpreted as indicating convergence. Additionally, we compared a null model, with just a random effects term, with a model containing the covariates. In this way, remaining variances after accounting for covariates were known. We calculated the proportion of variance explained by the covariates when modelled independently and combined.

Third, influence of variation across study sites on model fit for regression parameters was assessed using five-fold cross-validation where the model was refitted five times, each time withholding all data from one study site until all sites had been held out once.

Fourth, to assess the influence of the different types of citizen science data on the regression parameter we re-ran the analyses separately to contain just one type of citizen science data (survey IAM and report IAM) alongside the expert data. Only sites where data were available were included, this amounted to 157 sites in the survey IAM (five sites were excluded) and 134 sites in the report IAM (28 sites were included). The sites included in the survey IAM spanned the full range of IMD deciles (1–10) and human population densities (238–15,129 people per km²). Whereas, the sites in the report IAM only spanned the full range of IMD deciles (1–10), with population densities not incorporating the lowest and the highest density areas (390–13 847 people per km²).

Fifth, we assessed how prior specifications for regression parameters influenced the results. We varied the parameter range between 10 magnitudes lower to two magnitudes higher than the original by refitting the IAM with three different prior distributions for the regression parameters, the original (B ~ uniform (−5, 5)), a first alternative with a more narrow distribution (B ~ uniform (−0.5, 0.5)) and a second alternative with a wider distribution (B ~ uniform (−10, 10)).

Finally, we tested drivers of unowned cat abundance by fitting generalised linear models with logarithmic link and quasi-Poisson error that has known significance testing procedures.

Quantification of unowned cat abundance in England

We estimated the unowned cat population in the urban areas of England, accounting for uncertainty in our estimates, by multiplying data-derived posterior distributions of regression coefficients by deciles of deprivation and standardised human population density from urban areas in England. The calculation may be expressed as:

where μ is the posterior distribution of the intercept from the IAM, β_{IMD deciles} and β_{human pop dens}, are the posterior distributions of the regression parameters of IMD and standardised population density respectively, and IMD and PD are the true deprivation and human density values for the area, as sourced from the ONS (see supplementary table 2). Additionally, we incorporate a scaling parameter (SP), which is the area of the site relative to the area in the study.

At the smallest geographic unit we focussed our estimates on ONS defined lower Super Output Areas (LSOAs), which are the small area geographies for England designed to be socially homogeneous with a relatively even population size with 1500 residents on average, but they vary in their area size and consequently population density. All urban LSOAs in England (defined as towns, cities and conurbations with more than 10,000 residents according to Communities and Local Government guidelines) were classified into decile groups according to the level of deprivation and assigned human population density, which were standardised. Using this approach, we predicted the abundance and density (per km²) of unowned cat populations for 27,246 urban LSOA’s in England. The total unowned cat population was calculated as a summation across all sites. For each calculation we used the full posterior distributions from the IAM output, in doing so we maintain proper estimates of uncertainty in our predictions and present the mean values and 95% credible intervals for all results.

Quantification of unowned cat abundance in UK

We applied the same calculation described above to predict the number of unowned cats across urban areas in the UK. However, small-area statistical geographies differ between countries in the UK, defined by their respective national statistics agencies. Lower layer super output areas (LSOAs) are defined in England and Wales, super output areas (SOAs) in Northern Ireland and data zones in Scotland. LSOAs have populations of around 1500 people, while SOAs are slightly larger with typical populations of around 2000 people. Scottish data zones are smaller with populations of 500 to 1000 people.

Urban–Rural classifications differ across different countries in the UK. Consequently, using the ONS definition, we only included data zones in Scotland and super output areas in N. Ireland as urban areas if they were part of settlements of 10,000 people. This equated to 530 out of 890 SOA in Northern Ireland and 4909 out of 6976 data zones in Scotland. These were combined with 28,549 urban LSOA in England and Wales. Population densities for these areas were sourced from national statistics agencies (Supplementary Table 2).

Measures of socioeconomic deprivation differ across country borders in the UK and naively comparing across these measures can result in problems in analysis²⁷. In the absence of a consistent IMD decile across countries, we apply a previously published consistent measure of deprivation, in the form of adjusted IMD scores²⁷, based on 2011 indices. These quintiles of deprivation provided the means to inform on unowned cat abundance across the UK.

Validation of predictions

First, we tested the influence of different model assumptions on national population estimates. This included: (1) the influence of London on estimates; (2) the inclusion of areas with high population density and (3) the influence of the different measures of deprivation (Deciles vs. Quintiles) on England estimates, where both data are available. Second, we test the impact of using outcomes from the GLM approach vs. the IAM. Finally, in the absence of any prior estimates of unowned cats in these regions we tested the validity of population predictions by determining whether cat population density derived from predictions were comparable with those derived from the original IAM analysis of the raw data. We compared the overlap of credible intervals and correlation for cat density at three different scales: (1) across 44 LSOA where there was also spatial coverage of the raw data; (2) at the scale of the study town or city and (3) the average density across all study sites.

Source: Ecology - nature.com