Species distribution models: A comparison of statistical approaches for livestock and disease epidemics

Abstract

In livestock industries, reliable up-to-date spatial distribution and abundance records for animals and farms are critical for governments to manage and respond to risks. Yet few, if any, countries can afford to maintain comprehensive, up-to-date agricultural census data. Statistical modelling can be used as a proxy for such data but comparative modelling studies have rarely been undertaken for livestock populations. Widespread species, including livestock, can be difficult to model effectively due to complex spatial distributions that do not respond predictably to environmental gradients. We assessed three machine learning species distribution models (SDM) for their capacity to estimate national-level farm animal population numbers within property boundaries: boosted regression trees (BRT), random forests (RF) and K-nearest neighbour (K-NN). The models were built from a commercial livestock database and environmental and socio-economic predictor data for New Zealand. We used two spatial data stratifications to test (i) support for decision making in an emergency response situation, and (ii) the ability for the models to predict to new geographic regions. The performance of the three model types varied substantially, but the best performing models showed very high accuracy. BRTs had the best performance overall, but RF performed equally well or better in many simulations; RFs were superior at predicting livestock numbers for all but very large commercial farms. K-NN performed poorly relative to both RF and BRT in all simulations. The predictions of both multi species and single species models for farms and within hypothetical quarantine zones were very close to observed data. These models are generally applicable for livestock estimation with broad applications in disease risk modelling, biosecurity, policy and planning.

Fig 1. Spatial variogram of farm-level RMSPE, using Euclidean distance between farm centroids.

The solid line gives the variogram of the observed data, with the dotted lines indicating the 95% confidence intervals of the null distribution obtained by random permutation of RMSPE between the farm locations.

Fig 2. Maps of the actual livestock units (LSU) and the modelled region level livestock predictions for three regions.

Maps show results from Random Forests and Boosted Regression Trees for Waikato, Canterbury and Wellington for region predictions. The gradient colour axis is on a log scale for display purposes. KNN results are not shown due the extremely poor fit of the models relative to other model types.

Fig 3. Maps of the actual livestock units (LSU) and the modelled zone level livestock predictions for three regions.

Maps show results from Random Forests and Boosted Regression Trees for Waikato, Canterbury and Wellington for zone level predictions. The gradient colour axis is on a log scale for display purposes.

Fig 4. Scatterplot of the observed against the predicted farm-level.

Results are plotted by region. Total quarantine zone LSU was calculated by summing the observed and predicted values for all farms within the 3km quarantine zone. Cattle results are not shown as plots they are a subset of LSU.

Fig 5. Scatterplot of the observed against the predicted total quarantine zone LSU.

Results are plotted by region. Total quarantine zone LSU was calculated by summing the observed and predicted values for all farms within the 3km quarantine zone. Cattle results are not shown as plots they are a subset of LSU.

Fig 6. Relative influence of predictor variables from random forest models for LSU and cattle.

Plots show the increase in MSE of predictions if the variable of interest were randomly permuted. See S1 Table for full variable names and descriptions.