Random field calibration for the bare carrying capacity of bats in Africa

Abstract

Understanding the population dynamics of reservoirs of zoonotic diseases, such as bats, is a crucial first step to predict and prevent potential spillover of deadly viruses like Ebola. Due to the limited data on bats across Africa, their density and migrations can be studied with probabilistic numerical models based on samples of the ecological bare carrying capacity. To this purpose, the bare carrying capacity will be modeled as a random field and its statistics calibrated with the available data. The most popular methods for the calibration of the correlation of a random field are not applicable in the case of unevenly spaced data. We propose to use a least square regression model to estimate the autocorrelation function and remedy the problem of unevenly spaced data. The residuals (i.e., the differences between the predicted and actual values) of the regression model determining the bare carrying capacity were found to be weakly homogeneous across Africa. Correlation lengths of the residuals were found to be different along longitude and latitude. Along the longitude, the correlation length is 1.78 degrees (approximately 200 km) whereas along the latitude it is 1.40 degrees (approximately 150 km), which is expected as the climate and other parameters determining the carrying capacity change more rapidly along the latitude. The bare carrying capacity of bats was found to be more dense in central Africa. This is due to the fact that climatic and environmental conditions are more suitable for the survival of bats.

Random field calibration with data on irregular grid for regional analyses: A case study on the bare carrying capacity of bats in Africa

“…For this reason, such model was selected for estimating $$$ \mu $$$. Equation () shows the final model and Figure 5a provides its pictorial representation (see folder S3 in Mursel et al, 2023). The blue circles represent the included variables, and the edges represent the included cross terms; the size (i.e., the area) of the circles and the thickness of the edges are proportional to the weight of each term.…”

“…These functions were used in the SRM algorithm and samples representing the residuals were generated. Gaussian samples were translated into the non‐Gaussian distribution (Figure 6) calibrated empirically (see folder S1 in Mursel et al, 2023). Some samples superimposed to $$$ \hat{\mu} $$$ are presented in Figure 11.…”

“…Similarly, artificial observations were added in general areas of known presence (Fiorillo et al, 2018; IUCN, 2015). The result is a set of observations $$$ {K}_{\mathrm{obs}} $$$ at sparse locations $$$ \left({\tilde{x}}_1,{\tilde{x}}_2\right) $$$ (see folder S3 in Mursel et al, 2023).…”

“…Environmental and geographical data (i.e., features) were gathered using the Google Earth Engine tool to access the databases from the NASA Land Processes Distributed Active Archive Center (LP DAAC) at the USGS Earth Resources Observation and the Science (EROS) Center, Sioux Falls, South Dakota (NASALP‐DAAC, 2022). For this study, we considered eight variables: enhanced vegetation index ($$$ EVI $$$, dimensionless), precipitation ($$$ PRE $$$, in mm/5 days), daily air temperature ($$$ TMP $$$, in °C), land cover index ($$$ LND $$$, dimensionless), ground elevation ($$$ ELV $$$, in m), human population density ($$$ POP $$$, in individuals/km 2 ), latitude ($$$ LAT $$$, in °), and longitude ($$$ LON $$$, in °) (see folder S1 in Mursel et al, 2023). It should be noted that all the variables but $$$ LND $$$ are quantitative.…”

“…Similarly, artificial observations were added in general areas of known presence (Fiorillo et al, 2018;IUCN, 2015). The result is a set of observations K obs at sparse locations x1 , x2 (see folder S3 in Mursel et al, 2023). Environmental and geographical data (i.e., features) were gathered using the Google Earth Engine tool to access the databases from the NASA Land Processes Distributed Active Archive Center (LP DAAC) at the USGS Earth Resources Observation and the Science (EROS) Center, Sioux Falls, South Dakota (NASALP-DAAC, 2022).…”