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After preprocessing the data, methods consisted of spatial analyses to map areas at risk of conflict; statistical analyses to identify the most important factors affecting lion and elephant population numbers; economic analyses to estimate the EAA of building and maintaining mitigation fences in areas under severe and high risk of conflict, and fragmentation analyses to assess the impact of fences on migratory mammal species. We describe each step in detail below (see Supplementary Fig. 2 for a flowchart of the analysis). All spatial data were converted to vectors for analysis to reduce commission errors (when a species is mistakenly thought to be present) when converting the species-range maps from vector to raster. Data preprocessing was carried out using the open source database PostgreSQL 11.4 (https://www.postgresql.org/about/) with the GIS extensions of PostGIS 2.5 (https://postgis.net/); conflict mapping and range fragmentation analyses used PostgreSQL 11.4 and PostGIS 2.5, and Python v. 3.7.060; statistical and economic analyses used R v. 3.6.061; sensitivity analyses used PostgreSQL 11.4 and PostGIS 2.5, and Python v. 3.7.060 and R v. 3.6.061.PreprocessingHuman pressuresHuman pressure layers were independently generated from this study. We used Gridded Population of the World Version 4 (GPWv4) as a layer for human population density62. GPWv4 is a minimally modelled data set consisting of estimates of human population (number of persons per raster grid cell) based on non-spatial population data (i.e., tabular counts of population listed by administrative area) and spatially explicit administrative boundary data. Population input data are collected at the most detailed spatial resolution available from the results of the 2010 round of Population and Housing Censuses. The input data are then extrapolated to 2020 using calculated growth rates to produce future population estimates. A proportional allocation gridding algorithm, utilizing ~13.5 million national and subnational administrative units, assigned population counts to 30 arcsecond (~1 km at the equator) grid cells. The population density rasters were created by dividing the population count raster for a given target year by the land-area raster.We used the most recent version of the Gridded Livestock of the World database63, reflecting the compiled and harmonized subnational livestock distribution data for 2010, to extract information on cattle density. The data set provides global population densities of cattle, buffaloes, horses, sheep, goats, pigs, chickens, and ducks in each land pixel at a spatial resolution of 0.083333 decimal degrees (~10 km at the equator). Detailed livestock census statistics are mined from agricultural yearbooks or through direct contacts with ministries or statistical bureaus. The census statistics are usually found in the form of numbers per administrative unit that must be linked to corresponding geographic information system boundaries. Densities are estimated in each census polygon by dividing the number of animals from the census by the surface area of the administrative unit polygon (estimated in an Albert equal-area projection), corrected by a mask excluding unsuitable areas. Livestock densities were then extracted from the subnational census data and were used as the dependent variable in Random Forest models to estimate a density value in each pixel, based on raster predictor variables.We used spatially detailed crop maps available from the Copernicus Global Land Cover map at ~0.001° (~100 m) resolution64. The land-cover map is a discrete map with ten continuous cover fractions (nine base land-cover classes and seasonal water) to provide spatial information about land for a diversity of applications, including biodiversity conservation. Cropland (as percentage of 100 m pixel that is covered by cropland) refers to cultivated and managed agriculture, but does not include perennial woody crops that are classified under the appropriate forest or shrub land-cover type64. Cropland also refers to both irrigated and rainfed agriculture. The land-cover map was generated by compiling the 5-daily PROBA-V multi-spectral image data with a Ground Sampling Distance of ~0.001° as the primary earth observation data and PROBA-V UTM daily multi-spectral image data with a Ground Sampling Distance of ~0.003° (~300 m) as the secondary earth observation data. Next, the 5-daily PROBA-V 100 m and daily 300 m datasets were fused using a Kalman filtering approach. The global overall accuracy of the product for the base year 2015 was calculated through an independent pre-validation and reached 80%.Species-range mapsUpdated range maps showing current distribution for lions and elephants were provided by the International Union for Conservation of Nature (IUCN) Cat and African Elephant Specialist Groups65. In addition to the range maps, the specialist groups provided information on the number of African lions (2018) and elephants (2016) within sites where they are still extant. We also obtained species-range maps for all terrestrial mammal species in orders Cetartiodactyla, Perissodactyla, Primates, and Carnivora occurring in Africa from the IUCN Red List portal (www.iucnredlist.org/). Mammal species in these orders include migratory mammal species (e.g., the common wildebeest Connochaetes taurinus), which might be negatively affected by mitigation fences, e.g., by potentially blocking migratory routes.Protected areasThe data on protected areas were based on the May 2019 release of the World Database on Protected Areas66 (retrieved from http://www.protectedplanet.net). To prevent overestimation of the area coverage of protected areas caused by overlapping designations, we merged polygons into a single layer. We only included in the analysis IUCN categories Ia (Strict Nature Reserve), Ib (Wilderness Area), II (National Park), III (Natural Monument or Feature), and IV (Habitat/Species Management Area), because we wanted to prevent fences from excluding people from protected areas that had been modified by the interaction of nature and people over time (e.g., V, Protected Landscape/Seascape).Mapping potential risk of conflictA database on the spatial distribution of conflict locations between humans and lions and elephants is not available across Africa. We therefore mapped the most prominent factors known to affect conflict: human population density (for both lion and elephant), crop raiding (elephants), and cattle killing (lions)8. Furthermore, spatial modelling of range contractions in carnivores showed that contractions were significantly more likely in regions with high rural human population density, cattle density, and/or cropland4. Therefore, we only retained areas where human, cattle, and crop densities were in the first decile (in our case, the first decile is the decile with the highest human population, crop, and cattle densities) by PostgreSQL/PostGIS. Using only the highest decile likely resulted in a conservative map of spatial conflict.We further classified areas at the highest potential conflict into low, moderate, high, or severe risk of conflict. Specifically, areas at severe risk of conflict are those where the highest human population, crop, and cattle densities all overlap; areas at high risk of conflict are those with overlaps between the highest densities of human population and either crops or cattle; areas at moderate risk of conflict are the areas where the highest crop and cattle densities overlap; and areas at low risk of conflict are those with only one human pressure, i.e., the highest human population, or crop, or cattle density. The remainder was considered as being at no risk of conflict, as it did not meet any of the above criteria, but note the conservative nature of our analysis (see above).The lion and elephant range maps and the protected area layer were intersected to select all protected areas that contain parts of lion and elephant range and/or were adjacent to the species-range maps. The identified protected areas were then merged with the species-range maps to create a new extended range layer (see for an example in Supplementary Fig. 1). These extended range maps were used (i) to identify potential areas where lions and elephants could be restored, and (ii) to avoid interrupting ecological processes (e.g., migrations) and/or causing unintended consequences (e.g., fragment populations) to other biodiversity in neighbouring protected areas.We then identified areas at risk of conflict by intersecting the extended range map layer for lions and elephants with the classified conflict map. In all cases, the intersections were carried out so that the classified conflict areas were either adjacent to, or within a distance of 10 km from, the edge of the extended range map layer. We set this distance to consider the wide-ranging behaviour of both lions and elephants, to account for the fact that conflict decreases at greater distances from protected area boundaries37,38, and to account for the fact that future human pressures will likely increase before conservation actions take place2.We assessed how robust our results were to commission (where human pressure is mistakenly assumed to exist) and omission (where human pressure is mistakenly assumed to be absent) errors in the human pressure maps by carrying out a sensitivity analysis that randomly varied the distances between the extended range maps and the human pressure maps. We first used Latin hypercube sampling, which is a form of sampling used to reduce the number of runs necessary for a Monte Carlo simulation to achieve a reasonably accurate random distribution67, to randomly vary 100 times the distance values between the extended range and human pressure maps. Specifically, we divided the low, moderate, high, and severe conflict lines into 100 m segments, calculated the minimum distance for each segment to human pressure within a 10, 20, and 30 km buffer distance from the edge of the extended range map layer, and then randomly varied that distance 100 times across ±10% of the value. We then averaged the resulting 100 randomly created distance values for each segment and identified which segments fell outside of the analyzed buffer distances of 10, 20, and 30 km. We tested for 20 and 30 km buffer distances, as we wanted to assess the variability of the fencing distance to different buffer sizes. We also estimated the certainty of lion and elephant presence by identifying segments of the perimeter of the range maps of lion and elephant that overlapped with protected areas. We did this as we had information on certain presence of both species from within protected areas, as opposed to areas extending outside of protected areas.Statistical analysesWe used an information theoretic approach68 and Bayesian information criterion to calculate statistical models. We used generalized linear mixed models with a negative‐binomial error distribution to account for over-dispersed count data and a log‐link function to examine factors affecting lion (n = 77) and elephant (n = 191) population sizes in Africa. Generalized linear mixed models were fitted with both random and fixed effects, to capture the data structure. Country was included as a random intercept to represent the hierarchical structure of the data. All variables listed in Supplementary Table 8 were fitted as fixed effects, i.e., with constant regression coefficients across countries. The site-specific variables were calculated only for sites where lions and elephants are currently present and not for the extended ranges. For transboundary sites that stretch across countries, we used the value for Gross Domestic Product, Conservation expenditure, and the Ibrahim Index of African Governance, for the country making the largest area contribution to the site. We compared and ranked models using the Bayesian information criterion68. To avoid multicollinearity among variables, we only selected variables with the strongest effect on population numbers that correlated at r 0.7 was selected as an input into the modelling process. We assessed each model’s relative probability, using Bayesian information criterion weights and the structural goodness-of-fit from the percentage of deviance explained by the model. We determined the magnitude and direction of the coefficients for the independent variables with multi-model averaging implemented in the R package glmulti69. The relative importance of each predictor variable was measured as the sum of the weights over the six top‐ranked models with Bayesian information criterion values closer to that of the best model containing the parameter of interest. Finally, we used a 10-fold cross-validation (a bootstrap resampling procedure using 1000 iterations) to assess the predictive ability of the top-ranked model.Range fragmentation analysesWe assessed how the proposed mitigation fences affected species-range connectivity by calculating the perimeter length-to-area ratio for mammal species in orders Cetartiodactyla, Perissodactyla, Primates, and Carnivora, whose ranges were identified as intersecting with areas at severe risk of conflict. Minimizing the perimeter length-to-area ratio is an important method of optimizing protected area design, resulting in compact reserves with high connectivity that can enhance persistence of the species. The smaller the ratio, the greater the clumping and connectivity of the species ranges. Specifically, we calculated the ratios of perimeter length to area for the ranges of 20 migratory mammalian species (i) under current conditions without fences and (ii) under future conditions where the identified mitigation fences would pass through their ranges. In the latter case, we used a 20 m buffer around the identified fences to account for further habitat clearance due to maintaining clearances around the fences for management purposes.Economic analysesWe used EAA to estimate the return on investment of building and maintaining mitigation fences to reduce cattle loss and crop damage. EAA calculates the constant annual cash flow generated by a project over its lifespan if it were an annuity and the annuity can then be compared to other projects of similar or different lifespan. Therefore, the measure potentially provides an important means for funders/donors to compare different investment opportunities. EAA is calculated by dividing the NPV of a project by the present value of annuity factor39. We started by calculating NPV in countries with areas at severe and high risk of conflict as:$${{NPV}}={sum }_{i}^{n}frac{{R}_{i}}{{left(1+dright)}^{i}}-Z$$
(1)
where ({R}_{i}) is net cash flow, (d) is the discount rate specific to each country (Supplementary Table 9), n is the number of time periods, (i) is the cash flow period, and (Z) is the initial investment of building the fences. NPV was calculated over a 10-year investment period. ({R}_{i}) was calculated as:$${R}_{i}=B-C$$
(2)
where (B) is the economic benefit derived from mitigation fences and (C) is the cost of maintaining mitigation fences. The economic benefits of mitigation fences for countries with severe risk of conflict refer to the potential reduction in cattle loss (for lions) and crop damage (for elephants) derived from building fences:$$B=L+E$$
(3)
where (L) represents the economic benefits of reducing cattle loss and (E) measures the economic benefits of reducing crop damage. For countries with high risk of conflict, the benefit ((B)) is derived from one or the other, i.e., (B) = (L) or (B) = (E).$$L=v * w * P$$
(4)
where (v) is the number of cattle that are not lost because of the presence of fences, (w) is the average weight in kg of adult cattle in that country, and (P) is the price of meat per kg paid to producers in that country in 2017 (data can be downloaded from http://www.fao.org/faostat/en/#data/PP). (v) was calculated as the percentage of total cattle present in the 10 km buffer adjacent to severe and high conflict areas, which could potentially be killed, based on published estimates across Africa45. Estimates range from 0.8 to 2.6% of cattle losses, and we decided to use a conservative 1% loss in the analysis (see below for how we accounted for uncertainty in model parameters). (w) was based on the average weight of an adult cow with estimates available at a regional level (west Africa: 262 kg; central Africa: 281 kg; east Africa: 283 kg; and southern Africa: 339 kg)70.$$E=left(d * Aright) * y * P$$
(5)
where (d) is the percentage of crop area damaged by elephants; data are taken from published estimates (ranging from 0.2 to 4% and we used a conservative 1% in the analysis)44; (A) is the total area in km2 available as crops in the 10 km buffer adjacent to the areas at severe and high risk of conflict; (y) is the yield (ton/km2) for the crop known to be targeted by elephants (cassava, maize, millet, banana, sorghum, groundnuts)44, which covered the largest area size in that country in 2017 (data calculated from: http://www.fao.org/faostat/en/#data/PP); and (P) is the price per ton paid to producers for that crop in that country in 2017 (data can be downloaded from http://www.fao.org/faostat/en/#data/PP). Although there might be several crops available within the buffer, this information is currently not available at the continental scale. Therefore, we decided to use the most common cultivated crop known to be targeted by elephants in each country.The cost of maintaining mitigation fences ((C)) was calculated as:$$C=f * c$$
(6)
where f is the fence length in that country and (c) is the cost for maintaining the fence. We obtained cost estimates of building (Z) and maintaining ((c)) the fences from Pekor et al.33. We used the median estimated current cost of USD 9522 per km for building fences and the median stated annual budget cost of USD 487 per km for adequate fence inspection and maintenance. This is the most up-to-date information validated through peer review on the costs (converted to 2017 USD) across Africa33. Cost estimates varied across surveyed conservation areas because of fence height and materials but included relevant costs of electrification and predator-proof structures33. The data were collected from 29 partially fenced ( More

The author wishes to thank N. Haan, G. P. Robertson and N. Haddad for their valuable comments. Financial support was provided by USDA/NIFA (awards 2019-67012-29595 and 2015-68007-23133), the US National Science Foundation’s Long-term Ecological Research Program (award 1637653), the US Department of Energy, Office of Science, Office of Biological and Environmental Research (awards DESC0018409 and DE-FC02-07ER64494), and Michigan State University AgBioResearch. More