^{1}

^{2}

^{3}

^{1}

^{4}

^{1}

^{2}

^{5}

^{2}

^{2}

^{6}

^{7}

^{1}

^{1}

^{1}

^{8}

^{3}

^{3}

^{2}

^{2}

^{9}

^{2}

The authors have declared that no competing interests exist.

Broad scale population estimates of declining species are desired for conservation efforts. However, for many secretive species including large carnivores, such estimates are often difficult. Based on published density estimates obtained through camera trapping, presence/absence data, and globally available predictive variables derived from satellite imagery, we modelled density and occurrence of a large carnivore, the jaguar, across the species’ entire range. We then combined these models in a hierarchical framework to estimate the total population. Our models indicate that potential jaguar density is best predicted by measures of primary productivity, with the highest densities in the most productive tropical habitats and a clear declining gradient with distance from the equator. Jaguar distribution, in contrast, is determined by the combined effects of human impacts and environmental factors: probability of jaguar occurrence increased with forest cover, mean temperature, and annual precipitation and declined with increases in human foot print index and human density. Probability of occurrence was also significantly higher for protected areas than outside of them. We estimated the world’s jaguar population at 173,000 (95% CI: 138,000–208,000) individuals, mostly concentrated in the Amazon Basin; elsewhere, populations tend to be small and fragmented. The high number of jaguars results from the large total area still occupied (almost 9 million km^{2}) and low human densities (< 1 person/km^{2}) coinciding with high primary productivity in the core area of jaguar range. Our results show the importance of protected areas for jaguar persistence. We conclude that combining modelling of density and distribution can reveal ecological patterns and processes at global scales, can provide robust estimates for use in species assessments, and can guide broad-scale conservation actions.

Broad scale population estimates are desired for setting conservation goals and priorities (e.g. for IUCN assessments) [

When direct censuses are not possible, population estimates may be derived from known species distributions and spatial variation in population densities. However, as densities are usually highly variable in space, a large number of density studies would be needed to reliably estimate population size; similarly precise distributions of species are rarely known. An alternative approach would be to model density variation and distribution and combine spatial predictions of both models to derive population numbers at a given moment. Species distribution models have become a powerful tool in animal conservation. They can help to estimate current species range, identify factors determining species distribution, and indicate ecological corridors [

In our study we used the profusion of recently published density estimates to gain insight into the factors affecting the density and distribution of the jaguar at a global scale. To increase our sample size for the analysis of spatial variation in population densities, we proposed a method to rescale the estimates obtained with non-spatial methods to the level of densities obtained with spatial models. Using widely available data derived from satellite imagery, we modelled variation in jaguar density across the species’ range. Based on a second, independent presence-absence dataset, we also developed a distribution model and calculated the probability of jaguar occurrence across the Americas. With this approach, we separately revealed mechanisms and factors that determine population densities and distribution of jaguars. Finally, we combined these results in a hierarchical framework to estimate the current total population of jaguar across the entire species’ range.

Our study area covered the entire historical range of the jaguar in South and North America (17.6 million km^{2} [

Indicated are historical and current jaguar range (see

Jaguar densities were obtained using the published results of 117 camera-trap studies, conducted in 80 different study sites between 2002 and 2014. Our sources included studies published in peer reviewed journals, theses and dissertations, as well as government and non-governmental agency reports (

Spatial and non-spatial methods differ in how they calculate densities. To produce a density estimate, non-spatial methods calculate the total number of jaguars and divide that by an estimate of the sampled area, which consists of the study area plus a buffer. This buffer is usually calculated as half the mean maximum distance moved by individuals within the study (hereafter referred as 1/2MMDM) [

Of the 117 studies analysed here, 59 used non-spatial methods, 53 used both spatial and non-spatial methods simultaneously, and 5 studies presented only spatial methods. We treated 8 studies in which no jaguars were recorded by camera traps as zero density estimates (

We modelled jaguar density based on 17 candidate spatial variables (_{MEAN}), (b) mean gross primary productivity (GPP_{MEAN}), (c) mean normalized difference vegetation index (NDVI_{MEAN}), and (d) mean enhanced vegetation index (EVI_{MEAN}). Each of these indices reflects a slightly different component of vegetation productivity with potentially different effects on herbivore populations [

All covariate raster data were standardized to a 1 km × 1 km pixel. We used this resolution to account for the jaguars’ selection for certain habitats, (e.g., those related to water) [

We fit all subset models to the density data with the explanatory variables and selected the best model based on Bayesian Information Criterion (BIC) [^{2} is the coefficient of determination, t_{i} is the value of t-statistic for variable _{res} is the number of degrees of freedom for residuals [

We projected our top density model across the whole of North—South America.

All spatial analyses were conducted using ArcGIS 10.1 (ESRI Redlands CA, USA). All statistical analyses were performed with SYSTAT 13.0 (Systat Software, Inc., San Jose, CA, USA) and SPSS ver. 20 (IBM SPSS Statistics).

We gathered jaguar presence/absence data from 4 sources. First, we used 1,266 jaguar records collected by the Wildlife Conservation Society in 1999 and 2006, and published by Zeller [

We fit logistic regression models to the presence-absence data and used the same set of candidate predictive variables as for the density model (^{2} pixel being occupied [

We could not derive population numbers directly from our density model because researchers conducting camera trapping studies tend to select less disturbed study areas, where they expect to find jaguars and thus avoid areas with high human impacts. Therefore the predictions of our density model likely represent potential rather than actual jaguar densities. However, human impacts were accounted for in our occurrence model, which was developed with both presence as well as absence points (i.e. where jaguars have been extirpated). To generate a range-wide estimate of the jaguar population, we combined density and occurrence models. The rationale of our method is based on the assumption that variation in potential population density and probabilities of occurrence at large geographic scales are driven by different mechanisms. We assumed that variation in potential density in carnivore populations results from the strong dependence of home range sizes on productivity factors and this relationship is strong even in highly human impacted conditions [

To estimate the total jaguar population size we combined our density and occurrence models in a hierarchical modelling framework using programs R and JAGS, version 4.2.0 (R2Jags) [

Our estimate is hierarchical in that an estimate of density is conditional on the cell first being occupied. We defined the occurrence of jaguars in any given cell (_{i} is the probability of jaguar occurrence derived from logit g(_{1-k}: and the corresponding regression coefficients _{1-k}
_{1-k} of our top density model:
^{2}:

To validate our method of estimating the global population, we simulated a dataset using similar sampling effort and modelling techniques as in the empirical dataset [^{2} cells that makeup historical jaguar range. We then assigned to each row a randomly generated jaguar density and values of six randomly generated continuous and one binomial covariates corresponding to covariates from our density and occurrence models. Finally, to match our sampling level we randomly sampled 0.05% of the cells for density, and 2% of the cells for occurrence. We then used the same MCMC process as above to estimate the simulated population level. We replicated this simulation procedure 100 times. In each replicate, new “population” and covariate values were generated, sampled, and modelled. From the output, we could estimate bias and accuracy of our method [

Jaguar densities estimated by non-spatial methods (½MMDM) ranged from 0–18.3 per 100 km^{2} and were generally greater than SCR estimates (0–9.0 per 100 km^{2}). A regression of SCR and ½MMDM (SCR = 0.07391 + 0.54761 * 1/2MMDM) (^{2} = 0.76, SE = 1.06, N = 53). We used this model to predict SCR density estimates for studies reporting only non-spatial methods, essentially increasing our sample size and standardizing density estimates.

Data points represent 53 published studies in which both non-spatial and spatial density estimates were applied (

Based on the original (58 studies, 36 study sites) and reconstructed (59 studies, 44 study sites) SCR density estimates we developed a set of regression models explaining spatial variation in jaguar population density. Our top model included four variables: mean annual temperature, mean annual net primary productivity (NPP_{MEAN}), standard deviation of annual net primary productivity (NPP_{SD}), and a categorical variable distinguishing North and South America (^{2} = 0.45, SEE = 1.37, N = 80), and had robust regression coefficients (_{MEAN} had the greatest ability to explain variability in jaguar density, changing the R^{2} value by 24% and 14% respectively, as indicated by semi-partial correlations sr_{i}^{2} (

Presented are ten best-fitting multiple linear regression models based on 21 spatial variables (three anthropogenic variables, 13 environmental variables, an indicator variable for North and South America (NA-SA), and four variables measuring camera trap effort); definitions of the predictive variables are in

Model No | Predictive variables | BIC | ΔBIC | BIC weight | R^{2} |
Significance of covariates |
---|---|---|---|---|---|---|

1 | _{MEAN}_{SD} |
298.65 | 0.00 | 0.26 | 0.45 | All significant |

2 | TEMP, NPP_{MEAN}, NPP_{SD}, NA-SA, N_CamStations |
299.78 | 1.13 | 0.14 | 0.48 | N_CamStations not significant |

3 | TEMP, EVI_{MEAN} |
300.22 | 1.57 | 0.12 | 0.38 | All significant |

4 | TEMP, EVI_{MEAN}, N_CamStations |
300.61 | 1.96 | 0.10 | 0.41 | N_CamStations not significant |

5 | TEMP, NPP_{MEAN}, NPP_{SD}, EVI_{MEAN}, NA-SA |
300.64 | 1.99 | 0.09 | 0.47 | EVI_{MEAN} not significant |

6 | TEMP, EVI_{MEAN}, NA-SA |
301.22 | 2.57 | 0.07 | 0.40 | All significant |

7 | TEMP, NPP_{MEAN}, EVI_{MEAN}, NA-SA |
301.37 | 2.72 | 0.07 | 0.43 | All significant |

8 | TEMP, NPP_{MEAN}, NPP_{SD}, EVI_{MEAN}, NDVI_{SD}, NA-SA |
301.51 | 2.86 | 0.06 | 0.49 | NDVI_{SD} not significant |

9 | TEMP, NPP_{MEAN}, NPP_{SD}, EVI_{MEAN}, NA-SA, N_CamStations |
301.63 | 2.98 | 0.06 | 0.49 | N_CamStations and EVI_{MEAN} not significant |

10 | TEMP, NPP_{MEAN}, NPP_{SD}, EVI_{MEAN}, NDVI_{SD}, NA-SA, N_CamStations |
302.94 | 4.29 | 0.03 | 0.51 | N_CamStations and NDVI_{SD} not significant |

Density studies were conducted between 2002 and 2014. Bias and the standard error of the regression coefficients of the bootstrapped model (10,000 replications) are shown; definitions of the predictive variables are in

Effect | Coefficient | Standard Error | t | sr_{i}^{2} |
p-Value | bias | Standard Error |
---|---|---|---|---|---|---|---|

CONSTANT | -8.07747 | 1.92 | -4.20 | < 0.001 | -0.11 | 1.74 | |

TEMP | 0.38911 | 0.07 | 5.76 | 0.24 | < 0.001 | <0.01 | 0.05 |

NPP_{MEAN} |
0.00136 | <0.01 | 4.40 | 0.14 | < 0.001 | <0.01 | <0.01 |

NPP_{SD} |
0.01026 | <0.01 | 2.68 | 0.05 | 0.009 | <0.01 | <0.01 |

NA-SA | -1.07356 | 0.33 | -3.27 | 0.08 | 0.002 | <0.01 | 0.34 |

The spatial prediction of our top model across the Neotropics indicated that jaguars can reach the highest population densities in the most productive, humid areas and the lowest densities in dry areas or in higher altitudes (^{2}), and especially for the areas at the base of the Andes in Peru (≥3 jaguars/100 km^{2}). High densities were also predicted for the Yucatan Peninsula and eastern coast of Central America (≥3 jaguars/100 km^{2}). Our model predicts a clear gradient of declining jaguar potential density with distance from the equator, resulting in low densities at the northernmost and southernmost extremes of historical range. Low or zero densities in high altitude, mountainous regions including the Andes, were predicted (^{2} (

Densities were predicted with our top regression model based on four environmental variables (mean annual temperature, NPP_{MEAN}, NPP_{SD}, North America–South America code). See also

In contrast to the density model, our best supported jaguar occurrence model contained both anthropogenic and environmental variables (^{2} = 0.624, AUC = 0.912; sensitivity = 0.83, specificity = 0.85, N = 3,377). All coefficients had measurable effect sizes and biases were small (

Models were fitted with 17 spatial variables (three anthropogenic variables, 13 environmental variables, and North America–South America code); definitions of the predictive variables are in ^{2} and the area under the receiver operating characteristic curve (AUC ROC) are provided. Bold indicates the best model used for spatial prediction of jaguar occurrence.

Model No | Predictive variables | Nagel-kerke R^{2} |
AUC ROC | BIC | ΔBIC | BIC |
---|---|---|---|---|---|---|

2,616.45 | 0 | 0.9997 | ||||

2 | TEMP, CANOPY, HPDENLG, HFOOTP, PREC, PRAR | 0.619 | 0.910 | 2,632.92 | 16.47 | 0.0003 |

3 | TEMP, CANOPY, HPDENLG, HFOOTP, NA-SA, PRAR | 0.617 | 0.910 | 2,639.92 | 23.47 | 0.0000 |

4 | TEMP, CANOPY, HPDENLG, NA-SA, PREC, PRAR | 0.615 | 0.908 | 2,649.89 | 33.44 | 0.0000 |

Definitions of the predictive variables are in

Parameter | Estimate | Standard Error | Z | p-Value | Odds ratio | Bias | _{BOO} |
---|---|---|---|---|---|---|---|

CONSTANT | -6.26094 | 0.47 | -13.25 | < 0.001 | -0.033 | < 0.001 | |

TEMP | 0.27835 | 0.02 | 15.84 | < 0.001 | 1.03 | 0.001 | < 0.001 |

PREC | 0.00046 | <0.01 | 5.45 | < 0.001 | 1.00 | <0.001 | < 0.001 |

CANOPY_{MEAN} |
0.05481 | <0.01 | 18.49 | < 0.001 | 1.06 | <0.001 | < 0.001 |

HPDENLG | -0.56917 | 0.05 | -11.20 | < 0.001 | 0.57 | 0.003 | < 0.001 |

HFOOTP | -0.03480 | 0.01 | -6.32 | < 0.001 | 0.97 | <0.001 | < 0.001 |

PRAR | 1.19062 | 0.13 | 9.06 | < 0.001 | 3.29 | 0.005 | < 0.001 |

NA-SA | -0.68730 | 0.14 | -4.96 | < 0.001 | 0.50 | 0.002 | < 0.001 |

Spatial projection of the top occurrence model predicted the highest probabilities of jaguar occurrence in the Amazon basin from the eastern foothills of the Andes to the Atlantic coast and along the eastern coast of Central America (^{2}, and that with a probability of > 0.9 was 6.2 million km^{2}. The posterior standard deviations of the predicted probabilities were generally low. The spatial distribution of these standard deviations indicated that our predictions of jaguar occurrence were least variable for the Amazon basin and somewhat less certain for some parts of Central America (

Probability values were predicted by our top occurrence model that included seven spatial variables (mean annual temperature, annual precipitation, forest cover, human density, human footprint index, area protection status, and North America—South America code). See also

In our analysis of simulated data sets, all mean estimates resulting from the hierarchical modelling process were within +/-19.05% of the true value (range 0.01 to 19.05%), with a mean absolute error (MAE) of 6.60%. This indicates that on average the mean population estimate predicted by our model would be within 6.60% of the true simulated population (

Applying our hierarchical model to our jaguar dataset resulted in a mean posterior estimate of 173,151 jaguars (95% CI: 138,148–208,137) within the current range of the species (8.968 million km^{2}), (^{2} (

Results obtained from 100,000 iterations of a hierarchical model of jaguar occurrence and density; dashed vertical lines represent a 95% credible interval.

Adjusted jaguar population densities were estimated using a hierarchical model combining our density and occurrence models and thus accounting for human impacts.

Population estimates and 95% credible intervals for each country were derived from hierarchical combination of the best fitting jaguar occurrence and density models based on anthropogenic and environmental variables. Calculations were performed for the area of current jaguar range (Figs

NR | Country | Current jaguar range area (thousands km^{2}) |
Mean estimate of jaguar population size (95% Credible Interval) | Mean density N/100 km^{2} |
---|---|---|---|---|

1 | Brazil | 4,583.6 | 86,834 (66,865–106,105) | 1.89 (1.46–2.31) |

2 | Peru | 739.6 | 22,210 (17,843–26,788) | 3.00 (2.41–3.62) |

3 | Colombia | 872.8 | 16,598 (11,724–21,311) | 1.90 (1.34–2.44) |

4 | Bolivia | 743.1 | 12,845 (10,260–15,449) | 1.73 (1.38–2.08) |

5 | Venezuela | 589.5 | 11,592 (8,761–14,334) | 1.97 (1.49–2.43) |

6 | Guyana | 208.8 | 4,356 (3,233–5,462) | 2.09 (1.55–2.62) |

7 | Suriname | 142.7 | 3,190 (2,275–4,081) | 2.24 (1.59–2.86) |

8 | Ecuador | 93.7 | 1,969 (1,586–2,359) | 2.10 (1.69–2.52) |

9 | French Guiana | 82.2 | 1,602 (1,097–2,105) | 1.95 (1.33–2.56) |

10 | Paraguay | 233.3 | 1,589 (708–2,497) | 0.68 (0.30–1.07) |

11 | Argentina | 76.1 | 314 (107–550) | 0.41 (0.14–0.72) |

13 | Uruguay | 0 | 0 (0–0) | 0.00 (0.00–0.00) |

12 | Chile | 0 | 0 (0–0) | 0.00 (0.00–0.00) |

Total South America | 8,365.4 | 163,098 (127,893–197,494)) | 1.95 (1.53–2.36) | |

14 | Mexico | 339.1 | 4,343 (3,400–5,383) | 1.28 (1.00–1.59) |

15 | Nicaragua | 60.5 | 1,476 (1,184–1,795) | 2.44 (1.96–2.97) |

16 | Honduras | 49.1 | 1,218 (986–1,447) | 2.48 (2.01–2.95) |

17 | Guatemala | 43.1 | 1,013 (828–1,201) | 2.35 (1.92–2.79) |

18 | Panama | 43 | 869 (692–1,057) | 2.02 (1.61–2.46) |

19 | Costa Rica | 38.5 | 571 (440–716) | 1.48 (1.14–1.86) |

20 | Belize | 20.9 | 563 (463–665) | 2.69 (2.22–3.18) |

21 | United States | 7.9 | 0 (0–4) | 0.01 (0.00–0.05) |

22 | El Salvador | 0 | 0 (0–0) | 0.00 (0.00–0.00) |

Total North America | 602.1 | 10,054 (8,352–12,352) | 1.67 (1.39–2.05) | |

Total South and North Americas | 8,967.5 | 173,151 (138,148–208,137) | 1.93 (1.54–2.32) |

For comparison, we also estimated the current potential population size across the entire historical range of jaguar (approx. 17,758,200 km^{2}), assuming that in the future jaguars may recolonize some potentially suitable areas outside of their current range (compare Figs ^{2}), where presumably jaguars have the highest protection and therefore the greatest chance of persistence (

We have proposed a new method to estimate the range wide population of jaguars, using available density and presence/absence data. The models that we have presented may be used to predict jaguar population densities, probability of occurrence, and population size at a given moment across the Neotropics (i.e. geographic regions, specific protected areas, etc.). Thus, they could be applied to conservation planning of new protected areas or in determining the degree of connectivity between populations. Our results provide a reference for monitoring future trends in jaguar populations.

Our estimate of the total jaguar population, approximately 173,000 individuals (CI = 138,000–208,000), was greater than may be expected by many researchers. This estimate may be influenced by the large area (approximately 9 million km^{2}) that is still inhabited by jaguars. A large proportion of our estimate was attributed to the forested areas of the Amazon basin, which were characterized by relatively high probabilities of jaguar occurrence and moderate to high densities. In most of this forested area, human population densities are low (< 1 person/km^{2}). In such conditions hunting usually has no measurable effect on populations of jaguars and their prey base [

Although validating our total population estimate is difficult, the results of our simulations indicated that reasonable estimates at this scale and with this level of sampling are possible (see ^{2}). Thus, our results are similar to the prior estimates provided by local studies and our credible intervals contain all those estimates. Alternatively, De la Torre et al. [^{2}) to the whole of the “Amazonia” region, which was not based on any field study; this single density was applied to areas from northern Argentina and the Pantanal in the south, through the Amazon Basin to northern Venezuela, where 37 actual studies have been conducted, and where estimated densities range from 0 to 9 jaguars/100 km^{2} (based on spatial methods only, compare

Our best density model based on environmental variables explained approximately 45% of the variation in jaguar density estimates throughout their range. The remaining unexplained variation is related to process and sampling variance. In our analysis, density estimates were only slightly influenced by camera trapping study design, such as the size of the study area and the number of camera stations used (

Our density estimates were derived from 80 camera trapping study sites. Although they covered a wide range of habitats and environmental conditions, these estimates may not have captured all of the natural variation in jaguar densities. Further precision in the predictions of models such as ours will be obtained with more replicated and representative density estimates.

Our occurrence model was based on 3,377 presence/absence points, producing robust predictions of jaguar occurrence probability. However, possible bias could result from an uneven distribution of our data, with a higher concentration in some areas of Central America and Venezuela, which potentially could produce spatial autocorrelation and inflation in the estimates of significance of the logistic regression [

Our presence/absence data lacked temporally replicated samples at each site, thus we were unable to account for detection probability in our model [

Our models are designed to estimate global distribution and population size at a snapshot in time related to that at which the data was collected. They cannot predict future population changes or population dynamics. New presence/absence data would have to be collected to estimate population increases or declines over time.

Our analysis reveals the spatial mechanisms that determine jaguar population density and distribution across the species’ range. We demonstrate that jaguar potential (natural) densities are driven by factors related to primary productivity. This finding is in concordance with previous work showing that mean carnivore home range size, which can be viewed as the inverse to density, at large geographic scales is also determined by primary productivity [

Our results show that protected areas have an important positive impact on jaguar persistence. Given the strong, negative association between human activities and the probability of jaguar occurrence, creating more protected areas, like national parks, is among the most important conservation actions for this species and other large carnivores [

We conclude that combining modelling of density and distribution can reveal ecological patterns and processes at global scales, can provide robust estimates for use in species assessments (e.g., IUCN), and can guide broad-scale conservation actions, including planning of protected areas and their ecological corridors [

(DOCX)

(DOCX)

(DOCX)

(DOCX)

(DOCX)

(DOCX)

(DOCX)

(DOC)

(DOCX)

(DOCX)

(DOCX)

(RAR)

We direct special thanks to the direction of the Instituto Venezolano de Investigaciones Cientificas (IVIC) and coordinators and staff of IVIC’s Centro de Ecología for their kind support. We thank Luke Hunter and Lisanne Petracca (Panthera) for their comments on an earlier draft of this paper. We are grateful to Dr Christian Andrew Hagen, Dr. Guillaume Souchay, and to an anonymous Reviewer for their comments which helped us to improve this paper.