Kruger National Park (KNP), South Africa, provides protected habitats for the unique animals of the African savannah. For the past 40 years, annual aerial surveys of herbivores have been conducted to aid management decisions based on (1) the spatial distribution of species throughout the park and (2) total species populations in a year. The surveys are extremely time consuming and costly. For many years, the whole park was surveyed, but in 1998 a transect survey approach was adopted. This is cheaper and less time consuming but leaves gaps in the data spatially. Also the distance method currently employed by the park only gives estimates of total species populations but not their spatial distribution. We compare the ability of multiple indicator kriging and area-to-point Poisson kriging to accurately map species distribution in the park. A leave-one-out cross-validation approach indicates that multiple indicator kriging makes poor estimates of the number of animals, particularly the few large counts, as the indicator variograms for such high thresholds are pure nugget. Poisson kriging was applied to the prediction of two types of abundance data: spatial density and proportion of a given species. Both Poisson approaches had standardized mean absolute errors (St. MAEs) of animal counts at least an order of magnitude lower than multiple indicator kriging. The spatial density, Poisson approach (1), gave the lowest St. MAEs for the most abundant species and the proportion, Poisson approach (2), did for the least abundant species. Incorporating environmental data into Poisson approach (2) further reduced St. MAEs.

中文翻译：

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南非克鲁格国家公园草食动物物种丰度制图模式的多指标克里金法和区域到点泊松克里金法的比较

南非克鲁格国家公园 (KNP) 为非洲大草原的独特动物提供了受保护的栖息地。在过去的 40 年中，每年都会对食草动物进行空中调查，以帮助基于 (1) 整个公园物种的空间分布和 (2) 一年中的物种总数做出管理决策。调查非常耗时且成本高昂。多年来，对整个公园进行了调查，但在 1998 年采用了样带调查方法。这更便宜且耗时更少，但会在空间上留下数据空白。此外，公园目前采用的距离方法仅提供总物种种群的估计值，而不是它们的空间分布。我们比较了多指标克里金法和区域到点泊松克里金法准确绘制公园物种分布图的能力。留一法交叉验证方法表明，多指标克里金法对动物数量的估计很差，尤其是少数大计数，因为如此高阈值的指标变异函数是纯金块。泊松克里金法被应用于两种类型的丰度数据的预测：空间密度和给定物种的比例。两种泊松方法都具有动物计数的标准化平均绝对误差 (St. MAE)，至少比多指标克里金法低一个数量级。空间密度 Poisson 方法 (1) 为最丰富的物种提供最低的 St. MAE，而 Poisson 方法 (2) 的比例为最不丰富的物种提供。将环境数据纳入泊松方法 (2) 进一步减少了 St. MAE。