Data from: Elliptical Time-Density model to estimate wildlife utilization distributions
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We present a new animal space-use model (Elliptical Time-Density - ETD) that uses discrete-time tracking data collected in wildlife movement studies. The ETD model provides a trajectory-based, non-parametric approach to estimate the utilization distribution (UD) of an animal, using model parameters derived directly from the movement behavior of the species. The model builds on the theory of ‘time-geography’ whereby elliptical constraining regions are established between temporally-adjacent recorded locations. Using a Weibull speed distribution fitted for an animal's movement data, a time-density value (i.e., time per unit landscape) is determined from the expectation of all elliptical regions equal to, or greater-than, the minimum bounding ellipse for a given landscape point. We tested the ETD model using a tracking dataset for an African elephant (Loxodonta africana) and compared the resulting UDs for regularly sampled, frequently recorded locations, as well as irregular random time intervals between locations and also infrequent temporal-sampling regimes, providing insight to the method's performance with different resolution data. We compared the performance of the ETD model, the Brownian Bridge Movement Model (BBMM), the Time-Geography Density Estimator (TGDE) and the Kernel Density Estimator (KDE) by calculating omission/commission errors from the predicted space-use distribution of each model relative to the true known UD of our elephant test data. The comparison was made for the 10% to 99% percentile UD model areas. The ETD90 model (i.e., ETD model parameterized using the 90% percentile value of the Weibull speed distribution) resulted in the fewest errors of commission and omission with regards to locating the true movement path at the 99% percentile UD area. The ETD model provides an improved approach for estimating animal UDs since: i) parameters are derived directly from the tracking data rather than assumed; ii) parameter values are biologically interpretable; iii) the Weibull speed distribution is adaptable to various temporal-sampling regimes; and iv) the ETD model handles the case of degenerate ellipses thus preserving landscape connectivity in the UD. Software (freeware) for calculating the ETD and a Bayesian framework for estimating the Weibull distribution speed parameters are also introduced in the paper.
本研究提出一种全新的动物空间利用模型——椭圆时间密度模型（Elliptical Time-Density，ETD），该模型依托野生动物运动研究中采集的离散时间追踪数据构建。ETD模型采用基于轨迹的非参数方法估算动物的利用分布（utilization distribution，UD），其模型参数直接源自该物种的运动行为特征。该模型基于时间地理学（time-geography）理论，在时间上相邻的记录位置之间构建椭圆约束区域。通过拟合动物运动数据得到的威布尔速度分布（Weibull speed distribution），针对给定景观点，计算所有大于或等于其最小外接椭圆的椭圆区域的期望，即可得到时间密度值（即单位景观面积上的停留时间）。本研究利用非洲象（Loxodonta africana）的追踪数据集对ETD模型进行测试，并对比了规则采样高频记录位置、位置间不规则随机时间间隔以及低频时间采样方案下得到的利用分布，以此分析该方法在不同分辨率数据下的表现。通过计算各模型预测的空间利用分布相对于非洲象测试数据的真实已知利用分布的漏报误差与误报误差，本研究对比了ETD模型、布朗桥运动模型（Brownian Bridge Movement Model，BBMM）、时间地理学密度估计器（Time-Geography Density Estimator，TGDE）以及核密度估计器（Kernel Density Estimator，KDE）的性能。本次对比针对10%至99%分位数的利用分布模型区域展开。ETD90模型（即采用威布尔速度分布90%分位数参数化的ETD模型）在99%分位数利用分布区域内定位真实运动路径时，产生的误报与漏报误差最少。ETD模型为动物利用分布的估算提供了更优方法，原因如下：其一，参数直接源自追踪数据，而非人为假设；其二，参数值具备生物学可解释性；其三，威布尔速度分布可适配多种时间采样方案；其四，ETD模型可处理退化椭圆（degenerate ellipses）场景，从而保留利用分布中的景观连通性。本文还公开了用于计算ETD模型的免费软件，以及用于估算威布尔分布速度参数的贝叶斯框架。
