Data from: Model selection with overdispersed distance sampling data

1. Distance sampling (DS) is a widely-used framework for estimating animal abundance. DS models assume that observations of distances to animals are independent. Non-independent observations introduce overdispersion, causing model selection criteria such as AIC or AICc to favour overly complex models, with adverse effects on accuracy and precision. 2. We describe, and evaluate via simulation and with real data, estimators of an overdispersion factor (c ̂), and associated adjusted model selection criteria (QAIC) for use with overdispersed DS data. In other contexts, a single value of c ̂ is calculated from the “global” model, i.e., the most highly-parameterized model in the candidate set, and used to calculate QAIC for all models in the set; the resulting QAIC values, and associated ΔQAIC values and QAIC weights, are comparable across the entire set. Candidate models of the DS detection function include models with different general forms (e.g., half-normal, hazard rate, uniform), so it may not be possible to identify a single global model. We therefore propose a two-step model selection procedure by which QAIC is used to select among models with the same general form, and then a goodness-of-fit statistic is used to select among models with different forms. A drawback of this approach is that QAIC values are not comparable across all models in the candidate set. 3. Relative to AIC, QAIC and the two-step model selection procedure avoided overfitting and improved the accuracy and precision of densities estimated from simulated data. When applied to six real data sets, adjusted criteria and procedures selected either the same model as AIC or a model that yielded a more accurate density estimate in 5 cases, and a model that yielded a less accurate estimate in 1 case. 4. Many DS surveys yield overdispersed data, including cue counting surveys of songbirds and cetaceans, surveys of social species including primates, and camera-trapping surveys. Methods that adjust for overdispersion during the model selection stage of DS analyses therefore address a conspicuous gap in the DS analytical framework as applied to species of conservation concern.

1. 距离抽样（Distance Sampling，DS）是一种应用广泛的动物种群丰度估算框架。距离抽样模型假设对动物与观测者之间距离的观测值相互独立。非独立的观测数据会引入过度离散（overdispersion）现象，使得AIC、AICc等模型选择准则倾向于选择过于复杂的模型，进而对估算结果的准确性与精度产生负面影响。
2. 本研究描述了适用于过度离散距离抽样数据的过度离散因子（overdispersion factor，ĉ）估计量，以及与之配套的校正模型选择准则——准AIC（QAIC），并通过模拟实验与真实数据对其进行了评估。在其他研究场景中，通常从候选模型集合中参数最多的“全局模型”中计算得到单一的ĉ值，并利用该值计算集合内所有模型的QAIC；由此得到的QAIC值、与之对应的ΔQAIC值与QAIC权重，可在整个候选模型集合中进行横向比较。距离抽样检测函数（detection function）的候选模型包含多种通用形式（如半正态（half-normal）、风险率（hazard rate）、均匀（uniform）模型），因此可能无法确定唯一的全局模型。为此，我们提出了两步模型选择流程：首先利用QAIC在相同通用形式的模型间进行选择，随后借助拟合优度（goodness-of-fit）统计量在不同形式的模型间完成筛选。该方法的一项局限在于，候选集合内不同模型的QAIC值不再具备横向可比性。
3. 相较于传统的AIC准则，QAIC与本研究提出的两步模型选择流程有效避免了过拟合（overfitting）问题，并提升了模拟数据中种群密度估算的准确性与精度。将上述校正准则与流程应用于6组真实数据集时，在5组案例中，其选择的模型与AIC选出的模型一致，或选出了密度估算精度更高的模型；仅在1组案例中选出了精度更低的模型。
4. 许多距离抽样调查会产生过度离散的数据，例如鸣禽（songbirds）与鲸类（cetaceans）的鸣声计数调查（cue counting surveys）、包括灵长类（primates）在内的群居物种（social species）调查，以及红外相机陷阱调查（camera-trapping surveys）。因此，在距离抽样分析的模型选择阶段校正过度离散的方法，填补了当前距离抽样分析框架在应用于受保护关注物种（species of conservation concern）时存在的显著空白。