
Biodiv Sci ›› 2026, Vol. 34 ›› Issue (1): 25386. DOI: 10.17520/biods.2025386 cstr: 32101.14.biods.2025386
• Special Feature: Methods for Ecological Data Analysis • Previous Articles Next Articles
Chunying Wu1,#(
), Viorel D. Popescu2,#(
), Yinqiu Ji1,*(
)(
)
Received:2025-10-01
Accepted:2026-01-20
Online:2026-01-20
Published:2026-02-03
Contact:
Yinqiu Ji
About author:First author contact:#Co-first authors
Supported by:Chunying Wu, Viorel D. Popescu, Yinqiu Ji. Hierarchical occupancy models as solutions to challenges in biodiversity assessment[J]. Biodiv Sci, 2026, 34(1): 25386.
Fig. 2 Simulation of hierarchical occupancy model (HOM) performance in correcting for imperfect detection. (a) Comparison of occupancy probability (ψ) estimates among different methods (sample size n = 100). The naive estimate systematically underestimates occupancy by ignoring imperfect detection, whereas the HOM estimate is closer to the true value. (b) Distribution of detection frequency at sites where the species is truly present. The bar at “0 detections” indicated by the red arrow represents “false absences”, where the species exists at the site but remains undetected due to a detection probability P < 1. This phenomenon is the primary source of bias in occupancy estimation.
Fig. 3 Dual-level statistical framework of the hierarchical occupancy model. This figure illustrates the dual-level statistical framework of the hierarchical occupancy model, which centers on correcting for imperfect detection in species surveys by decoupling the ecological and observation processes. The ecological process on the left describes the true occupancy state (latent variable zi) driven by environmental factors; the occupancy probability ψ is influenced by environmental covariates—such as habitat type (e.g., forest cover, vegetation structure), abiotic factors, and human disturbance—and is modeled via a logit link function. The observation process on the right describes the detection probability P during field surveys, which is affected by observational covariates including survey effort (duration, intensity, and number of replicates), weather conditions, and observer experience, also linked through a logit function. Given that the observation y is strictly dependent on the true occupancy state z (meaning a species can only be detected if it is truly present), the model integrates these processes by marginalizing over the latent variable zi to construct a joint likelihood function. This approach mathematically accounts for false absences, thereby achieving an unbiased estimation of the true species distribution.
Fig. 4 Schematic diagram of multi-season occupancy dynamics and state transition trends. This diagram illustrates the quarterly dynamics (where Q1-Q4 represent the first to fourth quarters of each year, respectively) of a species based on simulated data between 2015 and 2019: The occupancy rate (ψ, blue solid line) is generally maintained between 0.6-0.8, indicating a high persistent probability of presence in the study area. The colonization probability (γ, orange dotted line) is stable at 0.3-0.4 with a slight upward trend, reflecting a relatively strong capacity for range expansion. The extinction probability (ε, green dashed line) is maintained at 0.1-0.2, suggesting potential habitat disturbance or environmental pressure. This figure is created using simulated data and serves to illustrate the application of the multi-season hierarchical occupancy model (MSOM) in revealing species dynamics. Please see Appendix 2 for the R code.
| 类别 Category | 核心假设 Core assumption | 描述 Description |
|---|---|---|
| 生态过程 Ecological process | 闭合假设 Closure assumption | 在调查期间, 站点占有状态无变化(单季节模型); 动态模型放松此假设(MacKenzie et al., |
| 生态过程 Ecological process | 独立站点 Site independence | 站点间占有率条件独立, 或通过随机效应建模空间相关 Occupancy is conditionally independent among sites, or spatial correlation is accounted for through random effects |
| 观测过程 Observation process | 无假阳性 No false positives | 检测到即真实存在; eDNA等场景需扩展模型处理假阳性(Guillera-Arroita et al., |
| 观测过程 Observation process | 检测独立 Independent detections | 重复调查间检测事件独立 Detection events are independent across replicate surveys |
| 参数估计 Parameter estimation | 局部识别 Local identifiability | 重复调查足够多以分离ψ和P (通常j ≥ 3) A sufficient number of replicate surveys are required to distinguish ψ from P (typically j ≥ 3) |
Table 1 Core assumptions of hierarchical occupancy models
| 类别 Category | 核心假设 Core assumption | 描述 Description |
|---|---|---|
| 生态过程 Ecological process | 闭合假设 Closure assumption | 在调查期间, 站点占有状态无变化(单季节模型); 动态模型放松此假设(MacKenzie et al., |
| 生态过程 Ecological process | 独立站点 Site independence | 站点间占有率条件独立, 或通过随机效应建模空间相关 Occupancy is conditionally independent among sites, or spatial correlation is accounted for through random effects |
| 观测过程 Observation process | 无假阳性 No false positives | 检测到即真实存在; eDNA等场景需扩展模型处理假阳性(Guillera-Arroita et al., |
| 观测过程 Observation process | 检测独立 Independent detections | 重复调查间检测事件独立 Detection events are independent across replicate surveys |
| 参数估计 Parameter estimation | 局部识别 Local identifiability | 重复调查足够多以分离ψ和P (通常j ≥ 3) A sufficient number of replicate surveys are required to distinguish ψ from P (typically j ≥ 3) |
| 类别 Category | 核心内容 Core item | 描述 Description |
|---|---|---|
| 模型选择 Model selection | AICc/WAIC/LOO-CV | 用于比较模型拟合与复杂度; AICc适用于小样本(Burnham & Anderson, |
| 模型选择 Model selection | 后验预测检查 Posterior predictive check (PPC) | 贝叶斯框架下评估模型拟合(Gelman et al., |
| 模型验证 Model selection | 交叉验证 Cross-validation (CV) | 使用k折交叉验证评估预测性能 Evaluating predictive performance using k-fold cross-validation (k-fold CV) |
| 残差诊断 Residual diagnostics | DHARMa残差 DHARMa residuals | 模拟残差检查拟合优度, 适用于层级模型(Hartig, |
Table 2 Framework for model selection and validation in hierarchical occupancy models
| 类别 Category | 核心内容 Core item | 描述 Description |
|---|---|---|
| 模型选择 Model selection | AICc/WAIC/LOO-CV | 用于比较模型拟合与复杂度; AICc适用于小样本(Burnham & Anderson, |
| 模型选择 Model selection | 后验预测检查 Posterior predictive check (PPC) | 贝叶斯框架下评估模型拟合(Gelman et al., |
| 模型验证 Model selection | 交叉验证 Cross-validation (CV) | 使用k折交叉验证评估预测性能 Evaluating predictive performance using k-fold cross-validation (k-fold CV) |
| 残差诊断 Residual diagnostics | DHARMa残差 DHARMa residuals | 模拟残差检查拟合优度, 适用于层级模型(Hartig, |
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