1. Joint species distribution models (JSDMs) are a recent development in biogeography and enable the spatial modelling of multiple species and their interactions and dependencies. However, most models do not consider imperfect detection, which can significantly bias estimates. This is one of the first papers to account for imperfect detection when fitting data with JSDMs and to explore the complications that may arise.
2. A multivariate probit JSDM that explicitly accounts for imperfect detection is proposed, and implemented using a Bayesian hierarchical approach. We investigate the performance of the JSDM in the presence of imperfect detection for a range of factors, including varied levels of detection and species occupancy, and varied numbers of survey sites and replications. To understand how effective this JSDM is in practice, we also compare results to those from a JSDM that does not explicitly model detection but instead makes use of ‘collapsed data’. A case study of owls and gliders in Victoria, Australia, is also illustrated.
3. Using simulations, we found that the JSDMs explicitly accounting for detection can accurately estimate intrinsic correlation between species with enough survey sites and replications. Reducing the number of survey sites decreases the precision of estimates, while reducing the number of survey replications can lead to biased estimates. For low probabilities of detection, the model may require a large number of survey replications to remove bias from estimates. However, JSDMs not explicitly accounting for detection may have a limited ability to disentangle detection from occupancy, which substantially reduces their ability to accurately infer the species distribution spatially. Our case study showed positive correlation between Sooty Owls and Greater Gliders, despite a low number of survey replications.
4. To avoid biased estimates of inter-species correlations and species distributions, imperfect detection needs to be considered. However, for low probability of detection, the JSDMs explicitly accounting for detection is data hungry. Estimates from such models may still be subject to bias. To overcome the bias, researchers need to carefully design surveys and choose appropriate modelling approaches. The survey design should ensure sufficient survey replications for unbiased inferences on species inter-dependencies and occupancy.

中文翻译：

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存在不完善检测时联合物种分布模型的有效性

1. 联合物种分布模型 (JSDM) 是生物地理学的最新发展，能够对多个物种及其相互作用和依赖性进行空间建模。然而，大多数模型不考虑不完美的检测，这会显着偏差估计。这是在用 JSDM 拟合数据时解释不完美检测并探讨可能出现的并发症的第一篇论文之一。
2. 提出了一种明确说明不完美检测的多元概率 JSDM，并使用贝叶斯分层方法实现。我们调查了 JSDM 在一系列因素存在不完善检测的情况下的性能，包括不同的检测水平和物种占有率，以及不同数量的调查站点和重复。为了理解这个 JSDM 在实践中的有效性，我们还将结果与 JSDM 的结果进行比较，后者没有明确地对检测进行建模，而是利用“折叠数据”。还说明了澳大利亚维多利亚的猫头鹰和滑翔机的案例研究。
3. 使用模拟，我们发现 JSDM 明确考虑检测可以准确估计具有足够调查站点和重复的物种之间的内在相关性。减少调查地点的数量会降低估计的精确度，而减少调查重复的数量会导致估计有偏差。对于低检测概率，该模型可能需要大量重复调查以消除估计偏差。然而，没有明确考虑检测的 JSDM 将检测与占用分开的能力可能有限，这大大降低了它们在空间上准确推断物种分布的能力。我们的案例研究表明，尽管重复调查的次数很少，但乌黑猫头鹰和大滑翔机之间存在正相关关系。
4. 为了避免物种间相关性和物种分布的偏差估计，需要考虑不完善的检测。然而，对于低检测概率，明确考虑检测的 JSDM 需要大量数据。来自此类模型的估计仍可能存在偏差。为了克服这种偏见，研究人员需要仔细设计调查并选择合适的建模方法。调查设计应确保对物种相互依赖性和占有率的无偏见推断有足够的调查重复。