A Ph.D. student entered my office at the University of Arizona and asked me to review a habitat model for a desert ungulate that was part of their dissertation. I gladly did so, and when the student returned for my comments, I gave my opinion and asked how they thought the habitat characteristics afield aligned with those in the model. The study area was only a few hours southwest of the university. The response puzzled me when the student stated “Oh, I did not realize they were that close and no, I have not ever seen the species and have never been to the area.” The entire model developed by the student was based on remote sensing and information of others that had not been verified, much of which was speculation.

In essence this is a problem with some models used in manuscripts submitted to the Journal of Wildlife Management. Many submitted models rely too much on unverified work of others, make no attempt to obtain information from the animals or their habitat, do not sample randomly, and do not attempt any form of ground truthing, verification, or validation to ensure that data are accurate and results are appropriate for the inferences made, and to justify that a model's intended use meets specified performance requirements (Rykiel 1996, Hastie et al. 2001, Roberts et al. 2017, Brice et al. 2020).

Models, each with different considerations, include statistical models, analytical models, and simulation models. Statistical models are more commonly used to test scientific theories when the data (e.g., observations, processes, boundary conditions) are subject to stochasticity (Hartig et al. 2011). Analytical models use mathematical equations to predict simple linear components of ecosystems and simulation models are somewhere between experimental methods and purely theoretical models. Simulation models are used to solve analytic equations computationally to capture and mimic real‐world systems that unlike real‐world systems can then be experimented upon (Winsberg 2003). All types of model have their place and are important tools to advance the science and practice of wildlife management. Models have been used in an array of arenas including those designed to better understand foraging, reproduction, predator avoidance, and other components of behavioral ecology (Mangel and Clark 1988); population modeling and translocation (Converse et al. 2013); determination of species occurrence (MacKenzie et al. 2009); wildlife habitat and habitat selection (McLane et al. 2011); crop damage (Retanosa et al. 2008); anthropogenic disturbances (Braunisch et al. 2011); estimation of probability of use, occurrence, and selection of habitats in time (Wisdom et al. 2020); harvest management (Boyce et al. 2012); and just about every other aspect of wildlife ecology and management. Özesmi and Özesmi (2003) even use fuzzy cognitive mapping models to include abstract and aggregate variables, model relationships that are not known with certainty, include complex relationships, and use different knowledge sources (e.g., people's knowledge in place of data). Model accuracy continues to improve as more data and types of data (e.g., citizen science) become available, but none are perfect and controversy will continue related to model selection, multimodel selection, and the inferences made (Fieberg and Johnson 2015, Hooten and Hobbs 2015). Yet fundamental to the reliability of any model is the sampling design that went into guiding model development in the first place (Thompson 1992, Reich 2020). There are dozens of examples of highly sophisticated models built with data collected by an underlying biased sampling design (Brice et al. 2020). Too often models are designed to be applied to a single population at a specific time and are not generally applicable (i.e., generality) to broaden knowledge across species or areas (Levins 1966, Wisdom et al. 2020). When using models, it is important to ensure that they are being used appropriately. Are they being used for prediction, a specific population, or generality so they can be applied elsewhere?

I realize that all models do not meet the needs of all researchers and managers. There are, however, some general guidelines that are important for anyone that uses statistical models. The purpose of this editorial is to briefly summarize some important considerations when using and understanding inferences made from models (Getz et al. 2017, Wisdom et al. 2020). Considering these tenets will improve the use of models and the understanding of inferences made from them.

First, models will be more useful than academic exercises if they are developed in cooperation with wildlife managers, administrators, and scientists (Wisdom et al. 2020). Managers often desire models that are simple and general, and can help explain management outcomes across ranges of settings not included in the original modeling data. This emphasizes the importance of guarding against overfitting and the principle of parsimony. Consulting people who might use the models makes sense, especially if managers are expected to apply models and interpret results to implement meaningful change. The purpose of the models used should be explicit with well‐defined performance criteria (e.g., goodness‐of‐fit testing, out‐of‐sample cross‐validation; Rykiel 1996).

Second, modelers must decide on the appropriate spatiotemporal scale (e.g., from molecules, macromolecules, cells, organs, organisms, populations, communities, and ecosystems) and from short to long periods (Getz et al. 2017, Wisdom et al. 2020). The selected resolution and extent of scale should be appropriate for the measured covariates and objectives, and be clearly identified in the methods.

Third, data used must be adequate (i.e., sufficient sample sizes and an appropriate sampling design) to estimate model parameters (Getz et al. 2017). Too often, researchers breeze through the data sources as if they are adequate without any reference to limitations or indication that they have been vetted to meet modeling assumptions and objectives. It is not merely sufficient to have large enough datasets to obtain precise estimates. Any modeling exercise should consider the underlying sampling design of the data collection. Large samples of biased data will lead to precise but biased model results. Many modern online data repositories (e.g., eBird, citizen science) are the result of convenience sampling designs with significant sampling biases that must be addressed in model development (Kramer‐Schadt et al. 2013). This is especially true when researchers use large datasets from different data sources that have been collected by others or use datasets obtained from web access to generic, open‐source formats. Biased data from even a single source can minimize the use and rigor of the model.

On the other hand, the advent of big data and meta‐replication approaches allow us to develop and evaluate models with multiple study areas and datasets (Griffin et al. 2011), which in turn expands inference space and can lead to more robust regional models with broader application than one‐off case studies. The model should be able to address the objectives and hypotheses formulated and should be based on adequate data related to sample size and sampling design (Wisdom et al. 2020). Also, there should be enough data available for model validation and evaluating model success (e.g., cross‐validation; Boyce et al. 2002, Hooten and Hobbs 2015, Getz et al. 2017). The most powerful types of validation will be true out‐of‐sample validation (Mladenoff et al. 1995, 1999). In some cases, only sparse data are available because of access limitations, small populations, or data that are difficult and expensive to collect. Even then, the limitations must be addressed in the discussion. Unfortunately, if the assumptions demanded by the model are not met, simply discussing them will not enhance the quality of the model. Inadequate data can result in models and inferences that are biased and inaccurate and often results are presented without estimates of accuracy or are too precise given the data. There is no excuse for using data that are not adequate (Lozier et al. 2009).

Fourth, models should include the state variables needed (e.g., nutrients, movement, environmental representation) and important biological elements (e.g., species, occupancy, population estimates) to represent the biological processes of interest without overfitting. Further, depending on the objectives of a study, age, sex, population relationships, population performance, and other variables should be included for assessing models and determining their adequacy, again without overfitting (McLane et al. 2011). The appropriate level of detail should be included for clarity and to ensure that the results of the model are not sensitive to perturbations in the parameters used (Getz et al. 2017, Wisdom 2020). In many studies, researchers use too many variables, given the effective sample size, and many of them will often be biased or spurious (Freedman 1983). Trying to fit numerous variables (e.g., 30) to limited observations (e.g., 100) is a recipe for overfitting, spurious results, and the opposite of parsimony (Freedman 1983). Often the simplest model is the best, most general, and easiest to test its assumptions (e.g., Ockhams' razor). For example, Hurley et al. (2017) examined overwinter survival of juvenile ungulates and used approximately 4,000 mule deer years. The top model (selected by sample cross‐validation) had only 3 parameters. The simpler model was more general and could be applied and better predicted across the entire state of Idaho, USA. The best model selected by Akaike's Information Criterion (AIC; Akaike 1974) had more than twice as many parameters. Some model selection methods (e.g., AIC) can often lead to over parameterization and are guilty of fitting data too well and failing to address generality (Levins 1966). It is important to understand the generality of a model (Levins 1966) so it can be applied to other systems with rigor. The model structure needs to be consistent with the available data (Boyce et al. 2012).

Fifth, models should ideally include experimental controls in their sampling design and consider ecologically plausible sets of competing models in their development and selection (Burnham and Anderson 2002, Getz et al. 2017, Wisdom et al. 2020). The controls might be necessary to evaluate how well a model can characterize an ecological process in question. Some sort of model selection approach should be used to compare potential models (Chamberlain 1890), but remember that approaches such as AIC were designed to approximate the performance of a model under true out‐of‐sample validation (Burnham and Anderson 2002). Thus, researchers should be on their guard that AIC can and often does select a model with spurious results as the top choice (Lukacs et al. 2009), and always aim to assess model performance using some sort of cross‐validation (Hastie et al. 2001). And finally, all models used to advance wildlife science should have reliable interpretations for ecological understanding and use in management. Too often, manuscripts are presented with complex models and detailed statistical analysis but fail to clearly address sampling design, biological objectives, hypotheses being tested, or limits of inference.

Sometimes models are developed by researchers who know little about the biology of the species being studied, the quality of the data used, or how managers or ecologists might apply or interpret results. Successfully running a model in a software package can sometimes become the default objective. Deficiencies in results are obvious, reflecting an approach of simply assimilating available data in a model without ecological thought or consideration. Use models with a purpose, quality data, and structured biological framework, and use them to advance the science of wildlife management.

博士学位 一位学生进入我在亚利桑那大学的办公室，要我复习一下沙漠有蹄类动物的栖息地模型，这是他们论文的一部分。我很高兴这样做，当学生返回我的评论时，我发表了意见，并询问他们如何看待该地区的栖息地特征与模型中的那些一致。研究区域位于大学西南仅几个小时的地方。当学生说：“哦，我没有意识到它们离那儿很近，没有，我从未见过这种物种，也从未去过该地区。” 该学生开发的整个模型是基于遥感和其他未经验证的信息，其中大部分是推测。

本质上，这是一些提交给《野生动物管理杂志》的手稿中使用的模型的问题。许多提交的模型过分依赖他人未经验证的工作，没有尝试从动物或其栖息地获取信息，没有进行随机抽样，也没有尝试进行任何形式的地面真实，验证或确认以确保数据准确结果适合于推论，并证明模型的预期用途满足指定的性能要求（Rykiel  1996，Hastie等 2001，Roberts等 2017，Brice等 2020）。

每个模型都有不同的考虑因素，包括统计模型，分析模型和仿真模型。当数据（例如观测值，过程，边界条件）受到随机性影响时，统计模型通常用于检验科学理论（Hartig等，  2011）。分析模型使用数学方程式来预测生态系统的简单线性组成部分，而仿真模型则介于实验方法和纯理论模型之间。仿真模型用于通过计算求解解析方程，以捕获和模拟与实际系统不同的实际系统，然后可以对其进行试验（Winsberg，  2003年）。）。所有类型的模型都有其位置，并且是促进野生动植物管理的科学和实践的重要工具。模型已经在一系列领域中使用，包括那些旨在更好地了解觅食，繁殖，避免捕食和行为生态学其他组成部分的模型（Mangel and Clark  1988）。种群建模和易位（Converse等，  2013）；确定物种的发生（MacKenzie等，  2009）；野生动物栖息地和栖息地选择（麦克莱恩等人 2011）; 作物损害（Retanosa等人。  2008年）; 人为干扰（Braunisch等人 2011）; 及时评估栖息地的使用，发生和选择的可能性（Wisdom等，  2020年）；收获管理（Boyce等人。  2012）; 以及野生动植物生态和管理的几乎所有其他方面。Özesmi和Özesmi（2003）甚至使用模糊认知映射模型来包括抽象变量和集合变量，不确定性的模型关系，复杂的关系以及使用不同的知识源（例如，人们的知识代替数据）。随着越来越多的数据和数据类型（例如，公民科学）的出现，模型的准确性继续提高，但是没有一个是完美的，关于模型选择，多模型选择以及所做的推论将继续引起争议（Fieberg和Johnson，  2015年），Hooten和Hobbs，  2015年）。然而，对于任何模型的可靠性而言，最根本的是抽样设计，该设计最初是用于指导模型开发的（Thompson  1992，Reich  2020）。有数十个高度复杂的模型示例，这些模型使用基础偏差采样设计收集的数据构建而成（Brice等人，  2020年）。太多时候，模型被设计为在特定时间应用于单个种群，而不能普遍应用于（即普遍性）来扩展跨物种或区域的知识（Levins  1966； Wisdom等人 2020）。）。使用模型时，确保正确使用它们很重要。它们是用于预测，特定人群还是普遍性，以便可以在其他地方应用？

我意识到所有模型都不能满足所有研究人员和管理人员的需求。但是，有一些通用准则对使用统计模型的任何人都非常重要。这篇社论的目的是简要总结使用和理解模型推论时的一些重要考虑因素（Getz等人，  2017； Wisdom等人，  2020）。考虑这些原则将改善模型的使用和对模型推论的理解。

首先，如果模型是与野生动物管理者，管理者和科学家合作开发的，那么它将比学术练习更有用（Wisdom等，  2020）。管理人员通常希望模型既简单又通用，并且可以帮助解释原始建模数据中未包含的各种设置范围内的管理结果。这强调了防止过度拟合和简约性原则的重要性。向可能使用这些模型的人咨询是有道理的，特别是如果期望管理人员应用模型并解释结果以实施有意义的变更。使用明确定义的性能标准（例如拟合优度测试，样本外交叉验证； Rykiel 1996）时，使用的模型的目的应该明确 。

其次，建模者必须决定适当的时空尺度（例如，从分子，大分子，细胞，器官，生物，种群，社区和生态系统）以及从短期到长期（Getz等人，  2017； Wisdom等人，  2020）。 。所选的分辨率和等级范围应适合所测协变量和目标，并在方法中明确标识。

第三，所使用的数据必须足够（即足够的样本量和适当的抽样设计）以估计模型参数（Getz等人 2017））。研究人员常常轻而易举地浏览数据源，就好像它们足够了一样，没有提及任何限制或表明它们已经过审核以满足模型假设和目标。拥有足够大的数据集以获得精确的估计不仅是足够的。任何建模练习都应考虑数据收集的基础抽样设计。有偏差数据的大量样本将导致精确但有偏差的模型结果。许多现代的在线数据存储库（例如，eBird，公民科学）是便利采样设计的结果，这些采样具有明显的采样偏差，必须在模型开发中加以解决（Kramer-Schadt等，  2013）。）。当研究人员使用来自其他人的不同数据源的大型数据集或使用通过Web访问的通用开放源格式获得的数据集时，尤其如此。即使来自单一来源的有偏数据也可以最大程度地减少模型的使用和严格性。

另一方面，大数据和元复制方法的出现使我们能够开发和评估具有多个研究领域和数据集的模型（Griffin等人，  2011年），这反过来又扩大了推理空间并可以导致更强大的区域模型比一次性案例研究具有更广泛的应用。该模型应能够解决制定的目标和假设，并应基于与样本数量和样本设计相关的足够数据（Wisdom等，  2020）。而且，应该有足够的数据可用于模型验证和评估模型成功（例如，交叉验证; Boyce等人 2002，Hooten and Hobbs  2015，Getz等人 2017）。最强大的类型的验证为真出的样本验证（Mladenoff等人。  1995年，  1999年）。在某些情况下，由于访问限制，人口少或收集困难且费用昂贵的数据，只有稀疏数据可用。即使这样，在讨论中也必须解决局限性。不幸的是，如果不满足模型要求的假设，那么简单地讨论它们将不会提高模型的质量。数据不足会导致模型和推论有偏差和不准确，并且在给出结果时往往没有准确度的估计或结果过于精确。没有使用不充分数据的借口（Lozier等，  2009）。

第四，模型应包括所需的状态变量（例如营养素，运动，环境表征）和重要的生物学要素（例如物种，占用率，种群估计），以表示感兴趣的生物过程而不会过度拟合。此外，根据研究的目的，年龄，性别，人口关系，人口表现以及其他变量也应包括在内，以评估模型并确定其适当性，而又不要过度拟合（McLane等，  2011）。为了清楚起见，应包括适当的详细程度，并确保模型的结果对所用参数的扰动不敏感（Getz等人 2017，Wisdom  2020）。在许多研究中，给定有效的样本量，研究人员使用了太多的变量，其中许多变量经常会带有偏见或虚假（Freedman  1983）。试图使众多变量（例如30）适合有限的观测值（例如100），是导致过度拟合，虚假结果和简约的对立面（Freedman  1983）。最简单的模型通常是检验其假设的最佳，最通用且最容易的模型（例如，奥克汉姆剃刀）。例如，Hurley等。（2017年）检查了有蹄类动物的越冬生存期，并使用了约4,000 ule年。顶级模型（通过样本交叉验证选择）只有3个参数。更简单的模型更通用，可以在美国爱达荷州的整个州应用和更好地预测。Akaike的信息标准（AIC; Akaike 1974）选择的最佳模型的 参数是其两倍多。一些模型选择方法（例如，AIC）通常会导致过度参数化，并且对数据拟合得太好并且无法解决一般性问题（Levins  1966）。理解模型的一般性很重要（Levins  1966），因此可以严格应用于其他系统。模型结构必须与可用数据保持一致（Boyce等，  2012）。

第五，理想情况下，模型应在其抽样设计中包括实验控制，并在其开发和选择中考虑竞争模型的生态上合理的集合（Burnham和Anderson  2002； Getz等人，  2017； Wisdom等人，  2020）。可能需要使用控件来评估模型可以很好地描述所讨论的生态过程。应该使用某种模型选择方法来比较潜在的模型（Chamberlain  1890），但请记住，诸如AIC之类的方法是为了在真实的样本外验证下近似模型的性能而设计的（Burnham和Anderson  2002））。因此，研究人员应该保持警惕，AIC可以并且经常确实选择带有假结果的模型作为首选（Lukacs等，2009），并且始终旨在通过某种交叉验证来评估模型的性能（Hastie等，2009）。  （  2001）。最后，用于促进野生动植物科学的所有模型都应具有对生态学理解和在管理中使用的可靠解释。稿件常常带有复杂的模型和详细的统计分析，但不能清楚地说明采样设计，生物学目的，要检验的假设或推断的局限性。

有时，模型是由研究人员开发的，他们对所研究物种的生物学，所用数据的质量，管理者或生态学家如何应用或解释结果知之甚少。在软件包中成功运行模型有时可以成为默认目标。结果的不足是显而易见的，反映出一种简单地吸收模型中可用数据而无需生态学思考或考虑的方法。使用具有目的，质量数据和结构化的生物学框架的模型，并将其用于推进野生动植物管理的科学。