Department of Biology, Duke University, Durham, North Carolina, 27708, USA.
Environmental Studies Program, University of Colorado-Boulder, Boulder, Colorado, 80301, USA.
Ecology. 2018 Oct;99(10):2308-2317. doi: 10.1002/ecy.2455. Epub 2018 Aug 27.
Integral projection and matrix population models are commonly used in ecological and conservation studies to assess the health and extinction risk of populations. These models use one (or more) measurable state variable(s), such as size or age, to predict individual performance, which, ideally, is the sole determinant of an individual's expected fate. However, even if ecologists successfully identify and measure the observable state variable(s) that best predicts individual fate, we are rarely, if ever, able to perfectly measure state for many species, especially those with size structure, where total plant biomass or starch stores, for example, may be the best predictors of fate. Here, we used a series of simulations to test how this imperfect quantification of actual state ("measurement error") leads to inaccurate prediction of state-dependent fates and influences the predictions of structured population models. We simulated 10 yr of best practice field data collection using known vital rate functions and incorporated measurement error of different magnitudes and types (completely random, temporal, and individual based) for two size-structured life histories. We found that even for conservative error rates, most types of measurement error increased the median predicted population growth rate by 1-2% growth per year. However, the magnitude of this error differed substantially with life history strategy and error type, with some scenarios resulting in >8% median overestimation of population growth rate. This effect arises largely from the well-known econometrics problem of "regression dilution" (overestimation of the intercept and underestimation of the slope of a regression when the predictor variable is measured with error), which in our simulations typically results in overly optimistic predictions of small or young individuals' vital rates. Our results suggest that the problem of measurement error for state variables, present in many demographic studies but virtually unacknowledged in the ecological literature, may lead to substantial misestimation of population behavior, resulting in erroneous inferences about not only growth, but also extinction risk and other aspects of population dynamics.
积分预测和矩阵种群模型常用于生态和保护研究中，以评估种群的健康状况和灭绝风险。这些模型使用一个（或多个）可测量的状态变量（如大小或年龄）来预测个体表现，而个体表现理想情况下是决定个体预期命运的唯一因素。然而，即使生态学家成功地识别和测量了最能预测个体命运的可观察状态变量，我们也很少能够完美地测量许多物种的状态，尤其是那些具有大小结构的物种，例如，植物总生物量或淀粉储量可能是预测命运的最佳指标。在这里，我们使用一系列模拟来测试这种对实际状态的不完美量化（“测量误差”）如何导致对状态相关命运的不准确预测，并影响结构化种群模型的预测。我们使用已知的生命表函数模拟了 10 年的最佳实践现场数据收集，并针对两种大小结构的生活史，纳入了不同大小和类型（完全随机、时间和个体）的测量误差。我们发现，即使对于保守的误差率，大多数类型的测量误差也会使中值预测种群增长率每年增加 1-2%。然而，这种误差的幅度与生活史策略和误差类型有很大的不同，有些情况下会导致中值高估种群增长率超过 8%。这种效应主要源于众所周知的计量经济学问题“回归稀释”（当预测变量存在测量误差时，对回归的截距高估和斜率低估），在我们的模拟中，这种效应通常会导致对小个体或年轻个体生命表率的过度乐观预测。我们的结果表明，状态变量测量误差的问题在许多人口研究中都存在，但在生态文献中几乎没有被承认，这可能导致对种群行为的严重估计错误，从而导致对生长、灭绝风险和其他种群动态方面的错误推断。
