To avoid the transformation of the dependent variable, which introduces bias when back-transformed, complex nonlinear forest models have the parameters estimated with heuristic techniques, which can supply erroneous values. The solution for accurate nonlinear models provided by Strimbu et al. (Ecosphere 8:e01945, 2017) for 11 functions (i.e., power, trigonometric, and hyperbolic) is not based on heuristics but could contain a Taylor series expansion. Therefore, the objectives of the present study are to present the unbiased estimates for variance following the transformation of the predicted variable and to identify an expansion of the Taylor series that does not induce numerical bias for mean and variance. We proved that the Taylor series expansion present in the unbiased expectation of mean and variance depends on the variance. We illustrated the new modeling approach on two problems, one at the ecosystem level, namely site productivity, and one at individual tree level, namely stem taper. The two models are unbiased, more parsimonious, and more precise than the existing less parsimonious models. This study focuses on research methods, which could be applied in similar studies of other species, ecosystem, as well as in behavioral sciences and econometrics.

为避免因变量的转换（在反向转换时引入偏差），复杂的非线性森林模型具有使用启发式技术估算的参数，这些参数可能会提供错误的值。Strimbu等人提供的精确非线性模型的解决方案。（Ecosphere 8：e01945，2017）的11个函数（即幂，三角函数和双曲线）不是基于启发式方法，而是可以包含泰勒级数展开式。因此，本研究的目的是提出预测变量转换后的方差无偏估计，并确定泰勒级数的展开，该展开不引起均值和方差的数值偏差。我们证明了存在于均值和方差的无偏期望中的泰勒级数展开取决于方差。我们针对两种问题说明了新的建模方法，一种是在生态系统级别，即站点生产力，另一种是在单个树级别，即茎锥度。与现有的较少简约模型相比，这两个模型是无偏的，更加简约和精确的。这项研究的重点是研究方法，可以将其应用于其他物种，生态系统的相似研究以及行为科学和计量经济学。