Fertilization is a common practice to increase the productivity and the stand value in the southeastern US. The decision to fertilize a given site is driven by site characteristics and the expected magnitude of response. To determine the magnitude, forest researchers typically rely on fertilization trials established throughout the region of interest and derive growth equations to reflect an increase in either site index or volume. Such equations lack an explicit spatial prediction component. To bridge this gap, we developed a modeling framework that explicitly evaluates the likelihood of a fertilization response as a binary process and the magnitude of such response as a separate model. The methodology relies on the non-parametric interpolator thin plate spines. To test the efficacy of this framework, both percent volume and dominant height response to repeated fertilizer treatments were estimated using data from long-term research trials in Georgia. Several environmental covariates were evaluated on their ability to reduce the models’ root mean square error and account for more of the variation in percent gain from fertilization regimes. Results showed that the inclusion of such covariates improved the model performance and reduced errors associated with interpolation. Thresholding expected responses from fertilization treatments allows practitioners to evaluate the probability of achieving a given response.

中文翻译：

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使用环境协变量估计火炬松人工林施肥反应的非参数框架

施肥是提高美国东南部生产力和林分价值的常见做法。对给定地点施肥的决定取决于地点特征和预期的响应幅度。为了确定规模，森林研究人员通常依赖于在整个感兴趣区域建立的施肥试验，并得出生长方程以反映场地指数或体积的增加。这样的方程缺乏明确的空间预测成分。为了弥合这一差距，我们开发了一个建模框架，该框架明确评估了作为二元过程的受精反应的可能性以及作为单独模型的这种反应的幅度。该方法依赖于非参数插值器薄板脊柱。为了测试这个框架的功效，使用佐治亚州长期研究试验的数据估计了对重复施肥处理的体积百分比和主要高度响应。评估了几个环境协变量降低模型的均方根误差的能力，并解释了施肥方案获得的百分比增益的更多变化。结果表明，包含这些协变量提高了模型性能并减少了与插值相关的错误。对受精治疗的预期反应设定阈值允许从业者评估实现给定反应的可能性。评估了几个环境协变量降低模型的均方根误差的能力，并解释了施肥方案获得的百分比增益的更多变化。结果表明，包含这些协变量提高了模型性能并减少了与插值相关的错误。对受精治疗的预期反应设定阈值允许从业者评估实现给定反应的可能性。评估了几个环境协变量降低模型的均方根误差的能力，并解释了施肥方案获得的百分比增益的更多变化。结果表明，包含这些协变量提高了模型性能并减少了与插值相关的错误。对受精治疗的预期反应设定阈值允许从业者评估实现给定反应的可能性。