We develop a model of honey bee colony collapse based on contamination of forager bees in pesticide contaminated spatial environments. The model consists of differential and difference equations for the spatial distributions of the uncontaminated and contaminated forager bees. A key feature of the model is incorporation of the return to the hive each day of forager bees. The model quantifies colony collapse in terms of two significant properties of honey bee colonies: (1) the fraction of contaminated forager bees that fail to return home due to pesticide contamination, and (2) the fraction of forager bees in the total forager bee population that return to the sites visited on the previous day. If the fraction of contaminated foragers failing to return home is high, then the total population falls below a critical threshold and colony collapse ensues. If the fraction of all foragers that return to previous foraging sites is high, then foragers who visit contaminated sites multiple times have a higher probability of becoming contaminated, and colony collapse ensues. This quantification of colony collapse provides guidance for implementing measures for its avoidance.

中文翻译：

---

由于觅食蜂的农药污染而导致的蜂群集落崩溃的空间模型。

我们基于农药污染的空间环境中觅食蜂的污染，开发了一种蜜蜂群体崩溃的模型。该模型由微分方程和微分方程组成，用于未污染和污染的觅食蜂的空间分布。该模型的一个关键特征是将每天觅食蜂的返还归入蜂巢。该模型根据蜜蜂殖民地的两个重要特性对殖民地崩溃进行了量化：（1）因农药污染而无法返回家园的受污染觅食蜂的比例，以及（2）占总觅食蜂种群的觅食蜂的比例返回到前一天访问的网站。如果受污染的觅食者未能返回家园的比例很高，然后总人口下降到临界阈值以下，随后发生殖民地崩溃。如果返回到先前觅食地点的所有觅食者所占比例很高，则多次访问受污染地点的觅食者被污染的可能性更高，随之而来的是殖民地崩溃。殖民地崩溃的量化为实施避免殖民地崩溃的措施提供了指导。