标题： 带有标记的更新过程模型用于描述蜂群的规模 显示英文标题

标题： A marked renewal process model for the size of a honey bee colony

摘要： 许多农业领域依赖于蜜蜂提供授粉服务，蜜蜂数量的减少可能会影响全球粮食安全。为了理解蜂群的动力学，我们提出了一个用于描述蜂群规模的离散时间标记更新过程模型。我们证明，在温和条件下，该模型达到一个依赖于每批卵数量分布、卵孵化概率以及批次之间时间和蜜蜂寿命分布的平稳分布。这使得可以分析性地研究这些数量变化的影响。然后我们将此模型扩展到具有周期性年度效应的情况，例如，每批卵的数量和{卵孵化的概率}可能随季节变化。 显示英文摘要

摘要： Many areas of agriculture rely on honey bees to provide pollination services and any decline in honey bee numbers can impact on global food security. In order to understand the dynamics of honey bee colonies we present a discrete time marked renewal process model for the size of a colony. We demonstrate that under mild conditions this attains a stationary distribution that depends on the distribution of the numbers of eggs per batch, the probability an egg hatches and the distributions of the times between batches and bee lifetime. This allows an analytic examination of the effect of changing these quantities. We then extend this model to cyclic annual effects where for example the numbers of eggs per batch and {the probability an egg hatches} may vary over the year.