瓦螨和蜜蜂的种群动力学：年龄结构和季节性对寄生的影响
Population dynamics of Varroa mite and honeybee: Effects of parasitism with age structure and seasonality
摘要：
蜜蜂在许多农作物的生产和维持不受干扰的生态系统中的植物多样性方面发挥着重要作用。蜜蜂数量的迅速减少引起了全世界的极大关注。先前的研究表明，寄生的瓦螨可能是菌落损失的主要原因。为了研究螨类对蜜蜂种群动力学和蜂群健康的影响，提出了一个考虑蜂螨从蜂到蜂的时滞的蜂螨育雏-成虫模型。注意到蜂群的动态随季节而变化，我们验证了模型并在恒定和波动的季节性情景下进行了参数估计。分析和数值计算结果表明：（a）在有寄生螨存在的情况下，从幼螨到成螨的大时滞会破坏种群动力学的稳定性，导致种群崩溃，但当时滞较小时或处于中等水平时，成螨的自然死亡率较低，可以促进无螨种群的形成;（b）在季节性不变的情况下，小的幼虫感染率可以使种群稳定在唯一的内部平衡，而在考虑季节性的情况下，小的幼虫感染率可能会使螨种群灭绝;（c）在恒定和季节性的条件下，高的幼蜂感染率会使蜂群动态不稳定，导致种群崩溃，这取决于最初的种群规模;（d）敏感性分析的结果表明，蚁后的产卵可能对蜂群规模产生最大的影响。育雏死亡率和育雏存活率的一半最大的殖民地规模也被证明是高度敏感的，与殖民地人口规模呈负相关。我们的研究结果提供了见解的动态季节性的影响。
英文摘要：
Honeybees play an important role in the production of many agricultural crops and in sustaining plant diversity in undisturbed ecosystems. The rapid decline of honeybee populations have sparked great concern worldwide. Previous studies have shown that the parasitic Varroa mite could be the main reason for colony losses. In order to understand how mites affect population dynamics of honeybees and a colony health, we propose a brood-adult bee-mite model in which the time lag from brood to adult is taken into account. Noting that the dynamics of a honeybee colony varies with respect to season, we validate the model and perform parameter estimations under both constant and fluctuating seasonality scenarios. Our analytical and numerical studies reveal the following: (a) In the presence of parasite mites, the large time lag from brood to adult could destabilize population dynamics and drive the colony to collapse; but the small natural mortality of the adult population can promote a mite-free colony when time lag is small or at an intermediate level; (b) Small brood' infestation rates could stabilize all populations at the unique interior equilibrium under constant seasonality while may drive the mite population to die out when seasonality is taken into account; (c) High brood' infestation rates can destabilize the colony dynamics leading to population collapse depending on initial population size under constant and seasonal conditions; (d) Results from sensitivity analysis indicate the queen's egg-laying may have the greatest effect on colony population size. The brood death rate and the colony size at which brood survivability is the half maximal were also shown to be highly sensitive with an inverse correlation to the colony population size. Our results provide insights on the effects of seasonality on the dynamics.
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