The dynamic interactions between predators and their prey have two fundamental processes: numerical and functional responses. Numerical response is defined as predator growth rate as a function of prey density or both prey and predator densities [dP/dt = f(N, P)]. Functional response is defined as the kill rate by an individual predator being a function of prey density or prey and predator densities combined. Although there are relatively many studies on the functional response in mammalian predators, the numerical response remains poorly documented. We studied the numerical response of Eurasian lynx (Lynx lynx) to various densities of its primary prey species, roe deer (Capreolus capreolus), and to itself (lynx). We exploited an unusual natural situation, spanning three decades where lynx, after a period of absence in central and southern Sweden, during which roe deer populations had grown to high densities, subsequently recolonized region after region, from north to south. We divided the study area into seven regions, with increasing productivity from north to south. We found strong effects of both roe deer density and lynx density on lynx numerical response. Thus, both resources and intraspecific competition for these resources are important to understanding the lynx population dynamic. We built a series of deterministic lynx–roe deer models, and applied them to the seven regions. We found a very good fit between these Lotka–Volterra type models and the data. The deterministic models produced almost cyclic dynamics or dampened cycles in five of the seven regions. Thus, we documented population cycles in this large predator–large herbivore system, which is rarely done. The amplitudes in the dampened cycles decreased toward the south. Thus, the dynamics between lynx and roe deer became more stable with increasing carrying capacity for roe deer, which is related to higher productivity in the environment. This increased stability could be explained by variation in predation risk, where human presence can act as prey refugia, and by a more diverse prey guild that will weaken the direct interaction between lynx and roe deer.

中文翻译：

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捕食者对猎物的数值响应：欧亚山猫和狍子的动态相互作用和种群周期

捕食者和猎物之间的动态相互作用有两个基本过程：数字响应和功能响应。数值响应定义为捕食者生长速率，作为猎物密度或猎物和捕食者密度的函数 [ dP/dt  =  f ( N , P )]。功能反应被定义为个体捕食者的杀死率是猎物密度或猎物和捕食者密度之和的函数。尽管关于哺乳动物捕食者的功能反应的研究相对较多，但数字反应的记录仍然很少。我们研究了欧亚山猫（ Lynx lynx）对其主要猎物物种狍（Capreolus capreolus）和其自身（山猫）不同密度的数值响应。我们利用了一种不寻常的自然环境，跨越了三十年，山猫在瑞典中部和南部消失了一段时间，在此期间狍子数量增长到很高的密度，随后从北到南一个又一个地区重新定居。我们将研究区域分为七个区域，生产力从北到南逐渐增加。我们发现狍子密度和山猫密度对山猫数值响应都有很强的影响。因此，资源和对这些资源的种内竞争对于理解山猫种群动态都很重要。我们建立了一系列确定性的山猫-狍模型，并将其应用于七个区域。我们发现这些 Lotka-Volterra 类型模型和数据之间非常吻合。确定性模型在七个区域中的五个区域中产生了几乎循环动态或减弱的循环。因此，我们记录了这个大型捕食者-大型食草动物系统中的种群周期，但这种情况很少发生。衰减周期的振幅向南减小。因此，随着狍子承载能力的增加，狍子和狍子之间的动态变得更加稳定，这与环境生产力的提高有关。这种稳定性的增加可以通过捕食风险的变化来解释，人类的存在可以充当猎物的避难所，并且猎物群体更加多样化，这将削弱山猫和狍子之间的直接互动。