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Theory of the dependence of population levels on environmental history for semelparous species with short reproductive seasons

机译：繁殖季节短的同性种种群水平对环境历史的依赖性理论

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A population that is strongly self-regulating through density-dependent effects is expected to be such that, if many generations have elapsed since its establishment, its present size should not be sensitive to its initial size but should instead be determined by the history of the variables that describe the influence of the environment on fecundity, mortality, and dispersal. Here we discuss the dependence of abundance on environmental history for a semelparous population in which reproduction is synchronous. It is assumed that at each instant t: (i) the rate of loss of members of age a by mortality and dispersal is given by a function ρ of t, a, and the present number x = x(a,t) of such members; and (ii) the number x(0,t) of members born in the population is given by a function F of t and the number of x(af,t) at a specified age af of fecundity. It is further assumed that the functions ρ and F have the forms ρ(x,a,t) = π1(a,t)x + π2(a,t)x2 and F(x(af,t),t) = νtx(af,t). For such a population, a change in the environment is significant only if it results in a change in νt π1(a,t), or π2(a,t), and, hence, the history of the environment up to time t is described by giving ντ, π1(a,τ), and π2(a,τ) for each τ ≤ t and all a in [0, af]. We show that the dependence of x on the history of the environment can be calculated explicitly and has certain properties of “fading memory”; i.e., environmental events that occurred in the remote past have less effect upon the present abundance than comparable events in the recent past.
机译：预期通过密度依赖性效应具有强烈自我调节作用的种群将是这样的：如果自种群建立以来已经过去了许多世代，那么种群的当前大小不应对其初始大小敏感，而应由种群的历史决定。这些变量描述了环境对繁殖力，死亡率和传播的影响。在这里，我们讨论了繁殖是同步的同性种群的丰富度对环境历史的依赖性。假设在每个时刻t：（i）由死亡率和分散度造成的年龄a成员的损失率由t的函数ρ给出，a的现值x = x（a，t）成员； （ii）人口中出生的成员人数x（0，t）由函数f为t给出，并且在指定生育年龄af时有x（af，t）人数。进一步假设函数ρ和F具有形式ρ（x，a，t）=π1（a，t）x +π2（a，t）x2和F（x（af，t），t）= νtx（af，t）。对于这样的人口，仅当环境变化导致νtπ1（a，t）或π2（a，t）发生变化时，环境变化才有意义，因此，直到时间t的环境历史为通过给每个τ≤t以及所有[0，af]中的a给出ντ，π1（a，τ）和π2（a，τ）来描述。我们证明了x对环境历史的依赖关系可以被明确地计算出来，并且具有“衰落记忆”的某些特性。即，与最近的可比事件相比，较远的过去发生的环境事件对当前丰度的影响较小。

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