捕食者——猎物功能反应模型初探

Study On Functional Response Models Of Predator To Prey

本文通过分析在捕食的情况下猎物种群的平均绝对增长速率与捕食效应的关系以及捕食者的捕食平均绝对速率与猎物密度的关系,建立了捕食者——猎物功能反应的一般模型:dHa/dHt=A(Ha/Ht)f(Ht) 其中,A为捕食者与猎物行为常数,f(Ht)为待定函数。 (1)在捕食速率与猎物密度无关时,这时f(Ht)=常数。其功能反应模型为: 其中,a为攻击速率,b^(-1)为猎物群体防御系数,H_k为捕食量阈值。当b=1时,即表示猎物无群体防御效应,这时模型即成为HollingI型反应模型。 (2)在捕食速率与猎物密度有关的情况下,通过对最大捕食率限制因素的分析,结果认为捕食平均绝对速率随着猎物密度的增加而下降。因而对f(Ht)进行了如下假设: (a)设f(Ht)=1/Ht,代入一般方程式后得Ha=ae^(b/Dt) 其中,a为最大捕食量,b为最佳寻找猎物密度。此模型是描述Ⅲ型曲线。但当b=1时,模型实际上是描述Ⅱ型反应。 (b)设f(Ht)=1/(1+bHt)时,得功能反应模型为:Ha=a(bHt/1+bHt)~e 其中,a为最大捕食量,(c—1)/b为最佳寻找猎物密度。当c>1时,模型描述Ⅲ型曲线。当c=1时模型即为圆盘方程。如果进一步对f(Ht)进行假设可以得到一系列的新的功能反应模型。通过对上面模型的分析,笔者认为功能反应模型按Holling的Ⅰ、Ⅱ、Ⅲ型反应相应划分是不方便的。建议按“捕食速率与猎物密度无关或有关”两个类型划分。并认为Ⅲ型模型在昆虫中也能得到较广泛的应用。

Through analyses of the relationships between the mean absolute rate of the prey population increase and the predatory efficiency (Ha/ Ht) and the relationships between the mean attack absolute rate (dHa/dt) and the prey population density (Ht),we have introduced a common model of the functional response of predator to prey: A is the behavioural constant of predator and prey (1)When the attack rate is irrelevant to the prey density,thus,f(Ht)= constant, and the functional response model is, in which, a is the attack rate; b^- is the coefficient of prey defence in society; Hk is the threshold of numbers eaten(if prey numbers are more than Hk,the predator will eat no more) When b=l, that is, the prey has’no defence in society, thus this model has become the"type l"response equation, (2) When the attack rate is relevant to the prey population density, through analyzing the limitation factors of the maximum attack rate, we have concluded that the mean attack absolute rate decrease with the prey population density increase. Thus we can assume that the function f(Ht) is following form: (a)assuming that, f(Ht)=l/Ht, and substituting it into common model gives us.H_e=ae-(b/Ht) where a is the maximum eating number, and b is the optimum prey density for searching by predator, This equation will describe a "type 3" response.But whsn b=l,it really will depict the "type 2" response. (b)assummg that,f(Ht) = 1/(1+bHt),as a result the response equation will be.Ha=a(bHt/1+bHt)~x(C≥1)where a is the maximum eating number, and (c-1)/b is the optimum prey density for searching by predator. When c>l, it will become Hoiling’ s disc equation We can get more new response models if further assuming the form of the function f(Ht). Through analyzing the response models above, the writer have considered that we classified the response models according to Holling’s"type 1,2 or 3" response was defective, and suggested that the functional response models could be divided into two types according to that the attack rate is irrelevant or relevant to the rey population density.