prey&quot; F. Population Dynamics of Predation we can look at effects of predation on the population dynamics (i.e., changes in density over time) of both the predator and its prey we will begin by considering a relatively simple model based on differential equations considering just one predator and one prey species: Lotka-Volterra Predator-Prey Model here we have two basic components : C = number (or density) of the consumer (= predator) population N = number (or density or biomass) of the prey or plant population here we have two simultaneous differential equations , one for the prey and one for the predator 1) PREY POPULATION GROWTH RATE: prey population growth rate = exponential birth rate - predator-caused death rate assumption #1 : in the absence of predators, the prey population increases exponentially, i.e., no density-dependence: dN/dt = r N but prey individuals are removed (i.e., killed) by predators: the rate of removal depends on the rate of predator-prey encounters and the efficiency of the predator encounters increase as: 1) the number of predators (C) increase 2) the number of prey (N) increases the predator&#146;s efficiency can be designated a', the &quot;attack rate&quot; of the predator&#151;a' increases with: 1) increasing search efficiency 2) increasing capture efficiency assumption #2 : a' comes from linear functional response: the rate of successful encounters (i.e., the consumption rate) will then be: a'CN and the overall equation for the prey population dynamics becomes: dN/dt = r N - a'CN (a) 2) PREDATOR POPULATION GROWTH RATE: predator population growth rate = birth rate - background mortality rate in the absence of food (prey), individual predators lose weight and starve to death therefore, in this model, predators are assumed to suffer a &quot;background&quot; mortality&#151;decline exponentially through starvation in absence of prey: dC/dt = -qC where: q = mortality rate this lose of predators is counteracted by predator birth, which depends on: 1) the rate at which food (prey) is consumed: a'CN 2) the predator's efficiency (f) of turning this food into predator offspring there are two additional assumptions here: assumption
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predators are assumed,List([1764, 1785)) s efficiency can be designated,List([1147, 1177)) s efficiency can be designated,List([1147, 1177)) the prey population increases exponentially , i.e. , no density - dependence the prey population increases exponentially , i.e. , no density - dependence we have the prey population increases exponentially , i.e. , no density - dependence we will begin we have the prey population increases exponentially , i.e. , no density - dependence we will begin we have the prey population increases exponentially , i.e. , no density - dependence
the number of predators predator birth individual predators we predators individual predators the consumption rate predators s efficiency individuals dN/dt = r N but prey individuals are removed (i.e., killed) by predators: the rate of removal depends on the rate of predator-prey encounters and the efficiency of the predator a relatively simple model the prey population increases exponentially, i.e., no density-dependence: dN/dt = r N but prey individuals are removed (i.e., killed) by predators: the rate of removal depends on the rate of predator-prey encounters and the efficiency of the predator encounters increase as: 1) the number of predators (C) increase 2) the number of prey (N) increases the predator&#146;s efficiency can be designated dN / dt = r N but prey individuals are removed ( i.e. , killed ) by predators : the rate of removal depends on the rate of predator - prey encounters and the efficiency of the predator encounters increase as : 1 ) the number of predators ( C ) increase 2 ) the number of prey ( N ) increases the predator & # 146  dN / dt = r N but prey individuals are removed ( i.e. , killed ) by predators : the rate of removal depends on the rate of predator - prey encounters and the efficiency of the predator encounters increase as : 1 ) the number of predators ( C ) increase 2 ) the number of prey ( N ) increases the predator & # 146  dN / dt = r N but prey individuals are removed ( i.e. , killed ) by predators : the rate of removal depends on the rate of predator - prey encounters and the efficiency of the predator encounters increase as : 1 ) the number of predators ( C ) increase 2 ) the number of prey ( N ) increases the predator & # 146  dN / dt = r N but prey individuals are removed ( i.e. , killed ) by predators : the rate of removal depends on the rate of predator - prey encounters and the efficiency of the predator encounters increase as : 1 ) the number of predators ( C ) increase 2 ) the number of prey ( N ) increases the predator & # 146  dN / dt = r N but prey individuals are removed ( i.e. , killed ) by predators : the rate of removal depends on the rate of predator - prey encounters and the efficiency of the predator encounters increase as : 1 ) the number of predators ( C ) increase 2 ) the number of prey ( N ) increases the predator & # 146  q = mortality rate differential equations
increase depends starve therefore have are assumed lose will be to suffer can be designated are removed encounters based becomes s efficiency can be designated becomes,List([778, 1520))):(a' s efficiency can be designated a ' comes becomes,List([778, 1520))):(we s efficiency can be designated a ' comes becomes,List([360, 1520))):(we s efficiency can be designated a ' comes becomes,List([181, 1520))):(we s efficiency can be designated a ' comes becomes,List([181, 1520))):(we is counteracted considering
the number of prey
on: 1) the rate
two simultaneous differential equations
L:in this model
weight L:dN/dt = r N - a'CN (a) 2) PREDATOR POPULATION GROWTH RATE
a'CN and the overall equation for the prey population dynamics T:then
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on differential equations
comes from linear functional response
have two basic components L:here
will begin by considering a relatively simple model
can look at effects of predation on the population dynamics (i.e., changes in density over time) of both the predator and its prey
will begin by considering a relatively simple model based on differential equations
by predator birth L:dC/dt = -qC
just one predator and one prey species