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Unformatted text preview: Notes on a juvenile-adult model Patrick De Leenheer * January 22, 2009 These notes describe a model of a population consisting of juveniles and adults. We will determine the fixed points and their stability. We denote J n and A n as the number of juveniles and adults at time n respectively and make the following assumptions: 1. A fraction f ∈ (0 , 1) of juveniles makes it to adulthood between two consecutive times. The rest, a fraction 1- f , remain juveniles. 2. The average number of off-spring per adult between consecutive times is b ∈ (0 , 1). 3. The survival chances of an adult between consecutive times depends on the current number of adults in the population (density dependence). For instance, food sources for adults could be scarce. If the population has A n adults, we assume that the probability that an adult survives to the next time step n + 1 is given by the following survival function: s ( A n ) = a 1 + kA n , a ∈ (0 , 1) and k > . The population model is: J n +1 = (1- f ) J n + bA n (1) A n +1 = fJ n + s ( A n ) A n (2) Fixed points Clearly ( J,A ) = (0 , 0) is a fixed point of (1)- (2), but are there any others? From (1) we find that at any fixed point there must hold that:...
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- Summer '06
- Assumption of Mary, Stability theory, Fixed points