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d_bio3 - Biomatemtica y Ecolog a a 26 de marzo de 2011 1...

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Biomatem´ atica y Ecolog´ ıa 26 de marzo de 2011 1. Dado el modelo de Ricker P t +1 = P t exp ( r ( 1 - P t K )) , pruebe por que en este modelo K se interpreta tambi´ en como la cpacidad de carga del medio. Adem´ as, discuta por que consid- erar, como en el modelo log´ ıstico, a r como la tasa de crecimiento intrinseco del modelo, tomamos la expresi´ on exp( r ) - 1. Mostremos que en efecto K es un punto de equilibrio : P * = F ( P * ) P * = P * exp r 1 - P * K 1 = exp r 1 - P * K Entonces r 1 - P * K = 0 De donde: P * = K Finalmente como si P t < K implica que Δ P < 0 , y P t > K implica que Δ P > 0; con- cluimos que K es la capacidad de carga. Ahora analicemos la tasa de crecimiento intrinseca: Δ P P = exp r 1 - P K - 1 Como P K -→ 0 tomando el l´ ımite se obtiene que : Δ P P = exp( r ) - 1 2. Comparar el modelo log´ ıstico discreto y el continuo. a. El modelo continuo b´ asicamente hac´ ıa que el tama˜no de la poblaci´ on se acercara asint´ oticamente a K, independientemente del tama˜no inicial de la poblaci´ on. La ve- locidad con que se produc´
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  • Winter '09
  • CarlosTrujillo
  • Bajo eléctrico, Selección K, Intrínseco, Catástrofe malthusiana, ıstico discreto, Percy Leroy Ricker

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