emery_Lecture_13

emery_Lecture_13 - Lecture 13 Density Dependence...

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Lecture 13 Density Dependence Calculating doubling time of a population that is exhibiting exponential growth: solution: N t = N o e rt let 2N o = N t 2N o = N o e rt 2 = e rt Continuous: ln2 = lne rt ln2 = rtlne (lne = 1) ln2 = rt t = ln2/r doesn’t matter what population size is, doubling time is same t = 0.7/r Discrete: t = 0.7/lnλ Review assumptions of geometric/exponential growth Discrete growth = N t = N o λ t Continuous growth = N t = N o e rt Assumptions: 1. pop. is “closed” – there is no immigration or emigration 2. birth and death rates (and therefore λ and r) are constant - unlimited resources - no environmental stoichasticity - no predators 3. all individuals are identical 4. no time lags Incorporate random noise - exponential growth and environmental stoichasticity N t = N o e rt N t = N o e rt average population size, average r σ 2 Nt = N o e e 2rt (e σ2rt -1) variants increase over time can predict mean pop size but variance increases over time and becomes harder to predict over time spread (variances) increases over time pop size
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   N t time Arim et al 2006 - density dependent population growth: the per capita growth rate is affected by the  density or  size of the population non-log non- log      N (1/N)dN/dt   time N      N
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emery_Lecture_13 - Lecture 13 Density Dependence...

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