January 18, 2011 - Types of resources their interaction and...

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Continuing from last class 1. Logistic equation A. (dN / dt) = rN (1-N/K) - - As opposed to growth rate where nothing ever changes, r is modified by (1-N/K) - This is simplest way to describe as population goes up and reaches the equilibrium (when N reaches K) - Large exponent > 1. there is not much effect on density on individual death and birth until it reaches close to carrying capacity in which it goes down very quickly Exponent less than 1, even at low density, the birth - death rate goes down quickly as population size goes up. There is wide range of high population size where there is not much growth but growth does not go down fast either. Adding exponent to (N/K), what happens to relationship between N & K? - About 1/3 of population has theta (exponent) less than 1 - Problems with the applicability of logistic growth to humans B. increased population size has many potentially positive effects on birth and death rates in human - Effects have time lags: they take time to be fully effective - That is ignored in simple model Age / size and spatial structure of populations not represented; different classes have different effects on and sensitivities to density - Many more. . - ** TRUE for logistics: if population size is high and long enough, something will get depleted that is important for human population growth such that growth will decline. (Cohan calls this "uncharacteristic kind") Resources 2. Set of entities are "resources" with respect to a set of consumers A. The entities can be consumed by a consumer individual, where consumption means that they are at least temporarily transformed to an state that is unavailable to other individuals - Consumption has a positive effect on the fitness of the consumer individual (allows survival or birthrate to go up) - Sufficient consumption has the potential to decrease resource abundance enough to decrease consumer per capital population growth (B-D rate goes down) - i.e. oxygen in normal environment is NOT resource b/c variation in oxygen amount affects survival rate very little nor does it affect abundance significance ** what is to be a resource or not depends on the environment** - Types of resources; their interaction and effect on population growth January-29-11 4:03 AM January 18, 2011 Page 1
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Why study resources? B. The ability to be reduced by consumption is part of the definition of a biological resources (the other part is that its greater abundance increases population growth) Resources limit population growth - Studying consumer-resource interactions (conceptual model with density-dependence) automatically accounts for delay in the impact of higher densities on birth / death - What keeps nonhuman populations from becoming huge? C. (what 'limits' or 'regulates' populations?)
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January 18, 2011 - Types of resources their interaction and...

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