We assume that at any given density birth rates and death rates do not change

We assume that at any given density birth rates and

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intersects the death rate curve. We assume that at any given density birth rates and death rates do not change overtime so the two curves intersect at a single point, k, which is constant overtime (invariant density dependent vital rates) We can also assume that at any given density, both the birth and death rates vary overtime, as indicated by the broad bands. As a result, the birth and death rate curves can intersect at a broad range of values causing k to take on a range of values as well (fuzzy density-dependent vital rates) o Population fluctuations (all pops. fluctuate – some erratically, some very regularly)
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Size rises and falls over time Population fluctuations in some populations can occur as erratic increases or decreases in abundance from an overall mean. In other populations fluctuations, can occur as deviations from a population growth pattern, such as exponential or logistic growth o Population cycles (regular fluctuations) Alternating periods of high and low abundance occur after constant intervals of time. Such regular cycles have been observed in populations of small rodents such as lemmings and voles whose abundances typically reach a peak every 3-5 years o Chaos (appears noise-like, but is constrained) – not in the textbook Delayed density dependence Variation in r and population growth o The effect of population density is often delayed in time o Delays or time lags, are an important feature of interactions in nature o Time lags can cause delayed density dependence which can result in population cycles o It is common for the number of individuals born in a given time period to be influenced by the population densities or other conditions that were present several time periods ago. o Delayed density dependence: delays in the effect that density has on population size o Instead of growth tracking current population size (as in logistic), growth tracks density at tau units back in time dN/dt = rN [1-(N (t-tau) /K)] If r(tau) is small, logistic If rtau is intermediate, damped oscillations If rtau is large, stable limit cycle
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