. Advances in herpetology and evolutionary biology : essays in honor of Ernest E. Williams. Williams, Ernest E. (Ernest Edward); Herpetology; Evolution. Figure 3. Stability regions for the exponential logistic (equation (6)). s = monotonic stability, o = oscillatory stability, u = unstable. The central line in the o region separates parameter choices where an increase in I decreases the rate of return to an equilibrium (to the left) from those parameters where I effects a faster return (to the right). In cyclic populations the appropriate value for T is one cycle length, whereas in a chaotic p
. Advances in herpetology and evolutionary biology : essays in honor of Ernest E. Williams. Williams, Ernest E. (Ernest Edward); Herpetology; Evolution. Figure 3. Stability regions for the exponential logistic (equation (6)). s = monotonic stability, o = oscillatory stability, u = unstable. The central line in the o region separates parameter choices where an increase in I decreases the rate of return to an equilibrium (to the left) from those parameters where I effects a faster return (to the right). In cyclic populations the appropriate value for T is one cycle length, whereas in a chaotic population a large number of generations per run starting from a num- ber of initial conditions may be required to fully characterize . What is the relationship between aver- age density and the rate of immigration? An example of a pattern that emerged repeatedly in the simulations is depicted in Figure 4. The model used for this figure has been extensively exploited by insect ecologists (, Hassell, 1975). With an added immigration term the growth model is N(t + 1) = N(t)er (1 + dN(t))-b + 1.(5) The four curves in the figure correspond to four values for the intrinsic growth rate, r. At 1=0 and high r, populations obeying equation (5) fluctuate, some- times greatly, around an unstable point equilibrium. In these unstable popula- tions, does not increase mono- tonically with I. The influx of a few immi- grants per generation may dramatically increase , and a yet greater rate of immigration may actually decrease . This nonmonotonic relation between and I has a simple explanation. In discrete-time growth models such as (5), populations with high intrinsic growth rates tend to exhibit chaotic behavior (May, 1976). Time-series of populations in chaos typically show overshoots of K followed by precipitous declines in abundance. Following each population crash, several generations may elapse before population numbers are suffi- ciently large to produce a high total growth rate, cul
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Keywords: ., bookauthorharvarduniver, bookcentury1900, booksubjectherpetology
