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With x = population size, the nonautonomous equation x = xf(t, x) provides a very general description of population growth in which any of the many factors that influence the growth rate may vary through time. If there is some fixed length of time (usually long) such that during any interval of this length the population experiences environmental… (More)

Larval settlement of a small coral-reef fish, the bridled goby (Coryphopterus glaucofraenum), to five entire reefs over 4 yr decreased with increasing cover of hard substrate (rock and coral). Experimentally increasing rock cover on these large reefs caused a reduction in settlement that lasted 3 yr, confirming that settling coral-reef fish discriminate… (More)

We give conditions under which two solutions x and y of the Kolmogorov equation ˙ x = xf (t, x) satisfy lim y(t)/x(t) = 1 as t → ∞. This conclusion is important for two reasons: it shows that the long-time behavior of the population is independent of the initial condition and it applies to ecological systems in which the coefficients are time dependent. Our… (More)

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