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We have discovered a severe problem with the current theory of species-area curves (SPARs). This theory claims that we should expect SPARs with z-values of about 0.26. However, that is wrong. The correct prediction turns out to be approximately 0.77. To make this prediction,we used a stochastic sampling scheme, and constructed species-area curves from a lognormal abundance distribution, exactly as previous theory meant to do. We arrived at our prediction using two independent methods: we performed computer simulations of the scheme and we derived its analytical equation. SPARs that result from the simulations are the same as those from the equation, validating the logic of our analysis. We explain what went awry with the previous theory. However, although logically accurate, the new theory has an empirical problem:real SPARs do not have z-values near 0.77. Rather. they tend to lie in the interval 0.1--0.2. To obtain these, we added an assumption to the lognormal abundance distribution. We assumed that range size and abundance are positively correlated. This new assumption is qualitatively similar to Hanski's (1982; Oikos 38: 210-221) pattern. Finally, we derive a simple relation connecting average point diversity, average range size and species diversity for a province. [ABSTRACT FROM AUTHOR]

We trained barn owls to fly over 2-ha field enclosures containing populations of Gerbillus allenbyi. Each 2-ha plot was divided into two equal parts by a fence with gates allowing easy passage of the gerbils. We varied the number of gerbils in the enclosure and the number ofowl flights on each side of the dividing fence. Gerbil foraging activity responded within two hours to the difference in number of owl flights over the subplots. The greater the difference, the more the gerbils shifted their foraging to the subplot with fewer flights. Gerbils did not reduce their total foraging effort but redistributed it between subplots. In the absence of owl flights, gerbils divided their foraging effort equally between the matched subplots. Thus, they appear to seek an ideal free distribution in the two halves of each plot. Therefore, based on the gerbils' distribution of activity in the presence of different numbers of owl flights over the two subplots we estimated the shapes and slopes of the gerbil victim isoclines in the middle and right hand side of the 'gerbil-activity vs number of owl flights' state space. The isoclines were parallel straight lines with slope equal to -0.57. We believe this to be the first estimate of a victim isocline for a population of vertebrates in the field. Using the isodar method of Morris, we also determined that the fitness cost of each additional gerbil, i.e., per capita intraspecific competition among the G. allenbyi, is constant. It does not depend on either owl flight frequencies or G. allenbyi densities. The isodar also shows thatthe fitness cost of added owl flights does not vary with G. allenbyipopulation densities. [ABSTRACT FROM AUTHOR]