Scaling of population density on body mass and a number-size trade-off

The energetic equivalence rule (EER), that is the negative relationship between population density and body mass with the body mass exponent of - 0.75, is often observed for mammal species assemblages studied at regional scales. Little, however, is known about the mechanism that may generate it. Here we attempt to explain EER in terms of demography and life-history theory, namely on the basis of an interspecific trade-off between total lifetime female offspring and relative mass at birth. Based on data on 85 species of non-flying mammals from the territory and coastal waters of the former Soviet Union, we show that the number of offspring per lifetime is approximately inversely proportional to the relative mass at birth (the exponent is not significantly different from - 1). Simple mathematics shows that given some other conditions, this minus-one trade-off entails the energetic equivalence rule. Two other consequences also follow. First, as an interspecific trade-off evolves From the intraspecific trade-off of the same type, the tendency for small-bodied species to be more abundant than large ones may have its evolutionary origin in the intraspecific trade-off between offspring number and size. Second, the trade-off may solve the paradox relating to EER: how could it be that in spite of probably unequal food availability for so different species as, for example, mice and elephants their populations consume, on average, equal amounts of energy, as the rule implies? We suggest that populations of different species consume the same amount of energy per unit area per unit time because their individual members require the same amount of energy per unit mass per lifetime, the latter being a somewhat different formulation of the minus-one trade-off between lifetime offspring number and relative mass at birth.