Plant energetics and population density

Abstract

Enquist et al. reply — Energy equivalence, as originally defined¹, was an empirical relationship observed in animals: species differing in body mass, M, by many orders of magnitude tend to have almost equal rates of energy use per unit area by the population, because of an inverse allometric scaling relationship between energy use by the individual, or its metabolic rate, B, and the maximal population density, N_max. Because B ∝M^3/4 and N_max∝M^−3/4, energy use is proportional to BN_max∝M^3/4M^−3/4∝M.

Main

We have shown that this also holds for plants², namely that the allometric scaling of both B and N_maxappear to be the same as in animals. Further, we showed that the scaling of population density, and the resulting energy equivalence, can be explained by a simple model that assumes that plants grow until the allometric rates of resource use by the population equals the rate of resource supply.

In previous work, this was far from clear. The traditional explanation of the thinning law was not based on rates of individual resource use, but was thought to result from the geometric packing of canopies³ so that N ∝M^-2/3, or to be due to biomechanical constraints and the accumulation of non-living material⁴ so that N ∝M^−3/4. None of these studies, including that of Dewar⁵, has predicted the scaling of individual resource use. We not only make this explicit prediction, but also derive it from a model of resource distribution in plants with fractal-like branching structures⁶.

Dewar implies that energy equivalence reflects the fact that essentially all of the light is intercepted by closed canopies, and that growth rates of plants per unit of radiation are invariant. We agree, and in fact this is a special case of our general argument. Furthermore, we now have a detailed quantitative whole-plant model of resource distribution from which the general derivation of energy equivalence follows⁷. This model assumes that the size and photosynthetic rate of leaves are independent of plant mass. It predicts the number of leaves to be proportional to B, which is proportional to M^3/4. This is exactly the condition needed to give the density-mass relationship and therefore energy equivalence. But our model is much more general because it also applies to populations in which canopies are not closed and where water or nutrients, as well as light (as claimed by Dewar), are the critical limiting resources.

Dewar correctly observes that there may be a slight decrease in production or growth following canopy closure during secondary succession. But this is a point of detail. The hundred-fold variation in resource use, including any possible decline in production associated with age, is very small compared with the trillion-fold variation in vascular plant size. We emphasized that ecosystems such as adjacent grasslands and forests, which have similar rates of resource supply but are dominated by plants differing by many orders of magnitude in mass, typically have similar rates of primary production. This does not seem to have been appreciated, despite work on relationships between population density and plant size and between individual plant performance and ecosystem productivity.

We agree with Magnani that transpiration and plant metabolism are influenced by local environmental conditions, especially when comparisons are made between individuals of relatively similar size^8,9. This accounts, for example, for the nearly two orders of magnitude variation in productivity of ecosystems dominated by similarly sized plants (our Fig. 4 in ref. 2); a good example would be to compare Arctic tundra with tropical grassland. Organism transpiration and metabolism, however, are even more strongly influenced by plant size (our Fig. 1). Thus, rates of xylem flux vary by only about two orders of magnitude as plant mass varies by 12 orders of magnitude from the smallest herbs and seedlings to the largest trees.

The rates of evaporation for ecosystems (our Fig. 4) are near-maximal short-term rates measured for individuals of known size of different plant species under near-optimal conditions. A few of these values are indeed higher than rates reported for ecosystems averaged over longer periods of months to years. Given this caveat, it is impressive that our estimates obtained by scaling up from individual plants (max, 82.4 l m^-2 per day; min, 1.0 l m^-2 per day; mean, 16.3 l m^-2 per day, s.d. 16.44) are within an order of magnitude of the maximum reported values. Most values fall within the range obtained using different sampling techniques, including remote sensing, for estimating the productivity of entire ecosystems¹⁰.

We therefore disagree with Magnani's objection to our extrapolation of the consequences of allometric scaling at the level of individual plants to processes that operate at the level of populations and ecosystems¹¹. Allometric relationships are not useful for understanding small differences in performance among similarly sized plants, such as forest trees following canopy closure. Allometry is invaluable, however, for understanding the pervasive effects of plant size on such diverse phenomena as the structure of single- and mixed-species stands, or on the productivity of ecosystems dominated by plants of contrasting size, such as adjacent agricultural fields, grasslands and forests. Understanding quarter-power allometric scaling relations at different levels of biological organization (in both plants and animals) will contribute to a common explanation of how body size influences the acquisition and allocation of resources and thereby affects the abundance, distribution and diversity of sizes.