Plant energetics and population density

Abstract

Enquist et al.¹ present data from 37 plant species showing that the use of resources by individual plants scales approximately as the 3/4 power of plant mass, as predicted previously from a model of resource use in fractal-like branching structures². Thus, Q ∝ M^3/4, where Q is the resource use, estimated as xylem transport, and M is the plant mass. In addition, their re-analysis of data from 251 populations¹ showed that the ‘thinning law’ between maximum plant population density (N_max) and plant mass also obeys 3/4-power scaling, with N_max∝ M^−3/4. From these two data sets, they inferred that population resource use per unit area is approximately independent of plant mass, with N_maxQ ∝M⁰, a relation termedenergy equivalence³.

Main

Conversely (and more generally), the thinning law (with exponent − y, say) can be viewed as the consequence of energy equivalence and allometric scaling of individual resource use (with exponent y). This resource-based interpretation of the thinning law has been proposed previously for both plant⁴ and animal⁵ populations, but the theoretical derivation² of y =3/4 is an important new insight. Energy equivalence itself cannot be explained in any mechanistic sense by allometric scaling of individual resource use, despite apparent claims to the contrary¹, and remains to be accounted for as an empirical observation³.

I suggest that, for plant populations, energy equivalence reflects the facts that: (1) once plant canopies have reached closure, most of the incident radiation per unit area is intercepted^6,7; and (2) for well-watered plants, growth rate per unit of intercepted radiation (that is,the light utilization efficiency, or LUE) is approximately independent of plant mass^8,10. There is now a mechanistic explanation for the latter observation in terms of leaf photosynthetic acclimation to light¹¹. It follows that, for closed canopies not subject to water limitation, population energy use for growth is roughly independent of plant mass, but may vary with incident radiation and LUE. An analogous argument, involving mass-independent population resource capture and utilization efficiency, might also explain energy equivalence in animal populations.

However, a word of caution is needed here. An important counter-example to energy equivalence is given by the welldocumented observation that the growth rate per unit area of evenly aged forests eventually declines as individual trees become larger^12,13. Above-ground net primary productivity typically reaches a maximum in young forest stands and then decreases by up to 76%, with an average reduction of 34% according to 13 studies of forest age sequences¹⁴. The rate of decline has important implications for sustainable forest management and the role of forests in the global carbon budget. This apparently universal phenomenon has been attributed, at least in part, to height-dependent hydraulic limitations on leaf stomatalconductance^14,15, implying that leaf photosynthetic rate and LUE may not always be independent of plant mass, particularly under water-limited conditions.

In summary, it is probably more appropriate to consider energy equivalence — like the thinning law — as an approximate rule of thumb, rather than as a fundamental law applicable to all plant types under all growth conditions.

Reply See Also - Magnan