Allometric Trajectories and "Stress": A Quantitative Approach

Abstract

The term "stress" is an important but vague term in plant biology. We show situations in which thinking in terms of "stress" is profitably replaced by quantifying distance from functionally optimal scaling relationships between plant parts. These relationships include, for example, the often-cited one between leaf area and sapwood area, which presumably reflects mutual dependence between sources and sink tissues and which scales positively within individuals and across species. These relationships seem to be so basic to plant functioning that they are favored by selection across nearly all plant lineages. Within a species or population, individuals that are far from the common scaling patterns are thus expected to perform negatively. For instance, "too little" leaf area (e.g., due to herbivory or disease) per unit of active stem mass would be expected to incur to low carbon income per respiratory cost and thus lead to lower growth. We present a framework that allows quantitative study of phenomena traditionally assigned to "stress," without need for recourse to this term. Our approach contrasts with traditional approaches for studying "stress," e.g., revealing that small "stressed" plants likely are in fact well suited to local conditions. We thus offer a quantitative perspective to the study of phenomena often referred to under such terms as "stress," plasticity, adaptation, and acclimation.

Keywords: fitness; morphospace; operationalization; plasticity; scaling.

FIGURE 1

How allometric trajectories can be used for quantitatively studying phenomena traditionally discussed in the context of “stress.” The simplest case is to consider a single species in a specific environment. Most individuals of a tree species have the typical proportionalities between traits (e.g., log Y = leaf mass and log X = mass of the sapwood), with some variation about this line frequently observed (white area), e.g., as heritable variants in natural populations or responses to differences in local conditions. Outside of this area, a wide “empty morphospace” (in gray) (sensu Olson, 2012) is potentially available for different morphotypes with allocation patterns that deviate from the commonly observed variants. Individuals in these areas are expected to have lower performance or fitness relative to those within the white zone. The prediction that distance from the white zone broadly correlates negatively with performance is readily testable. A tree at point A would be expected to have lower performance/fitness than a tree within the common morphospace (white band). For example, higher respiratory costs correlated with a larger body biomass per unit of leaf would decrease individual performance. Therefore, plants would be expected to recover the optimal trait combination. At some threshold level of damage, they presumably cannot recover (irreversible decline) and die. Selection is therefore expected not to favor variants that lie in empty morphospace, such as a tree in points A or B. Allometric trajectories with different intercepts within the white area likely represent different trait proportionalities favored in different environmental conditions, e.g., lower intercepts in resource-rich sites, indicating that a unit of leaf area supports a higher amount of consuming/supporting tissues because annual carbon gain (i.e., assimilation) is higher (see Figure 2B and text for further explanations).

FIGURE 2

Empirical relationships between traits and different notions of “stress.” (A) Defoliation in Moringa oleifera trees. As in most plants, undamaged shoots have a highly predictable relationship between stem mass and leaf mass (circles). Leaf harvesting temporarily diverts this relationship (diamonds), but plants stripped of their leaves sooner or later recover the pre-damage leaf mass vs. stem mass relationship (arrows). (B–D) Examples of “stressful” environments. (B) Possible variants at different elevations: in Pinus cembra from below (circles) vs. above (triangles) 1800 m a.s.l., the scaling of leaf mass vs. total body mass (roots included) follows the same exponent (∼0.85), but leaf mass per unit of body mass (i.e., Y intercept) is higher in high elevation trees. (C) Boxplot of annual shoot growth and needle length between wet (“favorable”) and dry (“stressful”) sites in Pinus sylvestris (dashed and solid lines are mean and median values respectively). This approach seems to show categorical differences between trees in sites that could be arbitrarily classified as stressed and unstressed. (D) However, when the same samples of Figure 2C are plotted as part of an allometric series, it is clear that the scaling of leaf mass vs. shoot mass (the last three growing years) converges on the same trajectory in both wet (circles) and dry (triangles) conditions. This result highlights that the species is able to build similar allometries of the distal parts of the plant in spite of different environments.