Physiological Variability in Stoichiometry

The theory sketched above treats each population's stoichiometry as fixed. This is often a reasonable approximation for animals that exhibit homeostatic composition, but autotrophs typically have highly variable composition. When a population's stoichiometry varies physiologically, the stoichiometric quantities Qjy are variables rather than constants. Their dynamics can be described by equations relating their time derivatives to the consumption, release, and use in net production of the nutrient in question. In a steady-state situation, these process balance, and the stoichiometric quantities Qj are constant. As a result, algebraic constraints representing mass conservation apply, and eqns [3] and [4] apply as steady-state approximations. The rigor of graphical analyses is somewhat diminished, but the key insights remain. In particular, graphical theory has been applied very successfully to algae competing for dissolved nutrients, despite demonstrations of potentially large physiological variations in the competitors' stoichiometry.

Physiological variation in stoichiometry can be an important determinant of a population's ability to compete for a nutrient, however. The growth rate of a population generally increases with organismal nutrient content, that is, with Q for that nutrient. At some low value Q min, population growth ceases, and as Q becomes very large, growth is maximal. Consider two populations that differ in Q min, but are otherwise equivalent (Figure 11). When population growth balances mortality, the population with lower Q min will have a lower steady-state quota. This in turn reduces the rate of nutrient consumption required for growth that balances mortality. The rate of nutrient consumption generally increases with nutrient concentration, so reducing this rate ultimately lowers steady-state nutrient concentration required by the species with the lower Qmin; that is, the quantity R* is reduced, making this species a better competitor.

Figure 11 Two populations with physiologically variable stoichiometry that differ only in minimal nutrient quota (Qmin). Each population's growth rate is an increasing function of nutrient quota, and at steady state each must grow at a rate balancing mortality.

Quota, Q

Figure 11 Two populations with physiologically variable stoichiometry that differ only in minimal nutrient quota (Qmin). Each population's growth rate is an increasing function of nutrient quota, and at steady state each must grow at a rate balancing mortality.

Now, if one species evolves a lower Q_min to become better for one nutrient, but owing to physiological constraints it then requires greater amounts of another nutrient, Qmin for that nutrient rises and this species becomes a worse competitor for it. In the graphical theory of competition for two resources (Figure 2), this makes intersections of ZNGI graphs likely for different species, and also imparts stabilizing slopes to their impact vectors. Thus, selection on the ability to compete for one resource likely produces the tradeoffs required for stable coexistence of populations competing for two resources. Experimentally, it has proven relatively easy to construct stable coexistence of algae competing for two resources, suggesting that the underlying tradeoffs are common for this group of autotrophs.

It is likely that physiological variations in stoichiome-try contribute to a population's ability to compete for a nutrient in variable environments, as well as those at steady state. Often, there is a physiological limit on the quota for a nutrient, Qmax, and the ratio of Qmax:Qmin then measures the capability to store the nutrient. Theoretical studies suggest that populations with high storage capability are favored when competition occurs in variable environments characterized by large, infrequent pulses of nutrient concentration. Such storage specialists can dominate even when they suffer disadvantages in their rates of nutrient consumption and population growth, compared to other species.

The physiological variation in stoichiometry characteristic of autotrophs plays many roles in their interactions with herbivores. Interestingly, it can theoretically permit stable coexistence of two herbivore species that compete by exploiting the same autotroph population. This result arises in mathematical models of two herbivore species consuming one algal species, whose nutrient:carbon ratio varies physiologically in response to the supply of the nutrient relative to the light intensity that supports photosynthetic carbon fixation. As is commonly observed for aquatic herbivores, their nutrient composition is homeostatic, and due to the varying composition of their food, the growth of herbivore populations can be either carbon- or nutrient-limited.

The steady states of such an interaction can be analyzed graphically through an adaptation of Figure 2. The resource axes represent the biomass densities of carbon and nutrient embodied in the algal population. Feasibility bounds and impact vectors arise in part from mass-conservation constraints, but also from other feedbacks in the interaction. When herbivores feed on algae whose composition does not meet their stoichiometric requirement, recycling of nutrient occurs, altering the supply experienced by algae and thus their nutrient:carbon ratio. Remarkably, theory predicts that these complex processes can stabilize with the algal nutrient:carbon ratio poised at a value permitting coexistence of both herbivores. In such a steady state, growth of one herbivore population is carbon-limited and that of the other is nutrient-limited. Representing this coexistence graphically requires some simplifying assumptions, but relaxing these does not change the essential prediction that two herbivores can coexist while exploiting one autotroph population. The surprise in this result is that such coexistence occurs due to stoichiometry, without any of the factors classically proposed to explain herbivore coexistence, such as spatial processes or differentiation of the autotroph individuals into various physical structures (e.g., leaves, stems, etc.).

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