Optimal defense strategies in an idealized microbial food web under trade-off between competition and defense

Abstract

Trophic mechanisms that can generate biodiversity in food webs include bottom-up (growth rate regulating) and top-down (biomass regulating) factors. The top-down control has traditionally been analyzed using the concepts of "Keystone Predation" (KP) and "Killing-the-Winner" (KtW), predominately occuring in discussions of macro- and micro-biological ecology, respectively. Here we combine the classical diamond-shaped food web structure frequently discussed in KP analyses and the KtW concept by introducing a defense strategist capable of partial defense. A formalized description of a trade-off between the defense-strategist's competitive and defensive ability is included. The analysis reveals a complex topology of the steady state solution with strong relationships between food web structure and the combination of trade-off, defense strategy and the system's nutrient content. Among the results is a difference in defense strategies corresponding to maximum biomass, production, or net growth rate of invading individuals. The analysis thus summons awareness that biomass or production, parameters typically measured in field studies to infer success of particular biota, are not directly acted upon by natural selection. Under coexistence with a competition specialist, a balance of competitive and defensive ability of the defense strategist was found to be evolutionarily stable, whereas stronger defense was optimal under increased nutrient levels in the absence of the pure competition specialist. The findings of success of different defense strategies are discussed with respect to SAR11, a highly successful bacterial clade in the pelagic ocean.

Figure 1. Killing-the-Winner (KtW) model with and without partial defense.

Original KtW model with complete defense (no predation on defense specialist, A) and modified version with partial defense analyzed here (B). The mortality rate of the predator or parasite is indicated with a horizontal arrow. The total nutrient content in the system is the sum of N, C, D and P.

Figure 2. Trade-off functions between competitive and defensive abilities of the defense strategist.

Relative affinity of defense strategist and clearance rate of predator on the defense strategist with respect to the defense strategy (0 pure competition, 1 pure defense). For a trade-off parameter of 1 (dashed line), a linear trade-off shape is obtained where the loss in competitive ability (i.e. reduction of affinity of the defense strategist) is proportional to the gain in defense (i.e. the reduction of the predator's clearance rate) as the strategy increases. For a trade-off parameter below 1 (solid lines, shown for ), a trade-off is obtained where the clearance rate drops initially more steeply than the affinity for increasing , illustrating that a lot is gained initially in terms of reduced predation for a small reduction in competitive ability. The extension to a high trade-off parameters () is trivial (i.e. the initial gain in defense is small relative to the loss in competition), but not of interest here since solutions with the defense strategist present only exist for (not shown).

Figure 3. Biomass distributions at steady state as a function of defense strategy and trade-off parameter .

Steady-state biomass distributions for the predator (P*, top), the defense strategist (D*, middle) and the competition specialist (C*, bottom) with respect to the defense strategy and trade-off parameter for three limiting nutrient contents (20, left, 50, middle, and 80, right). Other parameters as in Table 2.

Figure 4. Biomass sections as a function of the defense strategy for given trade-off parameters .

Steady-state biomass of competition specialist (C*, fine dotted lines), defense strategist (D*, dashed line) and predator (P*, solid line) as a function of defense strategy for different trade-offs ( top, middle, and bottom) for Other parameters as in Table 2.

Figure 5. Optimal defense strategies with respect to maximum biomass, maximum production and evolutionarily stable strategy (ESS).

Defense strategies corresponding to defense strategist's maximum biomass (blue), maximum production (defined as , green) and ESS (red) are shown as a function of the trade-off parameter for different nutrient contents. The ESS is defined by the maximum net growth rate of a invading mutant, which is found by critical point analysis of the first partial derivative of the net growth rate with respect to strategy (see Appendix S1). Different contours show the effect of the total nutrient content on the maximizing strategies. Other parameters as in Table 2.