Date Published: January 23, 2017
Publisher: Public Library of Science
Author(s): Amanda L. Caskenette, Kevin S. McCann, Andrea Belgrano.
Ecological theory has uncovered dynamical differences between food web modules (i.e. low species food web configurations) with only species-level links and food web modules that include within-species links (e.g. non-feeding links between mature and immature individuals) and has argued that these differences ought to cause food web theory that includes within-species links to contrast with classical food web theory. It is unclear, however, if life-history will affect the observed connection between interaction strength and stability in species-level theory. We show that when the predator in a species-level food chain is split into juvenile and adult stages using a simple nested approach, stage-structure can mute potentially strong interactions through the transfer of biomass within a species. Within-species biomass transfer distributes energy away from strong interactions promoting increased system stability consistent with classical food web theory.
Ecosystem stability, the ability of an ecosystem to persist through time and resist perturbations, depends on the biological structure inherent in these ecosystems [1–4]. Modular food web theory, the study of low species food web configurations within a food web, seeks to identify how structure and interactions act together to mediate the stability of ecosystems [5,6]. The successes of this modular approach to understand the links between network structure, interaction strengths, and food web stability are encouraging. For example, modular approaches have found that weak interactions between trophic levels [3,7], coupling of strong and weak energy channels , and omnivory [9,10] can stabilize systems. Nonetheless, focusing on modules within the larger food web may not capture all network properties and, importantly for this study, tends to concentrate on species level food web structure at the cost of ignoring other biological structures that occur within species (for example, stage-structure); in doing so, important within-species structural mechanisms may be concealed .
Here, in all our numerical experiments we always start from the end case of a food chain (i.e., m = 1 and s = 1). We use previous results to inform our starting conditions (whether we are starting from an equilibrium or non-equilibrium attractor). We then vary one, and only one parameter of interest (the bifurcation parameter), and follow the fate of the interior equilibrium and its local stability (i.e., real part of the largest eigenvalue) and/or the local maxima and local minima on the attractor. This latter approach allows us to unfold the bifurcation parameter and follow non-equilibrium attractors as well, effectively determining the existence of the interior equilibrium at each new step of the bifurcation parameter, and then calculates the Jacobian of the full system  and the eigenvalues associated with this new parameter set. By continuity, we know that very small values of the modified parameter preserve the feasibility of the equilibrium solution. Thus, we follow the equilibrium (or non-equilibrium) solutions explicitly as we increase the parameter of interest.
In order to generally test whether biomass transfer between stages has the potential to alter the stability of a LHIGP module, we choose parameter combinations in our numerical experiments that result in the entire range of possible dynamic outcomes for the initial food chain endpoint (i.e., chaotic, cyclic, or stable). We then ask whether the initial source of instability affects the qualitative stabilizing effect of biomass transfer between stages. The basic food chain module is an appropriate starting point (Fig 1A) as the dynamics of the system are well known  allowing us to look at the general influence of LHIGP under different dynamical scenarios, in essence performing a sensitivity analysis over the entire suite of possible starting conditions. In what follows, we therefore separate the dynamics into four informative cases where the initial food chain is: stable (Case 1); cyclic, where the cycle is driven primarily by a strong consumer-resource interaction (Case 2); cyclic, where the cycle is driven primarily by a strong predator-consumer interaction (Case 3) and; complex dynamics where the cycles are an interaction of strong consumer-resource and strong predator-consumer interactions (Case 4).
In general we found that intermediate levels of LHIGP were stabilizing (Fig 3) regardless of the initial sources of instability (Cases 1–4). While initial sources of instability (Cases 1–4) did not have a large effect on the dynamics of the real part of the dominant eigenvalue in the LHIGP module, there were implications regarding where the maximum stability of the LHIGP module occurred in relation to the distribution of biomass (Fig 3). Finally, the point of maximum stability (Fig 4) was affected by the juvenile consumption constant (aPR).
Recent work has argued that stage-structured food web theory may frequently contrast with classical food web theory . This notion comes from the fact that since stage-structured models have some unique dynamical properties (e.g., cohort cycles ), it is unclear if a unique topology of community interactions will be stabilized in a manner equivalent to the instabilities associated with classical food web models. Given that specific differences in dynamical outcomes exist, it becomes important to ask whether stage-structure actually changes the general underlying mechanisms that drive stable webs. Much species-level theory, for example, has shown that diverting energy away from strong interactions towards weak to intermediate interactions can mute potentially strong interactions driving increased stability . We showed that the transfer of energy through ontogeny to weak interactions can act as a powerful stabilizing agent in within-species models.