Soil food webs in agricultural ecosystems - Microbial Ecology in Sustainable Agroecosystems - page 71

the steady-state biomass of functional group i ( X * i in Equation 4.2 and Equation 4.3 ) in the
rate equations can be approximated from long-term seasonal averages of biomass of func-
tional group i ( B i ). Second, we assume that the consumption terms in the rate equations for
prey i to predator j represent the flux rates estimated as described in Equation 4.1 , that is,
F ij = f ( X i *) X j *. Under these assumptions, the off-diagonal interaction strengths are α ij = − F ij /
B j for the per capita effect of predator j on prey i , and α ji = a j p j F ij / B j for prey i on predator j
(Moore et al., 1993; de Ruiter et al., 1994, 1995).
The diagonal elements α ii of the matrix depicting the degree of self-limitation for a
group cannot be derived from field data or estimates of energy fluxes as described. Here,
we assume that all groups possess some degree of self-limitation, and that the magnitude
of the effect can be scaled s i in a density-dependent manner to the specific death rates d i ,
that is, α ii = − s i d i (de Ruiter et al., 1995), or can be set at levels that ensure stability (Neutel
et al., 2002).
Stability is assessed by evaluating the eigenvalues of the Jacobian matrix. If the real
parts of each of the eigenvalues are negative, then the system is deemed stable. In this case,
when the system is disturbed and populations deviate from their equilibrium, the popula-
tions and hence the system will return to their equilibrium. If the real part of any of the
eigenvalues is zero or positive, then the system is deemed unstable. In this case, the system
does not return to its original equilibrium state.
4.3 Patterns in energy flux and interaction strength
The food web descriptions of the shortgrass steppe and tillage agricultural systems reveal
three important patterns in the arrangement of interactions and the distribution of bio-
mass and energy flux within the food web that are important to their dynamic stability
(May, 1972; Coleman et al., 1983; Moore and Hunt, 1988; Rooney et al., 2006). First, the
biomasses of the functional groups and fluxes among the functional groups possess pyra-
midal arrangements with an ascending distribution of trophic position. With this arrange-
ment, the majority of biomass and the dominant fluxes are at the lower trophic positions.
Second, the food webs possess a distinct asymmetry in the pattern of interaction strength
when arranged by trophic position. The effects of prey on predators are large at the base of
the food web and decrease with increased trophic position, while the converse is true for
the effects of predators on prey ( Figure 4.5 ) .
The connectedness structure and energy fluxes reveal a third pattern; the functional
groups are compartmentalized into subsystems based on dominant flows of energy,
termed energy channels (Moore and Hunt 1988; Moore and de Ruiter, 1997; Table 4.4 ). The
energy channels originate from plant roots and continue through their consumers (root
energy channel) and from detritus through bacteria and their consumers (bacterial energy
channel) and fungi and their consumers (fungal energy channel). The boundaries of sub-
systems are often defined in terms of temporal or spatial scaling ( Table 4.5 ) . This follows
an arrangement that Coleman et al. (1983) recognized within the rhizosphere; the dynam-
ics of the transfer of C and N among plants and soil biota is mediated by a fast cycle
dominated by bacteria and their consumers and a slow cycle dominated by fungi and their
consumers. A spatial component is evident when considering the spatial extent, movement
patterns, and water requirement of the organisms within each channel.