Key words: predation, competition, exploitation, trophic dynamic model, ... Interspecific competition and intraspecific regulation had secondary roles in ...
Hydrobiologia 291 : 157-178, 1994 . © 1994 Kluwer Academic Publishers . Printed in Belgium .
157
The roles of predation, competition, and exploitation in the trophic dynamics of a warmwater stream : a model synthesis, analysis, and application Michael J . Roell1 & Donald J . Orth Department of Fisheries and Wildlife Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA ; ' Present address: Missouri Department of Conservation, Fish and Wildlife Research Center, 1110 South College Avenue, Columbia, MO 65201, USA Received 17 November 1993 ; accepted 24 November 1993
Key words: predation, competition, exploitation, trophic dynamic model, warmwater stream, food web analysis
Abstract We developed a trophic dynamic model of key populations and processes in the New River, West Virginia, to identify the mechanisms most responsible for maintaining food web structure . Key populations were represented by thirteen model components and were aquatic insects ; age-1 and age-2 crayfish (three species) ; age-1 and age-2 hellgrammites (Corydalus cornutus larvae) ; non-game fishes ; age-0, age-1, and adult smallmouth bass (Micropterus dolomieu) ; age-0, age-1, and adult rock bass (Ambloplites rupestris) ; and age-0, age-1 to age-3, and adult flathead catfish (Pylodictis olivaris) . In this system, crayfish and hellgrammites are harvested to provide bait for the recreational fishery that extensively exploits the three predatory fish species . Predation and intraspecific regulation were represented with nonlinear algorithms, and linear terms represented fishery harvests . Interspecific competition among components occurred through predation on shared prey . Error analysis of the model suggested that predation was the most important mechanism in maintaining system structure (the disposition of biomass among system components) . Further, the trophic relation between each component and its prey accounted for 34-64% of the variability in food web structure, whereas predation on each component explained 1-24% of food web structure variability. Therefore, so-called 'bottom-up' effects were more influential than 'top-down' effects . Interspecific competition and intraspecific regulation had secondary roles in maintaining New River food web structure, although intraspecific regulation was most important to aquatic insects, which were not predatory in our model . Both forms of competition are probably tempered by extensive predation and exploitation in the New River system . Exploitation was a secondary structuring agent to adult smallmouth bass, which experience a high rate of harvest in the New River .
Introduction Theoretical discussions of food web organization have suggested that prey-predator assemblages are structured by productivity at `lower' trophic levels (Lindeman, 1942; Hunter & Price, 1992 ; Power, 1992) and by population interactions at `higher' levels (Glasser, 1979 ; Huston, 1979 ; Tilman, 1982) . The underlying theme of the literature that addresses the structuring of natural communities is that productivity at lower levels and habitat quality at all levels provide the template for food web structure, and that population interactions at higher levels, principally predation and
competition, shape the biotic assemblage supported by the template . Considerable debate centers around which forces, productivity or population interactions, are most influential (Fretwell, 1987 ; Oksanen, 1988 ; Vadas, 1989 ; Hunter & Price, 1992 ; Karr et al., 1992 ; Menge, 1992 ; Power, 1992 ; Strong, 1992) . The extent to which productivity, predation, competition, and other processes shape natural assemblages in stream ecosystems is not well understood . Schlosser (1987) presented an initial conceptual framework for small warmwater streams . For lake communities, the concept of `cascading' trophic interactions (Carpenter et al., 1985 ; Kerfoot, 1987 ; Kitchell
158 & Carpenter, 1987 ; Mills et al., 1987) describes et al., 1987 ; Lobb & Orth, 1991 ; Roell & Orth, 1991, predation-mediated maintenance of food web struc1992, 1993), and trophic linkage between prey and ture or predation-caused transition from one commupredators (Roell & Orth, 1993) provided the basis for a nity structure to another. This 'top-down' regulation of preliminary concept of how exploited and unexploited trophic structure by predation also has been observed populations interact in the New River. Specific objecin stream communities (Peckarsky & Dodson, 1980 ; tives were : (1) to integrate the information on bait and Obendorfer et al., 1984 ; Walde & Davies, 1984 ; Bowlfish harvest and the age-specific dynamics of the prinby & Roff, 1986) . Among the biological processes that cipal predatory fishes and their prey into an energy flow influence food web structure, predation is best undermodel, (2) to identify the model parameters that constood, but the indirect effects of predation on communitribute most to the error of model predictions, and (3) ty structure have only recently been addressed (Kerfoot to identify the states and processes that are most influ& Sib, 1987 ; Northcote, 1988) . The effects of other ential in maintaining the structure of the prey-predator processes such as intraspecific regulation and interspeassemblage in the New River . cific competition have not been addressed simultaneously with the effects of predation, because the effects of competition alone are difficult to recognize and meaMethods sure, and because processes operating concurrently are difficult to distinguish quantitatively . In addition, fishWe developed an energy-based trophic dynamic model ery exploitation may play a role similar to predation to represent the interactions among key populations (or in shaping the structure of aquatic communities . May groups of functionally-similar populations) of prey and (1973) theorized that exploitation, particularly at high predators in the New River between Bluestone Dam rates, may destabilize community structure. and Sandstone Falls, an area of 408 ha . This sixthWe developed an energy-based trophic dynamic order river reach is 16 .4 km in length and receives model to address the roles that predation, interspean average discharge of 159 m 3 s -1 from Bluestone cific competition, intraspecific regulation, and fishery Dam, which is operated as a run-of-the-river faciliexploitation have in maintaining food web structure in ty. Roell & Orth (1991, 1992, 1993) provide more the New River, West Virginia, below Bluetone Dam . site-specific information . Model development and use This system, although simplified conceptually here, is involved four steps : (1) conceptual framework, (2) complex due to prey-predator interactions, exploitaquantitative specification, (3) model analysis, and (4) tion of benthic invertebrates and fishes, and oftensystem process analysis . conflicting management and resource use strategies . Smallmouth bass (Micropterus dolomieu), rock bass Conceptual framework (Ambloplites rupestris), and flathead catfish (Pylodictis olivaris) are the principal predatory fishes and Model components represented the principal predaare exploited heavily by anglers . These fishes prey tory fishes, which are smallmouth bass, rock bass, extensively on aquatic insects and crayfish (Decapoda : and flathead catfish, and their prey, which are aquatCambaridae) and to a lesser extent on hellgrammites is insects, crayfish, hellgrammites, and `prey' fishes . (Corydalus cornutus larvae) and fish (Roell & Orth, Energy inputs to this system were organic seston from 1993) . Productivity of the crayfish and hellgrammite Bluestone Lake and solar energy assimilated by primapopulations is high (Roell & Orth, 1991, 1992) and ry producers in the study reach . Energy outputs from supports a bait fishery (Nielsen & Orth, 1988) . Aquatthe system were waste losses, respiratory losses, nonic insect productivity is very high (Voshell, 1985) and predatory natural mortality (from intraspecific regulais supported primarily by the vast supply of energytion), and bait and fish harvest . For modeling purposrich seston from Bluestone Lake (Voshell et al., 1987), es, the detrital pool in the study reach was assumed to be relatively constant, given the considerable input but a bacterial larvicide (Bacillus thuringiensis israelensis) has been applied in the tailwaters since 1986 in of detrital material in the form of seston (see 'Quanan attempt to control nuisance adult black flies in the titative Specification' below) . Also, detritus dynamics were inconsequential in regard to our objectives . local area . Knowledge of invertebrate bait harvest (Nielsen & The structure of the model system was composed Orth, 1988), fish harvest (Pierce et al ., 1981), prey and of thirteen components . The four `prey' components were aquatic insects (other than hellgrammites), ages-1 predator population dynamics (Voshell, 1985 ; Voshell
159 and -2 crayfish, ages-1 and -2 hellgrammites, and prey fishes . Virtually all of the aquatic insect biomass was that of the collector-filterer and collector-gatherer functional guilds, so all aquatic insects except hellgrammites were modeled collectively as one component . The sizes of crayfish and hellgrammites caught for bait (Roell & Orth, 1991, 1992) and found in the diet of predatory fishes (Roell & Orth, 1993) corresponded primarily to age-1 and age-2 animals, so only those age groups were represented here . The prey fish component represented only those fishes of a size considered vulnerable to predatory fishes . The nine components representing predatory fishes were age-0, age-1, and age-2 to age-6 smallmouth bass ; age-0, age-1, and age-2 to age-5 rock bass ; and age-0, age-1 to age-3, and age-4 to age-8 flathead catfish . Age-0 fishes were considered separate components, because their diet differed from older fish (Roell & Orth, 1993) . Age-2 to age-6 smallmouth bass, age-2 to age-5 rock bass, and age-4 to age-8 flathead catfish were fully recruited to the recreational fishery and were treated as separate model components . Age groups older than age-0 fish and younger than fully-recruited age groups were considered individual components . Juvenile and/or adult fish of other fish species (white crappie Pomoxis annularis ; spotted bass Micropterus punctulatus ; sunfishes Lepomis spp . ; bigmouth chub Nocomis platyrhynchus ; common carp Cyprinus carpio ; and muskellunge Esox masquinongy) were not represented in the model, because they were relatively few in number (Lobb & Orth, 1991) .
processes . Our objectives did not require that we model seasonal aspects of the system . Component Biomasses . Four prey components and nine predator components were the state variables (X 1 , X2, . . ., X13 ; Table 1) in the model . Annual mean biomass of aquatic insects (X1) was estimated from total biomass (117 . 707 kg DW ha -1 ) reported by Voshell et al. (1987) for benthic macroinvertebrates in riffles of our study reach ; biomass was considered negligible in pools (J . R . Voshell, Jr., personal communication, 1989) . Total biomass was converted to an energy equivalent with a weight conversion factor of 6 g wet weight g -1 DW (Waters, 1977), an energy density of 5 .648 kJ g -1 wet weight (Roell & Orth, 1993), and the areas of riffles (197 ha) and pools (211 ha) in our study reach . Annual mean biomasses of ages-1 and -2 crayfish (4 .63 g m -2 =X2 ; Roell & Orth, 1992) and ages-1 and -2 hellgrammites (1 .83 g m -2 = X3 ; Roell & Orth, 1991) were converted to energy equivalents with energy densities of 3 .766 and 6 .565 kJ g - ' wet weight (Roell & Orth, 1993) . Annual mean biomass of prey fish (X4) was estimated from abundances reported by Lobb & Orth (1991) for several species/life stage groups counted along underwater transects in our study reach ; eight habitat types were sampled in approximate proportion to their areal extent . We recognized two size groups to produce a more accurate biomass estimate . The first group (9 .5 fish 100 m -2 ; 1 g mean live weight) included bluntnose minnow (Pimephales notatus), logperch (Percina caprodes), shiners (Notropis spp .), greenQuantitative specification side darter (Etheostoma blennioides), rainbow darter (Etheostoma caeruleum), sharpnose darter (Percina The state of each model component was representoxyrhyncha), unidentified darters, and age-0 bigmouth ed by the energy equivalent of annual mean biomass, chub . The second group (11 .5 fish 100 m -2 ; 3 g mean which was in terms of kilojoules per meter squared live weight) included age-0 and juvenile northern hog(kJ m -2 ) . Annual energy flows (consumption, waste sucker (Hypentelium nigricans), age-0 spotted bass, losses, respiratory losses, natural mortality, and har- and age-0 and juvenile sunfishes (Lepomis spp .) . An vest) and annual production were expressed in terms energy density of 4 .184 kJ g - ' wet weight was used for of kilojoules per meter squared per year (kJ m -2 y -1 ) . prey fish (Roell & Orth, 1993) . Annual mean biomassStates and flows were derived and employed as values es of prey fish and the nine components (X5 - Xt3 ) reprepresentative of an `average' m 2 in the study reach . resenting predatory fishes (Roell & Orth, 1993) were In addition, states and flows were represented to the converted to energy equivalents with 4 .184 kJ g -1 wet nearest 0 .001 unit to accommodate representation of weight. minor flows to or from key components and to facilSystem energy sources . Seston, periphyton, and itate balancing of all flows in the initial specification aquatic macrophytes were the principal energy sources of the model . Our use of these values does not necof the prey-predator system . The annual input of organessarily imply high measurement precision for these is seston from Bluestone Lake was derived from a convariables . We used the model to predict system equiservative estimate of 1 .64 109 kg AFDW y - ' (Voshell libriums resulting from changes to system states and et al., 1987), an energy density of 20 .083 kJ g -1
1 60 m_2) Table 1 . Annual mean biomass (Xi ; kJ and the coefficients for external feeding (Zi ; y -1 ), standard and activity metabolism y-1) (Mi ; y - 1 ) intraspecific regulation (Ri ; kJ-1 m-2 y -1 ), and annual harvest (Hi ; for each component in the New River energy flow model . (All values, except those of Xi have been rounded to the fourth decimal position) .
Component
Annual mean biomass (Xi)_
External feeding coefficient (Zi)
Respiration coefficient (Mi)
Regulation coefficient (Ri)
Annual harvest rate (Hi)
1 : Aquatic insects 2 : Ages 1-2 Crayfish 3 : Ages 1-2 Hellgrammites 4 : Prey fish 5 : Age 0 Smallmouth bass 6 : Age I Smallmouth bass 7 : Ages 2-6 Smallmouth bass 8 : Age 0 Rock bass 9 : Age 1 Rock bass 10 : Ages 2-5 Rock bass 11 : Age 0 Flathead catfish 12 : Ages 1-3 Flathead catfish 13 : Ages 4-8 Flathead catfish
192 .615 17 .435 12.012 1 .841 2 .372 2.498 4 .418 1 .753 1 .381 2.628 0.368 1 .142 0.757
403 .3821 13 .5680 0 0 0 0 0 0 0 0 0 0 0
26 .0451 6 .5665 1 .4328 8 .0621 2 .5258 1 .1458 0 .7219 4 .6374 2 .9925 2 .4720 2 .1420 1 .0060 0 .5741
0 .7280 0 .0680 0 .4615 2 .1488 3 .9410 2 .6038 0 .0771 4 .8986 4 .8209 1 .3109 17 .1746 3 .6764 0 .2442
0 0 .0778 0 .1313 0 0 0 0 .7358 0 0 0 .1115 0 0 0 .3757
Table 2 . Estimated values offi3 (y -1 ) for all trophic interactions represented in the New River energy flow model . (All values have been rounded to at least the third decimal position) .
Donor component
1 2
1 : Aquatic insects 0 2 : Ages 1-2 Crayfish 0 3 : Ages 1-2 Hellgrammites 0 4 : Prey fish 0 5 : Age 0 Smallmouth bass 0 6 : Age 1 Smallmouth bass 0 7 : Ages 2-6 Smallmouth bass 0 8 : Age 0 Rock bass 0 9 : Age 1 Rock bass 0 10 : Ages 2-5 Rock bass 0 11 : Age 0 Flathead catfish 0 12 : Ages 1-3 Flathead catfish 0 13 : Ages 4-8 Flathead catfish 0
3
4
5
5 .03 17 .06 54 .77 36 .26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
AFDW -1 (VPISU, 1985), and study reach area (408 ha) . Annual energy contribution by periphyton (and associated microbes) was estimated from Hill & Webster (1982), who reported an input of 1423 .4 103 kg AFDW for a 676 ha reach of the New River, Virginia .
6
Recipient component 9 7 8
12 .13 2 .71 0 2 .06 0 0 0 0 .20 0 0 0 0 0
10
11
1 .58 38 .45 21 .98 3 .34 23 .28 0 0 .76 6 .33 6 .01 0 0 .041 0 0 2 .05 0 1 .38 0 0 0 .006 0 0 .43 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .023 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .355 0 0 0 0 0 0 0 0 0 0 0 0 0
12
13
4 .43 1 .53 6 .79 10 .24 0 .82 0 .085 0 .47 0 .38 0 .92 0 .13 0 0 0 0 0 .10 0 .085 0 0 0 0 1 .69 0 0 0 0 0
We used a periphyton energy density of 18 .912 kJ g -1 AFDW (Cummins & Wuycheck, 1971) . Maximum summer biomass estimates were used to derive the annual energy contribution by aquatic macrophytes . Podostemum ceratophyllum biomass on rock outcrops immediately below Bluestone Dam in August 1983 (326 g DW m -2 ; Voshell, 1985) and
161
Table 3 . Estimated values of b2 ; (kJ m -2 ) for all trophic interactions represented in the New River energy flow model . (All values have been rounded to at least the third decimal position) . Recipient component Donor component
1 2
1 : Aquatic insects
0 207 .3 212 .7 222 .9 339 .1 286 .4
2 : Ages 1-2 Crayfish
0 0
3 : Ages 1-2 Hellgrammites 4 : Prey fish 5 : Age 0 Smallmouth bass
3
0
0
0 0
0 0
7 : Ages 2-6 Smallmouth bass 0 0 8 : Age 0 Rock bass
0 0
9 : Age I Rock bass
0
10 : Ages 2-5 Rock bass 11 : Age 0 Flathead catfish
6 : Age 1 Smallmouth bass
4
0 0
5
0
0
0 0
0
0
0
0 0
6
0 0
7
23 .7 0
8
243 .2 18 .0 11 .0
9
10
11
245 .9 203 .3 106 .0 0 0
17 .1 0
7 .2 4 .1
12
13
214 .0 340 .3
643 .8
0
29 .8
57 .6
20 .2 2 .1
39 .5 5 .4
0
0 .26
0 .004
0
0
0.004
0 0
0
0
0
0
0
0
3 .1
7 .2
0 0
0 0
0 .004
0
0
0 0
0
0
0
0
0
0 0
0
0
0
0
0
0
0 0
2 .0 0
5 .1 0
0
0 0
0
0 .13
0 0 .004
0
0
0
0
0
0
0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 .004
0
0
0
0
0 .004
0
0 0
0
0 0
0 0
12 : Ages 1-3 Flathead catfish 0
0
0
0
0
0
0
0 0
0
0
0 0
13 : Ages 4-8 Flathead catfish 0
0
0
0
0
0
0
immediately above Sandstone Falls in June 1987 (240 m_2 ; g DW Voshell et al., 1989) averaged 283 g DW m -2 . This species occupied 99 of 408 ha (Voshell etal.,
six dominant taxa of aquatic insects in riffles immediately below Bluestone Dam (13 .961 g DW m-2
y-1 )
1987), so biomass on a study reach basis was about 69 g DW m-2 and energy input was derived with 13 .000
and immediately above Sandstone Falls (608 g DW m -2 y -1 ) . Again, assuming negligible aquatic insect biomass in pools, these estimates were weighted by
kJ g -1 DW (based on energy densities reported for
surface area of riffles in the upper reach (127 ha) and
several submergent aquatic macrophytes by Cummins
the lower reach (70 ha) to achieve an estimate of aquat-
& Wuycheck, 1971) . Rodgers et al. (1983) estimated
is insect consumption (4450 g DW m -2 y -1 ) . We used a seston energy density of 17 .460 kJ g-1 DW,
maximum biomass and percentage of total colonized area occupied by six aquatic macrophytes in the New
which was based on the diet composition of New Riv-
River immediately upstream from Bluestone Lake ; we
er aquatic insects (Voshell, 1985) . Diet composition of
used the information for the four species that occur below Bluestone Dam to derive maximum biomass estimates for Justicia americana, Elodea nuttallii, Het-
the five dominant insect taxa was 2 .0% animal, 25 .7% diatoms, 19 .1% other algae, and 53 .2% fine detritus . Energy densities were derived from Cummins & Wuy-
eranthera dubia, and Potamogeton crispus (24 .1, 9 .5, 13 .0, and 0.1 g AFDW m -2 , respectively) . Energy
check (1971) for cladoceran zooplankton (21 .928 kJ g-1 DW), Chrysophyta (Bacillariophyceae ; 15 .958 kJ
densities of 18 .343, 17 .677, and 18 .489 kJ g -1 AFDW
g -1 DW), Chlorophyta (16 .108 kJ g -1 DW), and detri-
were estimated for E. nuttallii, H. dubia, and P. cris-
tus (18 .502 kJ g -1 DW) .
pus, respectively, from energy densities reported by Cummins & Wuycheck (1971) for the same species or
We assumed that consumption by ages-1 and -2 crayfish in the study reach was 80% seston, 10%
species in the same genus, and we assumed an energy
aquatic insects, 5% aquatic macrophyte detritus, and
density of 18 .000 kJ g -1 AFDW for J. americana . Consumption . Seston was assumed to be the exclu-
5% periphyton, which is in general agreement with other studies (Tack, 1941 ; Bovbjerg, 1952 ; Vannote & Ball, 1972) . Budd et al. (1978) demonstrated that crayfish, particularly young crayfish, are effi-
sive energy source of aquatic insects, because seston was 99 .9% of total energy inputs to the reach, and because the aquatic insect assemblage below the
cient filter-feeders, so crayfish downstream from Blue-
dam was dominated by collector- filterers and collector-
stone Dam probably consume the energy-rich seston
gatherers (Voshell et al., 1987) . Voshell (1985) and
released from the reservoir . Crayfish annual consumption (262 .839 kJ m -2 y -1 ) was derived from annual
Voshell et al. (1989) estimated consumption by the
1 62 _1;
production (6 .98 g m-2 y Roell & Orth, 1992), a gross growth efficiency of 0 .1, and crayfish energy density (see above) . Gross growth efficiency (annual production/annual consumption) was a compromise between efficiencies of 7 .3% for Orconectes limosus (Kossakowski & Orzechowski, 1975) and 15 .1% for Pacifastacus leniusculus (Mason, 1975) . Total consumption was apportioned among the four food types using the corresponding percentages . Seston, aquatic insects, aquatic macrophytes, and periphyton therefore provided 210 .271, 26 .284, 13 .142, and 13 .142 kJ m -2 y -1 to the crayfish component . Aquatic insects were assumed to be the only prey of ages-1 and -2 hellgrammites (Davis, 1903 ; Stewart et al., 1973 ; Kondratieff & Voshell, 1983 ; Merritt & Cummins, 1984) . Annual consumption by hellgrammites (61 .467 kJ m -2 y - 1 ) was estimated from annual y_1 ; production (3 .09 g m-2 Roell & Orth, 1991), gross growth efficiency (0 .33 ; Brown & Fitzpatrick, 1978), and energy density (see above), All of the prey fish species represented in our model were invertivores (Lobb & Orth, 1991) . Annual y_1) consumption by prey fish (30 .246 kJ m-2 was calculated as for hellgrammites . Prey fish annual production (4 .234 kJ m -2 y -1 ) was the product of annual mean biomass (1 .841 kJ m -2 ; see above) and a production/mean biomass (P/B) ratio of 2 .3, which was based on the average of P/B ratios reported by Neves (1981) for several small, non-game, stream fishes . Gross growth efficiency (0 .14) was computed from annual production and annual consumption reported by Small (1975) for two darter species in a Kentucky stream . Estimates of prey consumption by age groups of New River smallmouth bass, rock bass, and flathead catfish (Roell & Orth, 1993) were converted with the appropriate energy densities and then summed according to the representation of age groups in the model . Consumption of age-0 smallmouth bass, rock bass, and flathead catfish by age-1 and older smallmouth bass and flathead catfish was distinguished from the energy provided by prey fish using the species composition of fish in the diet (Roell & Orth, 1993) ; fish in the rock bass diet were unidentifiable and assumed to be from the prey fish component . Aquatic insects and crayfish were the only system components that fed on energy sources (seston, periphyton, and aquatic macrophytes) that were external to the defined model system . Consumption of external energy sources was represented as one energy flow, and was modeled as a linear, recipient-controlled function
of component biomass as follows : Coi = Zi
X
Xi
where - Coi =the consumption by component i of energy from external sources (kJ m -2 y -1 ) - Zi = the coefficient of annual energy transfer (y -1 ; Table 1), and - Xi = the annual mean biomass of component i (kJ m -2 ) . This formulation allows the component to acquire energy from external sources as needed ; therefore, the external energy source was assumed to be available in excess . This assumption was considered valid, because seston represented virtually all of the external sources of energy and was supplied in great quantity . The trophic interaction expression of DeAngelis et al. (1975), as modified by O'Neill et al. (1980), was used to represent predation by one component on another. The expression provides for predator feeding saturation at high prey abundance, intraspecific feeding interference of the predator, and availability of prey . Other trophic interaction terms (Lotka, 1925 ; Volterra, 1928 ; Holling, 1959 ; Watt, 1959 ; Ivlev, 1961) were insufficient in some respects (DeAngelis et al ., 1975 ; Hall, 1988) . DeAngelis et al. (1975) provided extensive analysis and justification for their expression . The expression has the form :
Ctij =
fij x wig x Xi
Xj bi3 + wi_j + Xi + X; X
where - Cij = the annual flow of energy from component i to component j (kJ m-2 y - 1 ) - Xi = the annual mean biomass of component i as prey (kJ m -2 ), - Xi =the annual mean biomass of component j as predators (kJ m -2 ), -fij = the coefficient of annual energy transfer (y -1 ; Table 2), - bid = a variable that relates the densities of the prey i and the predator j to the environment in which they interact (kJ m -2 ; Table 3), - wig = the fraction of prey biomass (Xi) available to predator j and reflects the foraging efficiency of the predator (unitless ; O'Neill et al., 1980) . The fij parameter defines the maximum per capita feeding rate of the predator when prey are superabun-
1 63 that a conversion factor of 6 g wet weight g - ' DW (Waters, 1977) and an energy density of 5 .648 kJ g - ' wet weight (Roell & Orth, 1993) were used . Aquatic insect egestion was estimated with a seston assimilation efficiency of 20% as found for benthic macroinvertebrates feeding on detritus (Webster, 1983) . We did not find published accounts of bioenergetics studies that distinguished SDA energy losses from other 13 metabolic losses in aquatic insects . Given that aquatic insect production and egestion accounted for 88 .5% of 1 Z-1 Ci ; annual consumption, the proportion of energy lost to x fi; = PR i; x excretion and SDA was assumed to be 5% of annual P, Xi consumption (22 .5% of assimilated energy) . By difference, energy lost to standard and activity metabolism where - PRi3 =the proportion of the total annual energy was 6 .5% of annual consumption . Thus, E01 was 0 .85 flow to component j that is from component i, and and M1 was 26 .05 y - ' . - P3 = the proportion of the maximum per capita The assimilation efficiency of Orconectes virilis feeding rate realized in nature . feeding on algae is about 70% (Jones & Momot, 1983), The P ; for the nine components representing New which was used to estimate egestion of New River River predatory fishes were the largest values of P crayfish feeding on energy sources external to the system . An assimilation efficiency of 85% (fish feeding on derived in the bioenergetics procedure used to estimate . This approach resulted in aquatic insects ; Roell & Orth, 1993) was used to esticonsumption (Roell 1989) conservative estimates of fi; . For crayfish, hellgrammate egestion of crayfish feeding on aquatic insects . mites, and prey fish feeding on aquatic insects, an Jones & Momot (1983) estimated SDA of O. virilis in three size groups ; SDA estimates for the two largestimate of P3 of 0 .3, similar to values of P ; for age-0 predatory fishes feeding on aquatic insects, was u sed . er groups, comparable to age-1 and age-2 New River Assuming an arbitrary value of 0 .5 for all wi ; (half of crayfish, were 10% and 20%, so we used 15% for the prey are available to the predator), estimates of bi3 SDA of New River crayfish . Crayfish excretion was were derived for all trophic interactions . assumed to be 10% of assimilated energy, which is comparable to fish (0 .088 ; Roell & Orth, 1993) . Thus, Metabolic energy losses . The annual metabolic energy loss from a component is the total of five fates : E02 was 0.48 and E12 was 0 .37 ; M2 was 6 .57 y -1 . egestion, excretion, apparent specific dynamic action Hellgrammites use about 28% of consumed energy (SDA), standard metabolism, and activity metabolism . for standard and activity metabolism (Brown & Fitzpatrick, 1978) . Using annual consumption and annual We modeled the sum of annual energy losses due to production (see above) to determine total metabolic egestion, excretion, and SDA as a proportion (Ei3) of the annual consumption of each prey type, which have energy losses, we estimated E13 (0.39) and M3 (1 .43 differences in digestibility . The sum of annual energy y -1 ) . losses due to standard and activity metabolism (heat Annual production values for the nine components of respiration) was modeled as a multiple (Mi ; Table representing New River predatory fishes (Roell & Orth, 1) of annual mean biomass . To specify these param1993) were converted to energy equivalents with 4 .184 eters, we estimated annual metabolic energy loss as kJ g - ' wet weight and then subtracted from correthe difference between annual consumption and annusponding annual consumption values (see above) to al production, and then apportioned this loss among estimate annual metabolic energy losses . Assimilation efficiencies of predatory fishes feeding on craythe five fates using information from previous studies . Voshell (1985) and Voshell et al. (1989) estimated fish, hellgrammites, aquatic insects, and fish were 82, production of the six dominant taxa of aquatic insects in 85, 85, and 90% (Roell & Orth, 1993) . Given the riffles immediately below Bluestone Dam (612 g DW proportions of assimilated energy excreted (0 .088) and m -2 y - ') and immediately above Sandstone Falls (31 used in SDA (0.17 ; Roell & Orth, 1993), the values g DW m -2 Y-1) . Annual production on a study reach of Ei3 for predatory fish feeding on crayfish, hellgrammites, aquatic insects, and all fish were 0 .39, 0.37, 0 .37, basis (6638 .046 kJ m -2 y - ') was estimated in a manner similar to that of consumption (see above) except and 0 .34 . We assumed an Ei3 value of 0.37 for prey dant (DeAngelis et al., 1975). The bi; parameter determines the rate at which the per capita feeding rate of the predator approaches its maximum as prey biomass increases . For example, the predator realizes a given per capita feeding rate at a lower prey biomass when the value of bi3 is large relative to when it is small . Given estimates of Ci ; and X; , thefi; parameters were estimated as follows :
E
1 64
d
fish feeding on aquatic insects . Values of Mi (Table - d t = the change in energy of component i over a given time interval (kJ m -2 y - ' ), 1) were estimated from the difference between annual metabolic energy loss and the total loss from egestion, 13 excretion, and SDA . ~ f,i x wji X Xj X X ) Ci = Zi X Xi + Intraspecific regulation and interspecific competi_ bji + wji x X1 + Xi 3=1 tion . Energy losses due to intraspecific regulation (nonpredatory natural mortality) within a component were the annual consumption of energy by component i modeled as a multiple (Ri, Table 1) of the squared value (kJ m -2 y - ' ), of component biomass (Kostitzin, 1939 ; Larkin, 1966) . For model specification, this loss was assumed equiv13 x 'wJ, x X; X Xi Eli) Fi = Zi x Xi x Eoi+'( b~, + w~i x X alent to that portion of annual production remaining . + Xi x after predation and harvest losses (O' Neill et al., 1980) . -' Therefore, an equilibrium was implied for all state varienergy lost to egestion, excretion, and SDA (kJ ables to aid model specification . For aquatic insects and m -2 y -1) crayfish, intraguild regulation is a more appropriate - Eji = the proportion of the energy consumed from description, because these components each representcomponent j that is lost from component i through ed several functionally similar species ; for clarity, we the processes of egestion, excretion, and SDA, refer to intraspecific regulation throughout this telling . - Mj = the multiple of annual mean biomass that Interspecific competition was not modeled explicitly, represents standard and activity metabolism (y - ' ), but was manifested through predators feeding on one or more of the same prey . 13 fij x wig x Xi X X3. ) Exploitation . Harvests from the crayfish, hellgramPi bi3 + wig x Xi + X 3 mite, and adult predatory fish components were each j-1 modeled as a multiple (Hi ; Table 1) of annual mean predation on component i by other components (kJ biomass . Annual harvests of ages-1 and -2 crayfish m -2 y - ' ), (0 .36 g m-2 y - ' ; Roell & Orth, 1992), ages-1 and -2 - Ri = the coefficient for intraspecific regulation hellgrammites (0 .24 g m -2 y - ' ; Roell & Orth, 1991), within component i (kJ m -2 Y_'), and and age-2 to age-6 smallmouth bass (0 .78 g m -2 y - ') - Hi = the multiple of annual mean biomass that is age-2 to age-5 rock bass (0 .07 g m-2 y-'), and ageharvested by people (y -1 ) . 4 to age-8 flathead catfish (0 .25 g m -2 y - ' ; Roell Simultaneous integration of the equations was & Orth, 1993) were transformed with the appropriaccomplished with a four-step Runge-Kutta numerical ate energy densities . Our estimate of flathead catfish integration procedure using a time step of 0 .001 year . harvest exceeded annual production, so harvest was Annual production and annual harvest also were calcuassumed to be 90% of annual production as found for lated by numerical integration . Annual production was adult smallmouth bass . Differential equations representthe difference between consumption and energy TossModel structure . es from egestion, excretion, SDA, and standard and ed inputs, outputs, and accumulation of energy in each activity metabolism . component . Net energy change during an interval of time (dXi dt -1 ) was a function of energy inputs from Model analysis consumption and energy losses due to egestion, excretion, SDA, standard and activity metabolism, predaError analysis (sensu O'Neill et al., 1980 ; Gardner tion, harvest, and intraspecific regulation : et al., 1980a ; Gardner et al., 1980b) was applied to the model for two purposes : (1) to identify parameters that most influence the variability of component dXi = C biomass, and (2) to identify the states and processi -Fi-(M.xXi)-Pi-(Rix X2)-(HixX2) dt es that most affect the structure of the New River prey-predator assemblage . Error analysis involved two steps . First, a Monte Carlo procedure was used to propagate error through the model with standardized variwhere ability in selected input parameters . Second, multiple
(
2
f7i
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1 65 regression analysis was used to identify input parameexplained by the independent variable after adjusting ters that explained substantial variation in component for the effects of all other independent variables . Thus, biomass . Thus, error analysis here addressed the prethe proportion of the total PSS accounted for by a single diction capabilities of this deterministic model, and independent variable (or group of variables) is a relwas not an attempt to represent stochastic phenomena ative measure of the expected improvement in model (Gardner et al ., 1980a) . precision associated with improved parameter estimaOne hundred thirty-nine input parameters were tion (Bartell et al., 1988) . chosen for the analysis . These parameters corresponded to states and processes representing interactions System process analysis among organisms in the system, and included all Xi, fij, bid, wig, Ri, and Hi parameters . Parameters repError analysis results also were used to infer the resenting physiological processes (Eij and Mi) and states and processes that most affected system strucenergy inputs to the system (Zi) were excluded from ture. From the perspective of an individual component, the analysis, because initial attempts to perform error model parameters could be grouped to collectively repanalysis including these parameters resulted in predicresent states or processes such as the biomasses of all tions of extreme values of component biomasses in the prey, predation on all prey, predation from all predamajority of the simulations . This suggested that these tors, and so on . The PSS of the parameters in each parameters are estimable with higher precision than group could then be pooled to provide a measure of that implied in the error analysis procedure . Exclusion the effect of that state or process on the biomass of of these parameters did not detract from identification each model component and, hence, system structure . of the key mechanisms that structure the model preyThe PSS were pooled for the following groups predator assemblage . of parameters : the fib , bij, and wig parameters repTwo hundred, one-year simulations of energy flow resenting predation by the component, predation on were conducted in the Monte Carlo procedure . Each the component, support of the component's prey by simulation used a different set of values for the aquatic insects, predation on alternative prey by the input parameters, and the value of the end-of-thecomponent's predators, predation by competitors on year biomass of each component was recorded . Inde- the component's prey, or predation by competitors on pendent values for input parameters were randomly non-mutual prey ; the Xi parameters representing the chosen for each simulation from normal distributions initial biomasses of all prey, all predators, and all using a stratified random sampling procedure (Iman competitors ; the Hi parameters representing the har& Conover, 1980), which ensured adequate sampling vest rates of all exploited prey, all exploited predators, from the entire distribution ; sampling was restricted and all exploited competitors ; and the Ri parameters to within three standard deviations of the mean . The representing the intraspecific regulation coefficients of distribution of each input parameter was defined by a all prey, all predators, and all competitors . Only the mean (the model estimate) and a variance correspondPSS of initial biomass, harvest rate, and the intraspeing to a 20% coefficient of variation (Bartell et al ., cific regulation coefficient of each component were 1988), which represents a reasonable level of variation considered individually (that is, not pooled with the for ecological parameters (O'Neill et al ., 1980) . PSS of other parameters) . In this manner, the contribuMultiple regression was used to relate end-of-thetions to prediction error by the parameters associated year biomass of each component (dependent variable) with predation, exploitation, interspecific competition to the input parameters (independent variables) . For for food, and intraspecific regulation could be identieach component, the two hundred estimates of endfied for each model component . Further, the effects of of-the-year biomass were regressed (via the method bottom-up versus topdown regulation on each compoof least squares) with the two hundred correspondnent's biomass could be addressed . From the perspecing values randomly chosen for each of the 139 input tive of a component, bottom-up regulation was effects parameters ; a first-order model (each independent varifrom changes in prey biomass or changes in the feedable included but no cross-product terms or terms in ing relation (described by fib, bid, and wig) with prey powers of the independent variables are included ; Ott, components, and top-down regulation was effects from 1984) was assumed . The partial sum of squares (PSS) changes in predator biomass or changes in the feeding was calculated for each input parameter . The PSS is a relation with predator components . measure of the amount of residual variation in biomass
1 66 Results System energy flow
Annual energy input to the New River between Bluestone Dam and Sandstone Falls was more than 8 million kJ m -2 Y-1 . Organic seston inputs to the reach from Bluestone Lake (8 .073 106 kJ m-2 y - ') represented 99.9% of the estimated annual input . Periphyton and aquatic macrophytes contributed about 3980 and 1737 kJ m-2 y-1 . Energy flow into the model system via aquatic insects and crayfish was 77 .934 kJ m -2 y - ' (Fig . 1) ; seston contributed 77 .908 kJ m -2 y - ' and periphyton and aquatic macrophytes each contributed 13 kJ m -2 Y' . Inter-component flows (predation) in the system totaled 209 kJ m -2 y - ' and ranged from 0.004 (prey fish fed on by age-2 to age-5 rock bass) to 61 .467 kJ m -2 y - ' (aquatic insects fed on by hellgrammites) . Predation on aquatic insects was 87% of total predation, but predation rates on crayfish (10%), hellgrammites (1%), prey fish (1%), and age-0 fishes (
