Dynamics of prey moving through a predator field: a model of migrating juvenile salmon
Introduction
Interactions between prey and their predators do not always take place in the ideal closed homogeneous system implicitly assumed by simple models. Frequently a population of prey or predators is moving in a definite direction through a field of a relatively stationary population of the other. A common situation is for patches of migrating prey to pass through a gauntlet of predators. This type of predator–prey interaction presents difficulties for modeling, as the interactions are transient and inherently inhomogeneous in space. Thus, it is difficult to apply standard predator–prey models such as simple Lotka–Volterra equations.
However, the dynamics of a prey population migrating through an array of predators is important to understand for practical reasons. For example, the case of special interest in this paper is migrating salmon. Stocks of Pacific salmon (Oncorhynchus spp.) have disappeared from about 40% of their historical breeding range in Washington, Oregon, Idaho, and California, and 74% of extant stocks face a ‘high’ or ‘moderate’ risk of extinction [1], [2]. The decrease in salmon numbers has been attributed to many factors – a decline in the spawning habitat for adult salmon because of mining, logging, and other development, increased pressure from commercial and sport fisheries, construction of hydroelectric projects on rivers such as the Columbia and Lower Snake, and ocean conditions [2]. However, one of the main sources of mortality to salmon is predation by relatively stationary piscivorous fish, such as the northern pikeminnow (Ptychocheilus oregonensis; previously called northern squawfish) during the downstream migration of juvenile salmon. The conversion of rivers, such as the Columbia, into a series of reservoirs may have increased the habitat and population size of such predators, and thus increased the predation-related mortality of salmon.
Fishery managers in the Columbia River Basin use various ‘passage’ models to simulate predation on juvenile salmon in rivers. Current passage models assume that large reservoirs can be treated as one or a few large homogeneous areas or partitions (modeling approaches are reviewed elsewhere [3], [4]). The number of juvenile salmon is represented by a single variable in each partition. Thus salmonids are assumed to be evenly distributed throughout the model partitions of the reservoirs and average predation rates are applied throughout these large areas.
We believe that such models lack the spatial resolution to realistically represent predator–prey interactions during the migration of salmon smolts. In real situations, predators will be exposed to a transient patch of prey. If a patch of prey is spatially narrow, a given stationary predator may be exposed to high densities of prey for only a few hours, even though the patch of prey may be in the reservoir for days. As the prey population changes in total size and spatial distribution through time, each predator will be exposed to a different temporal pattern of prey density. Thus, the assumptions of spatial ‘mixing’ of predators and prey implicit in most models may not even be approximately met. This, in combination with the fact that predators will be satiated by sufficiently high densities of prey (swamping), results in very complex dynamics that are poorly represented by models that treat a reservoir as one or a few well-mixed ‘pools’. Models used by fishery managers may need to include the density and narrowness of smolt patches, for example, if such features affect total predation.
We propose that an effective way to model such a system is through the spatially-explicit, individual-based (SEIB) modeling approach. In this approach, each predator and prey is individually modeled. This type of model allows a great deal of flexibility in building realism into the models, particularly in capturing the degree of spatial resolution needed to represent interactions in space. Further, even though computer simulations are necessary to derive results from SEIB models, we demonstrate that important theoretical generalizations can be derived from such models, in addition to their use in applied population ecology. For example, the model that we used produces a non-linear `swamping' effect on predators at high prey density through first principles, whereas this effect is generally described with type II or type III functional response models [5], [6].
In this paper, we formulate a model for a patch of prey moving through a predator field. We ask how the various characteristics of the prey patch, such as number of prey in the patch, its speed of movement, and its spatial size and configuration, affect the total mortality on the prey and the amount of prey caught by individual predators. Field data on Columbia and Snake River salmon smolts and their main predator, the northern pikeminnow, were used to parameterize the model. However, the model presented here is relatively simple. We were looking only for general properties of the system at this stage.
Section snippets
Model development
We developed a simulation model for the movement of a population of prey through an area occupied by a spatial distribution of predators and the predation interaction. The particular application in mind is a river reach containing predators distributed at relatively fixed locations along the reach and feeding on juvenile salmon migrating downstream through the reach. Most juvenile salmon enter reservoirs during brief periods during the day and we call such a group a `patch'. Our main purpose is
Individual predator feeding behavior
We simulated a pikeminnow's response to a brief pulse (patch) of smolts to examine how capture rate varied with time and prey density for a bout-feeding predator. First, we followed the response of the predator in Cell #1, the cell farthest upstream, to rapidly changing smolt density. No smolts entered Cell #1 for 83 h, 130 smolts were present in the cell at hour 84, and 870 smolts were present at hour 85. During hour 84, smolt density was relatively low (1.3 smolts per 2000 m3), but pikeminnow
Discussion
Our model results are interesting in light of empirical data on salmon smolts. Field studies and laboratory observations have shown that northern pikeminnow respond rapidly to transient patches of juvenile salmon by often capturing several smolts during a brief feeding bout [18], [23], [24], [25]. Predation rates in our modeling studies were sensitive to the dynamics of smolt patches and interactions between patch characteristics and river conditions such as flow. The size of patches entering
Acknowledgements
We appreciate critical reviews and helpful comments from Michele Adams, Tony Ives, Tom Poe, Rip Shively, and two anonymous reviewers. J.H.P. was supported by the Bonneville Power Administration through contracts administered by Bill Maslen. D. DeA.’s part in this work was supported in significant part by the Department of Interior's Critical Ecosystem Studies Initiative and in part by the USGS’s Florida Caribbean Science Center.
References (54)
- et al.
Index of predation on juvenile salmonids by northern squawfish in the lower and middle Columbia River and in the lower Snake River
Trans. Am. Fish. Soc.
(1995) - et al.
A stochastic predation model: application to largemouth bass observations
Ecol. Modelling
(1984) - et al.
Optimal foraging and arbitrary food distributions: patch models gain a lease on life
Trends Ecol. Evol.
(1988) - et al.
Modelling the linkages between flow management and salmon recruitment in rivers
Ecol. Modelling
(1997) - et al.
Finescale biological patchiness of 70 kHz acoustic scattering at the edge of the Gulf Stream-Echofront 85
Deep Sea Res.
(1990) - et al.
Pacific salmon at the crossroads: stocks at risk from California, Oregon, Idaho and Washington
Fisheries
(1991) - National Research Council, Upstream: Salmon and Society in the Pacific Northwest. National Academy Press, Washington,...
- D.H. Fickeisen, D.D. Dauble, D.A. Neitzel, Proceedings of the predator–prey workshop. Bonneville Power Administration,...
- L.W. Barnthouse, Expert initial review of Columbia River Basin salmonid management models: Summary report. Oak Ridge...
The functional response of predators to prey density and its role in mimicry and population regulation
Mem. Entomol. Soc. Can.
(1965)
Feeding of predaceous fishes on out-migrating juvenile salmonids in John Day Reservoir, Columbia River
Trans. Am. Fish. Soc.
Estimated loss of juvenile salmonids to predation by northern squawfish, walleyes, and smallmouth bass in John Day Reservoir, Columbia River
Trans. Am. Fish. Soc.
Rates of consumption of juveniles salmonids and alternative prey fish by northern squawfish, walleyes, smallmouth bass, and channel catfish in John Day Reservoir, Columbia River
Trans. Am. Fish. Soc.
Diel sampling of migratory juvenile salmonids in the Columbia River estuary
Fish. Bull. US
The feeding pattern and daily ration of a top carnivore the northern pike (Esox lucius)
Can. J. Zool.
Functional response and capture timing in an individual-based model: predation by northern squawfish (Ptychocheilus oregonensis) on juvenile salmonids in the Columbia River
Can. J. Fish. Aquat. Sci.
Adaptive flexibility in the foraging behavior of fishes
Can. J. Fish. Aquat. Sci.
Satiation time, appetite, and maximum food intake of sockeye salmon (Oncorhynchus nerka)
J. Fish. Res. Board Can.
Satiation amount, frequency of feeding and gastric emptying rate in Salmo gairdneri
J. Fish Biol.
Effects of multiple acute stressors on the predator avoidance ability and physiology of juvenile chinook salmon
Trans. Am. Fish. Soc.
Light-mediated predation by northern squawfish on juvenile chinook salmon
J. Fish Biol.
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