Dynamics of prey moving through a predator field: a model of migrating juvenile salmon

https://doi.org/10.1016/S0025-5564(00)00017-1Get rights and content

Abstract

The migration of a patch of prey through a field of relatively stationary predators is a situation that occurs frequently in nature. Making quantitative predictions concerning such phenomena may be difficult, however, because factors such as the number of the prey in the patch, the spatial length and velocity of the patch, and the feeding rate and satiation of the predators all interact in a complex way. However, such problems are of great practical importance in many management situations; e.g., calculating the mortality of juvenile salmon (smolts) swimming down a river or reservoir containing many predators. Salmon smolts often move downstream in patches short compared with the length of the reservoir. To take into account the spatial dependence of the interaction, we used a spatially-explicit, individual-based modeling approach. We found that the mortality of prey depends strongly on the number of prey in the patch, the downstream velocity of prey in the patch, and the dispersion or spread of the patch in size through time. Some counterintuitive phenomena are predicted, such as predators downstream capturing more prey per predator than those upstream, even though the number of prey may be greatly depleted by the time the prey patch reaches the downstream predators. Individual-based models may be necessary for complex spatial situations, such as salmonid migration, where processes such as schooling occur at fine scales and affect system predictions. We compare some results to predictions from other salmonid models.

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)

  • M.P. Hassell, The Dynamics of Arthropod Predator–Prey Systems, Princeton University, Princeton, NJ,...
  • T.P Poe et al.

    Feeding of predaceous fishes on out-migrating juvenile salmonids in John Day Reservoir, Columbia River

    Trans. Am. Fish. Soc.

    (1991)
  • B.E Rieman et al.

    Estimated loss of juvenile salmonids to predation by northern squawfish, walleyes, and smallmouth bass in John Day Reservoir, Columbia River

    Trans. Am. Fish. Soc.

    (1991)
  • S Vigg et al.

    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.

    (1991)
  • J.H. Petersen, C.A. Barfoot, S.T. Sauter, D.M. Gadomski, P.J. Connolly, T.P. Poe, Predicting the effects of dam...
  • D.A. Brege, W.T. Norman, G.A. Swan, J.G. Williams, Research at McNary Dam to improve fish guiding efficiency of...
  • L.A. Hawkes, R.D. Martinson, W.W. Smith, Monitoring of downstream salmon and steelhead at federal hydroelectric...
  • R.D Ledgerwood et al.

    Diel sampling of migratory juvenile salmonids in the Columbia River estuary

    Fish. Bull. US

    (1991)
  • R.W. Zabel, Spatial and temporal models of migrating juvenile salmon with applications, PhD dissertation, University of...
  • J.S Diana

    The feeding pattern and daily ration of a top carnivore the northern pike (Esox lucius)

    Can. J. Zool.

    (1979)
  • J.H Petersen et al.

    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.

    (1992)
  • L.M Dill

    Adaptive flexibility in the foraging behavior of fishes

    Can. J. Fish. Aquat. Sci.

    (1983)
  • J.R Brett

    Satiation time, appetite, and maximum food intake of sockeye salmon (Oncorhynchus nerka)

    J. Fish. Res. Board Can.

    (1971)
  • D.J Grove et al.

    Satiation amount, frequency of feeding and gastric emptying rate in Salmo gairdneri

    J. Fish Biol.

    (1978)
  • US Geological Survey, Water Resources Data, Washington, DC,...
  • M.G Mesa

    Effects of multiple acute stressors on the predator avoidance ability and physiology of juvenile chinook salmon

    Trans. Am. Fish. Soc.

    (1994)
  • J.H Petersen et al.

    Light-mediated predation by northern squawfish on juvenile chinook salmon

    J. Fish Biol.

    (1994)
  • Cited by (34)

    • The confluences of ideas leading to, and the flow of ideas emerging from, individual-based modeling of riverine fishes

      2018, Ecological Modelling
      Citation Excerpt :

      The need to grow beyond a certain size prior to a stressful period (e.g., winter), and the population resilience created by ‘contest’ competition (van Noordwijk and de Jong., 1986) and compensatory (density-dependent) mortality were two insights gained through individual-based modeling (DeAngelis et al., 1993). In rivers, the first application with a focus on size-mediated effects simulated predation on migrating salmon smolts (Petersen and Deangelis, 1992, 2000). These size-based algorithms were later incorporated into models of bass predation on salmon juveniles in rivers, particularly deep pools (Jager et al., 1997).

    • Mathematical analysis and validation of an exactly solvable model for upstream migration of fish schools in one-dimensional rivers

      2016, Mathematical Biosciences
      Citation Excerpt :

      Some other investigators have studied coarse-scaled macroscopic behavior of fish schools. Peterson and DeAngelis [58] mathematically modeled movements of prey fishes in a predator field using a conceptual model and analyzed relationships between the mortality of prey and hydrodynamic and biological conditions. Gao et al. [19] developed a horizontally 2-D numerical model of upstream fish migration in a vertical-slot fishway based on tracked trajectories of laboratorial experiments of individual fishes and a shallow water hydrodynamic model.

    • Forecasting Yangtze finless porpoise movement behavior using an Eulerian-Eulerian-diffusion method (EEDM)

      2016, Ecological Engineering
      Citation Excerpt :

      Although with significant limitations, several fish behavior models have been developed based on various theoretical systems and aiming at the fish responses to hydrodynamic. Nevertheless, there are other factors that affect fish movement behavior besides hydrodynamic patterns, e.g., mortality (Christie and Regier, 1988), water temperature (He, 2003), predation and predator avoidance (Petersen and DeAngelis, 2000) and dissolved gas (Matthews and Berg, 1997), etc. It is expected that the model would provide more insights on fish behavior when more of these factors are appropriately incorporated into the model.

    • Foraging ecology of walleye and brown trout in a Great Lakes tributary

      2016, Journal of Great Lakes Research
      Citation Excerpt :

      Further, the very small size of parr may have reduced the perceptual volume of walleye (through a reduced detection distance due to small size), thereby leading to lower encounter rates relative to rainbow trout and brown trout (Gerritsen and Strickler, 1977). The few walleyes that consumed large numbers of parr may have responded to transient dense patches of prey (e.g., Petersen and DeAngelis, 2000). Had we excluded these few walleyes that had likely encountered rare opportunities to feed on parr, mean consumption of parr by walleyes would have been considerably lower.

    • Modelling the complete life-cycle of Atlantic salmon (Salmo salar L.) using a spatially explicit individual-based approach

      2013, Ecological Modelling
      Citation Excerpt :

      Additionally, they do not require the simplification and mathematical derivations that may be required for GBMs (Huston et al., 1988; Railsback et al., 1999), effectively “bridging the gap” left by reductionist approaches (Schank, 2001). IBMs for salmonid fishes have been used to model habitat selection (Railsback and Harvey, 2002), growth rates (Smith et al., 2009), migration (Schonfisch and Kinder, 2002), predator–prey interactions (Petersen and DeAngelis, 2000), the effect of habitat fragmentation on population persistence (Morita and Yokota, 2002), the effect of turbidity on feeding (Harvey and Railsback, 2009), and life-history strategies (Satterthwaite et al., 2010). Usually, only part of the life-cycle of the fish is simulated.

    View all citing articles on Scopus
    View full text