Skip to main content
Log in

Predicting availability to consumers of spatially and temporally variable resources

  • Published:
Hydrobiologia Aims and scope Submit manuscript

Abstract

Ecological dynamics in many aquatic communities are strongly influenced by spatial and temporal variability of key limiting resources, and the extent to which consumers can locate and exploit concentrations of those resources. Intuitively, resource concentrations that are `close' and `long-lived' should typically be more available to consumers than `distant' and `ephemeral' resource concentrations. The speed and accuracy with which consumers can locate concentrations of their resources is in part determined by their movement characteristics and sensory constraints, which vary with taxon, life-history stage, physiological state, environmental conditions, and other factors. This has motivated detailed observation and modelling of individual-level foraging behaviors in a wide variety of taxa. However, our abilities to develop this intuitive concept of availability into empirically-based, quantitative predictions for consumer–resource interactions remain limited, largely due to the complexities of formulating and simulating spatially explicit models of consumer–resource interactions, and the difficulty of understanding how specific simulation results relate to broader ecological situations. This paper presents a non-dimensional index, the Frost number, that provides a simple prediction of availability to consumers of spatially and temporally varying resource concentrations. This index incorporates characteristics of both resource distributions and consumer movement behaviors. When Frost numbers characterizing consumer–resource interactions are much less than unity, resource concentrations are typically unavailable to consumers because travel time to reach them exceeds the longevity of the resource. Conversely, when Frost numbers are much greater than unity, resource longevity exceeds travel time so that resource concentrations are available. The Frost number may provide a preliminary identification of the length and time scales at which resources are available to consumers in complex ecological systems, even when detailed spatial observations and simulations are not available.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Alt, W., 1980. Biased random walk model for chemotaxis and related diffusion approximations. J. Mathematical Biol. 9: 147-177.

    Google Scholar 

  • Bearon, R. N. & T. J. Pedley, 1980. Modelling run-and-tumble chemotaxis in a shear flow. J. Mathematical Biol. 9: 147-177.

    Google Scholar 

  • Berg, H. C. & D. A. Brown, 1974. Chemotaxis in Escherichia coli analyzed by three-dimensional tracking. Nature 239: 500.

    Google Scholar 

  • Bernstein, C., A. Kacelnik & J. R. Krebs, 1988. Individual decisions and the distribution of predators in a patchy environment. J. anim. Ecol. 57: 1007-1026.

    Google Scholar 

  • Bernstein, C., A. Kacelnik & J. R. Krebs, 1991. Individual decisions and the distribution of predators in a patchy environment. ii. the influence of travel costs and the structure of the environment. J. anim. Ecol. 60: 205-225.

    Google Scholar 

  • Blackburn, N. & T. Fenchal, 1999. Modelling of microscale patch encounter by chemotactic protozoa. Protist 150: 337-343.

    Google Scholar 

  • Bollens, S. M., C. L. Speekman & S. R. Avent, 2000. The effect of ultraviolet radiation on the vertical distribution and mortality of estuarine zooplankton. J. Plankton Ecol. 22: 2325-2350.

    Google Scholar 

  • Boss, E., L. Karp-Boss & P. A. Jumars, 2000. Motion of dinoflagellates in a simple shear flow. Limnol. Oceanogr. 45: 1594-1602.

    Google Scholar 

  • Botte, V. & A. Key, 2000. A numerical study of plankton population dynamics in a deep lake during the passage of the spring thermal bar. J. mar. Syst. 26: 367-386.

    Google Scholar 

  • Buskey, E. J., 1997. Behavioral components of feeding selectivity of the heterotrophic dinoflagellate Protoperidinium pellucidum. Mar. Ecol. Prog. Ser. 153: 77-89.

    Google Scholar 

  • Caparroy, P. & F. Carlotti, 1996. A model for Acartia tonsa: effect of turbulence and consequences for the related physiological processes. J. Plankton Ecol. 18: 2139-2177.

    Google Scholar 

  • Crenshaw, H. C., 1996. A new look at locomotion in microorganisms: rotating and translating. Am. Zool. 36: 608-618.

    Google Scholar 

  • Cuddington, K. M. & E. McCauley, 1994. Food-dependent aggregation and mobility if the water fleas Ceriodaphnia dubia and Daphnia pulex. Can. J. Zool. 72: 1217-1226.

    Google Scholar 

  • Davis, L. H., D. K. Stoecker & D. M. Anderson, 1984. Fine scale spatial correlations between planktonic ciliates and dinoflagellates. J. Plankton Ecol. 6: 829-242.

    Google Scholar 

  • Dickinson, R. B. & R. T. Tranquillo, 1995. Transport equations and indices for random and biased cell migration based on single cell properties. Society of Industrial and Applied Mathematics Journal on Applied Mathematics 55 (5): 1419-1454.

    Google Scholar 

  • Doucet, P. G. and N. J. Drost, 1985. Theoretical studies on animal orientation. ii. directional displacement in kineses. J. theor. Biol. 117: 337-361.

    Google Scholar 

  • Fenchal, T. & N. Blackburn, 1999. Motile chemosensory behavior or phagotrophic protists: mechanisms for and efficiency in congregating at food patches. Protist 150: 325-336.

    Google Scholar 

  • Frost, B. W., 1972. Effects of size and concentration of food particles on the feeding behavior of the marine planktonic copepod, Calanus pacificus. Limnol. Oceanogr. 17: 805-815.

    Google Scholar 

  • Frost, B. W., M. J. Dagg & J. Newton, 1997. Vertical migration and feeding of Calanus pacificus females during a phytoplankton bloom in Dabob Bay, U.S. Limnol. Oceangr. 42: 974-980.

    Google Scholar 

  • Frost, B. W., M. J. Dagg & J. Newton, 1998. Diel vertical migration and feeding in adult female Calanus pacificus, Metridia lucens and Pseudocalanus newmani during a spring bloom in Dabob Bay, a fjord in Washington, U.S.A. J. mar. Syst. 15: 503-509.

    Google Scholar 

  • Frost, B.W., S.M. Bollens, K. Osgood & S. D. Watts, 1993. Vertical distributions and susceptibilities to vertebrate predation of the marine copepods Metridia lucens and Calanus pacificus. Limnol. Oceangr. 38: 1827-1837.

    Google Scholar 

  • Grünbaum, D., 1998. Using spatially explicit models to characterize foraging performance in heterogeneous landscapes. Am. Nat. 151 (2): 97-115.

    Google Scholar 

  • Grünbaum, D., 1999. Advection-diffusion equations for generalized tactic searching behaviors. J. Mathematical Biol. 38: 169-194.

    Google Scholar 

  • Grünbaum, D., 2000. Advection-diffusion equations internal statemediated random walks. Society of Industrial and Applied Mathematics Journal on Applied Mathematics 61: 43-73.

    Google Scholar 

  • Holliday, D. V., C. A. Barans, B. W. Stender & C.F. Greenlaw, 1997. Variation in the vertical distribution of zooplankton and fine particles in an estuarine inlet of South Carolina. Estuaries 20: 467-482.

    Google Scholar 

  • Jonsson, P. R., 1986. Particle size selection, feeding rate and growth dynamics of marine planktonic oligotrichous ciliates (ciliophora: Oligotrichina). Mar. Ecol. Prog. Ser. 33: 265-277.

    Google Scholar 

  • Jonsson, P. R., 1989. Vertical distribution of planktonic cililates-an experimental analysis of swimming behavior. Mar. Ecol. Prog. Ser. 52: 39-53.

    Google Scholar 

  • Jonsson, P. R., 1991. Swimming behaviour of marine bivalve larvae in a flume boundary-layer flow: evidence for near-bottom confinement. mar. Ecol. Prog. Ser. 79: 67-76.

    Google Scholar 

  • Jonsson, P.R., P. Tiselius & P. G. Verity, 1993. a model evaluation of the impact of food patchiness on foraging strategy and predation risk in zooplankton. Bull. mar. Sci. 53: 247-264.

    Google Scholar 

  • Keller, E. F. & L. A. Segel, 1971. Model for chemotaxis. J. theor. Biol. 30: 225-234.

    Google Scholar 

  • Larsson, P., 1997. Ideal free distribution in Daphnia? are daphnids able to consider both food patch quality and the position of competitors? Hydrobiologia 360: 143-152.

    Google Scholar 

  • Larsson, P. & O. T. Kleiven, 1996. Food search and swimming speed in Daphnia. In Purcell, J. E., P. H, Lenz, D. K. Hartline 191 & D. L. Macmillan (eds), Zooplankton: Sensory Ecology and Physiology. Gordon and Breach Publishers: 375-387.

  • Larsson, P., K. H, Jensen & G. Hogstedt, 2001. Detecting food search in Daphnia in the field. Limnol Oceanogr. 46: 1013-1020.

    Google Scholar 

  • Leising, A. W. & P. J. S. Franks, 2000. Copepod vertical distribution within a spatially variable food source: a simple foraging-strategy model. J. Plankton Ecol. 22: 999-1024.

    Google Scholar 

  • Leising, A. W., 2001. Copepod foraging in patchy habitats and thin layers using a 2-d individual-based model. Mar. Ecol. Prog. Ser. 216: 167-179.

    Google Scholar 

  • Mangel, M., 1990. Dynamic information in uncertain and changing worlds. J. theor. Biol. 146: 317-332.

    Google Scholar 

  • McNamara, J. M. &A. I. Houston, 1987. Memory and the efficient use of information. J. theor. Biol. 125: 385-395.

    Google Scholar 

  • Meneveau, C., H. Jiang & T. R. Osborn, 1999. Numerical study of the feeding current around a copepod. J. Plankton Ecol. 21: 1391-1421.

    Google Scholar 

  • Metaxis, A. & C. M. Young, 1998. Responses of echinoid larvae to food patches of different algal densities. Mar. Biol. 130: 433-445.

    Google Scholar 

  • Metcalfe, A. M. & T. J. Pedley, 1998. Bacterial bioconvection: weakly nonlinear theory for pattern selection. J. Fluid Mechanics 370: 249-270.

    Google Scholar 

  • Mitchell, M., M. Martinez-Alonso, J. Lalucat, I. Esteve & S. Brown, 1991. Velocity changes, long runs, and reversals in the Chromatium minus swimming response. J. Bacteriol. 173 (3): 997-1003.

    Google Scholar 

  • Moore, T. M., J. T. Pierce-Shimomoura & S. R. Lockery, 1999. The fundamental role of pirouettes in Caenorhabditis elegans chemotaxis. J. Neurophysiol. 19: 9557-9569

    Google Scholar 

  • Morgulis, A., R. Arditi, Y. Tyutyunov & V. Govorukhin, 2001. Directed movement of predators and the emergence of densitydependence in predator-prey models. Theor. Pop. Biol. 59: 207-221.

    Google Scholar 

  • Okubo, A., 1980. Diffusion and Ecological Problems: Mathematical Models, Vol 10 of Lecture Notes in Biomathematics. Springer-Verlag.

  • Othmer, H. G., S. R. Dunbar & W. Alt, 1988. Models of dispersal in biological systems. J. Mathematical Biol. 26: 263-298.

    Google Scholar 

  • Paffenhoffer, G. A., 1998. On the relation of structure, perception and activity in marine planktonic copepods. J. mar. Syst. 15: 457-473.

    Google Scholar 

  • Petersen, J. E. & A. Hastings, 2001. dimensional approaches to scaling experimental ecosystems: designing mousetraps to catch elephants. Am. Nat. 157: 324-333.

    Google Scholar 

  • Ploug, H., T. Kiorboe & U. H. Thygesen, 2001. Fluid motion and solute distribution around sinking aggregates. i. small-scale fluxes and heterogeneity of nutrients in the pelagic environment. Mar. Ecol. Prog. Ser. 211: 1-13.

    Google Scholar 

  • Schmitz, O. J., 2000. Combining field experiments and individualbased modeling to identify the dynamically relevant organizational scale in a field system. Oikos 89: 471-484

    Google Scholar 

  • Schmitz, O. J., 2001. From interesting details to dynamical relevance: toward more effective use of empirical insights in theory construction. Oikos 94: 39-50.

    Google Scholar 

  • Stianson, J. E. & S. Sundby, 2001. Improved methods for generating and estimating turbulence in tanks suitable for fish larvae experiments. Sci. Mar. 65: 151-167.

    Google Scholar 

  • Tester, P. A., D. E. Streans & R. L. Walker, 1989. Diel changes in the egg production rate of Acartia tonsa (copepoda, calanoida) and related environmental factors in two estuaries. Mar. Ecol. Prog. Ser. 52: 7-16.

    Google Scholar 

  • Thygesen, U. H., P. Caparroy & A. W. Visser, 2000. Modelling the attack success of planktonic predators: patterns and mechanisms of prey size selectivity. J. Plankton Ecol. 22: 1871-1900.

    Google Scholar 

  • Veit, R. R. & P. A. Prince, 1997. Individual and population level dispersal of black-browed and grey-headed albatrosses in response to Antarctic krill. Ardea 85: 129-134.

    Google Scholar 

  • Veit, R. R., 1997. Behavioral responses by foraging petrels to swarms of antarctic krill, Euphasia superba. Ardea 87: 41-50.

    Google Scholar 

  • Visser, A. W. & B. R. MacKenzie, 1998. Turbulence-induced contact rates of plankton: the question of scale. Mar. Ecol. Prog. Ser. 166: 307-310.

    Google Scholar 

  • Yamazaki, H., 1993. Lagrangian study of planktonic organisms. Bull. mar. Sci. 53: 265-278.

    Google Scholar 

  • Yamazaki, H., J. R. Strickler, K. D. Squires & A. H. Abib, 1997. Combining analog turbulence with digital turbulence. Sci. Mar. 61: 197-204.

    Google Scholar 

  • Yen, J., & J. R. Strickler, 1996. Advertisement and concealment in the plankton: what makes a copepod hydrodynamically conspicuous? Invert. Biol. 115: 191-205.

    Google Scholar 

  • Yen, J., 1982. Sources of variability in attack rates of Euchaeta elongata esterly, a carnivorous marine copepod. Biol. Ecol. 63: 105-117.

    Google Scholar 

  • Yen, J., 1983. Effects of prey concentration, prey size, predator life stage, predator starvation, and season on predation rates of the carnivorous copepod Euchaeta elongata. Mar. Biol. 75: 69-77.

    Google Scholar 

  • Yen, J., 1985. Selective predation by the carnivorous marine copepod Euchaeta elongata: laboratory measurements of predation rates verified by field observations of temporal and spatial feeding patterns. Limnol. Oceanogr. 30: 577-597.

    Google Scholar 

  • Yen, J., 1988. Directionality and swimming speeds in a predator-prey and male-female interactions of Euchaeta rimana, a subtropical marine copepod. Bull. mar. Sci. 43: 395-403.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grünbaum, D. Predicting availability to consumers of spatially and temporally variable resources. Hydrobiologia 480, 175–191 (2002). https://doi.org/10.1023/A:1021296103358

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1021296103358

Navigation