Skip to main content
Log in

Effects of branching spatial structure and life history on the asymptotic growth rate of a population

  • Original Paper
  • Published:
Theoretical Ecology Aims and scope Submit manuscript

Abstract

The dendritic structure of a river network creates directional dispersal and a hierarchical arrangement of habitats. These two features have important consequences for the ecological dynamics of species living within the network. We apply matrix population models to a stage-structured population in a network of habitat patches connected in a dendritic arrangement. By considering a range of life histories and dispersal patterns, both constant in time and seasonal, we illustrate how spatial structure, directional dispersal, survival, and reproduction interact to determine population growth rate and distribution. We investigate the sensitivity of the asymptotic growth rate to the demographic parameters of the model, the system size, and the connections between the patches. Although some general patterns emerge, we find that a species’ modes of reproduction and dispersal are quite important in its response to changes in its life history parameters or in the spatial structure. The framework we use here can be customized to incorporate a wide range of demographic and dispersal scenarios.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Anderson KE, Nisbet RM, Diehl S, Cooper SD (2005) Scaling population responses to spatial environmental variability in advection-dominated systems. Ecol Lett 8:933–943

    Article  Google Scholar 

  • Barbeau MA, Caswell H (1999) A matrix model for short-term dynamics of seeded populations of sea scallops. Ecol Appl 9(1):266–287

    Article  Google Scholar 

  • Bilton DT, Freeland JR, Okamura B (2001) Dispersal in freshwater invertebrates. Ann Rev Ecolog Syst 32(1):159–181

    Article  Google Scholar 

  • Burgner RL (1991) Life history of sockeye salmon (Oncorhynchus nerka). In: Groot C, Margolis L (eds) Pacific salmon life histories. University of British Columbia Press, Vancouver, pp 3–118

    Google Scholar 

  • Caswell H (1983) Phenotypic plasticity in life-history traits: demographic effects and evolutionary consequences. Am Zool 23(1):35–46

    Google Scholar 

  • Charles S, Parra RBDL, Mallet JP, Persat H, Auger P (1998) Population dynamics modelling in an hierarchical arborescent river network: an attempt with Salmo trutta. Acta Biotheor 46:223–234

    Article  Google Scholar 

  • Charles S, Parra RBDL, Mallet JP, Persat H, Auger P (2000) Annual spawning migrations in modelling brown trout population dynamics inside an arborescent river network. Ecol Model 133:15–31

    Article  Google Scholar 

  • Dunham JB, Rieman BE (1999) Metapopulation structure of bull trout: influences of physical, biotic, and geometrical landscape characteristics. Ecol Appl 9:642–655

    Article  Google Scholar 

  • Elliott JM (2003) A comparative study of the dispersal of 10 species of stream invertebrates. Freshw Biol 48:1652–1668

    Article  Google Scholar 

  • Fagan WF (2002) Connectivity, fragmentation, and extinction risk in dendritic metapopulations. Ecology 83:3243–3249

    Article  Google Scholar 

  • Fagan WF, Grant EHC, Lynch HJ, Unmack PJ (2009) Riverine landscapes: ecology for an alternative geometry. In: Ruan S, Cosner C, Cantrell S (eds) Spatial ecology. CRC/Chapman and Hall, Berlin

    Google Scholar 

  • Fairless D (2008) Muddy waters. Nature 452:278–281

    Article  CAS  PubMed  Google Scholar 

  • Fortuna M, Gómez-Rodríguez C, Bascompte J (2006) Spatial network structure and amphibian persistence in stochastic environments. Proc R Soc Lond Ser B 273:1429–1434

    Article  Google Scholar 

  • Froese R, Pauly D (2000) FishBase 2000: concepts, design and data sources. ICLARM, Los Baños, Laguna

    Google Scholar 

  • Gotelli NJ, Taylor CM (1999) Testing metapopulation models with stream-fish assemblages. Evol Ecol Res 1:835–845

    Google Scholar 

  • Goto A (1986) Movement and population size of the river sculpin Cottus hangiongensis in the Daitobetsu River of southern Hokkaido. Japanese Journal of Icthyology 32:421–430

    Google Scholar 

  • Graf W (2001) Damage control: restoring the physical integrity of America’s rivers. Ann Assoc Am Geogr 91:1–27

    Article  Google Scholar 

  • Grant EHC, Lowe WH, Fagan WF (2007) Living in the branches: population dynamics and ecological processes in dendritic networks. Ecol Lett 10:1–11

    Article  Google Scholar 

  • Hanski I (1994) A practical model of metapopulation dynamics. J Anim Ecol 63:151–162

    Article  Google Scholar 

  • Hastings A (2004) Transients: the key to long-term ecological understanding? Trends Ecol Evol 19:39–45

    Article  PubMed  Google Scholar 

  • Hill MF, Hastings A, Botsford LW (2002) The effects of small dispersal rates on extinction times in structured metapopulation models. Am Nat 160:389–402

    Article  PubMed  Google Scholar 

  • Hill MF, Witman JD, Caswell H (2004) Markov chain analysis of succession in a rocky subtidal community. Am Nat 164(2):E46–E61

    Article  PubMed  Google Scholar 

  • Holland MD, Hastings A (2008) Strong effect of dispersal network structure on ecological dynamics. Nature 456:792–795

    Article  CAS  PubMed  Google Scholar 

  • Humphries P (2005) Spawning time and early life history of Murray cod, Maccullochella peelii peelii (Mitchell) in an Australian river. Environ Biol Fisches 72:393–407

    Article  Google Scholar 

  • Hunter CM, Caswell H (2005) The use of the vec-permutation matrix in spatial matrix population models. Ecol Model 188:15–21

    Article  Google Scholar 

  • Johnson R (1977) The central Arizona project. University of Arizona Press, Tuscon

    Google Scholar 

  • Kareiva P, Marvier M, McClure M (2000) Recovery and management options for spring/summer chinook salmon in the Columbia River Basin. Science 290:977–979

    Article  CAS  PubMed  Google Scholar 

  • Koizumi I, Maekawa K (2004) Metapopulation structure of stream-dwelling Dolly Varden charr inferred from patterns of occurrence in the Sorachi River Basin, Hokkaido, Japan. Freshw Biol 49:973–981

    Article  Google Scholar 

  • Labonne J, Ravigne V, Parisi B, Gaucherel C (2008) Linking dendritic network structures to population demogenetics: the downside of connectivity. Oikos 117:1479–1490

    Article  Google Scholar 

  • Levine JM (2003) A patch modeling approach to the community-level consequences of directional dispersal. Ecology 84:1215–1224

    Article  Google Scholar 

  • Lowe WH (2002) Landscape-scale spatial population dynamics in human-impacted stream systems. Environ Manage 30:225–233

    Article  PubMed  Google Scholar 

  • Lowe WH (2003) Linking dispersal to local population dynamics: a case study using a headwater salamander system. Ecology 84:2145–2154

    Article  Google Scholar 

  • Lutscher F, McCauley E, Lewis MA (2007) Spatial patterns and coexistence mechanisms in systems with unidirectional flow. Theor Popul Biol 71:267–277

    Article  PubMed  Google Scholar 

  • MacCulloch RD, Secoy DM (1983) Movement in a river population of Chrysemys picta bellii in southern Saskatchewan. J Herpetol 17:283–285

    Article  Google Scholar 

  • Maitland P (2003) Ecology of the river, brook and sea lamprey, vol conserving natura 2000 rivers ecology series no. 5. English Nature, Peterborough

    Google Scholar 

  • Mallin MA, Williams KE, Esham EC, Lowe RP (2000) Effect of human development on bacteriological water quality in coastal watersheds. Ecol Appl 10:1047–1056

    Article  Google Scholar 

  • McClure MM, Holmes EE, Sanderson BL, Jordan CE (2003) A large-scale, multispecies status assessment: anadromous salmonids in the Columbia River Basin. Ecol Appl 13:964–989

    Article  Google Scholar 

  • McKeown BA (1984) Fish migration. Routledge, London

    Google Scholar 

  • Minckley WL, Marsh PC (2009) Inland fishes of the greater southwest. University of Arizona Press

  • Muneepeerakul R, Levin SA, Rinaldo A, Rodriguez-Iturbe I (2007a) On biodiversity in river networks: a trade-off metapopulation model and comparative analysis. Water Resour Res 43:W07,426

    Google Scholar 

  • Muneepeerakul R, Weitz JS, Levin SA, Rinaldo A, Rodriguez-Iturbe I (2007b) A neutral metapopulation model of biodiversity in river networks. J Theor Biol 245:351–363

    Article  PubMed  Google Scholar 

  • Muneepeerakul R, Bertuzzo E, Lynch HJ, Fagan WF, Rinaldo A, Rodriguez-Iturbe I (2008) Neutral metacommunity models predict fish diversity patterns in Mississippi-Missouri basin. Nature 453:220–223

    Article  CAS  PubMed  Google Scholar 

  • Nilsson C, Reidy C, Dynesius M, Revenga C (2005) Fragmentation and flow regulation of the world’s large river systems. Science 308:405–408

    Article  CAS  PubMed  Google Scholar 

  • Pachepsky E, Lutscher F, Nisbet R, Lewis M (2005) Persistence, spread and the drift paradox. Theor Popul Biol 67:61–73

    Article  CAS  PubMed  Google Scholar 

  • Perry RW, Brandes PL, Sandstrom PT, Ammann A, MacFarlane B, Klimley AP, Skalski JR (in press) Estimating survival and migration route probabilities of juvenile chinook salmon in the Sacramento-San Joaquin River Delta. North Am J Fish Manage (in press)

  • Planquette P, Keith P, Bail PYL (1996) Atlas des poissons d’eau douce de Guyane (tome 1). IEGB-Muséum National d’Histoire Naturelle, Paris, INRA, CSP, Min. Env., Paris

  • Pluto TW, Bellis ED (1988) Seasonal and annual movements of riverine map turtles, Graptemys geographica. J Herpetol 22:152–158

    Article  Google Scholar 

  • Pusey B, Arthington A, Bird J, Close P (2001) Reproduction in three species of rainbowfish (Melanotaeniidae) from rainforest streams in northern Queensland, Australia. Ecol Freshw Fish 10:75–87

    Article  Google Scholar 

  • Reynolds RF (1983) Migration patterns of five fish species in the Murray-Darling River system. Aust J Mar Freshw Res 34:857–871

    Article  Google Scholar 

  • Reznick D, Meyer A, Frear D (1993) Life history of Brachyraphis rhabdophora (pisces: Poeciliidae). Copeia 1993:103–111

    Article  Google Scholar 

  • Rieman BE, Dunham JB (2000) Metapopulations and salmonids: a synthesis of life history patterns and empirical observations. Ecol Freshw Fish 9:51–64

    Article  Google Scholar 

  • Roy M, Holt RD, Barfield M (2005) Temporal autocorrelation can enhance the persistence and abundance of metapopulations comprised of coupled sinks. Am Nat 166:246–261

    Article  PubMed  Google Scholar 

  • Russell AP, Bauer AM, Johnson MK (2005) Migration in amphibians and reptiles: an overview of patterns and orientation mechanisms in relation to life history strategies. In: Elewa AMT (ed) Migration of organisms: climate, geography, ecology. Springer, Berlin, pp 151–203

    Google Scholar 

  • Schick RS, Lindley ST (2007) Directed connectivity among fish populations in a riverine network. J Appl Ecol 44:1116–1126

    Article  Google Scholar 

  • Schneider DW, Lyons J (1993) Dynamics of upstream migration in two species of tropical freshwater snails. J North Am Benthic Soc 12:3–16

    Article  Google Scholar 

  • Schtickzelle N, Quinn TP (2007) A metapopulation perspective for salmon and other anadromous fish. Fish Fish 8:297–314

    Google Scholar 

  • Skalski GT, Gilliam JF (2000) Modeling diffusive spread in a heterogeneous population: a movement study with stream fish. Ecology 81:1685–1700

    Article  Google Scholar 

  • Smith M, Caswell H, Mettler-Cherry P (2005) Stochastic flood and precipitation regimes and the population dynamics of a threatened floodplain plant. Ecol Appl 15(3):1036–1052

    Article  Google Scholar 

  • Speirs DC, Gurney WSC (2001) Population persistence in rivers and estuaries. Ecology 82:1219–1237

    Article  Google Scholar 

  • Vindenes Y, Engen S, Saether BE (2008) Individual heterogeneity in vital parameters and demographic stochasticity. Am Nat 171(4):455–467

    Article  PubMed  Google Scholar 

  • Vuilleumier S, Possingham HP (2006) Does colonization asymmetry matter in metapopulations? Proc R Soc Lond Ser B 273:1637–1642

    Article  Google Scholar 

  • Watts DJ (1998) Small worlds. Princeton University Press, Princeton

    Google Scholar 

  • Williams DD, Williams NE (1993) The upstream/downstream movement paradox of lotic invertebrates: quantitative evidence from a Welsh mountain stream. Freshw Biol 30:199–218

    Article  Google Scholar 

  • Wilson PH (2003) Using population projection matrices to evaluate recovery strategies for snake river spring and summer chinook salmon. Conserv Biol 17:782–794

    Article  Google Scholar 

Download references

Acknowledgements

We thank Evan H. C. Grant and the anonymous reviewers for comments on the manuscript. Funding for this work came from the James S. McDonnell Foundation (EEG, HJL, WFF). MGN was supported by grants from the National Science Foundation (CMG-0530830, OCE-0326734, ATM-0428122).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Emma E. Goldberg.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goldberg, E.E., Lynch, H.J., Neubert, M.G. et al. Effects of branching spatial structure and life history on the asymptotic growth rate of a population. Theor Ecol 3, 137–152 (2010). https://doi.org/10.1007/s12080-009-0058-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12080-009-0058-0

Keywords

Navigation