Abstract
The chance of local extinction is high during periods of small population size. Accordingly, a metapopulation made of local communities that support internal population cycling may face the threat of regional extinction if the local dynamics is coherent (synchronized). These systems achieve maximum sustainability at an intermediate level of migration that allows recolonization but prevents synchronization. Here we implement an individual-based simulation technique to examine the maximum persistence condition for a system of patch habitats connected by passive migration. The models discussed in this paper take into consideration realistic elements of metapopulations, such as migration cost, disordered spatial structure, frustration and environmental noise. It turns out that the state with maximum anti-correlation between neighboring patches is the most sustainable one, even in the presence of these complications. The results suggest, at least for small systems, a model independent conservation strategy: coherence between neighboring local communities has, in general, a negative impact, and population will benefit from intervention that increases anti-correlations.
Similar content being viewed by others
References
Abbott KC (2011) A dispersal-induced paradox: synchrony and stability in stochastic metapopulations. Ecol Lett. doi:10.1111/j.1461-0248.2011.01670.x.
Abta R, Schiffer M, Shnerb NM (2007) Amplitude-dependent frequency, desynchronization, and stabilization in noisy metapopulation dynamics. Phys Rev Lett 98:098,104
Abta R, Schiffer M, Ben-Ishay A, Shnerb NM (2008) Stabilization of metapopulation cycles: toward a classification scheme. Theor Popul Biol 74(3):273–282
Adler FR (1993) Migration alone can produce persistence of host-parasitoid models. Am Nat 141:642–650
Allen JC, Schaffer WM, Rosko D (1993) Chaos reduces species extinction by amplifying local population noise. Nature 364:229–232
Andren H (1994) Effects of habitat fragmentation on birds and mammals in landscapes with different proportions of suitable habitat: a review. Oikos 71(3):355–366
Barkham JP, Hance CE (1982) Population dynamics of the wild daffodil (narcissus pseudonarcissus) iii. implications of a computer model of 1000 years of population change. J Ecol 70:323
Bascompte J, Sole RV (1996) Habitat fragmentation and extinction thresholds in spatially explicit models. J Anim Ecol 65(4):465–473
Beier P, Noss RF (1998) Do habitat corridors provide connectivity? Conserv Biol 12(6):1241–1252
Ben-Zion Y, Cohen Y, Shnerb NM (2010a) Modeling epidemics dynamics on heterogenous networks. J Theor Biol 264(2):197–204
Ben-Zion Y, Yaari G, Shnerb NM (2010b) Optimizing metapopulation sustainability through a checkerboard strategy. PLoS Comput Biol 6(1):e1000,643
Bonsall M, Hastings A (2004) Demographic and environmental stochasticity in predator-prey metapopulation dynamics. J Anim Ecol 73:1043–1055
Briggs C, Hoopes M (2004) Stabilizing effects in spatial parasitoid-host and predator-prey models: a review. Theor Popul Biol 65:299–315
Comins H, Hamilton W, May R (1980) Evolutionary stable dispersal strategies. J Theor Biol 82:82
Debinski DM, Holt RD (2000) A survey and overview of habitat fragmentation experiments. Conserv Biol 14(2):342–355
Dey S, Joshi A (2006) Stability via asynchrony in drosophila metapopulations with low migration rates. Science 312(5772):434–436
Durrett R, Levin SA (1994) Stochastic spatial models: a user’s guide to ecological applications. Philos Trans R Soc London 343:327
Earn DJ, Levin SA, Rohani P (2000) Coherence and conservation. Science 290(5495):1360
Elgart V, Kamenev A (2004) Rare event statistics in reaction-diffusion systems. Phys Rev E 70(4):41,106
Ellner SP, McCauley E, Kendall BE, Briggs CJ, Hosseini PR, Wood SN, Janssen A, Sabelis MW, Turchin P, Nisbet RM, Murdoch WW (2001) Habitat structure and population persistence in an experimental community. Nature 412:538–543
Etienne RS, ter Braak CJ, Vos CC (2004) Application of stochastic patch occupancy models to real metapopulations. Ecology, Genetics, and Evolution of Metapopulations, p 105–132
Fahrig L (2003) Effects of habitat fragmentation on biodiversity. Annu Rev Ecol Evol Syst 34:487–515
Gonzalez A, Lawton JH, Gilbert FS, Blackburn TM, Evans-Freke I (1998) Metapopulation dynamics, abundance, and distribution in a microecosystem. Science 281(5385):2045
Hamilton WD, May RM (1977) Dispersal in stable habitats. Nature 269(5629):578–581
Hanski I (1991) Single-species metapopulation dynamics: concepts, models and observations. Biol J Linn Soc 42(1–2):17–38
Hanski I (1994a) Patch-occupancy dynamics in fragmented landscapes. Trends Ecol Evol 9(4):131–135
Hanski I (1994b) A practical model of metapopulation dynamics. J Anim Ecol 63(1):151–162
Hanski I (1999) Metapopulation ecology. Oxford University Press, USA
Hanski I, Gilpin M (1991) Metapopulation dynamics - brief-history and conceptual domain. Biol J Linn Soc 42:3–16
Hanski I, Ovaskainen O (2000) The metapopulation capacity of a fragmented landscape. Nature 404:755–758
Hastings A (1996) Population biology: concepts and models. Springer
Hastings A, Wysham DB (2010) Regime shifts in ecological systems can occur with no warning. Ecol Lett 13(4):464–472
Heino M, Kaitala V, Ranta E, Lindström J (1997) Synchronous dynamics and rates of extinction in spatially structured populations. In: Proceedings of the Royal Society of London Series B: Biological Sciences 264(1381):481–486
Holland MD, Hastings A (2008) Strong effect of dispersal network structure on ecological dynamics. Nature 456:792–794
Holling CS (1965) The functional response of predators to prey density and its role in mimicry and population regulation. Mem Entomol Soc Can 45(1):60
Holyoak M, Lawler SP (1996) Persistence of an extinction-prone predator-prey interaction through metapopulation dynamics. Ecology 77(6):1867–1879
Kaneko K (1990a) Clustering, coding, switching, hierarchical ordering, and control in network of chaotic elements. Physica D 41:137–172
Kaneko K (1990b) Globally coupled chaos violates law of large numbers. Phys Rev Lett 65:1391–1394
Kaneko K, Tsuda I (2000) Complex systems: chaos and beyond. Springer, New York
Kareiva P (1987) Habitat fragmentation and the stability of predator-prey interactions. Nature 326:388–390
Keeling M, Wilson H, Pacala S (2000) Reinterpreting space, time lags, and functional responses in ecological models. Science 290:1758–1761
Kerr B, Riley MA, Feldman MW, Bohannan BJM (2002) Local dispersal promotes biodiversity in a real-life game of rock-paper-scissors. Nature 418:171–174
Kerr B, Neuhauser C, Bohannan BJM, Dean AM (2006) Local migration promotes competitive restraint in a host-pathogen ‘tragedy of the commons’. Nature 442:75–78
Kessler DA, Shnerb NM (2007) Extinction rates for fluctuation-induced metastabilities: a real-space wkb approach. J Stat Phys 127(5):861–886
Kessler DA, Shnerb NM (2010) Globally coupled chaotic maps and demographic stochasticity. Phys Rev E 81(3):036,111
Keymer JE, Marquet PA, Velasco-Hernandez JX, Levin SA (2000) Extinction thresholds and metapopulation persistence in dynamic landscapes. Am Nat 156(5):478–494
Kneitel J, Miller T (2003) Dispersal rates affect species composition in metacommunities of sarracenia purpurea inquilines. Am Nat 162(2):165–171
Kruess A, Tscharntke T (1994) Habitat fragmentation, species loss, and biological control. Science 264(5165):1581
Levins R (1969) Some demographic and genetic consequences of environmental heterogeneity for biological control. Bull Entomol Soc Am 15:237–240
Liebhold A, Koenig WD, Bjornstad ON (2004) Spatial synchrony in population dynamics. Annu Rev Ecol Evol Syst 35:467–490
Lindenmayer D, Fischer J (2006) Habitat fragmentation and landscape change: an ecological and conservation synthesis. Island Press
Lotka AJ (1920) Analytical note on certain rhythmic relations in organic systems. Proc Natl Acad Sci U S A 6(7):410–415
Matter SF, Roland J (2010) Local extinction synchronizes population dynamics in spatial networks. Proc R Soc B 277(1682):729–737
Matthies D, Brauer I, Maibom W, Tscharntke T (2004) Population size and the risk of local extinction: empirical evidence from rare plants. Oikos 105:481–488
May RM, Oster GF (1976) Bifurcations and dynamic complexity in simple ecological models. Am Nat 110(974):573–599
Moilanen A (1999) Patch occupancy models of metapopulation dynamics: efficient parameter estimation using implicit statistical inference. Ecology 80(3):1031–1043
Moilanen A (2004) SPOMSIM: software for stochastic patch occupancy models of metapopulation dynamics. Ecol Model 179(4):533–550
Molofsky J, Ferdy JB (2005) Extinction dynamics in experimental metapopulations. PNAS 102(10):3726–3731
Moran PAP (1953) Noise colour and the risk of population extinctions. Aust J Zool 1:291–298
Motro U (1982) Optimal rates of dispersal II. diploid populations. Theor Popul Biol 21(3):412–429
Motro U (1983) Optimal rates of dispersal. III. parent-offspring conflict. Theor Popul Biol 23(2):159–168
Murray JD (1993) Mathematical Biology. Springer
Nicholson AJ, Bailey VA (1935) The balance of animal populations. Proc Zool Soc Lond 3:551–598
Ovaskainen O, Meerson B (2010) Stochastic models of population extinction. Trends Ecol Evol 25(11):643–652
Pimm SL (1998) The forest fragment classic. Nature 393(6680):23–24
Ranta E, Kaitala V (2006) Comment on “stability via asynchrony in drosophila metapopulations with low migration rates”. Science 314:420
Ranta E, Kaitala V, Lindstrom J, Linden H (1995) Synchrony in population dynamics. Proc R Soc Lon, B Biol Sci 262(1364):113–118. doi:10.1098/rspb.1995.0184
Ranta E, Lundberg P, Kaitala V (2006) Ecology of populations. Cambridge University Press, Cambridge UK
Reichenbach T, Mobilia M, Frey E (2007) Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games. Nature 448:1046–1049
Ricker WE (1954) Stock and recruitment. J Fish Res Bd Can 11:559–623
Ricklefs RE, Miller GL (2000) Ecology. Freeman and Co
Ripa J, Lundberg P (1996) Noise colour and the risk of population extinctions. Proceedings of the Royal Society B 1377:1751–1753
Rosenzweig M, MacArthur R (1963) Graphical representation and stability conditions of predator-prey interactions. Am Nat 97:209–223
Seri E, Shnerb N (2010) Sustainability without coexistence state in durrett-levin hawk-dove model. Theor Ecol. doi:10.1007/s12080-010-0099-4
Snyder R, Nisbet R (2000) Spatial structure and fluctuations in the contact process and related models. Bull Math Biol 62:959
Sutcliffe OL, Thomas CD, Yates TJ, Greatorex-Davies JN (1997) Correlated extinctions, colonizations and population fluctuations in a highly connected ringlet butterfly metapopulation. Oecologia 109:235
Taylor PD (1988) An inclusive fitness model for dispersal of offspring. J Theor Biol 130(3):363–378
Tewksbury JJ, Levey DJ, Haddad NM, Sargent S, Orrock JL, Weldon A, Danielson BJ, Brinkerhoff J, Damschen EI, Townsend P (2002) Corridors affect plants, animals, and their interactions in fragmented landscapes. Proc Natl Acad Sci U S A 99(20):12923–12926
Thouless DJ, Anderson PW, Palmer RG (1977) Solution of solvable model of a spin glass. Philos Mag 35(3):593–601
Vasseur D, Fox J (2009) Phase-locking and environmental fluctuations generate synchrony in a predator-prey community. Nature 460:1007
Volterra V (1931) Lecon sur la Theorie Mathematique de la Lutte pour le via. Gauthier-Villars
Yaari G, Solomon S, Schiffer M, Shnerb NM (2008) Local enrichment and its nonlocal consequences for victim-exploiter metapopulations. Phys D 237(20):2553–2562
Acknowledgements
The authors would like to thank Gur Yaari for helpful discussions. This work was supported by the Israeli Ministry of science TASHTIOT program and by the Israeli Science Foundation BIKURA grant no. 1026/11.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ben-Zion, Y., Fried, Y. & Shnerb, N.M. Migration, coherence and persistence in a fragmented landscape. Theor Ecol 5, 481–493 (2012). https://doi.org/10.1007/s12080-011-0140-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12080-011-0140-2