Population Ecology

, Volume 54, Issue 1, pp 213–223 | Cite as

Analyzing Taylor’s Scaling Law: qualitative differences of social and territorial behavior on colonization/extinction dynamics

  • Horacio Samaniego
  • Guillaume Sérandour
  • Bruce T. Milne
Original Article

Abstract

The power law relation between the mean population count and its variance (Taylor’s Power Law, TPL) is among the few general patterns in population ecology. While the TPL has been described to be pervasive across taxa, the causes of variation of the exponent describing this relation is not well understood. We compare the TPL exponents for two species with different social systems and behavior: Piñon jays (Gymnorhinus cyanocephalus) and Western scrub-jays (Aphelocoma californica). We analyze the underlying processes that generate the expected values of population size and its variance. Using a probabilistic model, we identify and estimate important processes involved in the generation of the TPL exponents. While both species show a scaling relationship between their mean and abundance, share a common negative relation between mean abundance and colonization–extinction rates, they differ greatly in the statistical distributions of colonization, extinction, the mean number of colonists, the probability of zero abundance and population sizes. We show how different aspects of the processes that generate abundance affect the TPL exponent, thereby providing empirical guidelines to interpret differences in the scaling relation between mean and variance of population size.

Keywords

Invariant scaling Mean–variance Population dynamics Population variability Taylor’s Power Law 

Notes

Acknowledgments

We would like to thank the hundreds of volunteer that make the BBS database an invaluable tool to better understand the functioning of nature. James H. Brown, Scott L. Collins, Pablo A. Marquet and Bernardo Broitman provided valuable comments to this manuscript. Funding for this research was provided through the Alvin R. and Caroline G. Grove doctoral scholarship and project DID S-2009-20 of the Research and Development office, Universidad Austral de Chile to HS.

Supplementary material

10144_2011_287_MOESM1_ESM.pdf (183 kb)
PDF (182 KB)
10144_2011_287_MOESM2_ESM.pdf (55 kb)
PDF (55 KB)

References

  1. Anderson RM, Gordon DM, Crawley MJ, Hassel MP (1982) Variability in the abundance of animal and plant species. Nature 296:245–248CrossRefGoogle Scholar
  2. Balda R (2002) Pinyon jay: Gymnorhinus cyanocephalus. In: Poole A, Gill F (eds) The birds of North America, vol 605. Cornell Laboratory of Ornithology, Ithaca. http://bna.birds.cornell.edu/
  3. Balda R, Kamil A, Bednekoff P (1997) Predicting cognitive capacities from natural histories: examples from four corvid species. Curr Ornithol 13:33–66Google Scholar
  4. Ballantyne F IV (2005) The upper limit for the exponent of Taylor’s power law is a consequence of deterministic population growth. Evol Ecol Res 7:1213–1220Google Scholar
  5. Ballantyne F IV, Kerkhoff AJ (2005) Reproductive correlation and mean–variance scaling of reproductive output for a forest model. J Theor Biol 235:373–380PubMedCrossRefGoogle Scholar
  6. Ballantyne F IV, Kerkhoff AJ (2007) The observed range of temporal mean–variance scaling exponents can be explained by reproductive correlation. Oikos 116:174–180CrossRefGoogle Scholar
  7. Both C, Visser M (2003) Density dependence, territoriality, and divisibility of resources: from optimality models to population processes. Am Nat 161:326–336PubMedCrossRefGoogle Scholar
  8. Brown JH, Kodric-Brown A (1977) Turnover rates in insular biogeography: effect of migration on extinction. Ecology 58:445–449CrossRefGoogle Scholar
  9. Brown JL (1964) The evolution of diversity in avian territorial systems. Wilson Bull 76:160–169Google Scholar
  10. Burt DB (1996) Habitat-use patterns in cooperative an non-cooperative breeding birds: testing predictions with western scrub-jays. Wilson Bull 108:712–727Google Scholar
  11. Cade BS, Terrell JW, Schroeder RL (1999) Estimating effects of limiting factors with regression quantiles. Ecology 80:311–323CrossRefGoogle Scholar
  12. Clark CW, Rosenzweig ML (1994) Extinction and colonization processes: parameters estimates from sporadic surveys. Am Nat 143:583–596CrossRefGoogle Scholar
  13. Curry R, Peterson A, Langen T (2002) Western scrub-jay: Aphelocoma californica. In: Poole A, Gill F (eds) The birds of North America, vol 712. Cornell Laboratory of Ornithology, Ithaca. http://bna.birds.cornell.edu/
  14. de Kort S, Clayton N (2006) An evolutionary perspective on caching by corvids. Proc R Soc B 273:417–423PubMedCrossRefGoogle Scholar
  15. de los Monteros A, Cracraft J (1997) Intergeneric relationships of the new world jays inferred from cytochrome-b gene sequences. Condor 99:490–502CrossRefGoogle Scholar
  16. Engen S, Lande R, Sæther B (2008) A general model for analyzing Taylor’s spatial scaling laws. Ecology 89:2612–2622PubMedCrossRefGoogle Scholar
  17. Engen S, Lande R, Sæther B, Dobson F (2009) Reproductive value and the stochastic demography of age-structured populations. Am Nat 174:795–804PubMedCrossRefGoogle Scholar
  18. Fortin M, Dale M (2005) Spatial analysis: a guide for ecologists. Cambridge University Press, CambridgeGoogle Scholar
  19. Fretwell SD, Lucas HL (1969) On territorial behavior and other factors influencing habitat distribution in birds I. Theoretical development. Acta Biotheor 19:16–36CrossRefGoogle Scholar
  20. Gillis D, Kramer D, Bell G (1986) Taylor’s power law as a consequence of Fretwell’s ideal free distribution. J Theor Biol 123:281–287CrossRefGoogle Scholar
  21. Hanski I, Tiainen J (1989) Bird ecology and Taylor’s variance–mean regression. Ann Zool Fenn 26:213–217Google Scholar
  22. Holt RD (1983) Models for peripheral populations: the role of immigration. In: Freedman HI, Strobeck C (eds) Lecture notes in biomathematics. Springer, Berlin, pp 25–32Google Scholar
  23. Holt RD, Barfield M (2001) On the relationship between the ideal-free distribution and the evolution of dispersal. In: Danchin E, Dhont AA, Nichols JD, Clobert J (eds) Dispersal. Oxford University Press, Oxford, pp 83–95Google Scholar
  24. Keeling M, Grenfell B (2000) Individual-based perspectives on R0. J Theor Biol 203:51–61PubMedCrossRefGoogle Scholar
  25. Keitt TH, Amaral LA, Buldyrev SV, Stanley HE (2002) Scaling in the growth of geographically subdivided populations: invariant patterns from a continent-wide biological survey. Proc R Soc B 357:627–633Google Scholar
  26. Kendal WS (1992) Fractal scaling in the geographic distribution of populations. Ecol Model 64:65–69CrossRefGoogle Scholar
  27. Kendal WS (1995) A probabilistic model for the variance to mean power law in ecology. Ecol Model 80:293–297CrossRefGoogle Scholar
  28. Kendal WS (2002) Spatial aggregation of the Colorado potato beetle described by an exponential dispersion model. Ecol Model 151:261–269CrossRefGoogle Scholar
  29. Kendal WS (2004) Taylor’s ecological power law as a consequence of scale invariant exponential dispersion models. Ecol Complex 1:193–209CrossRefGoogle Scholar
  30. Kerkhoff AJ, Ballantyne F IV (2003) The scaling of reproductive variability in trees. Ecol Lett 6:850–856CrossRefGoogle Scholar
  31. Kerkhoff AJ, Enquist BJ (2007) The implications of scaling approaches for understanding resilience and reorganization in ecosystems. Bioscience 57:489–499CrossRefGoogle Scholar
  32. Kilpatrick AM, Ives AR (2003) Species interactions can explain Taylor’s power law for ecological time series. Nature 422:65–68PubMedCrossRefGoogle Scholar
  33. Koenker R, Bassett G Jr (1978) Regression quantiles. Econometrica 46:33–50CrossRefGoogle Scholar
  34. Krasnov B, Stanko M, Miklisova D, Morand S (2006) Host specificity, parasite community size and the relation between abundance and its variance. Evol Ecol 20:75–91CrossRefGoogle Scholar
  35. Legendre P, Legendre L (1998) Numerical ecology, 2nd edn. Elsevier, AmsterdamGoogle Scholar
  36. López-Sepulcre A, Kokko H (2005) Territorial defense, territory size, and population regulation. Am Nat 166:317–329PubMedCrossRefGoogle Scholar
  37. Marzluff JM, Balda RP (1989) Causes and consequences of female-based dispersal in a flock-living bird, the Piñon jay. Ecology 70:316–328CrossRefGoogle Scholar
  38. Marzluff JM, Balda RP (1992) The pinyon jay: behavioral ecology of a colonial and cooperative corvid. T & AD Poyser, LondonGoogle Scholar
  39. Maurer BA, Taper ML (2002) Connecting geographical distributions with population processes. Ecol Lett 5:223–231CrossRefGoogle Scholar
  40. McArdle BH, Gaston KJ, Lawton JH (1990) Variation in the size of animal populations patterns, problems and artifacts. J Anim Ecol 59:439–454CrossRefGoogle Scholar
  41. Peterson AT, Burt DB (1992) Phylogenetic history of social evolution and habitat use in the Aphelocoma jays. Anim Behav 44:859–866CrossRefGoogle Scholar
  42. Pitelka FA (1951) Speciation and ecologic distribution in American jays of the genus Aphelocoma. Univ Calif Publ Zool L:195–435Google Scholar
  43. R Development Core Team (2010) R: a language and environment for statistical computing. R Foundation for Statistical Computing. http://www.r-project.org
  44. Ritter LV (1983) Nesting ecology of scrub-jays in Chico, California. Western Birds 14:147–158Google Scholar
  45. Sauer JR, Hines JE, Fallon J (2005) The north american breeding bird survey, results and analysis 1966–2005. version 6.2.2006, Tech. rep., USGS Patuxent Wildlife Research Center, Laurel, MDGoogle Scholar
  46. Saunders M, Edwards S (2000) Dynamics and phylogenetic implications of mtDNA control region sequences in new world jays (aves: Corvidae). J Mol Evol 51:97–109PubMedGoogle Scholar
  47. Silverman BW (1986) Density estimation for statistics and data analysis. Chapman & Hall/CRC Press, London/New YorkGoogle Scholar
  48. Soberón J, Loevinsohn M (1987) Patterns of variation in the numbers of animal populations and the biological foundations of Taylor’s law of the mean. Oikos 48:249–252CrossRefGoogle Scholar
  49. Taylor HM, Karlin S (1984) Introduction to stochastic modelling. Academic Press, LondonGoogle Scholar
  50. Taylor LR, Woiwod I, Perry J (1978) The density-dependence of spatial behaviour and the rarity of randomness. J Anim Ecol 47:383–406CrossRefGoogle Scholar
  51. Taylor LR (1961) Aggregation, variance and the mean. Nature 189:732–735CrossRefGoogle Scholar
  52. Taylor LR, Taylor RA (1977) Aggregation, migration and population mechanics. Nature 265:415–421PubMedCrossRefGoogle Scholar
  53. Taylor LR, Woiwod IP (1982) Comparative synoptic dynamics. I. Relationships between inter- and intra-specific spatial and temporal variance/mean population parameters. J Anim Ecol 51:879–906CrossRefGoogle Scholar
  54. Venables WN, Ripley BD (2002) Modern applied statistics with S-PLUS, 3rd edn. Springer, New YorkGoogle Scholar
  55. Warton D, Wright I, Falster D, Westoby M (2006) A review of bivariate line-fitting methods for allometry. Biol Rev 81:259–291PubMedCrossRefGoogle Scholar

Copyright information

© The Society of Population Ecology and Springer 2011

Authors and Affiliations

  • Horacio Samaniego
    • 1
    • 2
  • Guillaume Sérandour
    • 3
  • Bruce T. Milne
    • 4
  1. 1.Facultad de Ciencias Forestales y Recursos Naturales, Instituto de SilviculturaUniversidad Austral de ChileValdiviaChile
  2. 2.Los Alamos National LaboratoryCenter for Nonlinear StudiesLos AlamosUSA
  3. 3.Facultad de Ciencias de la IngenieríaUniversidad Austral de ChileValdiviaChile
  4. 4.Department of BiologyUniversity of New MexicoAlbuquerqueUSA

Personalised recommendations