Advertisement

Conservation Genetics

, Volume 14, Issue 2, pp 287–298 | Cite as

Implications of incomplete networks on estimation of landscape genetic connectivity

  • Ilona R. Naujokaitis-LewisEmail author
  • Yessica Rico
  • John Lovell
  • Marie-Josée Fortin
  • Melanie A. Murphy
Research Article

Abstract

Understanding processes and landscape features governing connectivity among individuals and populations is fundamental to many ecological, evolutionary, and conservation questions. Network analyses based on graph theory are emerging as a prominent approach to quantify patterns of connectivity with more recent applications in landscape genetics aimed at understanding the influence of landscape features on gene flow. Despite the strong conceptual framework of graph theory, the effect of incomplete networks resulting from missing nodes (i.e. populations) and their genetic connectivity network interactions on landscape genetic inferences remains unknown. We tested the violation of this assumption by subsampling from a known complete network of breeding ponds of the Columbia Spotted Frog (Rana luteiventris) in the Bighorn Crags (Idaho, USA). Variation in the proportion of missing nodes strongly influenced node-level centrality indices, whereas indices describing network-level properties were more robust. Overall incomplete networks combined with network algorithm types used to link nodes appears to be critical to the rank-order sensitivity of centrality indices and to the Mantel-based inferences made regarding the role of landscape features on gene flow. Our findings stress the importance of sampling effort and topological network structure as they both affect the estimation of genetic connectivity. Given that failing to account for uncertainty on network outcomes can lead to quantitatively different conclusions, we recommend the routine application of sensitivity analyses to network inputs and assumptions.

Keywords

Network theory Uncertainty Network indices Landscape genetics Sampling issue 

Notes

Acknowledgments

This work was conducted as part of the Distributed Graduate Seminar (DGS) course on Landscape Genetics, supported in part by the National Center for Ecological Analysis and Synthesis, a Center funded by NSF (Grant #EF-0553768), the University of California, Santa Barbara, and the State of California. INL was supported by NSERC, YR by CONACYT, MJF by NSERC Discovery grant, and MAM by Colorado State University (W. C. Funk) and University of Wyoming. The authors thank Rodney Dyer for assistance with programming enquiries and the DGS Landscape Genetics group for valuable input.

Supplementary material

10592_2012_385_MOESM1_ESM.docx (20 kb)
Supplementary material 1 (DOCX 20 kb)

References

  1. Anderson BS, Butts C, Carley K (1999) The interaction of size and density with graph-level indices. Soc Netw 21(3):239–267CrossRefGoogle Scholar
  2. Anderson CD, Epperson BK, Fortin MJ, Holderegger R, James PMA, Rosenberg MS, Scribner KT, Spear S (2010) Considering spatial and temporal scale in landscape-genetic studies of gene flow. Mol Ecol 19(17):3565–3575PubMedCrossRefGoogle Scholar
  3. Bowcock AM, Ruizlinares A, Tomfohrde J, Minch E, Kidd JR, Cavallisforza LL (1994) High-resolution of human evolutionary trees with polymorphic microsatellites. Nature 368(6470):455–457PubMedCrossRefGoogle Scholar
  4. Brassel KE, Reif D (1979) A procedure to generate Thiessen polygons. Geogr Anal 325:31–36Google Scholar
  5. Clauset A, Moore C, Newman MEJ (2008) Hierarchical structure and the prediction of missing links in networks. Nature 453(7191):98–101PubMedCrossRefGoogle Scholar
  6. Conover WJ, Johnson ME, Johnson MM (1981) A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data. Technometrics 23:351–361CrossRefGoogle Scholar
  7. Costenbader E, Valente TW (2003) The stability of centrality measures when networks are sampled. Soc Netw 25(4):283–307CrossRefGoogle Scholar
  8. Dale MRT, Fortin MJ (2010) From graphs to spatial graphs. Annu Rev Ecol Evol Syst 41:21–38CrossRefGoogle Scholar
  9. Dijkstra EW (1959) A note on two problems in connexion with graphs. Numer Math 1:269–271CrossRefGoogle Scholar
  10. Dunne JA, Williams RJ, Martinez ND (2002) Network structure and biodiversity loss in food webs: robustness increases with connectance. Ecol Lett 5(4):558–567CrossRefGoogle Scholar
  11. Dyer RJ, Nason JD (2004) Population graphs: the graph theoretic shape of genetic structure. Mol Ecol 13:1713–1727Google Scholar
  12. Evans I (1972) In: Chorley RJ (ed) Spatial analysis in geomorphology. Harper & Row, New York, pp 17–90Google Scholar
  13. Fedor A, Vasas V (2009) The robustness of keystone indices in food webs. J Theor Biol 260(3):372–378PubMedCrossRefGoogle Scholar
  14. Fogelqvist J, Niittyvuopio A (2010) Cryptic population genetic structure: the number of inferred clusters depends on sample size. Mol Ecol Resour 10(2):314–323PubMedCrossRefGoogle Scholar
  15. Fortin MJ, Dale MRT (2005) Spatial analysis: a guide for ecologists. Cambridge University Press, CambridgeGoogle Scholar
  16. Fortuna MA, Albaladejo RG, Fernandez L, Aparicio A, Bascompte J (2009) Networks of spatial genetic variation across species. Proc Natl Acad Sci USA 106(45):19044–19049PubMedCrossRefGoogle Scholar
  17. Freeman LC (1977) Set of measures of centrality based on betweenness. Sociometry 40(1):35–41CrossRefGoogle Scholar
  18. Freeman LC (1979) Centrality in social networks 1: conceptual clarification. Soc Netw 1(3):215–239CrossRefGoogle Scholar
  19. Funk WC, Blouin MS, Corn PS, Maxell BA, Pilliod DS, Amish S, Allendorf FW (2005) Population structure of Columbia spotted frogs (Rana luteiventris) is strongly affected by the landscape. Mol Ecol 14(2):483–496PubMedCrossRefGoogle Scholar
  20. Gabriel KR, Sokal RR (1969) A new statistical approach to geographic variation analysis. Syst Zool 18(3):259–278CrossRefGoogle Scholar
  21. Garroway CJ, Bowman J, Carr D, Wilson PJ (2008) Applications of graph theory to landscape genetics. Evol Appl 1:620–630Google Scholar
  22. Griffith D, Amrhein C (1997) Multivariate statistical analysis for geographers. Prentice Hall, Upper Saddle RiverGoogle Scholar
  23. Holderegger R, Wagner HH (2006) A brief guide to landscape genetics. Landsc Ecol 21(6):793–796CrossRefGoogle Scholar
  24. Koen EL, Bowman J, Garroway CJ, Mills SC, Wilson PJ (2012) Landscape resistance and American marten gene flow. Landsc Ecol 27:29–43Google Scholar
  25. Kossinets G (2006) Effects of missing data in social networks. Soc Netw 28(3):247–268CrossRefGoogle Scholar
  26. Laita A, Monkkonen M, Kotiaho JS (2010) Woodland key habitats evaluated as part of a functional reserve network. Biol Conserv 143(5):1212–1227CrossRefGoogle Scholar
  27. Legendre P, Dale MRT, Fortin MJ, Gurevitch J, Hohn M, Myers D (2002) The consequences of spatial structure for the design and analysis of ecological field surveys. Ecography 25(5):601–615CrossRefGoogle Scholar
  28. Mantel N (1967) Detection of disease clustering and a generalized regression approach. Cancer Res 27(2P1):209–220PubMedGoogle Scholar
  29. Minor ES, Urban DL (2008) A graph-theory framework for evaluating landscape connectivity and conservation planning. Conserv Biol 22(2):297–307PubMedCrossRefGoogle Scholar
  30. Murphy M, Evans J, Cushman S, Storfer A (2008) Evaluation of a novel approach for representing “populations” as continuous surfaces in landscape genetics. Ecography 31:685–697CrossRefGoogle Scholar
  31. Murphy MA, Dezzani R, Pilliod DS, Storfer A (2010a) Landscape genetics of high mountain frog metapopulations. Mol Ecol 19(17):3634–3649PubMedCrossRefGoogle Scholar
  32. Murphy MA, Evans JS, Storfer A (2010b) Quantifying Bufo boreas connectivity in Yellowstone National Park with landscape genetics. Ecology 91(1):252–261PubMedCrossRefGoogle Scholar
  33. Pilliod DS, Peterson CR (2001) Local and landscape effects of introduced trout on amphibians in historically fishless watersheds. Ecosystems 4:322–333CrossRefGoogle Scholar
  34. Pilliod DS, Peterson CR, Ritson PI (2002) Seasonal migration of Columbia spotted frogs (Rana luteiventris) among complementary resources in a high mountain basin. Can J Zool 80:1849–1862CrossRefGoogle Scholar
  35. R Development Core Team (2009) R: a language and environment for statistical computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
  36. Rayfield B, Fortin M-J, Fall A (2011) Connectivity for conservation: a framework to classify network measures. Ecology 92:847–858PubMedCrossRefGoogle Scholar
  37. Regan HM, Colyvan M, Burgman MA (2002) A taxonomy and treatment of uncertainty for ecology and conservation biology. Ecol Appl 12(2):618–628CrossRefGoogle Scholar
  38. Rehfeldt GE (2006) A spline model of climate for the Western United States. Gen. Tech. Rep. RMRS-GTR-165. U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station, Fort Collins, COGoogle Scholar
  39. Rozenfeld AF, Arnaud-Haond S, Hernandez-Garcia E, Eguiluz VM, Serrao EA, Duarte CM (2008) Network analysis identifies weak and strong links in a metapopulation system. Proc Natl Acad Sci USA 105(48):18824–18829PubMedCrossRefGoogle Scholar
  40. Sole RV, Montoya JM (2001) Complexity and fragility in ecological networks. Proc R Soc Lond B Biol Sci 268(1480):2039–2045CrossRefGoogle Scholar
  41. Spear S, Balkenhol N, Fortin MJ, McRae BH, Scribner KT (2010) Use of resistance surfaces for landscape genetic studies: considerations for parameterization and analysis. Mol Ecol 19:3576–3591PubMedCrossRefGoogle Scholar
  42. Storfer A, Murphy MA, Evans JS, Goldberg CS, Robinson S, Spear SF, Dezzani R, Delmelle E, Vierling L, Waits LP (2007) Putting the ‘landscape’ in landscape genetics. Heredity 98(3):128–142PubMedCrossRefGoogle Scholar
  43. Tabachnick BG, Fidell LS (2007) Using multivariate statistics, 5th edn. Allyn and Bacon, Inc., BostonGoogle Scholar
  44. Taylor PD, Fahrig L, Henein K, Merriam G (1993) Connectivity is a vital element of landscape structure. Oikos 68(3):571–573CrossRefGoogle Scholar
  45. Van Oppen MJ, Peplow LM, Kininmonth S, Berkelmans R (2011) Historical and contemporary factors shape the population genetic structure of the broadcast spawning coral, Acropora millepora, on the Great Barrier Reef. Mol Ecol 20:4899–4914PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Ilona R. Naujokaitis-Lewis
    • 1
    Email author
  • Yessica Rico
    • 2
  • John Lovell
    • 3
  • Marie-Josée Fortin
    • 1
  • Melanie A. Murphy
    • 4
  1. 1.Department of Ecology and Evolutionary BiologyUniversity of TorontoTorontoCanada
  2. 2.Department of Ecology and Evolutionary BiologyUniversity of TorontoMississaugaCanada
  3. 3.Graduate Degree Program in EcologyColorado State UniversityFort CollinsUSA
  4. 4.Ecosystem Science and ManagementUniversity of WyomingLaramieUSA

Personalised recommendations