Skip to main content
SpringerLink
Log in

Graph-theoretic connectivity measures: what do they tell us about connectivity?

  • Research Article
  • Published:
Landscape Ecology Aims and scope Submit manuscript

Abstract

Graph-theoretic connectivity analyses have received much attention in connectivity evaluation during the last few years. Here, we explore the underlying conceptual differences of various graph-theoretic connectivity measures. Based on connectivity analyses from three reserve networks in forested landscapes in Central Finland, we illustrate how these conceptual differences cause inconsistent connectivity evaluations at both the landscape and patch level. Our results also illustrate how the characteristics of the networks (patch density) may affect the performance of the different measures. Many of the connectivity measures react to changes in habitat connectivity in an ecologically undesirable manner. Patch prioritisations based on a node removal analysis were sensitive to the connectivity measure they were based on. The patch prioritisations derived from different measures showed a disparity in terms of how much weight they put on patch size versus patch location and how they value patch location. Although graphs operate at the interface of structure and function, there is still much to do for incorporating the inferred ecological process into graph structures and analyses. If graph analyses are going to be used for real-world management and conservation purposes, a more thorough understanding of the caveats and justifications of the graph-theoretic connectivity measures will be needed.

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

Access this article

Log in via an institution

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

Similar content being viewed by others

References

  • Andersson E, Bodin O (2009) Practical tool for landscape planning? An empirical investigation of network based models of habitat fragmentation. Ecography 32:123–132

    Article  Google Scholar 

  • Andren H (1994) Effects of habitat fragmentation on birds and mammals in landscapes with different proportions of suitable habitat: a review. Oikos 71:355–366

    Article  Google Scholar 

  • Bélisle M (2005) Measuring landscape connectivity: the challenge of behavioral landscape ecology. Ecology 86:1988–1995

    Article  Google Scholar 

  • Bender DJ, Contreras TA, Fahrig L (1998) Habitat loss and population decline: a meta-analysis of the patch size effect. Ecology 79:517–533

    Article  Google Scholar 

  • Bodin Ö, Saura S (2010) Ranking individual habitat patches as connectivity providers: integrating network analysis and patch removal experiments. Ecol Model 221:2393–2405

    Article  Google Scholar 

  • Borgatti SP (2005) Centrality and network flow. Soc Netw 27:55–71

    Article  Google Scholar 

  • Borgatti SP (2006) Identifying sets of key players in a social network. Comput Math Organ Theory 12:21–34

    Article  Google Scholar 

  • Bunn A, Urban D, Keitt T (2000) Landscape connectivity: a conservation application of graph theory. J Environ Manag 59:265–278

    Article  Google Scholar 

  • Castellon TD, Sieving KE (2007) Patch network criteria for dispersal-limited endemic birds of South American temperate rain forest. Ecol Appl 17:2152–2163

    Article  PubMed  Google Scholar 

  • Estrada E, Bodin O (2008) Using network centrality measures to manage landscape connectivity. Ecol Appl 18:1810–1825

    Article  PubMed  Google Scholar 

  • Fahrig L (1997) Relative effects of habitat loss and fragmentation on population extinction. J Wildl Manag 61:603–610

    Article  Google Scholar 

  • Fahrig L (2003) Effects of habitat fragmentation on biodiversity. Annu Rev Ecol Evol Syst 34:487–515

    Article  Google Scholar 

  • Fahrig L, Merriam G (1994) Conservation of fragmented populations. Conserv Biol 8:50–59

    Article  Google Scholar 

  • Fall A, Fall J (2001) A domain-specific language for models of landscape dynamics. Ecol Model 141:1–18

    Article  Google Scholar 

  • Fall A, Fortin M, Manseau M, O’Brien D (2007) Spatial graphs: principles and applications for habitat connectivity. Ecosystems 10:448–461

    Article  Google Scholar 

  • Ferrari J, Lookingbill T (2009) Initial conditions and their effect on invasion velocity across heterogeneous landscapes. Biol Invasions 11:1247–1258

    Article  Google Scholar 

  • Ferrari J, Lookingbill T, Neel M (2007) Two measures of landscape-graph connectivity: assessment across gradients in area and configuration. Landscape Ecol 22:1315–1323

    Article  Google Scholar 

  • Fuller T, Munguia M, Mayfield M, Sanchez-Cordero V, Sarkar S (2006) Incorporating connectivity into conservation planning: a multi-criteria case study from central Mexico. Biol Conserv 133:131–142

    Article  Google Scholar 

  • Gardner R, Milne B, Turnei M, O’Neill R (1987) Neutral models for the analysis of broad-scale landscape pattern. Landscape Ecol 1:19–28

    Article  Google Scholar 

  • Goodwin BJ (2003) Is landscape connectivity a dependent or independent variable? Landscape Ecol 18:687–699

    Article  Google Scholar 

  • Gross JL, Yellen J (2006) Graph theory and its applications. Chapman & Hall/CRC Press, Boca Raton, FL

    Google Scholar 

  • Hanski I (1999) Metapopulation ecology. Oxford University Press, Oxford

    Google Scholar 

  • Jordán F, Báldi A, Orci K, Rácz I, Varga Z (2003) Characterizing the importance of habitat patches and corridors in maintaining the landscape connectivity of a Pholidoptera transsylvanica (Orthoptera) metapopulation. Landscape Ecol 18:83–92

    Article  Google Scholar 

  • Keitt T, Urban D, Milne B (1997) Detecting critical scales in fragmented landscapes. Conserv Ecol 1:4

    Google Scholar 

  • Kindlmann P, Burel F (2008) Connectivity measures: a review. Landscape Ecol 23:879–890

    Google Scholar 

  • Laita A, Mönkkönen M, Kotiaho JS (2010) Woodland key habitats evaluated as part of a functional reserve network. Biol Conserv 143:1212–1227

    Article  Google Scholar 

  • Lookingbill TR, Gardner RH, Ferrari JR, Keller CE (2010) Combining a dispersal model with network theory to assess habitat connectivity. Ecol Appl 20:427–441

    Article  PubMed  Google Scholar 

  • Matisziw T, Murray A (2008) Connectivity change in habitat networks. Landscape Ecol 24:89–100

    Article  Google Scholar 

  • McRae BH, Beier P (2007) Circuit theory predicts gene flow in plant and animal populations. Proc Natl Acad Sci USA 104:19885–19890

    Article  PubMed  CAS  Google Scholar 

  • McRae BH, Dickson BG, Keitt TH, Shah VB (2008) Using circuit theory to model connectivity in ecology, evolution and conservation. Ecology 89:2712–2724

    Article  PubMed  Google Scholar 

  • Minor ES, Urban DL (2007a) Graph theory as a proxy for spatially explicit population models in conservation planning. Ecol Appl 17:1771–1782

    Article  PubMed  Google Scholar 

  • Minor ES, Urban DL (2007b) A graph-theory framework for evaluating landscape connectivity and conservation planning. Conserv Biol 22:297–307

    Article  Google Scholar 

  • Minor ES, Tessel SM, Engelhardt KAM, Lookingbill TR (2009) The role of landscape connectivity in assembling exotic plant communities: a network analysis. Ecology 90:1802–1809

    Article  PubMed  Google Scholar 

  • Moilanen A, Hanski I (2001) On the use of connectivity measures in spatial ecology. Oikos 95:147–151

    Article  Google Scholar 

  • Mönkkönen M, Reunanen P (1999) On critical thresholds in landscape connectivity: a management perspective. Oikos 84:302–305

    Article  Google Scholar 

  • O’Brien D, Manseau M, Fall A, Fortin M (2006) Testing the importance of spatial configuration of winter habitat for woodland caribou: an application of graph theory. Biol Conserv 130:70–83

    Article  Google Scholar 

  • Pascual-Hortal L, Saura S (2006) Comparison and development of new graph-based landscape connectivity indices: towards the priorization of habitat patches and corridors for conservation. Landscape Ecol 21:959–967

    Article  Google Scholar 

  • Pascual-Hortal L, Saura S (2008) Integrating landscape connectivity in broad-scale forest planning through a new graph-based habitat availability methodology: application to capercaillie (Tetrao urogallus) in Catalonia (NE Spain). Eur J For Res 127:23–31

    Google Scholar 

  • Pinto N, Keitt T (2009) Beyond the least-cost path: evaluating corridor redundancy using a graph-theoretic approach. Landscape Ecol 24:253–266

    Article  Google Scholar 

  • Rothley KD, Rae C (2005) Working backwards to move forwards: graph-based connectivity metrics for reserve network selection. Environ Model Assess 10:107–113

    Article  Google Scholar 

  • Saura S, Pascual-Hortal L (2007) A new habitat availability index to integrate connectivity in landscape conservation planning: comparison with existing indices and application to a case study. Landscape Urban Plan 83:91–103

    Article  Google Scholar 

  • Saura S, Rubio L (2010) A common currency for the different ways in which patches and links can contribute to habitat availability and connectivity in the landscape. Ecography 33:523–537

    Google Scholar 

  • Saura S, Torné J (2009) Conefor Sensinode 2.2: a software package for quantifying the importance of habitat patches for landscape connectivity. Environ Model Softw 24:135–139

    Article  Google Scholar 

  • Stauffer D (1987) Introduction to percolation theory. Taylor & Francis, London

    Google Scholar 

  • Taylor PD, Fahrig L, Henein K, Merriam G (1993) Connectivity is a vital element of landscape structure. Oikos 68:571–573

    Article  Google Scholar 

  • Tischendorf L, Fahrig L (2000a) On the usage and measurement of landscape connectivity. Oikos 90:7–19

    Article  Google Scholar 

  • Tischendorf L, Fahrig L (2000b) How should we measure landscape connectivity? Landscape Ecol 15:633–641

    Article  Google Scholar 

  • Tischendorf L, Fahrig L (2001) On the use of connectivity measures in spatial ecology. A reply. Oikos 95:152–155

    Article  Google Scholar 

  • Urban D, Keitt T (2001) Landscape connectivity: a graph-theoretic perspective. Ecology 82:1205–1218

    Article  Google Scholar 

  • Urban DL, Minor ES, Treml EA, Schick RS (2009) Graph models of habitat mosaics. Ecol Lett 12:260–273

    Article  PubMed  Google Scholar 

  • van Langevelde F (2000) Scale of habitat connectivity and colonization in fragmented nuthatch populations. Ecography 23:614–622

    Article  Google Scholar 

  • Vogt P, Ferrari JR, Lookingbill TR, Gardner RH, Riitters KH, Ostapowicz K (2009) Mapping functional connectivity. Ecol Indic 9:64–71

    Article  Google Scholar 

  • Wiegand T, Revilla E, Moloney KA (2005) Effects of habitat loss and fragmentation on population dynamics. Conserv Biol 19:108–121

    Article  Google Scholar 

  • With KA, Crist TO (1995) Critical thresholds in species’ responses to landscape structure. Ecology 76:2446–2459

    Article  Google Scholar 

  • With KA, King AW (1997) The use and misuse of neutral landscape models in ecology. Oikos 79:219–229

    Article  Google Scholar 

Download references

Acknowledgments

This research was started as part of The Finnish Environmental Cluster Research Programme “Talousmetsät, pienialaiset suojelukohteet ja suojelualueet monimuotoisuuden suojelussa: Integroitu ekologinen vaikuttavuus ja kustannustehokkuus.” The research was partially funded by Kone Foundation as a grant (to AL). We are also grateful to the Academy of Finland for funding (project #7115560, to MM). We thank the Forest and Park Service, the Regional Forestry Centre in Central Finland, the Regional Council, UPM Kymmene, and the Regional Environment Centre for providing data for our study. Pasi Reunanen helped us in network analyses conducted with the SELES program.

Author information

Authors and Affiliations

  1. Department of Biological and Environmental Science, University of Jyväskylä, PO Box 35, Survontie 9, Jyväskylä, 40014, Finland

    A. Laita, J. S. Kotiaho & M. Mönkkönen

Authors
  1. A. Laita
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. S. Kotiaho
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Mönkkönen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Laita.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Laita, A., Kotiaho, J.S. & Mönkkönen, M. Graph-theoretic connectivity measures: what do they tell us about connectivity?. Landscape Ecol 26, 951–967 (2011). https://doi.org/10.1007/s10980-011-9620-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10980-011-9620-4

Keywords

Search

Navigation