Skip to main content
SpringerLink
Log in

Taking a moment to measure networks—an approach to species conservation

Landscape Ecology volume 37, pages 2551–2569 (2022)Cite this article

Abstract

Context

Network-theoretic tools contribute to understanding real-world system dynamics, such as species survival or spread. Network visualization helps illustrate structural heterogeneity, but details about heterogeneity are lost when summarizing networks with a single mean-style measure. Researchers have indicated that a system composed of multiple metrics may be a more useful determinant of structure, but a formal method for grouping metrics is still lacking.

Objectives

Our objective is to present a tool that can account for multiple properties of network structure, which can be related to model outcomes.

Methods

We develop an approach using the statistical concept of moments and systematically test the hypothesis that this system of metrics is sufficient to explain variation in processes that take place on networks, using an ecological system as an example.

Results

Our results indicate that the moments approach outperforms single summary metrics by adjusted-R2 and AIC model fit criteria, and accounts for a majority of the variation in process outcomes.

Conclusions

Our scheme is helpful for indicating when additional structural information is needed to describe system process outcomes such as survival or spread.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

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

Data availability

Simulation data can be accessed on the Open Science Framework (osf.io/5y7fu).

Code availability

All source code can be accessed on the Open Science Framework (osf.io/5y7fu).

References

  • Albert R, Barabasi A (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97

    Article  Google Scholar 

  • Albert R, Jeong H, Barabasi A (2000) Error and attack tolerance of complex networks. Nature 406:378–382

    Article  CAS  PubMed  Google Scholar 

  • Amarasekare P (2004) The role of density-dependent dispersal in source-sink dynamics. J Theor Biol 226:159–168

    Article  PubMed  Google Scholar 

  • Ames GM, George DB, Hampson CP, Kanarek AR, McBee CD, Lockwood DR, Achter JD, Webb CT (2011) Using network properties to predict disease dynamics on human contact networks. Proc R Soc Biol Sci 278:3544–3550

    Article  Google Scholar 

  • Antolin MF, Savage LT, Eisen RJ (2006) Landscape features influence genetic structure of black-tailed prairie dogs (Cynomys ludovicianus). Landsc Ecol 21:867–875

    Article  Google Scholar 

  • Baggio JA, Schoon ML, Valury S (2019) Managed network landscapes: conservation in a fragmented, regionally connected world. Reg Environ Change 19:2551–2562

    Article  Google Scholar 

  • Baggio JA, Salau K, Janssen MA, Schoon ML, Bodin O (2011) Landscape connectivity and predator-prey population dynamics. Landsc Ecol 26:33–45

    Article  Google Scholar 

  • Barrat A, Barthélemy M, Pastor-Satorras R, Vespignani A (2004) The architecture of complex weighted networks. Proc Natl Acad Sci 101:3747–3752

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Barthélemy M (2011) Spatial networks. Phys Rep 499:1–84

    Article  Google Scholar 

  • Beissinger SR, Westphal MI (1998) On the use of demographic models of population viability in endangered species management. J Wildl Manag 62:821–841

    Article  Google Scholar 

  • Bevers M, Hof J, Uresk DW, Schenbeck GL (1997) Spatial optimization of prairie dog colonies for black-footed ferret recovery. Oper Res 45:495–507

    Article  Google Scholar 

  • Blonder B, Wey TW, Dornhaus A, James R, Sih A (2012) Temporal dynamics and network analysis. Methods Ecol Evol 3:958–972

    Article  Google Scholar 

  • Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D-U (2006) Complex networks: structure and dynamics. Phys Rep 424:175–308

    Article  Google Scholar 

  • Boit A, Martinez ND, Williams RJ, Gaedke U (2012) Mechanistic theory and modeling of complex food-web dynamics in lake constance. Ecol Lett 15:594–602

    Article  PubMed  Google Scholar 

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

    Article  Google Scholar 

  • Bunn AG, Urban DL, Keitt TH (2000) Landscape connectivity: a conservation application of graph theory. J Environ Manage 59:265–278

    Article  Google Scholar 

  • Campbell TM, Clark TW, Richardson L, Forrest S, Houston BR (1987) Food habits of wyoming black-footed ferrets. Am Midl Nat 117:208–210

    Article  Google Scholar 

  • Casella G, Berger RL (2002) Statistical inference. Duxbury Press, Pacific Grove. California

  • Dixon JD, Oli MK, Wooten MC, Eason TH, McCown JW, Paetkau D (2006) Effectiveness of a regional corridor in connecting two Florida black bear populations. Conserv Biol 20:155–162

    Article  PubMed  Google Scholar 

  • Durrett R, Levin S (1994) The importance of being discrete (and spatial). Theor Popul Biol 46:363–394

    Article  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • Frank K (2004) Ecologically differentiated rules of thumb for habitat network design—lessons from a formula. Biodivers Conserv 13:189–206

    Article  Google Scholar 

  • Friesen SK, Martone R, Rubidge E, Baggio JA, Ban NC (2019) An approach to incorporating inferred connectivity of adult movement into marine protected area design with limited data. Ecol Appl 29:e01890

    Article  PubMed  PubMed Central  Google Scholar 

  • Gai P, Kapadia S (2010) Contagion in financial networks. Proc Royal Society A 466:2401–2423

    Article  Google Scholar 

  • Garrett MG, Franklin WL (1988) Behavioral ecology of dispersal in the black-tailed prairie dog. J Mammal 69:236–250

    Article  Google Scholar 

  • Garrett MG, Hoogland JL, Franklin WL (1982) Demographic differences between an old and a new colony of black-tailed prairie dogs (Cynomys ludovicianus). Am Midl Nat 108:51–59

    Article  Google Scholar 

  • Germain RM, Strauss SY, Gilbert B (2017) Experimental dispersal reveals characteristic scales of biodiversity in a natural landscape. Proc Natl Acad Sci 114:4447–4452

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Gilarranz LJ, Rayfield B, Linan-Cembrano G, Bascompte J, Gonzalez A (2017) Effects of network modularity on the spread of perturbation impact in experimental metapopulations. Science 357:199–201

    Article  CAS  PubMed  Google Scholar 

  • Gilbert F, Gonzalez A, Evans-Freke I (1998) Corridors maintain species richness in the fragmented landscapes of a microecosystem. Proc R Soc London 265:577–582

    Article  Google Scholar 

  • Gonzalez A, Lawton JH, Gilbert FS, Blackburn TM, Evans-Freke I (1998) Metapopulation dynamics, abundance, and distribution in a microecosystem. Science 281:2045–2047

    Article  CAS  PubMed  Google Scholar 

  • Gotelli NJ (1995) A Primer of Ecology. Sinauer Associates, Sunderland

    Google Scholar 

  • Griffin PC, Mills LS (2009) Sinks without borders: snowshoe hare dynamics in a complex landscape. Oikos 118:1487–1498

    Article  Google Scholar 

  • Grimm V, Railsback SF (2005) Individual-based modeling and ecology. Princeton University Press, Princeton

    Book  Google Scholar 

  • Haldane AG, May RM (2011) Systemic risk in banking ecosystems. Nature 469:351–355

    Article  CAS  PubMed  Google Scholar 

  • Hanski I (1998) Connecting the parameters of local extinction and metapopulation dynamics. Oikos 83:390–396

    Article  Google Scholar 

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

    Google Scholar 

  • Harrison S, Murphy D, Ehrlich PR (1988) Distribution of the bay checkerspot butterfly, Euphydryas editha bayensis: evidence for a metapopulation model. Am Nat 132:360–382

    Article  Google Scholar 

  • Hof J, Bevers M, Uresk DW, Schenbeck GL (2002) Optimizing habitat location for black-tailed prairie dogs in southwestern South Dakota. Ecol Model 147:11–21

    Article  Google Scholar 

  • Holmes BE (2008) A review of black-footed ferret reintroduction in northwest Colorado. 2001–2006. In: Bo LM (ed) US Department of the Interior Technical Note 426, White River Field Office. Colorado

  • Hoogland JL, Angell DK, Daley JG, Radcliffe MC (1987) Demography and population dynamics of prairie dogs. Eighty Great Plains Wildlife Damage Control Workshop, Rapid City

    Google Scholar 

  • Jacobi MN, Jonsson PR (2011) Optimal networks of nature reserves can be found through eigenvalue perturbation theory of the connectivity matrix. Ecol Appl 21:1861–1870

    Article  PubMed  Google Scholar 

  • Johnson WC, Collinge SK (2004) Landscape effects on black-tailed prairie dog colonies. Biol Cons 115:487–497

    Article  Google Scholar 

  • Klebanoff A, Minta S, Hastings A, Clark TW (1991) Age-dependent predation model of black-footed ferrets and prairie dogs. SIAM J Appl Math 51:1053–1073

    Article  Google Scholar 

  • Knowles CJ (1982) Habitat affinity, populations, and control of black-tailed prairie dogs on the Charles M. Russel national wildlife refuge. Zoology, University of Montana, Vol. Ph.D

  • Laughlin SB, Sejnowski TJ (2003) Communication in neuronal networks. Science 301:1870–1874

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Legrand D, Guillaume O, Baguette M, Cote J, Trochet A, Calvez O, Zajitschek S, Zajitschek F, Lecomte J, Bénard Q, Le Galliard J-F, Clobert J (2012) The metatron: an experimental system to study dispersal and metaecosystems for terrestrial organisms. Nat Methods 9:828–833

    Article  CAS  PubMed  Google Scholar 

  • Liebold MA, Holyoak M, Mouquet N, Amarasekare P, Chase JM, Hoopes MF, Holt RD, Shurin JB, Law R, Tilman D, Loreau M, Gonzalez A (2004) The metacommunity concept: a framework for multi-scale community ecology. Ecol Lett 7:601–613

    Article  Google Scholar 

  • Liu Y, Yu C, Zhang X, Liu J, Duan Y, Alexander-Bloch AF, Liu B, Jiang T, Bullmore E (2013) Impaired long distance functional connectivity and weighted network architecture in Alzheimer’s disease. Cereb Cortex 24:1422–1435

    Article  PubMed  PubMed Central  Google Scholar 

  • Loreau M (2010) From populations to ecosystems: theoretical foundations for a new ecological synthesis. Princeton University Press, Princeton

    Book  Google Scholar 

  • Loreau M, Daufresne T, Gonzalez A, Gravel D, Guichard F, Leroux SJ, Loeuille N, Massol F, Mouquet N (2013) Unifying sources and sinks in ecology and earth sciences. Biol Rev 88:365–379

    Article  PubMed  Google Scholar 

  • May RM (2006) Network structure and the biology of populations. Trends Ecol Evol 21:394–399

    Article  PubMed  Google Scholar 

  • Miller B, Reading RP, Forrest S (1996) Prairie night: Black-footed ferrets and the recovery of endangered species. Smithsonian Institution Press, Washington

    Google Scholar 

  • Minor ES, Urban DL (2008) A graph-theory framework for evaluating landscape connectivity and conservation planning. Conserv Biol 22:297–307

    Article  PubMed  Google Scholar 

  • Minor ES, McDonald RI, Treml EA, Urban DL (2008) Uncertainty in spatially explicit population models. Biol Cons 141:956–970

    Article  Google Scholar 

  • Moilanen A (2011) On the limitations of graph-theoretic connectivity in spatial ecology and conservation. J Appl Ecol 48:1543–1547

    Article  Google Scholar 

  • Morris WF, Doak DF (2002) Quantitative conservation biology: Theory and practice of population viability analysis. Sinaeur Associates, Sunderland

    Google Scholar 

  • Mouquet N, Gravel D, Massol F, Calcagno V (2013) Extending the concept of keystone species to communities and ecosystems. Ecol Lett 16:1–8

    Article  PubMed  Google Scholar 

  • Newman MEJ (2003) The structure and function of complex networks. SIAM Rev 45:167–256

    Article  Google Scholar 

  • Newman MEJ (2006) Modularity and community structure in networks. Proc Natl Acad Sci 103:8577–8582

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Nier E, Yang J, Yorulmazer T, Alentorn A (2007) Network models and financial stability. J Econ Dyn Control 31:2033–2060

    Article  Google Scholar 

  • O’Connor LMJ, Fugère V, Gonzalez A (2020) Evolutionary rescue is mediated by the history of selection and dispersal in diversifying metacommunities. Front Ecol Evol 8:517434

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Phillips SJ, Williams P, Midgley G, Archer A (2008) Optimizing dispersal corridors for the cape Proteaceae using network flow. Ecol Appl 18:1200–1211

    Article  PubMed  Google Scholar 

  • Rayfield B, Fortin M, Fall A (2011) Conncectivity for conservation: a framework to classify network measures. Ecology 92:847–858

    Article  PubMed  Google Scholar 

  • Reading RP (1993) Toward an endangered species reintroduction paradigm: a case study of the black-footed ferret. Vol. Ph.D. Yale University

  • Rebaudo F, Rouzic AL, Dupas S, Silvain J-F, Harry M, Dangles O (2013) SimAdapt: an individual-based genetic model for simulating landscape management impacts on populations. Methods Ecol Evol 4:595–600

    Article  Google Scholar 

  • Roach JL, Stapp P, Horne BV, Antolin MF (2001) Genetic structure of a metapopulation of black-tailed prairie dogs. J Mammal 82:946–959

    Article  Google Scholar 

  • Russ GR, Alcala AC (2011) Enhanced biodiversity beyond marine reserve boundaries: the cup spillith over. Ecol Appl 21:241–250

    Article  PubMed  Google Scholar 

  • Salau KR, Schoon M, Baggio JA, Janssen MA (2012) Varying effects of connectivity and dispersal on interacting species dynamics. Ecol Model 242:81–91

    Article  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 

  • Schoon M, Baggio JA, Salau K, Janssen MA (2014) Insights for managers from modeling species interactions across multiple scales in an idealized landscape. Environ Model Softw 54:53–59

    Article  Google Scholar 

  • Shanafelt DW, Salau KR, Baggio JA (2017) Do-it-yourself networks: a novel algorithm of generating weighted networks. Royal Society Open Science 4:171227

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Sheets RG, Linder RL, Dahlgren RB (1972) Food habits of two litters of black-footed ferrets in South Dakota. Am Midl Nat 87:249–251

    Article  Google Scholar 

  • Sibly RM, Grimm V, Martin BT, Johnston ASA, Kułakowska K, Topping CJ, Calow P, Nabe-Nielsen J, Thorbek P, DeAngelis DL (2013) Representing the acquisition and use of energy by individuals in agent-based models of animal populations. Methods Ecol Evol 4:151–161

    Article  Google Scholar 

  • Srivastava DS, Kolasa J, Bengtsson J, Gonzalez A, Lawler SP, Miller TE, Munguia P, Romanuk T, Schneider DC, Trzcinski MK (2004) Are natural microcosms useful model systems for ecology. Trends Ecol Evol 19:379–384

    Article  PubMed  Google Scholar 

  • Staddon P, Lindo Z, Crittenden PD, Gilbert F, Gonzalez A (2010) Connectivity, non-random extinction and ecosystem function in experimental metacommunities. Ecol Lett 13:543–552

    Article  PubMed  Google Scholar 

  • Tang W, Bennett DA (2010) Agent-based modeling of animal movement: a review. Geogr Compass 4:682–700

    Article  Google Scholar 

  • Thompson PL, Shurin JB (2012) Regional zooplankton biodiversity provides limited buffering of pond ecosystems against climate change. J Anim Ecol 81:251–259

    Article  PubMed  Google Scholar 

  • Thompson PL, Rayfield B, Gonzalez A (2017) Loss of habitat and connectivity erodes species diversity, ecosystem functioning, and stability in metacommunity networks. Ecography 40:98–108

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Urban DL, Minor ES, Tremi E, A., Schick, R. S., (2009) Graph models of habitat mosaics. Ecol Lett 12:260–273

    Article  PubMed  Google Scholar 

  • USFWS (2013) Recovery plan for the black-footed ferret (Mustela nigripes). In: USF a W (ed) Service. U.S. Fish and Wildlife Service. Denver. Colorado

  • van Mieghem P (2011) Graph spectra for complex networks. Cambridge University Press, Cambridge

    Google Scholar 

  • Watts DJ (2002) A simple model of global cascades on random networks. Proc Natl Acad Sci 99:5766–5771

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • West AD, Stillman RA, Drewitt A, Frost NJ, Mander M, Miles C, Langston R, Sanderson WG, Willis J (2011) WaderMORPH—a user-friendly individual-based model to advise shorebird policy and management. Methods Ecol Evol 2:95–98

    Article  Google Scholar 

  • Wilensky U (1999) NetLogo Center for Connected Learning and Computer-Based Modeling. Northwestern University, Illinois

    Google Scholar 

Download references

Acknowledgements

B. Morin and E. Morales contributed helpful discussions about coding structure and statistical analysis. We are grateful to the INRAE MIGALE bioinformatics facility (MIGALE, INRAE, 2020. Migale bioinformatics Facility, https://doi.org/10.15454/1.5572390655343293E12) for providing help and computing resources.

Funding

JAB acknowledges support from the Center for Behavior, Institutions and the Environment. KRS acknowledges support from the NSF Alliance for faculty diversity postdoctoral fellowship [NSF Grant DMS-0946431].

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Arizona, 617 N Santa Rita Ave, Tucson, AZ, 85721, USA

    Kehinde R. Salau

  2. School of Politics, Security, and International Affairs, University of Central Florida, Orlando, FL, 32816, USA

    Jacopo A. Baggio

  3. National Center for Integrated Coastal Research, University of Central Florida, Orlando, FL, 32816, USA

    Jacopo A. Baggio

  4. Université de Lorraine, Université de Strasbourg, AgroParisTech, Centre National de la Recherche Scientifique (CNRS), L’Institut National de Recherche pour l’Agriculture, l’Alimentation, et l’Environnement (INRAE), Bureau d’Économie Théorique et Appliquée (BETA), AgroParis Tech - Centre de Nancy, 14 Rue Girardet - CS 14216, 54042, Nancy Cedex, France

    David W. Shanafelt

  5. School of Sustainability, Arizona State University, 777 E. University Dr., Tempe, AZ, 85281, USA

    Marco A. Janssen & Joshua K. Abbott

  6. School of Complex Adaptive Systems, College of Global Futures, Arizona State University, 1031 S Palm Walk, Tempe, AZ, 85281, USA

    Marco A. Janssen

  7. Yale School of the Environment, Yale University, 195 Prospect St, New Haven, CT, 06511, USA

    Eli P. Fenichel

Authors
  1. Kehinde R. Salau
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jacopo A. Baggio
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David W. Shanafelt
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Marco A. Janssen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Joshua K. Abbott
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Eli P. Fenichel
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

KRS, JAB and DWS analyzed the model simulations and drafted the manuscript; KRS solved the proofs relating the first and second moments of eigenvector centrality, and connecting eigenmetrics to other network metrics; KRS and JAB conceived the study with input from MAJ, JKA and EPF; MAJ, JKA and EPF helped develop and write the manuscript; all authors gave final approval for submission.

Corresponding author

Correspondence to David W. Shanafelt.

Ethics declarations

Conflict of interests

We have no competing interests to declare.

Ethics approval

Not applicable.

Consent to participate

Not applicable.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (DOCX 819 KB)

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Salau, K.R., Baggio, J.A., Shanafelt, D.W. et al. Taking a moment to measure networks—an approach to species conservation. Landsc Ecol 37, 2551–2569 (2022). https://doi.org/10.1007/s10980-022-01490-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10980-022-01490-0

Keywords

search

Navigation