Comparing forest governance models against invasive biological threats. (English) Zbl 1406.92657

Summary: In order to take account of the negative effects of invasive species and pathogens on networked forest areas, we study the dynamics of stochastic closed-loop input-output systems faced with the risk of external random perturbations. The extension of previous works on robustness is carried out by introducing a negative feedback mechanism, such that the output from an element contained in the system behaves as a negative input toward elements to which it is connected. Through the study of an overall network divided into compartments barely connected to one another, we first consider the pathway pertaining to monofunctional zoning. By looking at a single aggregated structure, we then move our focus to the pathway proper to multifunctionality. Our results show that, at significant time scales, the monofunctional-zoning mode of forest governance, generally applied in Australasia, performs robustly against invasive biological threats at all levels of outbreak probability. The multifunctional mode of forest governance, further practiced in Western Europe, is mainly sturdy when the probability of invasion verges into certainty. Should this not be the case, robustness is ensured would disturbers and perturbations be uncorrelated. Accordingly, the monofunctional pathway can afford adopting control strategies for outbreak avoidance, which is only acceptable in case the expected invasion can be halted. For the sake of maintaining low likelihood of invasion, the multifunctional pathway is compelled to applying preventive strategies.


92D40 Ecology
92C80 Plant biology
92C42 Systems biology, networks
93D25 Input-output approaches in control theory
93B52 Feedback control
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
Full Text: DOI


[1] Häggman, H.; Raybould, A.; Borem, A.; Fox, T.; Handley, L.; Hertzberg, M.; Lu, M.-Z.; Macdonald, P.; Oguchi, T.; Pasquali, G.; Pearson, L.; Peter, G.; Quemada, H.; Seguin, A.; Tattersall, K.; Ulian, E.; Walter, C.; McLean, M., Genetically engineered trees for plantation forests: key considerations for environmental risk assessment, Plant Biotechnol. J., 11, 785-798, (2013)
[2] Al Zamal, F.; Ruths, D., On the contributions of topological features to transcriptional regulatory network robustness, BMC Bioinform., 13, 1-12, (2012)
[3] Aleksander, I.; Taylor, J., Artificial Neural Networks, 2: Proceedings of the International Conference on Artificial Neural Networks, (1992), Elsevier: Elsevier New York
[4] Alexandre, S., 2017. Rapport de Mission de la Déléguée Interministerielle à la Forêt et au Bois, Rapport n^{o}011010-01, Conseil Général de l’Environnement et du Développement Durable, Paris.
[5] Arenas, A.; Diaz-Guilera, A.; Pérez-Vicente, C., Synchronization reveals topological scales in complex networks, Phys. Rev. Lett., 96, 114102, (2006)
[6] Barthod, C., La multifonctionnalité des forêts entre discours et pratiques: illusion ou réalité à assumer?, Revue Forestière Française, 67, 293-319, (2015)
[7] Bauschke, H.; Borwein, J., Continuous linear monotone operators on banach spaces, CiteSeer^{X}, 1-48, (1995)
[8] Beland Lindahl, K.; Sandström, C.; Sténs, A., Alternative pathways to sustainability? Comparing forest governance models, Forest Policy Econ., 77, 69-78, (2017)
[9] Booth, K., Recreation on public lands in new zealand - past, present and future, GeoJournal, 29, 299-305, (1993)
[10] Bremer, L.; Farley, K., Does plantation forestry restore biodiversity or create green deserts? a synthesis of the effects of land-use transitions on plant species richness, Biodivers. Conserv., 19, 3893-3915, (2010)
[11] Brockerhoff, E.; Jactel, H.; Parrotta, J.; Quine, C.; Sayer, J., Plantation forests and biodiversity: oxymoron or opportunity?, Biodivers. Conserv., 17, 925-951, (2008)
[12] Buldygin, V., Random Elements and their Convergence, Asymptotic Behaviour of Linearly Transformed Sums of Random Variables, (1997), Springer Netherlands, Dordrecht · Zbl 0906.60002
[13] Bulman, L., Pest detection surveys on high-risk sites in new zealand, Austr. Forestry, 71, 242-244, (2008)
[14] Callaway, R., Positive Interactions and Interdependence in Plant Communities, (2007), Springer: Springer New York
[15] Chen, A.; Silver, P., Designing biological compartmentalization, Trends Cell Biol., 22, 662-670, (2012)
[16] Clayton, R.; Cowan, P., Management of animal and plant pests in new zealand - patterns of control and monitoring by regional agencies, Wildlife Res., 37, 360-371, (2010)
[17] Cojocaru, M. G.; Daniele, P.; Nagurney, A., Projected dynamical systems and evolutionary variational inequalities via hilbert spaces with applications, J. Optim. Theory Appl., 27, 1-15, (2005) · Zbl 1093.49004
[18] Crowl, T.; Crist, T.; Parmenter, R.; Belovsky, G.; Lugo, A., The spread of invasive species and infectious disease as drivers of ecosystem change, Front. Ecol. Environ., 6, 238-246, (2008)
[19] Déthée, A., 2017. Marchiennes: L’ONF renonce aux coupes rases en forêt pour s’Éviter les foudres des promeneurs. La Voix du Nord, L’Édition du 7 Décembre 2017.
[20] Dix, M.; Johnson, R.; Harrell, M.; Case, R.; Wright, R.; Hodges, L.; Brandle, J.; Schoeneberger, M.; Sunderman, N.; Fitzmaurice, R.; Young, L.; Hubbard, K., Influences of trees on abundance of natural enemies of insect pests: a review, Agrofor. Syst., 29, 303-311, (1995)
[21] Dragicevic, A., Bayesian population dynamics of spreading species, Environ. Model. Assess., 20, 17-27, (2015)
[22] Dragicevic, A., From robustness to resilience: a network price identity approach, Ecol. Complex., 28, 47-53, (2016)
[23] Dragicevic, Functional diversity from network response dynamics, J. Bioecon., 18, 1-15, (2016)
[24] Dragicevic, A.; Shogren, J., Sustainability narrowness, Adv. Complex Syst., 20, (2017)
[25] Early, R.; Bradley, B.; Dukes, J.; Lawler, J.; Olden, J.; Blumenthal, D.; Gonzalez, P.; Grosholz, E.; Ibañez, I.; Miller, L.; Sorte, C.; Tatem, A., Global threats from invasive alien species in the twenty-first century and national response capacities, Nat Commun, 7, 12485, 1-9, (2016)
[26] Eiswerth, M.; Darden, T.; Johnson, W.; Agapoff, J.; Harris, T., Input-output modeling, outdoor recreation, and the economic impacts of weeds, Weed Sci., 53, 130-137, (2005)
[27] Epanchin-Niell, R.; Brockerhoff, E.; Kean, J.; Turner, J., Designing cost-efficient surveillance for early detection and control of multiple biological invaders, Ecol. Appl., 24, 1258-1274, (2014)
[28] Evans, A., The speed of invasion: rates of spread for thirteen exotic forest insects and diseases, Forests, 7, (2016)
[29] Eviner, V.; Hawkes, C., The Effects of Plant-Soil Feedbacks on Invasive Plants: Mechanisms and Potential Management Options, Invasive Plant Ecology and Management: Linking Processes to Practice, (2012), CAB International, Wallingford, Oxon
[30] FAO, 2001. Protecting plantations from pests and diseases, forest resources division. Working Paper 10, Rome.
[31] Farcy, C., Peyron, J. L., Poss, Y., 2011. Forêts et foresterie, mutations et décloisonnements. Éditions L’Harmattan, Paris.
[32] Farkas, B.; Wegner, S. A., Variations on barbalat’s lemma, Am. Math. Mon., 123, 825-830, (2017) · Zbl 1391.26005
[33] FBF, 2018. La gestion forestière, france bois forêt - interprofession nationale. Available at: https://franceboisforet.fr.
[34] Fiduccia, C.; Scheinerman, E.; Trenk, A.; Zito, J., Dot product representations of graphs, Discrete Math., 181, 113-138, (1998) · Zbl 0974.05058
[35] Franklin, J.; Shugart, H.; Harmon, M., Tree death as an ecological process, Bioscience, 37, 550-556, (1987)
[36] Ginzburg, L.; Inchausti, P., Asymmetry of population cycles: abundance-growth representation of hidden causes of ecological dynamics, Oikos, 80, 435-447, (1997)
[37] Guimera, R.; Stouffer, D.; Sales-Pardo, M.; Leicht, E.; Newman, M.; Amaral, L., Origin of compartmentalization in food webs, Ecology, 91, 2941-2951, (2010)
[38] Heij, C.; Ran, A.; van Schagen, F., Introduction to Mathematical Systems Theory: Linear Systems, Identification and Control, (2007), Birkhäuser, Basel · Zbl 1127.93004
[39] Hellmann, J.; Byers, J.; Bierwagen, B.; Dukes, J., Five potential consequences of climate change for invasive species, Conserv. Biol., 22, (2008)
[40] Hill, D.; Moylan, P., Stability results for nonlinear feedback systems, Automatica, 13, (1977) · Zbl 0356.93025
[41] Horie, T.; Haight, R.; Homans, F.; Venette, R., Optimal strategies for the surveillance and control of forest pathogens: a case study with oak wilt, Ecol. Econ., 86, 78-85, (2013)
[42] Hulme, P., Climate change and biological invasions: evidence, expectations, and response options, Biol. Rev., 92, 1297-1313, (2017)
[43] IFIJ, 2018. Code forestier (nouveau), institut français d’information juridique. Available at: http://codes.droit.org.
[44] Jactel, H.; Brockerhoff, E., Tree diversity reduces herbivory by forest insects, Ecol. Lett., 10, 835-848, (2007)
[45] Jensen, M.; Reynolds, K.; Langner, U.; Hart, M., Application of Logic and Decision Models in Sustainable Ecosystem Management, Proceedings of the 42nd Hawaii International Conference on Systems Sciences, Waikoloa, (2009)
[46] Kanowski, P., Australia’s forests: contested past, tenure-driven present, uncertain future, Forest Policy Econ., 77, 56-68, (2017)
[47] Kerr, B.; Godfrey-Smith, P., Generalization of the price equation for evolutionary change, Evolution, 63, 531-536, (2008)
[48] Kitano, H., Biological robustness, Nat. Rev. Genet., 5, 826-837, (2004)
[49] Klapwijk, M.; Bylund, H.; Schroeder, M.; Björkman, C., Forest management and natural biocontrol of insect pests, Forestry, 89, 253-262, (2016)
[50] Kovac, M.; Hladnik, D.; Kutnar, L., Biodiversity in (the natura 2000) forest habitats is not static: its conservation calls for an active management approach, J. Nature Conserv., 43, 250-260, (2018)
[51] Krause, A.; Frank, K.; Mason, D.; Ulanowicz, R.; Taylor, W., Compartments revealed in food-web structure, Nature, 426, 282-285, (2003)
[52] Landmann, G.; Gosselin, F.; Gosselin, M., Produire plus de bois tout en préservant mieux la biodiversité, apports de l’étude ”biomasse et biodiversité forestières”, Sciences Eaux et Territoires, 3, 50-55, (2010)
[53] Larson, D.; Philips-Mao, L.; Quiram, G.; Sharpe, L.; Stark, R.; Sugita, S.; Weiler, A., A framework for sustainable invasive species management: environmental, social, and economic objectives, J. Environ. Manage., 92, 14-22, (2011)
[54] Leach, M., Scoones, I., Stirling, A., 2010. Dynamic sustainabilities: technology, environment, social justice, earthscan. London.
[55] Lee, K., Compass and Gyroscope: Integrating Science and Politics for the Environment, (1993), Island Press: Island Press Washington
[56] Liebhold, A., Forest pest management in a changing world, Int. J. Pest Manag., 58, 289-295, (2012)
[57] L’IF, La forêt plantée en france: état des lieux, La Feuille de l’Inventaire Forestier, 40, (2017)
[58] Liu, T.; Hill, D.; Zhao, J., Incremental-dissipativity-based synchronization of interconnected systems, Proc. IFAC World Congress, 18, 8890-8895, (2011)
[59] Lourdes Torres, M.; Mena, C., Understanding Invasive Species in the Galapagos Islands: From the Molecular to the Landscape, (2018), Springer, Berlin
[60] Lovett, G.; Weiss, M.; Liebhold, A.; Holmes, T.; Leung, B.; Lambert, K.; Orwig, D.; Campbell, F.; Rosenthal, J.; McCullough, D.; Wildova, R.; Ayres, M.; Canham, C.; Foster, D.; LaDeau, S.; Weldy, T., Nonnative forest insects and pathogens in the united states: impacts and policy options, Ecol. Appl., 26, 1437-1455, (2016)
[61] Macpherson, M.; Kleczkowski, A.; Healey, J.; Quine, C.; Hanley, N., The effects of invasive pests and pathogens on strategies for forest diversification, Ecol. Modell., 350, 87-99, (2017)
[62] Manion, P., Tree Disease Concepts, (1991), Prentice Hall, Upper Saddle River
[63] Martínez-Jauregui, M.; Soliño, M.; Martínez-Fernández, J.; Touza, J., Managing the early warning systems of invasive species of plants, birds, and mammals in natural and planted pine forests, Forests, 9, 1-11, (2018)
[64] May, R., Will a large complex system be stable?, Nature, 238, 413-414, (1972)
[65] McCrone, J., 2015. The biosecurity threats to the new zealand economy. Stuff.co.nz, Issue of April 18, 2015.
[66] Melián, C.; Bascompte, J., Complex networks: two ways to be robust?, Ecol. Lett., 5, 705-708, (2002)
[67] Mestre, L.; Toro-Manríquez, M.; Soler, R.; Huertas-Herrera, A.; Martínez-Pastur, G.; Lencinas, M., The influence of canopy-layer composition on understory plant diversity in southern temperate forests, Forest Ecosyst., 4, (2017)
[68] Mitsuda, Y.; Ito, S.; Takata, K., Effects of competitive and cooperative interaction among neighboring trees on tree growth in a naturally regenerated even-aged larix sibirica stand in considering height stratification, J. Forest Res., 7, 185-191, (2002)
[69] Morbidi, F.; Kibangou, A distributed solution to the network reconstruction problem, Syst. Control Lett., 70, 85-91, (2014) · Zbl 1290.93009
[70] Nadkarni, N., Diversity of species and interactions in the upper tree canopy of forest ecosystems, Am. Zool., 34, 70-78, (1994)
[71] Nagurney, A., Network Economics: A Variational Inequality Approach, (1993), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0873.90015
[72] Newman, M., Modularity and community structure in networks, Proc. Natl. Acad. Sci., 103, 8577-8582, (2006)
[73] Norberg, J.; Cumming, G., Complexity Theory for a Sustainable Future, (2008), Columbia University Press: Columbia University Press New York
[74] ONF, 2012. La gestion durable des forêts domaniales, office national des forêts. Paris.
[75] Orion, T., Beyond the War on Invasive Species: A Permaculture Approach to Ecosystem Restoration, (2015), Chelsea Green Publishing: Chelsea Green Publishing Chelsea
[76] Panda, T.; Theodore, T.; Arun Kumar, R., Statistical Optimization of Biological Systems, (2015), CRC Press, Boca Raton
[77] Pastorella, F.; Giacovelli, G.; Maesano, M.; Paletto, A.; Vivona, S.; Veltri, A.; Pellicone, G.; Mugnozza, G., Social perception of forest multifunctionality in southern italy: the case of calabria region, J. Forest Sci., 62, 366-379, (2016)
[78] Pimentel, D.; Zuniga, R.; Morrison, D., Update on the environmental and economic costs associated with alien-invasive species in the united states, Ecol. Econ., 52, 273-288, (2005)
[79] Price, G., Selection and covariance, Nature, 227, 520-521, (1970)
[80] Quack, S.; Morgan, G.; Whitley, R., National Capitalisms, Global Competition, and Economic Performance, (2000), John Benjamins Publishing, Amsterdam
[81] Ren, J.; Wang, W. X.; Li, B.; Lai, Y. C., Noise bridges dynamics correlation and topology in coupled oscillator networks, Phys. Rev. Lett., 104, 058701, (2010)
[82] Ricciardi, A.; Cohen, J., The invasiveness of an introduced species does not predict its impact, Biol. Invasions, 9, 309-315, (2007)
[83] Rivière, C., De la ressource bois à la forêt multifonctionnelle?, Développement Durable et Territoires, 8, (2017)
[84] Roche, M., Forest governance and sustainability pathways in the absence of a comprehensive forest policy - the case of new zealand, Forest Policy Econ., 77, 33-43, (2017)
[85] Roy, B.; Alexander, H.; Davidson, J.; Campbell, F.; Burdon, J.; Sniezko, R.; Brasier, C., Increasing forest loss worldwide from invasive pests requires new trade regulations, Front. Ecol. Environ., 12, 457-465, (2014)
[86] Scardovi, L.; Arcak, M.; Sontag, E., Synchronization of interconnected systems with applications to biochemical networks: an input-output approach, IEEE Trans. Automat. Contr., 55, 1367-1379, (2010) · Zbl 1368.93651
[87] Scion, 2016. The importance of forests to people, new zealand planted forest portal. Available at: http://www.nzplantedforests.org.
[88] de Sèze, M. A., Pour une gestion durable de la forêt française, Géoéconomie, 65, 195-202, (2013)
[89] Skorohod, A., Random Linear Operators, Asymptotic Behaviour of Linearly Transformed Sums of Random Variables, (1984), Springer Netherlands, Dordrecht
[90] Smith, L.; Schmitz, O., Invasive plants may promote predator-mediated feedback that inhibits further invasion, Ecol. Evol., 5, 2411-2419, (2015)
[91] Steiner, A., 2010. Counting the cost of alien invasions. BBC News Online, 13 April 2010.
[92] Stouffer, D.; Bascompte, J., Compartmentalization increases food-web persistence, Proc. Natl. Acad. Sci., 108, 3648-3652, (2011)
[93] Strayer, D.; Eviner, V.; Jeschke, J.; Pace, M., Understanding the long-term effects of species invasions, Trends Ecol. Evol., 21, 645-651, (2006)
[94] Teng, J.; McCann, K., Dynamics of compartmented and reticulate food webs in relation to energetic flows, Am. Nat., 164, 85-100, (2004)
[95] Towsley, A.; Pakianathan, J.; Douglass, D., Correlation angles and inner products: application to a problem from physics, ISRN Appl. Math., 12, (2011) · Zbl 1237.62077
[96] Tran, X.; Dang, H.; Nguyen, T., Abstract random linear operators on probabilistic unitary spaces, J. Korean Math. Soc., 53, 347-362, (2016) · Zbl 1341.60067
[97] Vallina, S.; Le Quéré, C., Stability of complex food webs: resilience, resistance and the average interaction strength, J. Theor. Biol., 272, 160-173, (2011) · Zbl 1405.92305
[98] Wang, P., Information Linkage Between Applied Mathematics and Industry, (1979), Academic Press, Cambridge
[99] Wang, S.; Brose, U., Biodiversity and ecosystem functioning in food webs: the vertical diversity hypothesis, Ecol. Lett., 21, 9-20, (2018)
[100] Whitley, R., Divergent Capitalisms: The Social Structuring and Change of Business Systems, (1999), Oxford University Press, Oxford
[101] Wittenberg, R.; Cock, M., Invasive Alien Species: A Toolkit of Best Prevention and Management Practices, (2001), CAB International, Wallingford, Oxon
[102] Wu, C., Algebraic connectivity of directed graphs, Linear Multilinear Algebra, 53, 203-223, (2005) · Zbl 1065.05048
[103] Wu, C., On rayleigh-ritz ratios of a generalized laplacian matrix of directed graphs, Linear Algebra Appl., 402, 207-227, (2005) · Zbl 1063.05065
[104] Zhang, J.; Huang, S.; He, F., Half-century evidence from western canada shows forest dynamics are primarly driven by competition followed by climate, Proc. Natl. Acad. Sci., 112, 4009-4014, (2015)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.