Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-24T07:53:35.712Z Has data issue: false hasContentIssue false

5 - Network Transitions

Published online by Cambridge University Press:  05 May 2022

Cang Hui  and
David Richardson
Cang Hui
Affiliation:
Stellenbosch University, South Africa
David Richardson
Affiliation:
Stellenbosch University, South Africa
Get access

Summary

Astrologists have predicted the occurrence of solar eclipses with increasing precision through the ages. Predicting celestial motions invokes the dynamics of a relatively simple and rigid system; it is straightforward and akin to identifying regularities in recurrent records. Discovering regularities, however, does not necessarily impart true comprehension. While we can speculate about the mechanisms and forces at work to fill gaps as we edge towards comprehension, such conjectured theories are often misleading. In early 2020, epidemiologists were confronted with a once-in-a-lifetime challenge: forecasting the number of infections of COVID-19 both regionally and globally. With little understanding of the viral transmission at the time, most forecasts failed miserably. Failed forecasts abound, especially for systems that are complex and adaptive; the bet between ecologist Paul Ehrlich and economist Julian Simon on the swings of metal price anticipated from socioeconomic impacts of overpopulation (Sabin 2013) is a good example. The forecasting conundrum is both typical and perplexing to ecologists and invasion scientists; hindsight is an exact science, while forecasting is no easier than catching the Cheshire Cat.

Type
Chapter
Information
Invading Ecological Networks , pp. 265 - 317
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andrae, B, et al. (2010) Entropy production of cyclic population dynamics. Physical Review Letters 104, 218102.Google Scholar
Armstrong, JS (2009) Principles of Forecasting. Boston: Springer.Google Scholar
Arnoldi, J, Loreau, M, Haegeman, B (2019) The inherent multidimensionality of temporal variability: How common and rare species shape stability patterns. Ecology Letters 22, 1557–1567.Google Scholar
Beckage, B, Gross, LJ, Kauffman, S (2011) The limits to prediction in ecological systems. Ecosphere 2, 1–12.Google Scholar
Benincà, E, et al. (2015) Species fluctuations sustained by a cyclic succession at the edge of chaos. Proceedings of the National Academy of Sciences USA 112, 6389–6394.Google Scholar
Boettiger, C, Hastings, A (2012) Quantifying limits to detection of early warning for critical transitions. Journal of the Royal Society Interface 9, 2527–2539.Google Scholar
Boettiger, C, Ross, N, Hastings, A (2013) Early warning signals: The charted and uncharted territories. Theoretical Ecology 6, 255–264.Google Scholar
Bosc, C, et al. (2018) Interactions among predators and plant specificity protect herbivores from top predators. Ecology 99, 1602–1609.CrossRefGoogle ScholarPubMed
Bosc, C, et al. (2019) Importance of biotic niches versus drift in a plant-inhabiting arthropod community depends on rarity and trophic group. Ecography 42, 1926–1935.Google Scholar
Boughton, D, Malvadkar, U (2002) Extinction risk in successional landscapes subject to catastrophic disturbances. Ecology and Society 6, 2.Google Scholar
Box, GEP (1976) Science and statistics. Journal of the American Statistical Association 71, 791–799.Google Scholar
Brown, JH, Kodric-Brown, A (1977) Turnover rates in insular biogeography: Effect of immigration on extinction. Ecology 58, 445–449.Google Scholar
Cadotte, MW, et al. (2015) Predicting communities from functional traits. Trends in Ecology & Evolution 30, 510–511.Google Scholar
Capinha, C, et al. (2018) Models of alien species richness show moderate predictive accuracy and poor transferability. NeoBiota 38, 77–96.Google Scholar
CaraDonna, PJ, et al. (2017) Interaction rewiring and the rapid turnover of plant–pollinator networks. Ecology Letters 20, 385–394.Google Scholar
Carboni, M, et al. (2016) What it takes to invade grassland ecosystems: Traits, introduction history and filtering processes. Ecology Letters 19, 219–229.Google Scholar
Cardinale, BJ, Palmer, MA, Collins, SL (2002) Species diversity enhances ecosystem functioning through interspecific facilitation. Nature 415, 426–429.Google Scholar
Carpenter, SR, Brock, WA (2006) Rising variance: A leading indicator of ecological transition. Ecology Letters 9, 311–318.Google Scholar
Carpenter, SR, et al. (2011) Early warnings of regime shifts: A whole-ecosystem experiment. Science 332, 1079–1082.Google Scholar
Carpenter, SR, et al. (2008) Leading indicators of trophic cascades. Ecology Letters 11, 128–138.Google Scholar
Carroll, L (1865) Alice’s Adventures in Wonderland. London: Macmillan.Google Scholar
Caswell, H, Vindenes, Y (2018) Demographic variance in heterogeneous populations: Matrix models and sensitivity analysis. Oikos 127, 648–663.Google Scholar
Cauchy, A (1829) Sur la resolution des équivalences don’t lest modules se réduisent à des nombres premiers. Exercices de Mathematiques 4, 174–195.Google Scholar
Chakrabarti, CG, Ghosh, K (2009) Non-equilibrium thermodynamics of ecosystems: Entropic analysis of stability and diversity. Ecological Modelling 220, 1950–1956.Google Scholar
Chakrabarti, CG, Ghosh, K (2010) Maximum-entropy principle: Ecological organization and evolution. Journal of Biological Physics 36, 175–183.Google Scholar
Chapin, FS, et al. (1998) Ecosystem consequences of changing biodiversity. BioScience 48, 45–52.Google Scholar
Chapman, ASA, Tunnicliffe, V, Bates, AE (2018) Both rare and common species make unique contributions to functional diversity in an ecosystem unaffected by human activities. Diversity and Distributions 24, 568–578.Google Scholar
Chen, X, Cohen, JE (2001) Global stability, local stability and permanence in model food webs. Journal of Theoretical Biology 212, 223–235.Google Scholar
Chesson, P, et al. (2005) Scale transition theory with special reference to species coexistence in a variable environment. In Holyoak, M, Leibold, MA, Holt, RD (eds.), Metacommunities: Spatial Dynamics and Ecological Communities, pp. 279–306. Chicago: The University of Chicago Press.Google Scholar
Colautti, RI, et al. (2017) Invasions and extinctions through the looking glass of evolutionary ecology. Philosophical transactions of the Royal Society B: Biological Sciences 372, 20160031.Google Scholar
Cortez, MH, Abrams, PA (2016) Hydra effects in stable communities and their implications for system dynamics. Ecology 97, 1135–1145.Google Scholar
Crone, EE, et al. (2011) How do plant ecologists use matrix population models? Ecology Letters 14, 1–8.Google Scholar
Cuddington, K, Hastings, A (2016) Autocorrelated environmental variation and the establishment of invasive species. Oikos 125, 1027–1034.CrossRefGoogle Scholar
Dakos, V, et al. (2011) Slowing down in spatially patterned ecosystems at the brink of collapse. The American Naturalist 177, E153–E166.Google Scholar
Dakos, V, van Nes, EH, Scheffer, M (2013) Flickering as an early warning signal. Theoretical Ecology 6, 309–317.CrossRefGoogle Scholar
Dana, ED, et al. (2019) Common deficiencies of actions for managing invasive alien species: A decision-support checklist. NeoBiota 48, 97–112.Google Scholar
Davis, MA (2003) Biotic globalization: Does competition from introduced species threaten biodiversity? BioScience 53, 481–489.Google Scholar
Diamond, JM (1969) Avifaunal equilibria and species turnover rates on the channel islands of California. Proceedings of the National Academy of Sciences USA 64, 57–63.Google Scholar
Diamond, JM, May, RM (1977) Species turnover rates on islands: Dependence on census interval. Science 197, 266–270.Google Scholar
Ditlevsen, PD, Johnsen, SJ (2010) Tipping points: Early warning and wishful thinking. Geophysical Research Letters 37, L19703.Google Scholar
Doak, D, Kareiva, P, Kleptka, B (1994) Modeling population viability for the desert tortoise in the Western Mojave Desert. Ecological Applications 4, 446–460.Google Scholar
Dornelas, M, Madin, JS (2020) Novel communities are a risky business. Science 370, 164–165.Google Scholar
Drake, JM, Griffen, BD (2010) Early warning signals of extinction in deteriorating environments. Nature 467, 456–459.Google Scholar
Elliot-Graves, A (2016) The problem of prediction in invasion biology. Biology & Philosophy 31, 373–393.Google Scholar
Enquist, BJ, et al. (2019) The commonness of rarity: Global and future distribution of rarity across land plants. Science Advances 5, eaaz0414.Google Scholar
Evans, JM, Wilkie, AC, Burkhardt, J (2008) Adaptive management of nonnative species: Moving beyond the “either-or” through experimental pluralism. Journal of Agricultural and Environmental Ethics 21, 521–539.Google Scholar
Ezard, THG, et al. (2010) Matrix models for a changeable world: The importance of transient dynamics in population management. Journal of Applied Ecology 47, 515–523.CrossRefGoogle Scholar
Flather, CH, Sieg, CH (2007) Species rarity: Definition, causes, and classification. In Raphael, MG, Molina, R (eds.), Conservation of Rare or Little-Known Species: Biological, Social, and Economic Considerations, pp. 40–66. Washington: Island Press.Google Scholar
Fletcher, DH, et al. (2016) Predicting global invasion risks: A management tool to prevent future introductions. Scientific Reports 6, 26316.Google Scholar
Fournier, A, et al. (2019) Predicting future invaders and future invasions. Proceedings of the National Academy of Sciences USA 116, 7905–7910.Google Scholar
Frank, SA (2017) Universal expressions of population change by the Price equation: Natural selection, information, and maximum entropy production. Ecology and Evolution 7, 3381–3396.Google Scholar
Gaertner, M, et al. (2014) Invasive plants as drivers of regime shifts: Identifying high-priority invaders that alter feedback relationships. Diversity and Distributions 20, 733–744.Google Scholar
Gaston, KJ (2010) Valuing common species. Science 327, 154–155.Google Scholar
Gilbert, FS (1980) The equilibrium theory of island biogeography: Fact or fiction? Journal of Biogeography 7, 209–235.Google Scholar
Gilpin, ME, Diamond, JM (1982) Factors contributing to non-randomness in species co-occurrences on islands. Oecologia 52, 75–84.Google Scholar
Gould, SJ (1989) Wonderful Life: The Burgess Shale and the Nature of History. New York: Norton & Company.Google Scholar
Gravel, D, et al. (2011) Trophic theory of island biogeography. Ecology Letters 14, 1010–1016.CrossRefGoogle ScholarPubMed
Green, KC, Armstrong, JS (2015) Simple versus complex forecasting: The evidence. Journal of Business Research 68, 1678–1685.Google Scholar
Gurevitch, J, et al. (2011) Emergent insights from the synthesis of conceptual frameworks for biological invasions. Ecology Letters 14, 407–418.Google Scholar
Hanski, I (1982) Dynamics of regional distribution: The core and satellite species hypothesis. Oikos 38, 210–221.CrossRefGoogle Scholar
Hanski, I, Gyllenberg, M (1997) Uniting two general patterns in the distribution of species. Science 275, 397–400.Google Scholar
Harper, JL (1977) Population Biology of Plants. London: Academic Press.Google Scholar
Hastings, A (2001) Transient dynamics and persistence of ecological systems. Ecology Letters 4, 215–220.CrossRefGoogle Scholar
Hastings, A (2004) Transients: The key to long-term ecological understanding? Trends in Ecology & Evolution 19, 39–45.Google Scholar
Hastings, A, et al. (2018) Transient phenomena in ecology. Science 361, eaat6412.Google Scholar
Hastings, A, Wysham, DB (2010) Regime shifts in ecological systems can occur with no warning. Ecology Letters 13, 464–472.Google Scholar
He, F, Hubbell, SP (2011) Species–area relationships always overestimate extinction rates from habitat loss. Nature 473, 368–371.Google Scholar
Hector, A, et al. (2001) Conservation implications of the link between biodiversity and ecosystem functioning. Oecologia 129, 624–628.Google Scholar
Heino, J, Melo, AS, Bini, LM (2015) Reconceptualising the beta diversity-environmental heterogeneity relationship in running water systems. Freshwater Biology 60, 223–235.Google Scholar
Hewitt, JE, et al. (2016) Species and functional trait turnover in response to broad-scale change and an invasive species. Ecosphere 7, ee01289.Google Scholar
Hilbert, D (1904) Über eine Anwendung der Integralgleichungen auf eine Problem der Funktionentheorie. In Krazer, A (ed.), Verhandlungen des 3. Internationalen Mathematiker-Kongresses: in Heidelberg vom 8. bis 13, pp. 233–240. Leipzig: Teubner.Google Scholar
Hirota, M, et al. (2011) Global resilience of tropical forest and savanna to critical transitions. Science 334, 232–235.Google Scholar
Hirsch, H, Richardson, DM, Le Roux, JJ (2017). Tree invasions: Towards a better understanding of their complex evolutionary dynamics. AoB Plants 9, plx014.Google Scholar
Hui, C, McGeoch, MA (2014) Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist 184, 684–694.Google Scholar
Hui, C, Richardson, DM (2017) Invasion Dynamics. Oxford: Oxford University Press.Google Scholar
Hui, C, Richardson, DM (2019a) How to invade an ecological network. Trends in Ecology & Evolution 34, 121–131.Google Scholar
Hui, C, Richardson, DM (2019b) Network invasion as an open dynamical system: Response to Rossberg and Barabás. Trends in Ecology & Evolution 34, 386–387.Google Scholar
Hui, C, Fox, GA, Gurevitch, J (2017) Scale-dependent portfolio effects explain growth inflation and volatility reduction in landscape demography. Proceedings of the National Academy of Sciences USA 114, 12507–12511.Google Scholar
Hui, C, et al. (2014) Macroecology meets invasion ecology: Performance of Australian acacias and eucalypts around the world foretold by features of their native ranges. Biological Invasions 16, 565–576.Google Scholar
Hui, C, et al. (2016) Defining invasiveness and invasibility in ecological networks. Biological Invasions 18, 971–983.Google Scholar
Johnson, CN (1998) Species extinction and the relationship between distribution and abundance. Nature 394, 272–274.Google Scholar
Kahneman, D (2013) Thinking, Fast and Slow. New York: Farrar, Straus and Giroux.Google Scholar
Kato, M (1995) Numerical analysis of the Nernst-Planck-Poisson system. Journal of Theoretical Biology 177, 299–304.Google Scholar
Legault, G, et al. (2019) Demographic stochasticity alters expected outcomes in experimental and simulated non-neutral communities. Oikos 128, 1704–1715.Google Scholar
Legendre, P, Legendre, L (1998) Numerical Ecology, 2nd edition. Amsterdam: Elsevier.Google Scholar
Leitão, RP, et al. (2016) Rare species contribute disproportionately to the functional structure of species assemblages. Proceedings of the Royal Society B: Biological Sciences 283, 20160084.Google Scholar
Lenton, TM, et al. (2012) Early warning of climate tipping points from critical slowing down: Comparing methods to improve robustness. Philosophical transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, 1185–1204.Google Scholar
Lindegren, M, et al. (2012) Early detection of ecosystem regime shifts: A multiple method evaluation for management application. PLoS ONE 7, e38410.Google Scholar
Loreau, M, et al. (2001) Biodiversity and ecosystem functioning: Current knowledge and future challenges. Science 294, 804–808.Google Scholar
Low-Décarie, E, Chivers, C, Granados, M (2014) Rising complexity and falling explanatory power in ecology. Frontiers in Ecology and the Environment 12, 412–418.Google Scholar
Lurgi, M, et al. (2014) Network complexity and species traits mediate the effects of biological invasions on dynamic food webs. Frontiers in Ecology and Evolution 2, 36.Google Scholar
Lyons, KG, et al. (2005) Rare species and ecosystem functioning. Conservation Biology 19, 1019–1024.Google Scholar
MacArthur, RH, Wilson, EO (1967) The Theory of Island Biogeography. Princeton: Princeton University Press.Google Scholar
Mace, GM, Lande, R (1991) Assessing extinction threats: Toward a re-evaluation of IUCN threatened species categories. Conservation Biology 5, 148–157.Google Scholar
Martín, PV, et al. (2015) Eluding catastrophic shifts. Proceedings of the National Academy of Sciences USA 112, E1828–E1836.Google Scholar
Martyushev, LM, Seleznev, VD (2006) Maximum entropy production principle in physics, chemistry and biology. Physics Reports 426, 1–45.Google Scholar
Matthies, D, et al. (2004) Population size and the risk of local extinction: Empirical evidence from rare plants. Oikos 105, 481–488.Google Scholar
May, RM (1976) Simple mathematical models with very complicated dynamics. Nature 261, 459–467.Google Scholar
McCollin, D (2017) Turnover dynamics of breeding land birds on islands: Is island biogeographic theory ‘true but trivial’ over decadal time-scales? Diversity 9, 3.Google Scholar
McGeoch, MA, Latombe, G (2016) Characterizing common and range expanding species. Journal of Biogeography 43, 217–228.Google Scholar
McGeoch, MA, et al. (2019) Measuring continuous compositional change using decline and decay in zeta diversity. Ecology 100, ee02832.Google Scholar
McKinney, ML (1997) Extinction vulnerability and selectivity: Combining ecological and paleontological views. Annual Review of Ecology and Systematics 28, 495–516.Google Scholar
Miele, V, Ramos-Jiliberto, R, Vázquez, DP (2020) Core–periphery dynamics in a plant–pollinator network. Journal of Animal Ecology 89, 1670–1677.Google Scholar
Milkoreit, M, et al. (2018) Defining tipping points for social-ecological systems scholarship: An interdisciplinary literature review. Environmental Research Letters 13, 033005.Google Scholar
Miller, JT, et al. (2017) Is invasion success of Australian trees mediated by their native biogeography phylogenetic history or both? AoB Plants 9, plw080.Google Scholar
Muñoz, MA (2018) Criticality and dynamical scaling in living systems. Reviews of Modern Physics 90, 031001.Google Scholar
Nnakenyi, CA, Hui, C, Minoarivelo, HO, Dieckmann, U (2021) Leading eigenvalue of block-structured random matrices. In prep.Google Scholar
O’Sullivan, JD, Knell, RJ, Rossberg, AG (2019) Metacommunity-scale biodiversity regulation and the self-organised emergence of macroecological patterns. Ecology Letters 22, 1428–1438.Google Scholar
Olesen, JM, Stefanescu, C, Traveset, A (2011) Strong, long-term temporal dynamics of an ecological network. PLoS ONE 6, e26455.Google Scholar
Pärtel, M, et al. (2005) Grouping and prioritization of vascular plant species for conservation: combining natural rarity and management need. Biological Conservation 123, 271–278.Google Scholar
Perretti, CT, Munch, SB (2012) Regime shift indicators fail under noise levels commonly observed in ecological systems. Ecological Applications 22, 1772–1779.Google Scholar
Pettersson, S, Savage, VM, Jacobi, MN (2020) Predicting collapse of complex ecological systems: Quantifying the stability–complexity continuum. Journal of the Royal Society Interface 17, 20190391.Google Scholar
Pilgrim, ES, Crawley, MJ, Dolphin, K (2004) Patterns of rarity in the native British flora. Biological Conservation 120, 161–170.Google Scholar
Poincaré, H (1894) Sur la théorie cinétique des gaz. Revue générale des sciences pures et appliquées 5, 513–521.Google Scholar
Poisot, T, et al. (2012) The dissimilarity of species interaction networks. Ecology Letters 15, 1353–1361.Google Scholar
Purvis, A, et al. (2000) Nonrandom extinction and the loss of evolutionary history. Science 288, 328–330.Google Scholar
Pyšek, P, Richardson, DM (2007). Traits associated with invasiveness in alien plants: Where do we stand? In Nentwig, W (ed.), Biological Invasions, pp. 97–125. Berlin: Springer.Google Scholar
Rabinowitz, D (1981) Seven forms of rarity In Synge, H (ed.), The Biological Aspects of Rare Plant Conservation, pp. 205–217. New York: John Wiley & Sons Ltd.Google Scholar
Rittel, HW, Webber, MM (1973) Dilemmas in a general theory of planning. Policy Sciences 4, 155–169.Google Scholar
Romanuk, TN, et al. (2017) Robustness trade-offs in model food webs: Invasion probability decreases while invasion consequences increase with connectance. Advances in Ecological Research 56, 263–291.Google Scholar
Rossberg, AG (2013) Food Webs and Biodiversity: Foundations, Models, Data. Chichester: John Wiley & Sons Ltd.Google Scholar
Rossberg, AG, Barabás, G (2019) How carefully executed network theory informs invasion ecology. Trends in Ecology & Evolution 34, 385–386.Google Scholar
Rouget, M, et al. (2016) Invasion debt: Quantifying future biological invasions. Diversity and Distributions 22, 445–456.Google Scholar
Sabin, P (2013) The Bet: Paul Ehrlich, Julian Simon, and Our Gamble over Earth’s Future. New Haven: Yale University Press.Google Scholar
Sakai, AK, et al. (2001) The population biology of invasive species. Annual Review of Ecology and Systematics 32, 305–332.Google Scholar
Säterberg, T, et al. (2019) A potential role for rare species in ecosystem dynamics. Scientific Reports 9, 11107.Google Scholar
Scheffer, M, et al. (2001) Catastrophic shifts in ecosystems. Nature 413, 591–596.Google Scholar
Scheffer, M, et al. (2009) Early-warning signals for critical transitions. Nature 461, 53–59.Google Scholar
Scheffer, M, et al. (2012) Anticipating critical transitions. Science 338, 344–348.Google Scholar
Schoener, T, Spiller, D (1987) High population persistence in a system with high turnover. Nature 330, 474–477.Google Scholar
Schooler, SS, et al. (2011) Alternative stable states explain unpredictable biological control of Salvinia molesta in Kakadu. Nature 470, 86–89.Google Scholar
Schwartz, MW, Simberloff, D (2008) Taxon size predicts rates of rarity in vascular plants. Ecology Letters 4, 464–469.Google Scholar
Schwartz, MW, et al. (2000) Linking biodiversity to ecosystem function: Implications for conservation ecology. Oecologia 122, 297–305.CrossRefGoogle ScholarPubMed
Schwarz, B, et al. (2020) Temporal scale-dependence of plant-pollinator networks. Oikos 129, 1289–1302.Google Scholar
Seastedt, TR (2014) Biological control of invasive plant species: A reassessment for the Anthropocene. New Phytologist 205, 490–502.Google Scholar
Seekell, DA, et al. (2013) Evidence of alternate attractors from a whole-ecosystem regime shift experiment. Theoretical Ecology 6, 385–394.Google Scholar
Shackleton, RT, et al. (2018) Social-ecological drivers and impacts of invasion-related regime shifts: Consequences for ecosystem services and human wellbeing. Environmental Science and Policy 89, 300–314.Google Scholar
Smith, MD, Knapp, AK (2003) Dominant species maintain ecosystem function with non-random species loss. Ecology Letters 6, 509–517.Google Scholar
Staver, AC, Archibald, S, Levin, SA (2011) The global extent and determinants of savanna and forest as alternative biome states. Science 334, 230–232.Google Scholar
Stokstad, E (2009) On the origin of ecological structure. Science 326, 33–35.Google Scholar
Stone, L (2018) The feasibility and stability of large complex biological networks: a random matrix approach. Scientific Reports 8, 8246.Google Scholar
Stott, I (2016) Perturbation analysis of transient population dynamics using matrix projection models. Methods in Ecology and Evolution 7, 666–678.Google Scholar
Stott, I, Hodgson, DJ, Townley, S (2012) Beyond sensitivity: Nonlinear perturbation analysis of transient dynamics. Methods in Ecology and Evolution 3, 673–684.Google Scholar
Stott, I, Townley, S, Hodgson, DJ (2011) A framework for studying transient dynamics of population projection matrix models. Ecology Letters 14, 959–970.Google Scholar
Strayer, DL, et al. (2006) Understanding the long-term effects of species invasions. Trends in Ecology & Evolution 21, 645–651.Google Scholar
Suweis, S, et al. (2013) Emergence of structural and dynamical properties of ecological mutualistic networks. Nature 500, 449–452.Google Scholar
Sylvester, JJ (1852) A demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares. Philosophical Magazine IV, 138–142.Google Scholar
Tetlock, PE (2005) Political Judgment: How Good Is It? How Can We Know? Princeton: Princeton University Press.Google Scholar
Tilman, D, et al. (1994) Habitat destruction and the extinction debt. Nature 371, 65–66.Google Scholar
Ulrich, W (2005) Regional species richness of families and the distribution of abundance and rarity in a local community of forest Hymenoptera. Acta Oecologia 28, 71–76.Google Scholar
Van Kleunen, M, Richardson, DM (2007) Invasion biology and conservation biology: Time to join forces to explore the links between species traits and extinction risk and invasiveness. Progress in Physical Geography 3, 447–450.Google Scholar
Van Kleunen, M, Weber, E, Fischer, M (2010) A meta-analysis of trait differences between invasive and non-invasive plant species. Ecology Letters 13, 235–345.Google Scholar
Van Ruijven, J, Berendse, F (2003) Positive effects of plant species diversity on productivity in the absence of legumes. Ecology Letters 6, 170–175.Google Scholar
Veraart, AJ, et al. (2012) Recovery rates reflect distance to a tipping point in a living system. Nature 481, 357–359.Google Scholar
Violle, C, et al. (2017) Functional rarity: The ecology of outliers. Trends in Ecology & Evolution 32, 356–367.Google Scholar
Walters, C, Kitchell, JF (2001) Cultivation/depensation effects on juvenile survival and recruitment: Implications for the theory of fishing. Canadian Journal of Fisheries and Aquatic Sciences 58, 39–50.Google Scholar
Wang, R, et al. (2012) Flickering gives early warning signals of a critical transition to a eutrophic lake state. Nature 492, 419–422.Google Scholar
Whittaker, RH (1960) Vegetation of the Siskiyou Mountains, Oregon and California. Ecological Monographs 30, 279–338.Google Scholar
Whittaker, RH (1965) Dominance and diversity in land plant communities. Science 147, 250–260.Google Scholar
Williamson, GB (1978) A comment on equilibirium turnover rates for islands. The American Naturalist 112, 241–243.Google Scholar
Woodford, DJ, et al. (2016) Confronting the wicked problem of managing biological invasions. NeoBiota 31, 63–86.Google Scholar
Wright, SJ (1985) How isolation affects rates of turnover of species on islands. Oikos 44, 331–340.Google Scholar
Zhang, F, Dieckmann, U, Metz, JAJ, Hui, C (2021) Condition for evolutionary branching and trapping in multidimensional adaptive dynamics. In prep.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Network Transitions
  • Cang Hui, Stellenbosch University, South Africa, David Richardson, Stellenbosch University, South Africa
  • Book: Invading Ecological Networks
  • Online publication: 05 May 2022
  • Chapter DOI: https://doi.org/10.1017/9781108778374.006
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Network Transitions
  • Cang Hui, Stellenbosch University, South Africa, David Richardson, Stellenbosch University, South Africa
  • Book: Invading Ecological Networks
  • Online publication: 05 May 2022
  • Chapter DOI: https://doi.org/10.1017/9781108778374.006
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Network Transitions
  • Cang Hui, Stellenbosch University, South Africa, David Richardson, Stellenbosch University, South Africa
  • Book: Invading Ecological Networks
  • Online publication: 05 May 2022
  • Chapter DOI: https://doi.org/10.1017/9781108778374.006
Available formats
×