References
Andrewartha, H.G. & Birch, L.C. (1954). The distribution and abundance of animals. University of Chicago press.
Barros, C., Thuiller, W., Georges, D., Boulangeat, I. & Münkemüller, T. (2016). N- dimensional hypervolumes to study stability of complex ecosystems. Ecology Letters , 19, 729–742.
Blonder, B., Lamanna, C., Violle, C. & Enquist, B.J. (2014). The n -dimensional hypervolume. Global Ecology and Biogeography , 23, 595–609.
Blonder, B., Morrow, C.B., Maitner, B., Harris, D.J., Lamanna, C., Violle, C., et al. (2018). New approaches for delineating n ‐dimensional hypervolumes. Methods in Ecology and Evolution , 9, 305–319.
Blüthgen, N., Simons, N.K., Jung, K., Prati, D., Renner, S.C., Boch, S.,et al. (2016). Land use imperils plant and animal community stability through changes in asynchrony rather than diversity.Nature Communications , 7, 10697–10697.
Brown, J.H. (1984). On the Relationship between Abundance and Distribution of Species. The American Naturalist , 124, 255–279.
Cardinale, B.J., Duffy, J.E., Gonzalez, A., Hooper, D.U., Perrings, C., Venail, P., et al. (2012). Biodiversity loss and its impact on humanity. Nature , 486, 59–67.
Chamberlain, S., Barve, V., Mcglinn, D., Oldoni, D., Desmet, P., Geffert, L., et al. (2020). rgbif: Interface to the Global Biodiversity Information Facility .
Clavel, J., Julliard, R. & Devictor, V. (2011). Worldwide decline of specialist species: toward a global functional homogenization?Frontiers in Ecology and the Environment , 9, 222–228.
Craven, D., Eisenhauer, N., Pearse, W.D., Hautier, Y., Isbell, F., Roscher, C., et al. (2018). Multiple facets of biodiversity drive the diversity–stability relationship. Nature Ecology and Evolution , 2, 1579–1587.
Dapporto, L. & Dennis, R.L.H. (2013). The generalist–specialist continuum: Testing predictions for distribution and trends in British butterflies. Biological Conservation , 157, 229–236.
De Palma, A., Dennis, R.L.H., Brereton, T., Leather, S.R. & Oliver, T.H. (2017). Large reorganizations in butterfly communities during an extreme weather event. Ecography , 40, 577–585.
Dennis, E.B., Freeman, S.N., Brereton, T. & Roy, D.B. (2013). Indexing butterfly abundance whilst accounting for missing counts and variability in seasonal pattern. Methods in Ecology and Evolution , 4, 637–645.
Dı́az, S. & Cabido, M. (2001). Vive la différence: plant functional diversity matters to ecosystem processes. Trends in Ecology & Evolution , 16, 646–655.
Doak, D.F., Bigger, D., Harding, E.K., Marvier, M.A., O’Malley, R.E. & Thomson, D. (1998). The Statistical Inevitability of Stability‐Diversity Relationships in Community Ecology. The American Naturalist , 151, 264–276.
Donohue, I., Hillebrand, H., Montoya, J.M., Petchey, O.L., Pimm, S.L., Fowler, M.S., et al. (2016). Navigating the complexity of ecological stability. Ecology Letters , 19, 1172–1185.
Elith, J. & Leathwick, J.R. (2009). Species distribution models: ecological explanation and prediction across space and time.Annual review of ecology, evolution, and systematics , 40, 677–697.
Elton, C.S. (1958). The Ecology of Invasions by Animals and Plants . Springer US, Boston, MA.
Enrique, G., Violle, C., Pérez-Ramos, I.M., Marañón, T., Navarro-Fernández, C.M., Olmo, M., et al. (2018). A multidimensional functional trait approach reveals the imprint of environmental stress in Mediterranean woody communities.Ecosystems , 21, 248–262.
Eskildsen, A., Carvalheiro, L.G., Kissling, W.D., Biesmeijer, J.C., Schweiger, O. & Høye, T.T. (2015). Ecological specialization matters: long-term trends in butterfly species richness and assemblage composition depend on multiple functional traits. Diversity and Distributions , 21, 792–802.
Fick, S.E. & Hijmans, R.J. (2017). WorldClim 2: new 1‐km spatial resolution climate surfaces for global land areas. International Journal of Climatology , 37, 4302–4315.
Grime, J.P. (1998). Benefits of plant diversity to ecosystems: immediate, filter and founder effects. Journal of Ecology , 86, 902–910.
Hillebrand, H. (2004). On the Generality of the Latitudinal Diversity Gradient. The American Naturalist , 163, 192–211.
Hirzel, A.H. & Le Lay, G. (2008). Habitat suitability modelling and niche theory. Journal of Applied Ecology , 45, 1372–1381.
Hutchinson, G.E. (1957). Concluding remarks. Cold spring harbor symposium on quantitative biology , 22, 415–427.
Isbell, F., Tilman, D., Reich, P.B. & Clark, A.T. (2019). Deficits of biodiversity and productivity linger a century after agricultural abandonment. Nat Ecol Evol , 3, 1533–1538.
Ives, A.R., Gross, K. & Klug, J.L. (1999). Stability and Variability in Competitive Communities. Science , 286, 542–544.
Jiang, L. & Pu, Z. (2009). Different Effects of Species Diversity on Temporal Stability in Single‐Trophic and Multitrophic Communities.The American Naturalist , 174, 651–659.
Jucker, T., Bouriaud, O., Avacaritei, D. & Coomes, D.A. (2014). Stabilizing effects of diversity on aboveground wood production in forest ecosystems: linking patterns and processes. Ecology Letters , 17, 1560–1569.
Kilpatrick, A.M. & Ives, A.R. (2003). Species interactions can explain Taylor’s power law for ecological time series. Nature , 422, 65–68.
Kuussaari, M., Bommarco, R., Heikkinen, R.K., Helm, A., Krauss, J., Lindborg, R., et al. (2009). Extinction debt: a challenge for biodiversity conservation. Trends in ecology & evolution , 24, 564–571.
Lawton, J.H. (1993). Range, population abundance and conservation.Trends in Ecology & Evolution , 8, 409–413.
Lefcheck, J.S. (2016). piecewiseSEM : Piecewise structural equation modelling in r for ecology, evolution, and systematics. Methods in Ecology and Evolution , 7, 573–579.
Lehman, C.L. & Tilman, D. (2000). Biodiversity, Stability, and Productivity in Competitive Communities. The American Naturalist , 156, 534–552.
Ma, Z., Liu, H., Mi, Z., Zhang, Z., Wang, Y., Xu, W., et al.(2017). Climate warming reduces the temporal stability of plant community biomass production. Nature Communications , 8, 15378–15378.
MacArthur, R.H. & Wilson, E.O. (1967). The theory of island biogeography . Princeton University Press, Princeton.
Mammola, S. (2019). Assessing similarity of n‐ dimensional hypervolumes: Which metric to use? Journal of Biogeography , 46, 2012–2023.
May, R.M. (1972). Will a large complex system be stable? Nature , 238, 413–414.
May, R.M. (1974). Biological populations with non-overlapping generations: stable points,stable cycles and chaos, 186, 645–647.
McDermott Long, O., Warren, R., Price, J., Brereton, T.M., Botham, M.S. & Franco, A.M.A. (2017). Sensitivity of UK butterflies to local climatic extremes: which life stages are most at risk? Journal of Animal Ecology , 86, 108–116.
Metzger, M.J., Bunce, R.G.H., Jongman, R.H.G., Sayre, R., Trabucco, A. & Zomer, R. (2013). A high-resolution bioclimate map of the world: a unifying framework for global biodiversity research and monitoring.Global Ecology and Biogeography , 22, 630–638.
Millennium Ecosystem Assessment. (2005). Ecosystems and human well-being: Synthesis . Ecosystems . Island Press, Washington DC.
Mills, S.C., Oliver, T.H., Bradbury, R.B., Gregory, R.D., Brereton, T., Kühn, E., et al. (2017). European butterfly populations vary in sensitivity to weather across their geographical ranges. Global Ecology and Biogeography , 26, 1374–1385.
Oliver, T.H., Brereton, T. & Roy, D.B. (2013). Population resilience to an extreme drought is influenced by habitat area and fragmentation in the local landscape. Ecography , 36, 579–586.
Oliver, T.H., Roy, D.B., Brereton, T. & Thomas, J.A. (2012). Reduced variability in range-edge butterfly populations over three decades of climate warming. Global Change Biology , 18, 1531–1539.
Oliver, T.H., Stefanescu, C., Páramo, F., Brereton, T. & Roy, D.B. (2014). Latitudinal gradients in butterfly population variability are influenced by landscape heterogeneity. Ecography , 37, 863–871.
Osorio‐Olvera, L., Yañez‐Arenas, C., Martínez‐Meyer, E. & Peterson, A.T. (2020). Relationships between population densities and niche‐centroid distances in North American birds. Ecology Letters , 23, 555–564.
Palmer, G., Platts, P.J., Brereton, T., Chapman, J.W., Dytham, C., Fox, R., et al. (2017). Climate change, climatic variation and extreme biological responses. Philosophical Transactions of the Royal Society B: Biological Sciences , 372, 20160144–20160144.
Papuga, G., Gauthier, P., Pons, V., Farris, E. & Thompson, J.D. (2018). Ecological niche differentiation in peripheral populations: a comparative analysis of eleven Mediterranean plant species.Ecography , 41, 1650–1664.
Pennekamp, F., Pontarp, M., Tabi, A., Altermatt, F., Alther, R., Choffat, Y., et al. (2018). Biodiversity increases and decreases ecosystem stability. Nature , 563, 109–112.
Pianka, E.R. (1970). On r- and K-Selection. The American Naturalist , 104, 592–597.
Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D., & R Core Team. (2019).nlme: linear and nonlinear mixed-effects models. R package version 3.1-103 .
van der Plas, F. (2019). Biodiversity and ecosystem functioning in naturally assembled communities. Biological Reviews , 94, brv.12499-brv.12499.
Poggiato, G., Münkemüller, T., Bystrova, D., Arbel, J., Clark, J.S. & Thuiller, W. (2021). On the Interpretations of Joint Modeling in Community Ecology. Trends in Ecology & Evolution , 1–11.
Pollard, E. & Yates, T. (1993). Monitoring Butterflies for Ecology and Conservation . Chapman and Hall, London.
R Core Development Team. (2019). R: A language and environment for statistical computing (Version 3.6. 1)[Software package] . Vienna, Austria: R Foundation for Statistical Computing. Retrieved from ….
Roscher, C., Weigelt, A., Proulx, R., Marquard, E., Schumacher, J., Weisser, W.W., et al. (2011). Identifying population- and community-level mechanisms of diversity-stability relationships in experimental grasslands. Journal of Ecology , 99, 1460–1469.
Roy, D.B., Rothery, P., Moss, D., Pollard, E. & Thomas, J. a. (2001). Butterfly numbers and weather: predicting historical trends in abundance and the future effects of climate change. Journal of Animal Ecology , 70, 201–217.
Schmucki, R., Pe’er, G., Roy, D.B., Stefanescu, C., Van Swaay, C.A.M., Oliver, T.H., et al. (2016). A regionally informed abundance index for supporting integrative analyses across butterfly monitoring schemes. Journal of Applied Ecology , 53, 501–510.
Settele, J., Kudrna, O., Harpke, A., Kühn, I., Van Swaay, C., Verovnik, R., et al. (2008). Climatic risk atlas of European butterflies . Pensoft Sofia.
Shipley, B. (2000). A New Inferential Test for Path Models Based on Directed Acyclic Graphs. Structural Equation Modeling: A Multidisciplinary Journal , 7, 206–218.
Stefanescu, C., Torre, I., Jubany, J. & Páramo, F. (2011). Recent trends in butterfly populations from north-east Spain and Andorra in the light of habitat and climate change. J Insect Conserv , 15, 83–93.
Taylor, L.R. (1961). Aggregation, Variance and the Mean. Nature , 189, 732–735.
Thibaut, L.M. & Connolly, S.R. (2013). Understanding diversity–stability relationships: towards a unified model of portfolio effects. Ecology Letters , 16, 140–150.
Tilman, D. (1999). The ecological consequences of changes in biodiversity: A search for general principles. Ecology , 80, 1455–1474.
Tilman, D. & Downing, J.A. (1994). Biodiversity and stability in grasslands. Nature , 367, 363–365.
Tilman, D., Lehman, C.L. & Bristow, C.E. (1998). Diversity‐Stability Relationships: Statistical Inevitability or Ecological Consequence?The American Naturalist , 151, 277–282.
Tilman, D., May, R.M., Lehman, C.L. & Nowak, M.A. (1994). Habitat destruction and the extinction debt. Nature , 371, 65–66.
Ummenhofer, C.C. & Meehl, G.A. (2017). Extreme weather and climate events with ecological relevance: a review. Philosophical Transactions of the Royal Society B: Biological Sciences , 372, 20160135–20160135.
WallisDeVries, M.F., Baxter, W. & Van Vliet, A.J.H. (2011). Beyond climate envelopes: effects of weather on regional population trends in butterflies. Oecologia , 167, 559–571.
Wang, S. & Loreau, M. (2014). Ecosystem stability in space: α, β and γ variability. Ecology Letters , 17, 891–901.
White, L., O’Connor, N.E., Yang, Q., Emmerson, M.C. & Donohue, I. (2020). Individual species provide multifaceted contributions to the stability of ecosystems. Nature Ecology & Evolution .
White, P. & Kerr, J.T. (2006). Contrasting spatial and temporal global change impacts on butterfly species richness during the 20th century.Ecography , 29, 908–918.
Yachi, S. & Loreau, M. (1999). Biodiversity and ecosystem productivity in a fluctuating environment: The insurance hypothesis.Proceedings of the National Academy of Sciences , 96, 1463–1468.
Figure 1