title: Midpoint attractors and species richness: Modelling the interaction between environmental drivers and geometric constraints.
abstract: We introduce a novel framework for conceptualising, quantifying and unifying discordant patterns of species richness along geographical gradients. While not itself explicitly mechanistic, this approach offers a path towards understanding mechanisms. In this study, we focused on the diverse patterns of species richness on mountainsides. We conjectured that elevational range midpoints of species may be drawn towards a single midpoint attractor - a unimodal gradient of environmental favourability. The midpoint attractor interacts with geometric constraints imposed by sea level and the mountaintop to produce taxon-specific patterns of species richness. We developed a Bayesian simulation model to estimate the location and strength of the midpoint attractor from species occurrence data sampled along mountainsides. We also constructed midpoint predictor models to test whether environmental variables could directly account for the observed patterns of species range midpoints. We challenged these models with 16 elevational data sets, comprising 4500 species of insects, vertebrates and plants. The midpoint predictor models generally failed to predict the pattern of species midpoints. In contrast, the midpoint attractor model closely reproduced empirical spatial patterns of species richness and range midpoints. Gradients of environmental favourability, subject to geometric constraints, may parsimoniously account for elevational and other patterns of species richness.
authors.affiliation: Department of Ecology and Evolutionary Biology, University of Connecticut, Storrs, CT, 06269, USA.|Departmento de Ecologia, Universidade Federal de Goiás, CP 131, Goiânia, GO, 74.001-970, Brasil.|University of Colorado Museum of Natural History, Boulder, CO, 80309, USA.
authors.forename: Robert K
authors.initials: RK
authors.lastname: Colwell
authors.affiliation: Department of Biology, University of Vermont, Burlington, VT, 05405, USA.
authors.forename: Nicholas J
authors.initials: NJ
authors.lastname: Gotelli
authors.affiliation: Environmental Futures Research Institute, Griffith University, Nathan, Qld, 4111, Australia.|Life Sciences Department, Natural History Museum, South Kensington, London, SW7 5BD, UK.
authors.forename: Louise A
authors.initials: LA
authors.lastname: Ashton
authors.affiliation: University of Colorado Museum of Natural History, Boulder, CO, 80309, USA.|Department of Environmental Science (Biogeography), University of Basel, Basel, Switzerland.
authors.forename: Jan
authors.initials: J
authors.lastname: Beck
authors.affiliation: Phyletisches Museum, Friedrich-Schiller Universität, Jena, 07743, Germany.
authors.forename: Gunnar
authors.initials: G
authors.lastname: Brehm
authors.affiliation: Institute of Entomology, Biology Centre of the Czech Academy of Sciences and Faculty of Science, University of South Bohemia, Branišovská 31, 370 05, České Budějovice, Czech Republic.|Forest Ecology and Conservation Group, Imperial College London, Silwood Park Campus, Buckhurst Road, Ascot, Berkshire, SL5 7PY, UK.|Institute for Tropical Biology and Conservation, Universiti Malaysia Sabah, 88400 Kota Kinabalu, Sabah, Malaysia.
authors.forename: Tom M
authors.initials: TM
authors.lastname: Fayle
authors.affiliation: Department of Botany & Biodiversity Research, University of Vienna, Rennweg 14, 1030, Vienna, Austria.
authors.forename: Konrad
authors.initials: K
authors.lastname: Fiedler
authors.affiliation: Program in Ecology, Evolution, and Conservation Biology, Department of Biology, University of Nevada, Reno, NV, 89557, USA.
authors.forename: Matthew L
authors.initials: ML
authors.lastname: Forister
authors.affiliation: Institute of Systematic Botany, University of Zurich, 8008, Zurich, Switzerland.
authors.forename: Michael
authors.initials: M
authors.lastname: Kessler
authors.affiliation: Environmental Futures Research Institute, Griffith University, Nathan, Qld, 4111, Australia.
authors.forename: Roger L
authors.initials: RL
authors.lastname: Kitching
authors.affiliation: Institute of Entomology, Biology Centre of the Czech Academy of Sciences and Faculty of Science, University of South Bohemia, Branišovská 31, 370 05, České Budějovice, Czech Republic.
authors.forename: Petr
authors.initials: P
authors.lastname: Klimes
authors.affiliation: Department of Geography, University of Marburg, 35032, Marburg, Germany.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kluge
authors.affiliation: Department of Biology, University of Utah, Salt Lake City, UT, 84112, USA.
authors.forename: John T
authors.initials: JT
authors.lastname: Longino
authors.affiliation: Environmental Futures Research Institute, Griffith University, Nathan, Qld, 4111, Australia.
authors.forename: Sarah C
authors.initials: SC
authors.lastname: Maunsell
authors.affiliation: University of Colorado Museum of Natural History, Boulder, CO, 80309, USA.|Department of Ecology and Evolutionary Biology, University of Colorado, Boulder, CO, 80309, USA.
authors.forename: Christy M
authors.initials: CM
authors.lastname: McCain
authors.affiliation: New Guinea Binatang Research Center, P.O. Box 604, Madang, Papua New Guinea.|School of Natural and Physical Sciences, University of Papua New Guinea, P.O. Box 320, National Capital District, Papua New Guinea.
authors.forename: Jimmy
authors.initials: J
authors.lastname: Moses
authors.affiliation: Institute of Systematic Botany, University of Zurich, 8008, Zurich, Switzerland.
authors.forename: Sarah
authors.initials: S
authors.lastname: Noben
authors.affiliation: Institute of Entomology, Biology Centre of the Czech Academy of Sciences and Faculty of Science, University of South Bohemia, Branišovská 31, 370 05, České Budějovice, Czech Republic.
authors.forename: Katerina
authors.initials: K
authors.lastname: Sam
authors.affiliation: Environmental Futures Research Institute, Griffith University, Nathan, Qld, 4111, Australia.|Institute of Entomology, Biology Centre of the Czech Academy of Sciences and Faculty of Science, University of South Bohemia, Branišovská 31, 370 05, České Budějovice, Czech Republic.
authors.forename: Legi
authors.initials: L
authors.lastname: Sam
authors.affiliation: Center for Population Biology, University of California, Davis, CA, 95616, USA.
authors.forename: Arthur M
authors.initials: AM
authors.lastname: Shapiro
authors.affiliation: College of Forestry, Beijing Forestry University, Beijing, 100083, China.
authors.forename: Xiangping
authors.initials: X
authors.lastname: Wang
authors.affiliation: Institute of Entomology, Biology Centre of the Czech Academy of Sciences and Faculty of Science, University of South Bohemia, Branišovská 31, 370 05, České Budějovice, Czech Republic.|New Guinea Binatang Research Center, P.O. Box 604, Madang, Papua New Guinea.
authors.forename: Vojtech
authors.initials: V
authors.lastname: Novotny
mesh_terms: D000818:Animals; D001499:Bayes Theorem; D044822:Biodiversity; D017753:Ecosystem; D007313:Insecta / Q000502:physiology; D008954:Models, Biological; D018521:Plant Physiological Phenomena; D014714:Vertebrates / Q000502:physiology
keywords: Bayesian model; Biogeography; elevational gradients; geometric constraints; mid-domain effect; midpoint predictor model; stochastic model; truncated niche