Theoretical Ecology

, Volume 10, Issue 2, pp 181–193 | Cite as

Single species dynamics under climate change

  • Mauricio Tejo
  • Sebastián Niklitschek-Soto
  • Cristin Vásquez
  • Pablo A. MarquetEmail author


We propose a general mathematical model describing the growth and dispersal of a single species living in a 1-D spatially discrete array of habitat patches affected by a sustained and directional change in climate. Our model accounts for two important characteristics of the climate change phenomenon: (1) Scale dependency: different species may perceive the change in the environment as occurring at different rates because they perceive the environment at different scales, and (2) measure dependency: different species measure the environment differently in the sense that they may be sensible to or cue in on different aspects of it (e.g., maximum temperature, minimum temperature, accumulated temperature) which is associated with their physiological, ecological, and life history attributes, which renders some characteristics of the environment more biologically relevant than others. We show that the deterioration in the quality of habitable patches as a consequence of climate change drives the species to extinction when dispersal is not possible; otherwise, we proof and provide a numerical example that, depending on the velocity of climate change, the scale at which a species measures it, and the particular attribute of the environment that is more biologically relevant to the species under analysis, there is always a migration strategy that allows the persistence of the species such that it tracks its niche conditions through space, thus shifting its geographic range. Our mathematical analysis provides a general framework to analyze species’ responses to climate change as a relational property of a given species in interaction with a change in climate. In particular, we can analyze the persistence of species by taking into account the ways in which they measure and filter the environment. Indeed, one of our main conclusions is that there is not a single climate change but many, as it depends on the interaction between a particular species and climate. Thus, the problem is more complex than assumed by analytically tractable models of species responses to climate change.


Climate change Species dynamics Temporal scale dependency Allee effect threshold Species’ fundamental niche Migration strategies Threshold migration rate 



We acknowledge the main funding from FONDECYT 3140613 postdoctoral grant to Mauricio Tejo, and the partial support of CONICYT 21110386 Ph.D scholarship program to Cristián Vásquez, projects ICM-MINECOM, P05-002 IEB, Programa de Financiamiento Basal, CONICYT PFB-23 and FONDECYT 1161023 to Pablo A. Marquet and project “Stochastic Analysis Research Network” PIA-CONICYT-ACT1112, PIA-CONICYT-SOC1405, and VRI-PUC Program on Biostochastics. We thank Rolando Rebolledo and the members of the ANESTOC center for insightful and stimulating discussion during the preparation of our work.

Supplementary material

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Mauricio Tejo
    • 1
  • Sebastián Niklitschek-Soto
    • 2
  • Cristin Vásquez
    • 3
  • Pablo A. Marquet
    • 4
    • 5
    • 6
    • 7
    • 8
    Email author
  1. 1.Facultad de Ciencias Naturales y Exactas, Universidad de Playa AnchaValparaísoChile
  2. 2.Facultad de Ciencias Físicas y MatemáticasUniversidad de ConcepciónConcepciónChile
  3. 3.Departamento de Estadística, Facultad de MatemáticasPontificia Universidad Católica de ChileMaculChile
  4. 4.Departamento de Ecología, Facultad de Ciencias BiológicasPontificia Universidad Católica de ChileSantiagoChile
  5. 5.Instituto de Ecología, Biodiversidad (IEB)MaculChile
  6. 6.Laboratorio Internacional en Cambio Global (LINCGlobal, CSIC-PUC)Pontificia Universidad Católica de ChileSantiagoChile
  7. 7.Centro de Cambio Global UC (PUCGlobal)Pontificia Universidad Católica de ChileMaculChile
  8. 8.The Santa Fe InstituteSanta FeUSA

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