Adaptive dynamics on an environmental gradient that changes over a geological time-scale Mikael Fortelius a,1 , Stefan Geritz b,2 , Mats Gyllenberg b,3 , Jaakko Toivonen b,n Q1 a Department of Geosciences and Geography, University of Helsinki, FI-00014, Finland b Department of Mathematics and Statistics, University of Helsinki, FI-00014, Finland HIGHLIGHTS  We use bifurcation plots of adaptive dynamics to construct evolutionary trees.  Environmental history can have significant effect to evolutionary outcomes.  A monomorphic population can not branch on a steep environmental gradient.  However, polymorphic populations can evolve to inhabit steep gradients.  Intermediate phenotypes are more prone to branching and extinction than extreme ones. article info Article history: Received 21 October 2014 Received in revised form 3 March 2015 Accepted 30 March 2015 Keywords: Environmental change Mathematical modeling Spatial model Patterns of the fossil record abstract The standard adaptive dynamics framework assumes two timescales, i.e. fast population dynamics and slow evolutionary dynamics. We further assume a third timescale, which is even slower than the evolutionary timescale. We call this the geological timescale and we assume that slow climatic change occurs within this timescale. We study the evolution of our model population over this very slow geological timescale with bifurcation plots of the standard adaptive dynamics framework. The bifurcation parameter being varied describes the abiotic environment that changes over the geological timescale. We construct evolutionary trees over the geological timescale and observe both gradual phenotypic evolution and punctuated branching events. We concur with the established notion that branching of a monomorphic population on an environmental gradient only happens when the gradient is not too shallow and not too steep. However, we show that evolution within the habitat can produce polymorphic populations that inhabit steep gradients. What is necessary is that the environmental gradient at some point in time is such that the initial branching of the monomorphic population can occur. We also find that phenotypes adapted to environments in the middle of the existing environ- mental range are more likely to branch than phenotypes adapted to extreme environments. & 2015 Published by Elsevier Ltd. 1. Introduction In recent years there have been several research papers on evo- lution on an environmental gradient (Kirkpatrick and Barton, 1997; Meszena et al., 1997; Case and Taper, 2000; Doebeli and Dieckmann, 2003; Mizera and Meszena, 2003; Leimar et al., 2008; Heinz et al., 2009; Ispolatov and Doebeli, 2009; Debarre and Gandon, 2010; Payne et al., 2011; Haller et al., 2013). So far most papers on evolution on an environmental gradient have assumed the grad- ient to be fixed in time. Also, many papers have only investigated whether a monomorphic population can branch or not. The evolu- tion and further branching of polymorphic populations have not yet received as much attention. The theory of adaptive dynamics (Metz et al., 1992; Dieckmann and Law, 1996; Geritz et al., 1998) assumes two different timescales, i.e. fast population dynamics and slow evolutionary dynamics. In this paper we assume a third timescale called the geological time- scale, which is even slower than the timescale for evolutionary 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/yjtbi Journal of Theoretical Biology http://dx.doi.org/10.1016/j.jtbi.2015.03.036 0022-5193/& 2015 Published by Elsevier Ltd. n Corresponding author. Tel.: þ358 50355 3983. E-mail addresses: mikael.fortelius@helsinki.fi (M. Fortelius), stefan.geritz@helsinki.fi (S. Geritz), mats.gyllenberg@helsinki.fi (M. Gyllenberg), jaakko.toivonen@alumni.helsinki.fi (J. Toivonen). 1 Tel.: þ358 9191 50837. 2 Tel.: þ358 9191 51489. 3 Tel.: þ358 2941 51480. Please cite this article as: Fortelius, M., et al., Adaptive dynamics on an environmental gradient that changes over a geological time- scale. J. Theor. Biol. (2015), http://dx.doi.org/10.1016/j.jtbi.2015.03.036i Journal of Theoretical Biology ∎ (∎∎∎∎) ∎∎∎–∎∎∎