title: Constrained growth flips the direction of optimal phenological responses among annual plants.
abstract: Phenological changes among plants due to climate change are well documented, but often hard to interpret. In order to assess the adaptive value of observed changes, we study how annual plants with and without growth constraints should optimize their flowering time when productivity and season length changes. We consider growth constraints that depend on the plant's vegetative mass: self-shading, costs for nonphotosynthetic structural tissue and sibling competition. We derive the optimal flowering time from a dynamic energy allocation model using optimal control theory. We prove that an immediate switch (bang-bang control) from vegetative to reproductive growth is optimal with constrained growth and constant mortality. Increasing mean productivity, while keeping season length constant and growth unconstrained, delayed the optimal flowering time. When growth was constrained and productivity was relatively high, the optimal flowering time advanced instead. When the growth season was extended equally at both ends, the optimal flowering time was advanced under constrained growth and delayed under unconstrained growth. Our results suggests that growth constraints are key factors to consider when interpreting phenological flowering responses. It can help to explain phenological patterns along productivity gradients, and links empirical observations made on calendar scales with life-history theory.
authors.affiliation: Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, SE-901 87, Sweden.
authors.forename: Magnus
authors.initials: M
authors.lastname: Lindh
authors.affiliation: Department of Biology, Theoretical Population Ecology and Evolution Group, Lund University, Lund, SE-223 62, Sweden.
authors.forename: Jacob
authors.initials: J
authors.lastname: Johansson
authors.affiliation: Unit for Field-based Forest Research, Swedish University of Agricultural Sciences, Lammhult, SE-360 30, Sweden.|Department of Ecology, Environment and Plant Sciences, Stockholm University, Stockholm, SE-106 91, Sweden.
authors.forename: Kjell
authors.initials: K
authors.lastname: Bolmgren
authors.affiliation: Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, SE-901 87, Sweden.
authors.forename: Niklas L P
authors.initials: NL
authors.lastname: Lundström
authors.affiliation: Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, SE-901 87, Sweden.|Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), Laxenburg, A-2361, Austria.
authors.forename: Åke
authors.initials: Å
authors.lastname: Brännström
authors.affiliation: Department of Biology, Theoretical Population Ecology and Evolution Group, Lund University, Lund, SE-223 62, Sweden.
authors.forename: Niclas
authors.initials: N
authors.lastname: Jonzén
mesh_terms: D057231:Climate Change; D035264:Flowers / Q000502:physiology; D008962:Models, Theoretical; D018515:Plant Leaves / Q000502:physiology; D018521:Plant Physiological Phenomena; D012621:Seasons; D013997:Time Factors
keywords: climate change; constrained growth; flowering; life history; optimal control theory; phenology; productivity; season