Constrained growth flips the direction of optimal phenological responses among annual plants

Abstract

SummaryPhenological 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.

Latitudinal clines in the timing and temperature‐sensitivity of photoperiodic reproductive diapause in Drosophila montana

“…in the seasonal timing of biological events, are among the most conspicuous signs of global warming, and longer and warmer growing seasons enable many insect populations to complete more generations per year than in the past (Forest ). Moreover, evolutionary forces may drive insect phenologies into different directions than what is expected as a plastic response to global warming (Lindh et al ). Increased temperature may, for example, modify the normal rates of development and lead to a decoupling of synchrony between diapause‐sensitive life‐cycle stages and CDL (Bale and Hayward ).…”

Is timing of reproduction according to temperature sums an optimal strategy?

“…We studied the robustness of our predictions above by comparing how TSR and OCR respond to variation in p ( t ) depends on different assumptions in the plant growth model. Specifically, we compared predictions of the basic growth model analyzed above (Equations and ) with a model version where the plant growth rates slow down as the plant grows larger, for example, due to self‐shading or competition among conspecifics growing densely together (see e.g., Lindh et al, ) and a model version representing plant biomass being lost due to herbivory or senescence (King & Roughgarden, ). Overall we find only subtle differences between the predictions of the different models.…”

“…Firstly, we consider the fact that growth rates may slow down with the size of the developing plant, for example, due to self-shading or competition within dense stands of conspecific plants. Following Deng et al (2012) and Lindh et al (2016) we consider that the plant grows logistically according to:…”

Evolution of Reproduction Periods in Seasonal Environments

“…In this article, we have devised and analyzed a biomass-based stage-structured consumer-resource model to study the evolution of consumer reproductive strategies in seasonal environments. Contrary to earlier evolutionary models of reproductive phenology that have focused on only the starting time of reproduction (e.g., Iwasa and Levin 1995;Yamamura et al 2007;Lindh et al 2016), our model additionally allows for the duration of the reproduction period to evolve independently. We have focused on the effects of changing the seasonality of the environment through changing the temporal pattern of resource growth in terms of oscillation amplitude and peak width.…”

“…The evolution of reproductive strategies in seasonal environments has also attracted theoretical interest. Early studies focused on environmental variability in general (e.g., King and Roughgarden 1982;Iwasa and Levin 1995;Yamamura et al 2007), while more recent ones focused on climate change in particular (e.g., Jonzén et al 2007;Johansson et al 2013;Kristensen et al 2015;Lindh et al 2016). The models studied until now typically involve a number of simplifications that restrict the questions they can address and have often been geared to situations motivated by the phenologies of annual plants or seasonally breeding birds: (1) organisms can decide when to start reproducing but have no further flexibility to adjust the time course of their reproductive activity; (2) feedback between organisms and their environment is one-directional: organisms are affected by the environment, but there is no feedback from the organisms back to the environment, such as exhaustion of resources; and (3) adult and juvenile individuals do not compete for the same resources.…”