Predicting phenological shifts in a changing climate Katherine Scrantona,1,2 and Priyanga Amarasekarea,1 aDepartment of Ecology and Evolutionary Biology, University of California, Los Angeles, CA 90095 Edited by Nils Chr. Stenseth, University of Oslo, Oslo, Norway, and approved October 26, 2017 (received for review June 21, 2017) Phenological shifts constitute one of the clearest manifestations selection drives thermal optima of lower-latitude ectotherms to of climate warming. Advanced emergence is widely reported in coincide with the mean temperature while that of higher-latitude high-latitude ectotherms, but a significant number of species ectotherms evolves to exceed the mean habitat temperature (20). exhibit delayed, or no change in, emergence. Here we present a This difference in thermal optima is well documented in the mechanistic theoretical framework that reconciles these disparate empirical literature (12, 15, 20, 21). observations and predicts population-level phenological patterns These latitudinal differences in thermal adaptation suggest based solely on data on temperature responses of the underly- that warming should have differential effects on lower-latitude ing life history traits. Our model, parameterized with data from and higher-latitude species. Because tropical ectotherms’ ther- insects at different latitudes, shows that peak abundance occurs mal optima coincide with the mean habitat temperature, an earlier in the year when warming increases the mean environ- increase in the mean temperature will cause these optima to mental temperature, but is delayed when warming increases the fall below the mean, with the result that the birth rate will be amplitude of seasonal fluctuations. We find that warming does below its optimal value, and the mortality rate will be higher, for not necessarily lead to a longer activity period in high-latitude most of the year. If the mean temperature increases to a level species because it elevates summer temperatures above the upper at which the mortality rate exceeds the birth rate, the species limit for reproduction and development. Our findings both con- will go extinct. In contrast, because temperate ectotherms’ ther- firm and confound expectations for ectotherm species affected mal optima exceed the mean habitat temperature, a moder- by climate warming: an increase in the mean temperature is more ate increase in the mean temperature is likely to be beneficial. detrimental to low-latitude species adapted to high mean tem- Hence, warming involving an increase in the mean tempera- peratures and low-amplitude seasonal fluctuations; an increase ture is likely to be more detrimental to tropical ectotherms in seasonal fluctuations is more detrimental to high-latitude than to temperate ectotherms. In contrast, warming involving an species adapted to low mean temperatures and high-amplitude increase in seasonal temperature fluctuations [e.g., an increase fluctuations. in warm and cold extremes (22)] is likely to be more detrimen- tal to temperate ectotherms than to tropical ectotherms. This is because the concave-up nature of the mortality response dic- phenological shifts j stage-structured population model j variable tates that the average mortality rate must be higher when sea- developmental delay j climate change j life history traits sonal fluctuations are larger. At the same time, the concave- down nature of the birth rate response means a lower average emperature is the major abiotic factor that affects phenol- birth rate. If warming causes the magnitude of fluctuations to Togy, the seasonal timing of life history events. Climate warm- exceed the species’ response breadths, the average mortality rate ing is increasingly disrupting natural phenological patterns, but will exceed the average birth rate, predisposing the species to the consequences of such disruptions on population dynamics and species interactions are poorly understood (1, 2). Given Significance that ectotherms (microbes, plants, invertebrates, fish, amphib- ians, and reptiles) constitute the vast majority of biodiversity Changes in species’ phenology, the seasonal timing of life his- on the planet, elucidating the connection between their phe- tory events, constitute one of the most unambiguous conse- nology and population dynamics is a crucial research priority quences of climate warming and one of the least understood. (3–5). Ectotherm life history traits such as fecundity, develop- As our climate continues to warm and become more vari- ment, and survivorship exhibit plastic responses to tempera- able, we need theory that can explain the current phenologi- ture variation (6): when the temperature changes, the response cal patterns and predict future changes. We present a mathe- changes accordingly (7, 8). These responses are the result of tem- matical framework that translates temperature effects on the perature effects on the underlying biochemical processes (e.g., phenotypic traits of individual organisms to the population- reaction kinetics, enzyme inactivation, hormonal regulation) and level phenological patterns observed in ectotherms. It is suf- take qualitative forms (monotonic, unimodal) that are conserved ficiently mechanistic to yield accurate predictions and suffi- across ectotherm taxa (9–15). It is these trait responses that we ciently broad to apply across ectothermic taxa. Its power lies must focus on if we are to predict how warming-induced pheno- in generating predictions based solely on life history trait logical changes influence ectotherm population dynamics. responses to temperature and hence completely independent The nature of thermal adaptation dictates that trait responses of the population-level observations of phenological changes. be concave-up or concave-down functions of temperature (7, 16– 18). Based on Jensen’s inequality (19), we know that a tem- Author contributions: K.S. and P.A. designed research, performed research, analyzed perature response function that is concave up (e.g., exponen- data, and wrote the paper. tial) will yield a higher average response in a more variable The authors declare no conflict of interest. environment while a function that is concave down (e.g., uni- This article is a PNAS Direct Submission. modal) will yield a lower average response in a more variable Published under the PNAS license. environment. Per capita birth rate of all ectotherms exhibits Data deposition: Python code used to create and analyze the DDE model and R code a unimodal (i.e., concave-down) response to temperature. A used to fit thermal response curves and seasonal temperature fluctuations are available concave-down response means that higher-latitude (e.g., tem- at https://github.com/drscranto/doi.10.1073.PNAS.1711221114. perate) species, which have wider response breadths (greater 1K.S. and P.A. contributed equally to this work. plasticity), will exhibit lower average performance than lower- 2To whom correspondence should be addressed. Email: [email protected]. latitude (e.g., tropical) species, a necessary cost of thermal adap- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. tation to higher-latitude environments. In this case stabilizing 1073/pnas.1711221114/-/DCSupplemental. 13212–13217 j PNAS j December 12, 2017 j vol. 114 j no. 50 www.pnas.org/cgi/doi/10.1073/pnas.1711221114 Downloaded by guest on September 28, 2021 extinction. Thus, the qualitative nature of life history trait A dynamical model that incorporates mechanistic descriptions responses to temperature allows us to anticipate the differen- of trait responses, combined with quantitative differences in trait tial effects that climate warming can have on the viability of parameters that reflect latitudinal variation in thermal adapta- ectotherm species inhabiting different latitudes. tion, should therefore predict the qualitative effects of warm- Predicting warming effects on phenology, however, is a more ing on the phenology and population dynamics of ectotherm complicated proposition because it involves considering temper- species inhabiting any latitude. To link this general theory with ature effects on development. Over 80% of metazoan animals data, we parameterize the population dynamics model with ther- exhibit complex life cycles (23) characterized by temperature- mal response data from Hemipteran insect species from trop- driven developmental delays. It is these developmental delays ical, Mediterranean, and temperate latitudes (Fig. 1, Materials that ultimately determine the phenological events (e.g., timing and Methods, and SI Materials and Methods). of emergence and breeding) that we observe at the population Importantly, we find that the warming regime (increase in level. To predict how warming influences phenology, we need to mean temperature vs. increase in fluctuations) has opposite understand how the temperature response of development inter- effects on species’ abundances and activity patterns and that the acts with the temperature responses of birth and mortality rates magnitude of these differences increases as a function of lati- to determine species’ per capita growth rates (fitness), the metric tude (Figs. 2–4). An increase in the mean environmental tem- that translates temperature effects on species’ life history traits perature of 3−6 ◦C over 100 y decreases peak abundance and into population-level outcomes. Doing this requires developing mean annual abundance in the tropical species, and a 10 ◦C a mathematical framework that can scale up from trait responses