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Fluctuating Environments Favor Extreme Reproductive Delays and Penalize Intermediate Ones

Jorge Hidalgo1,2,*, Lorenzo Fant3,4, Rafael Rubio de Casas5,6, and Miguel A. Muñoz2,7

  • *Contact author: jorge.hidalgo@uco.es
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PRX Life 4, 033019 – Published 25 August, 2026

DOI: https://doi.org/10.1103/8hh4-2x4c

Abstract

The timing of reproduction is crucial for biological fitness. Reproductive delays carry an inherent demographic cost: an individual that takes longer to reproduce contributes later to population growth, a priori, without any compensating benefit. However, natural selection favors delayed reproduction under certain environmental conditions, a phenomenon that remains poorly understood. Here, we investigate how the environment can determine the evolution of particular life histories using a parsimonious delayed-logistic model. Individuals become reproductive only after a fixed lag whereas birth rates fluctuate under temporally correlated stochasticity. Numerical integration, analytical calculations and evolutionary simulations reveal that the joint effect of demographic memory and colored multiplicative noise generate a strongly nonmonotonic dependence of fitness on life history, with three distinct regimes of population performance: rapid reproduction maximizes linear growth but amplifies fluctuations and extinction risk; delayed reproduction buffers environmental variability, substantially increasing mean extinction times despite slower growth; strikingly, and central to our results, there is a broad band of maladaptive intermediate life histories that simultaneously reduce both growth and persistence, an effect that arises generically from the mismatch between reproductive timing and environmental autocorrelation. Our results show that reproductive timing is not merely a life-history parameter but an adaptive mechanism tuned to environmental time scales, and that “dangerous middle” maturation times can be inherently disfavored, with implications for understanding reproductive strategies across the tree of life.

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References (68)

  1. S. C. Stearns, The Evolution of Life Histories (Oxford University Press, Oxford, 1992).
  2. Y. Iwasa and S. A. Levin, The timing of life history events, J. Theor. Biol. 172, 33 (1995).
  3. J. W. Horn, B. W. van Ee, J. J. Morawetz, R. Riina, V. W. Steinmann, P. E. Berry, and K. J. Wurdack, Phylogenetics and the evolution of major structural characters in the giant genus Euphorbia L. (Euphorbiaceae), Mol. Phylogenet. Evol. 63, 305 (2012).
  4. S.-R. Lee, A. Oh, and D. C. Son, Characterization, comparison, and phylogenetic analyses of chloroplast genomes of Euphorbia species, Sci. Rep. 14, 15352 (2024).
  5. J. T. Lennon and S. E. Jones, Microbial seed banks: The ecological and evolutionary implications of dormancy, Nat. Rev. Microbiol. 9, 119 (2011).
  6. C. C. Baskin and J. M. Baskin, Seeds: Ecology, Biogeography, and Evolution of Dormancy and Germination (Academic, New York, 2000).
  7. D. L. Denlinger, Regulation of diapause, Annu. Rev. Entomol. 47, 93 (2002).
  8. O. Fridman, A. Goldberg, I. Ronin, N. Shoresh, and N. Q. Balaban, Optimization of lag time underlies antibiotic tolerance in evolved bacterial populations, Nature (London) 513, 418 (2014).
  9. J. Camacho Mateu, M. Sireci, and M. A. Muñoz, Phenotypic-dependent variability and the emergence of tolerance in bacterial populations, PLoS Comput. Biol. 17, e1009417 (2021).
  10. M. Lloyd and H. S. Dybas, The periodical cicada problem. I. Population ecology, Evolution 20, 133 (1966).
  11. J. T. Lennon, F. den Hollander, M. Wilke-Berenguer, and J. Blath, Principles of seed banks and the emergence of complexity from dormancy, Nat. Commun. 12, 4807 (2021).
  12. W. R. Shoemaker and J. T. Lennon, Evolution with a seed bank: The population genetic consequences of microbial dormancy, Evol. Appl. 11, 60 (2018).
  13. M. Rees, Evolutionary ecology of seed dormancy and seed size, Philos. Trans. R. Soc. London Ser. B 351, 1299 (1996).
  14. D. L. Venable and L. Lawlor, Delayed germination and dispersal in desert annuals: Escape in space and time, Oecologia 46, 272 (1980).
  15. C. G. Willis, C. C. Baskin, J. M. Baskin, J. R. Auld, D. L. Venable, J. Cavender-Bares, K. Donohue, R. Rubio de Casas, and NGW Group, The evolution of seed dormancy: Environmental cues, evolutionary hubs, and diversification of the seed plants, New Phytol. 203, 300 (2014).
  16. A. Măgălie, D. A. Schwartz, J. T. Lennon, and J. S. Weitz, Optimal dormancy strategies in fluctuating environments given delays in phenotypic switching, J. Theor. Biol. 561, 111413 (2023).
  17. K. Donohue, R. Rubio de Casas, L. Burghardt, K. Kovach, and C. G. Willis, Germination, postgermination adaptation, and species ecological ranges, Annu. Rev. Ecol. Evol. Syst. 41, 293 (2010).
  18. R. Rubio de Casas, C. G. Willis, W. D. Pearse, C. C. Baskin, J. M. Baskin, and J. Cavender-Bares, Global biogeography of seed dormancy is determined by seasonality and seed size: A case study in the legumes, New Phytol. 214, 1527 (2017).
  19. N. A. Sweet and C.-K. Hu, Using diapause as a platform to understand the biology of dormancy, Open Biol. 15, 250104 (2025).
  20. K. Wilsterman, M. Ballinger, and C. Williams, A unifying, eco‐physiological framework for animal dormancy, Funct. Ecol. 35, 11 (2021).
  21. R. Sachidanandham and K. Y.-H. Gin, A dormancy state in nonspore-forming bacteria, Appl. Microbiol. Biotechnol. 81, 927 (2009).
  22. M. D. Mcdonald, C. Owusu-Ansah, J. B. Ellenbogen, Z. D. Malone, M. P. Ricketts, S. E. Frolking, J. G. Ernakovich, M. Ibba, S. C. Bagby, and J. L. Weissman, What is microbial dormancy? Trends Microbiol. 32, 142 (2024).
  23. J. A. Aguirre-Ghiso, Models, mechanisms and clinical evidence for cancer dormancy, Nat. Rev. Cancer 7, 834 (2007).
  24. T. G. Phan and P. I. Croucher, The dormant cancer cell life cycle, Nat. Rev. Cancer 20, 398 (2020).
  25. Y. Wang, L. Liu, X. Zhang, T. Liang, and X. Bai, Cancer dormancy and metabolism: From molecular insights to translational opportunities, Cancer Lett. 635, 218097 (2025).
  26. D. Cohen, Optimizing reproduction in a randomly varying environment, J. Theor. Biol. 12, 119 (1966).
  27. E. Kussell and S. Leibler, Phenotypic diversity, population growth, and information in fluctuating environments, Science 309, 2075 (2005).
  28. T. M. Norman, N. D. Lord, J. Paulsson, and R. Losick, Stochastic switching of cell fate in microbes, Annu. Rev. Microbiol. 69, 381 (2015).
  29. K. Jops and J. P. O'Dwyer, Life history complementarity and the maintenance of biodiversity, Nature (London) 618, 986 (2023).
  30. G. E. Hutchinson et al., Circular causal systems in ecology, Ann. N. Y. Acad. Sci. 50, 221 (1948).
  31. M. Bulmer, Delayed germination of seeds: Cohen's model revisited, Theor. Popul. Biol. 26, 367 (1984).
  32. Y. Himeoka and N. Mitarai, When to wake up? The optimal waking-up strategies for starvation-induced persistence, PLoS Comput. Biol. 17, e1008655 (2021).
  33. S. Moreno-Gámez, D. J. Kiviet, C. Vulin, S. Schlegel, K. Schlegel, G. S. van Doorn, and M. Ackermann, Wide lag time distributions break a trade-off between reproduction and survival in bacteria, Proc. Natl. Acad. Sci. 117, 18729 (2020).
  34. E. Şimşek and M. Kim, Power-law tail in lag time distribution underlies bacterial persistence, Proc. Natl. Acad. Sci. 116, 17635 (2019).
  35. J. Baranyi, Stochastic modelling of bacterial lag phase, Int. J. Food Microbiol. 73, 203 (2002).
  36. R. C. Lewontin and D. Cohen, On population growth in a randomly varying environment, Proc. Natl. Acad. Sci. 62, 1056 (1969).
  37. S. Tuljapurkar, Delayed reproduction and fitness in variable environments, Proc. Natl. Acad. Sci. 87, 1139 (1990).
  38. S. Tuljapurkar, Population Dynamics in Variable Environments (Springer Science & Business Media, New York, 2013), Vol. 85.
  39. W. C. Ratcliff and R. F. Denison, Bacterial persistence and bet hedging in Sinorhizobium meliloti, Commun. Integr. Biol. 4, 98 (2011).
  40. Z. Wang, J. M. Baskin, C. C. Baskin, G. Liu, X. Ye, X. Yang, and Z. Huang, Soil salinity regulates spatial-temporal heterogeneity of seed germination and seedbank persistence of an annual diaspore-trimorphic halophyte in northern China, BMC Plant Biology 24, 604 (2024).
  41. D. Cao, C. C. Baskin, J. M. Baskin, F. Yang, and Z. Huang, Comparison of germination and seed bank dynamics of dimorphic seeds of the cold desert halophyte Suaeda corniculata subsp. mongolica, Ann. Bot. 110, 1545 (2012).
  42. A. Berkvens, P. Chauhan, and F. J. Bruggeman, Integrative biology of persister cell formation: Molecular circuitry, phenotypic diversification and fitness effects, J. R. Soc. Interface. 19, 20220129 (2022).
  43. C. E. Cáceres and A. J. Tessier, How long to rest: The ecology of optimal dormancy and environmental constraint, Ecology 84, 1189 (2003).
  44. L. F. Lafuerza and R. Toral, Stochastic description of delayed systems, Philos. Trans. R. Soc. A 371, 20120458 (2013).
  45. D. A. Vasseur and P. Yodzis, The color of environmental noise, Ecology 85, 1146 (2004).
  46. I. Bena, Dichotomous Markov noise: Exact results for out-of-equilibrium systems, Int. J. Mod. Phys. B 20, 2825 (2006).
  47. Y. Kuang, Delay Differential Equations (Academic, New York, 1993).
  48. H. Wernecke, B. Sándor, and C. Gros, Chaos in time delay systems, an educational review, Phys. Rep. 824, 1 (2019).
  49. M. A. Muñoz, Nature of different types of absorbing states, Phys. Rev. E 57, 1377 (1998).
  50. W. Genovese and M. A. Muñoz, Recent results on multiplicative noise, Phys. Rev. E 60, 69 (1999).
  51. S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Chapman and Hall/CRC, Boca Raton, FL, 2024).
  52. T. Frank, Delay Fokker-Planck equations, perturbation theory, and data analysis for nonlinear stochastic systems with time delays, Phys. Rev. E 71, 031106 (2005).
  53. P. Jung and P. Hänggi, Dynamical systems: A unified colored-noise approximation, Phys. Rev. A 35, 4464 (1987).
  54. T. Spanio, J. Hidalgo, and M. A. Muñoz, Impact of environmental colored noise in single-species population dynamics, Phys. Rev. E 96, 042301 (2017).
  55. J. Hidalgo, S. Suweis, and A. Maritan, Species coexistence in a neutral dynamics with environmental noise, J. Theor. Biol. 413, 1 (2017).
  56. D. T. Gillespie, A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comput. Phys. 22, 403 (1976).
  57. J.-W. Veening, W. K. Smits, and O. P. Kuipers, Bistability, epigenetics, and bet-hedging in bacteria, Annu. Rev. Microbiol. 62, 193 (2008).
  58. D. Z. Childs, C. Metcalf, and M. Rees, Evolutionary bet-hedging in the real world: Empirical evidence and challenges revealed by plants, Proc. R. Soc. B 277, 3055 (2010).
  59. E. Rotem, A. Loinger, I. Ronin, I. Levin-Reisman, C. Gabay, N. Shoresh, O. Biham, and N. Q. Balaban, Regulation of phenotypic variability by a threshold-based mechanism underlies bacterial persistence, Proc. Natl. Acad. Sci. 107, 12541 (2010).
  60. C. E. Tarnita, A. Washburne, R. Martínez-García, A. E. Sgro, and S. A. Levin, Fitness tradeoffs between spores and nonaggregating cells can explain the coexistence of diverse genotypes in cellular slime molds, Proc. Natl. Acad. Sci. 112, 2776 (2015).
  61. R. Martínez-García and C. E. Tarnita, Seasonality can induce coexistence of multiple bet-hedging strategies in Dictyostelium discoideum via storage effect, J. Theor. Biol. 426, 104 (2017).
  62. M. Loreau, M. Barbier, E. Filotas, D. Gravel, F. Isbell, S. J. Miller, J. M. Montoya, S. Wang, R. Aussenac, R. Germain, et al., Biodiversity as insurance: From concept to measurement and application, Biol. Rev. 96, 2333 (2021).
  63. P. Villa Martín, M. A. Muñoz, and S. Pigolotti, Bet-hedging strategies in expanding populations, PLoS Comput. Biol. 15, e1006529 (2019).
  64. M. Hooper, J. Musgrove, and F. Gilbert, Can long‐term diapause/dormancy improve persistence in a positively autocorrelated environment? Ecol. Entomol. 50, 717 (2025).
  65. H. Ten Brink, J. R. Gremer, and H. Kokko, Optimal germination timing in unpredictable environments: The importance of dormancy for both among-and within-season variation, Ecol. Lett. 23, 620 (2020).
  66. J. Hidalgo, L. Fant, R. Rubio de Casas, and M. A. Muñoz, Code for: Fluctuating environments favor extreme reproductive delays and penalize intermediate ones [Computer software], Zenodo, 2026, doi:10.5281/zenodo.21217955.
  67. Y. Tu, G. Grinstein, and M. A. Muñoz, Systems with multiplicative noise: Critical behavior from KPZ equation and numerics, Phys. Rev. Lett. 78, 274 (1997).
  68. C. Gardiner, Stochastic Methods: A Handbook for the Natural and Social Sciences, Springer Series in Synergetics (Springer, Berlin, 2009).

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PRX Life 4, 033019– Published 25 August, 2026
  • Received 5 December 2025
  • Accepted 14 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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