Abstract
Nearly all wild populations live in seasonal environments in which they experience regular fluctuations in environmental conditions that drive population dynamics. Recent empirical evidence from experimental populations of Drosophila suggests that demographic signals inherent in the counts of seasonal populations, including reproduction and survival, can indicate when in the annual cycle habitat loss occurred. However, it remains unclear whether these signatures of season-specific decline are detectable under a wider range of demographic conditions and rates of habitat loss. Here, we use a bi-seasonal Ricker model to examine season-specific signals of population decline induced by different rates of habitat loss in the breeding or non-breeding season and different strengths of density dependence. Consistent with the findings in Drosophila, breeding habitat loss was accompanied by reduced reproductive output and a density-dependent increase in survival during the subsequent non-breeding period. Non-breeding habitat loss resulted in reduced non-breeding survival and a density-dependent increase in reproduction in the following breeding season. These season-specific demographic signals of decline were present under a wide range of habitat loss rates (2–25% per generation) and different density-dependent regimes (weak, moderate, and strong). We show that stronger density dependence can negatively influence time to extinction when non-breeding habitat is lost, whereas the strength of density dependence does not influence time to extinction with breeding habitat loss (although, in all cases, density dependence itself was an important modulator of population dynamics). Our results illustrate the need to incorporate seasonality in theoretical models to better understand when populations are being driven to decline.
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The simulated data used in the analyses have been made available on Figshare: https://doi.org/10.6084/m9.figshare.14515194 (Burant and Norris 2023).
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The code for the theoretical model is publicly available on Figshare: https://doi.org/10.6084/m9.figshare.14515194 (Burant and Norris 2023). https://figshare.com/s/cdc05a8b819f74110544
References
Agrawal AA, Underwood N, Stinchcombe JR (2004) Intraspecific variation in the strength of density dependence in aphid populations. Ecol Entomol 29:521–526. https://doi.org/10.1111/j.0307-6946.2004.00635.x
Allee WC (1927) Animal Aggregations Quart Rev Biol 2:367–398. https://doi.org/10.1086/394281
Beissinger SR, Westphal MI (1998) On the use of demographic models of population viability in endangered species management. J Wildl Manage 62:821–841. https://doi.org/10.2307/3802534
Betini GS, Griswold CK, Norris DR (2013a) Carry-over effects, sequential density dependence and the dynamics of populations in a seasonal environment. Proc R Soc Lond B 280:20130110. https://doi.org/10.1098/rspb.2013.0110
Betini GS, Griswold CK, Norris DR (2013b) Density-mediated carry-over effects explain variation in breeding output across time in a seasonal population. Biol Lett 9:20130582. https://doi.org/10.1098/rsbl.2013.0582
Betini GS, Griswold CK, Prodan L, Norris DR (2014) Body size, carry-over effects and survival in seasonal environment: consequences for population dynamics. J Anim Ecol 3:1313–1321. https://doi.org/10.1111/1365-2656.12225
Bolser DG, Grüss A, Lopez MA, Reed EM, Mascareñas-Osorio I, Erisman BE (2018) The influence of sample distribution on growth model output for a highly exploited marine fish, the Gulf corvina (Cynoscion othonopterus). Peer J 6:e5582. https://doi.org/10.7717/peerj.5582
Borlestean A, Frost PC, Murray DL (2015) A mechanistic analysis of density dependence in algal population dynamics. Front Ecol Evol 3:37. https://doi.org/10.3389/fevo.2015.00037
Burant JB, Betini GS, Norris DR (2019) Simple signals indicate which period of the annual cycle drives declines in seasonal populations. Ecol Lett 22:2141–2150. https://doi.org/10.1111/ele.13393
Burant JB, Griffin A, Betini GS, Norris DR (2020) An experimental test of the ecological mechanisms driving density-mediated carry-over effects in a seasonal population. Can J Zool 96:425–432. https://doi.org/10.1139/cjz-2019-0271
Burant JB, Norris DR (2023) Code and data from: Demographic signals of population decline and time to extinction in a seasonal, density-dependent model. Figshare. https://doi.org/10.6084/m9.figshare.14515194
Burant JB, Park C, Betini GS, Norris DR (2021) Early warning indicators of population collapse in a seasonal environment. J Anim Ecol 90:1538–1549. https://doi.org/10.1111/1365-2656.13474
Bury T (2020) Detecting and distinguishing transitions in ecological systems: model and data-driven approaches. Dissertation, University of Waterloo, Waterloo
Colchero F, Jones OR, Conde DA, Hodgson D, Zajitschek F, Schmidt BR, Malo AF, Alberts SC, Becker PH, Bouwhuis S, Bronikowski AM, De Vleeschouwer KM, Delahay RJ, Dummermuth S, Fernández-Duque E, Frisenvænge J, Hesseilsøe M, Larson S, Lemaître J-F, McDonald J, Miller DAW, O’Donnell C, Packer C, Raboy BE, Reading CJ, Wapstra E, Weimerskirch H, While GM, Baudisch A, Flatt T, Coulson T, Gaillard J-M (2018) Diversity of population responses to environmental change. Ecol Lett 22:342–353. https://doi.org/10.1111/ele.13195
Dey S, Joshi A (2006) Stability via asynchrony in Drosophila metapopulations with low migration rates. Science 312:434–436. https://doi.org/10.1126/science.1125317
Díaz S, Settele J, Brondízio ES, Ngo HT, Agard J, Arneth A, Balvanera P, Brauman KA, Butchart SHM, Chan KMA, Garibaldi LA, Ichii K, Liu J, Subramanian SM, Midgley GF, Miloslavich P, Molnár Z, Obura D, Pfaff A, Polasky S, Purvis A, Razzaque J, Reyer B, Roy Chowdhury R, Shin Y-J, Visseren-Hamakers I, Willis KJ, Zayas CN (2019) Pervasive human-driven decline of life on Earth points to the need for transformative change. Science 266:eaax3100. https://doi.org/10.1126/science.aax3100
Drake JM (2005) Density-dependent demographic variation determines extinction rate of experimental populations. PLoS Biol 3:e222. https://doi.org/10.1371/journal.pbio.0030222
Elaydi SN, Sacker RJ (2009) Population models with Allee effect: a new model. J Biol Dynam 4:397–408. https://doi.org/10.1080/17513750903377434
Estay SA, Lima M, Harrington R (2009) Climate mediated exogenous forcing and synchrony in populations of the oak aphid in the UK. Oikos 118:175–182. https://doi.org/10.1111/j.1600-0706.2008.17043.x
Fahrig L (2003) Effects of habitat fragmentation on biodiversity. Annu Rev Ecol Evol Syst 34(1):487–515. https://doi.org/10.1146/ecolsys.2003.34.issue-1, https://doi.org/10.1146/annurev.ecolsys.34.011802.132419
Fahrig L (2019) Habitat fragmentation: A long and tangled tale. Glob Ecol Biogeogr 28(1):33–41. https://doi.org/10.1111/geb.v28.1, https://doi.org/10.1111/geb.12839
Ferguson JM, Ponciano JM (2013) Predicting the process of extinction in experimental microcosms and accounting for interspecific interactions in single-species time series. Ecol Lett 17:251–259. https://doi.org/10.1111/ele.12227
Fisher RA (1930) The genetic theory of natural selection. The Clarendon Press, Oxford
Fretwell SD (1972) Populations in a seasonal environment. Princeton University Press, Princeton
García-Díaz P, Prowser TAA, Anderson DP, Lurgi M, Binny RN, Cassey P (2019) A concise guide to developing and using quantitative models in conservation management. Conserv Sci Practice 1:e11. https://doi.org/10.1111/csp2.11
Geritz SAH, Kisdi É (2004) On the mechanistic underpinning of discrete-time population models with complex dynamics. J Theor Biol 228:261–269. https://doi.org/10.1016/j.jtbi.2004.01.003
Gimona A (1999) Theoretical framework and practical tools for conservation o biodiversity at the landscape scale. Planning in Ecological Network (PLANECO) Newsletter, 2: 1–3.
Griffen B, Drake J (2008) Effects of habitat quality and size on extinction in experimental populations. Proc R Soc Lond B 275:2251–2256. https://doi.org/10.1098/rspb.2008.0518
Hassell MP (1986) Detecting density dependence. Trends Ecol Evol 1:90–93. https://doi.org/10.1016/0169-5347(86)90031-5
Hastings A (2014) Temporal scales of resource variability: effects on dynamics of structured populations. Ecol Complex 18:6–9. https://doi.org/10.1016/j.ecocom.2013.08.003
Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) (2019) Global assessment report on biodiversity and ecosystem services. Díaz S, Settele J, Brondízio ES, Ngo HT, Guèze M, Argard J et al (eds). IPBES Secretariat, Bonn
Kilgour RJ, McAdam AG, Betini GS, Norris DR (2018) Experimental evidence that density mediates negative frequency-dependent selection on aggression. J Anim Ecol 87:1091–1101. https://doi.org/10.1111/1365-2656.12813
Kilgour RJ, McAdam AG, Norris DR (2020) Carry-over effects of resource competition and social environment on aggression. Behav Ecol 31:140–151. https://doi.org/10.1093/beheco/arz170
Kot M, Schaffer WM (1984) The effects of seasonality on discrete models of population growth. Theor Popul Biol 26:340–360. https://doi.org/10.1016/0040-5809(84)90038-8
Lande R, Engen S, Sæther B-E (2003) Stochastic population dynamics in ecology and conservation. Oxford University Press, Oxford
Leatherbury KN, Travis J (2019) The effects of food level and social density on reproduction in the least killifish, Heterandria formosa. Ecol Evol 9:100–110. https://doi.org/10.1002/ece3.4634
Liz E (2017) Effects of strength and timing of harvest on seasonal population models: stability switches and catastrophic shifts. Theor Ecol 10:235–244. https://doi.org/10.1007/s12080-016-0325-9
Liz E, Ruiz-Herrera A (2016) Potential impact of carry-over effects in the dynamics and management of seasonal populations. PLoS One e0155579. https://doi.org/10.1371/journal.pone.0155579
Ludwig D (1996) The distribution of population survival times. Am Nat 147:506–526. https://doi.org/10.1086/285863
May RM (1987) Chaos and the dynamics of biological populations. Proc R Soc Lond A 413:27–44. https://doi.org/10.1098/rspa.1987.0098
May RM, Oster GF (1976) Bifurcations and dynamic complexity in simple ecological models. Am Nat 110:573–799. https://doi.org/10.1086/283092
Mueller LD, Joshi A (2000) Stability in model populations. Princeton University Press, Princeton
Myers RA, Bowen KG, Barrowman NJ (1999) Maximum reproductive rate of fish at low population sizes. Can J Fish Aquat Sci 56:2404–2419. https://doi.org/10.1139/f99-201
Norris DR (2005) Carry-over effects and habitat quality in migratory populations. Oikos 109:178–186. https://doi.org/10.1111/j.0030-1299.2005.13671.x
Norris K (2004) Managing threatened species: the ecological toolbox, evolutionary theory and declining-population paradigm. J Appl Ecol 41:413–426. https://doi.org/10.1111/j.0021-8901.2004.00910.x
O’Connor CM, Cooke SJ (2015) Ecological carryover effects complicate conservation. Ambio 44:582–591. https://doi.org/10.1007/s13280-015-0630-3
O’Connor CM, Norris DR, Crossin GT, Cooke SJ (2014) Biological carryover effects: linking common concepts and mechanisms in ecology and evolution. Ecosphere 5:1–11. https://doi.org/10.1890/ES13-00388.1
Otso O, Meerson B (2010) Stochastic models of population extinction. Trends Ecol Evol 25:643–652. https://doi.org/10.1016/j.tree.2010.07.009
Pearl R, Reed LJ (1920) On the rate of growth of the population of the United States since 1790 and its mathematical representation. Proc Natl Acad Sci USA 6:275–288. https://doi.org/10.1073/pnas.6.6.275
Pimm SL, Jenkins CN, Abell R, Brooks TM, Gittleman JL, Joppa LN, Raven PH, Roberts CM, Sexton JO (2014) The biodiversity of species and their rates of extinction, distribution, and protection. Science 344:1245752. https://doi.org/10.1126/science.1246752
Ratikainen II, Gill JA, Gunnarsson TG, Sutherland WJ, Kokko H (2007) When density dependence is not instantaneous: theoretical developments and management implications. Ecol Lett 11:184–198. https://doi.org/10.1111/j.1461-0248.2007.01122.x
R Core Team (2020) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna
Ricker WE (1954) Stock and recruitment. J Fish Board Can 559–623. https://doi.org/10.1139/f54-039
Ricker WE (1963) Big effects from small causes: two examples from fish population dynamics. J Fish Board Can 20:257–264. https://doi.org/10.1139/f63-022
Romero MA, Grandi MF, Koen-Alonso M, Svendsen G, Ocampo Reinaldo M, García NA, Dans SL, González R, Crespo EA (2017) Analysing the natural population growth of a large marine mammal after a depletive harvest. Sci Rep 7:5271. https://doi.org/10.1038/s41598-017-05577-6
Sacker RJ (2007) A note on periodic Ricker maps. J Differ Equ Appl 13:89–92. https://doi.org/10.1080/10236190601008752
Skellam JG (1967) Seasonal periodicity in theoretical population ecology. Proc 5th Berkley Symp Math Stat Probab 4:179–205
Sokolowski MB, Pereira HS, Hughes K (1997) Evolution of foraging behaviour in Drosophila by density-dependent selection. Proc Natl Acad Sci USA 94:7373–7377. https://doi.org/10.1073/pnas.94.14.7373
Stephens PA, Sutherland WJ, Freckleton RP (1999) What is the Allee effect? Oikos 87:185–190. https://doi.org/10.2307/3547011
Sutherland WJ (1996) Predicting the consequences of habitat loss for migratory populations. Proc R Soc Lond B 263:1325–1327. https://doi.org/10.1098/rspb.1996.0194
Turchin P (2003) Complex population dynamics: a theoretical/empirical synthesis. Princeton University Press, Princeton
Twombly S, Wang G, Hobbs NT (2007) Composite forces shape population dynamics of copepod crustaceans. Ecology 88:658–670. https://doi.org/10.1890/06-0423
Verhulst P-F (1845) Recherches mathématiques sur la loi d’accroissement de la population [French; mathematical researches into the law of population growth increase]. Nouveaux Mémoires De L’académie Royale Des Sciences Et Belles-Lettres De Bruxelles 18:8
White ER, Hasting A (2020) Seasonality in ecology: progress and prospects in theory. Ecol Complex 44:100867. https://doi.org/10.1016/j.ecocom.2020.100867
World Wildlife Fund (WWF) (2018) Living planet report – 2018: aiming higher. Grooten M, Almond REA (eds). World Wildlife Fund, Gland, Switzerland
Wysham DB, Hastings A (2008) Sudden shifts in ecological systems: intermittency and transients in the coupled Ricker population model. Bull Math Biol 70:1013–1031. https://doi.org/10.1007/s11538-007-9288-8
Funding
This research was funded by a Discovery Grant to DRN from the Natural Sciences and Engineering Research Council of Canada. JBB was supported by an Ontario Graduate Scholarship and Queen Elizabeth II Graduate Scholarship in Science and Technology from the Ontario Government and a Graduate Tuition Scholarship from the University of Guelph.
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Both authors were involved in initial discussions to develop the theoretical population model. JBB constructed the model, performed the analyses, and wrote the first draft. Both authors revised the manuscript for publication.
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Burant, J.B., Norris, D.R. Demographic signals of population decline and time to extinction in a seasonal, density-dependent model. Theor Ecol 16, 181–194 (2023). https://doi.org/10.1007/s12080-023-00562-4
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DOI: https://doi.org/10.1007/s12080-023-00562-4