Analytical thresholds reveal mechanisms of cross-scale dynamics in adaptive mutualistic networks
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Abstract
Cross-scale integration remains a persistent challenge in ecology. Mechanistic network models can advance this integration by linking individual- and population-level processes with emergent community structure and dynamics, but their complexity often leaves their implications understood primarily through computer simulations. Here, I analyze a consumer-resource model of plant--pollinator interactions with adaptive foraging to show how simulation-discovered patterns can be translated into analytical threshold relationships. The model connects individual-level foraging, floral rewards, visitation, and pollination quality to population dynamics, competition for shared resources and services, and emergent community and network structure. Analytical decomposition identifies threshold conditions for population persistence, finite-density establishment, sustained pollination services, and community-level effects of network structure mediated by adaptive foraging. These relationships clarify how rewards, visitation, pollination quality, recruitment, and network architecture jointly constrain community outcomes. By connecting simulation-motivated patterns to analytical threshold conditions, this work shows how mechanistically detailed models can produce general insight into the biological processes and constraints that shape ecological communities.
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References
Simon A Levin. The problem of pattern and scale in ecology: the Robert H. MacArthur Award lecture. Ecology, 73 (6): 1943–1967, 1992. https://doi.org/10.2307/1941447
Debra P C Peters, Roger A Pielke, Brandon T Bestelmeyer, Craig D Allen, Stuart Munson-McGee, and Kris M Havstad. Cross-scale interactions, nonlinearities, and forecasting catastrophic events. Proceedings of the National Academy of Sciences, 101 (42): 15130–15135, 2004. https://doi.org/10.1073/pnas.0403822101
William J Sutherland, Robert P Freckleton, H Charles J Godfray, Steven R Beissinger, Tim Benton, Duncan D Cameron, Yohay Carmel, David A Coomes, Tim Coulson, Mark C Emmerson, et al. Identification of 100 fundamental ecological questions. Journal of Ecology, 101 (1): 58–67, 2013. https://doi.org/10.1111/1365-2745.12025
James B Heffernan, Patricia A Soranno, Michael J Angilletta, Lauren B Buckley, Daniel S Gruner, Timothy H Keitt, James R Kellner, John S Kominoski, Ankur V Rocha, Jingfeng Xiao, et al. Macrosystems ecology: understanding ecological patterns and processes at continental scales. Frontiers in Ecology and the Environment, 12 (1): 5–14, 2014. https://doi.org/10.1890/130017
Kim Cuddington, Marie-Josée Fortin, Leah R Gerber, Alan Hastings, Andrew Liebhold, Mary O’Connor, and Chris Ray. Process-based models are required to manage ecological systems in a changing world. Ecosphere, 4 (2): 1–12, 2013. https://doi.org/10.1890/ES12-00178.1
Mark C Urban, Greta Bocedi, Andrew P Hendry, Jean-Baptiste Mihoub, Guy Pe’er, Alexander Singer, Jon R Bridle, Lisa G Crozier, Luc De Meester, William Godsoe, et al. Improving the forecast for biodiversity under climate change. Science, 353 (6304): aad8466, 2016. https://doi.org/10.1126/science.aad8466
Richard Levins. The strategy of model building in population biology. American Scientist, 54 (4): 421–431, 1966.
Matthew R Evans, Mike Bithell, Stephen J Cornell, Sasha RX Dall, Sandra Díaz, Stephen Emmott, Bruno Ernande, Volker Grimm, David J Hodgson, Simon L Lewis, et al. Predictive systems ecology. Proceedings of the Royal Society B: Biological Sciences, 280 (1771): 20131452, 2013. https://doi.org/10.1098/rspb.2013.1452
Robert M May. Will a large complex system be stable? Nature, 238 (5364): 413–414, 1972. https://doi.org/10.1038/238413a0
Robert MacArthur. Species packing and competitive equilibrium for many species. Theoretical Population Biology, 1 (1): 1–11, 1970. https://doi.org/10.1016/0040-5809(70)90039-0
Stefano Allesina and Si Tang. Stability criteria for complex ecosystems. Nature, 483 (7388): 205–208, 2012. https://doi.org/10.1038/nature10832
Pablo A Marquet, Andrew P Allen, James H Brown, Jennifer A Dunne, Brian J Enquist, James F Gillooly, Patricia Adair Gowaty, Jessica L Green, John Harte, Stephen P Hubbell, et al. On theory in ecology. BioScience, 64 (8): 701–710, 2014. https://doi.org/10.1093/biosci/biu098
Michio Kondoh. Foraging adaptation and the relationship between food-web complexity and stability. Science, 299 (5611): 1388–1391, 2003. https://doi.org/10.1126/science.1079154
Fernanda S Valdovinos, Rodrigo Ramos-Jiliberto, Leslie Garay-Narváez, Pasquinell Urbani, and Jennifer A Dunne. Consequences of adaptive behaviour for the structure and dynamics of food webs. Ecology Letters, 13 (12): 1546–1559, 2010. https://doi.org/10.1111/j.1461-0248.2010.01535.x
Ulrich Brose, Richard J Williams, and Neo D Martinez. Allometric scaling enhances stability in complex food webs. Ecology Letters, 9 (11): 1228–1236, 2006. https://doi.org/10.1111/j.1461-0248.2006.00978.x
Amrei Binzer, Christian Guill, Björn C Rall, and Ulrich Brose. Interactive effects of warming, eutrophication and size structure: impacts on biodiversity and food-web structure. Global Change Biology, 22 (1): 220–227, 2016. https://doi.org/10.1111/gcb.13086
Benoit Gauzens, Björn C Rall, Vanessa Mendonça, Catarina Vinagre, and Ulrich Brose. Biodiversity of intertidal food webs in response to warming across latitudes. Nature Climate Change, 10: 264–269, 2020. https://doi.org/10.1038/s41558-019-0679-2
Fernanda S Valdovinos, Pablo Moisset de Espanés, José D Flores, and Rodrigo Ramos-Jiliberto. Adaptive foraging allows the maintenance of biodiversity of pollination networks. Oikos, 122 (6): 907–917, 2013. https://doi.org/10.1111/j.1600-0706.2012.20830.x
Fernanda S Valdovinos, Berry J Brosi, Heather M Briggs, Pablo Moisset de Espanes, Rodrigo Ramos-Jiliberto, and Neo D Martinez. Niche partitioning due to adaptive foraging reverses effects of nestedness and connectance on pollination network stability. Ecology Letters, 19 (10): 1277–1286, 2016. https://doi.org/10.1111/ele.12664
Fernanda S Valdovinos and Robert Marsland III. Niche theory for mutualism: A graphical approach to plant-pollinator network dynamics. The American Naturalist, 197 (4): 393–404, 2021. https://doi.org/10.1086/712831
Fernanda S Valdovinos, Eric L Berlow, Pablo Moisset de Espanés, Rodrigo Ramos-Jiliberto, Diego P Vázquez, and Neo D Martinez. Species traits and network structure predict the success and impacts of pollinator invasions. Nature Communications, 9 (1): 2153, 2018. https://doi.org/10.1038/s41467-018-04593-y
Fernanda S Valdovinos, Sabine Dritz, and Robert Marsland. Transient dynamics in plant–pollinator networks: fewer but higher quality of pollinator visits determines plant invasion success. Oikos, 2023 (6): e09634, 2023. https://doi.org/10.1111/oik.09634
Fernanda S Valdovinos. Effect of network structure and adaptive foraging on pollination services of species-rich plant–pollinator communities. Integrative and Comparative Biology, 65 (4): 981–990, 2025. https://doi.org/10.1093/icb/icaf024
Stephen D Fretwell and Henry L Lucas. On territorial behavior and other factors influencing habitat distribution in birds. I. Theoretical development. Acta Biotheoretica, 19 (1): 16–36, 1969. https://doi.org/10.1007/BF01601953
Alan Hastings. Transients: the key to long-term ecological understanding? Trends in Ecology & Evolution, 19 (1): 39–45, 2004. https://doi.org/10.1016/j.tree.2003.09.007
Alan Hastings, Karen C Abbott, Kim Cuddington, Tessa B Francis, Gabriel Gellner, Ying-Cheng Lai, Andrew Morozov, Sergei Petrovskii, Katherine Scranton, and Mary Lou Zeeman. Transient phenomena in ecology. Science, 361 (6406): eaat6412, 2018. https://doi.org/10.1126/science.aat6412
Kayla RS Hale, Fernanda S Valdovinos, and Neo D Martinez. Mutualism increases diversity, stability, and function of multiplex networks that integrate pollinators into food webs. Nature Communications, 11 (1): 2182, 2020. https://doi.org/10.1038/s41467-020-15688-w
David Tilman. Resource competition and community structure. Princeton University Press, 1982.
Peter Chesson. Mechanisms of maintenance of species diversity. Annual Review of Ecology and Systematics, 31 (1): 343–366, 2000. https://doi.org/10.1146/annurev.ecolsys.31.1.343
Bernd Heinrich. Bumblebee economics. Harvard University Press, 1979.
Sarah S Greenleaf, Neal M Williams, Rachael Winfree, and Claire Kremen. Bee foraging ranges and their relationship to body size. Oecologia, 153 (3): 589–596, 2007. https://doi.org/10.1007/s00442-007-0752-9
James H Brown, James F Gillooly, Andrew P Allen, Van M Savage, and Geoffrey B West. Toward a metabolic theory of ecology. Ecology, 85 (7): 1771–1789, 2004. https://doi.org/10.1890/03-9000
Evan P Kelemen, N Cao, T Cao, Goggy Davidowitz, and Anna Dornhaus. Metabolic rate predicts the lifespan of workers in the bumble bee Bombus impatiens. Apidologie, 50 (2): 195–203, 2019. https://doi.org/10.1007/s13592-018-0630-y
Laura A Burkle, John C Marlin, and Tiffany M Knight. Plant-pollinator interactions over 120 years: loss of species, co-occurrence, and function. Science, 339 (6127): 1611–1615, 2013. https://doi.org/10.1126/science.1232728
Paul J CaraDonna, William K Petry, Ross M Brennan, James L Cunningham, Judith L Bronstein, Nickolas M Waser, and Nathan J Sanders. Interaction rewiring and the rapid turnover of plant–pollinator networks. Ecology Letters, 20 (3): 385–394, 2017. https://doi.org/10.1111/ele.12740
Ignasi Bartomeus, John S Ascher, David Wagner, Bryan N Danforth, Sheila Colla, Sarah Kornbluth, and Rachael Winfree. Climate-associated phenological advances in bee pollinators and bee-pollinated plants. Proceedings of the National Academy of Sciences, 108 (51): 20645–20649, 2011. https://doi.org/10.1073/pnas.1115559108
Marília P Gaiarsa, Claire Kremen, and Lauren C Ponisio. Pollinator interaction flexibility across scales affects patch colonization and occupancy. Nature Ecology & Evolution, 5 (7): 787–793, 2021. https://doi.org/10.1038/s41559-021-01434-y
Paul Glaum, Thomas J Wood, Jonathan R Morris, and Fernanda S Valdovinos. Phenology and flowering overlap drive specialisation in plant–pollinator networks. Ecology Letters, 24 (12): 2648–2659, 2021. https://doi.org/10.1111/ele.13884
Rodrigo Ramos-Jiliberto, Fernanda S Valdovinos, Pablo Moisset de Espanés, and José D Flores. Topological plasticity increases robustness of mutualistic networks. Journal of Animal Ecology, 81 (4): 896–904, 2012. https://doi.org/10.1111/j.1365-2656.2012.01960.x
Christopher N Kaiser-Bunbury, Stefanie Muff, Jane Memmott, Christine B Müller, and Amedeo Caflisch. The robustness of pollination networks to the loss of species and interactions: a quantitative approach incorporating pollinator behaviour. Ecology Letters, 13 (4): 442–452, 2010. https://doi.org/10.1111/j.1461-0248.2009.01437.x