Benincà, E., Ballantine, B., Ellner, S.P. & Huisman, J. Species fluctuations sustained by a cyclic succession at the edge of chaos. Proc. Natl. Acad. Sci. 112, 6389–6394 (2015).
Lande, R. et al. Stochastic Population Dynamics in Ecology and Conservation (Oxford University Press, 2003).
Bonsall, M. B. & Hastings, A. Demographic and environmental stochasticity in predator-prey metapopulation dynamics. J. Anim. Ecol. 73, 1043–1055 (2004).
Google Scholar
Nisbet, R. M. & Gurney, W. Modelling Fluctuating Populations: reprint of first Edition (1982) (Blackburn Press, 2003).
Hening, A. & Nguyen, D. H. Stochastic Lotka–Volterra food chains. J. Math. Biol. 77(1), 135–163 (2018).
Google Scholar
Khasminskii, R. et al. Long term behavior of solutions of the Lotka–Volterra system under small random perturbations. Ann. Appl. Probab. 11(3), 952–963 (2001).
Google Scholar
Huang, W., Hauert, C. & Traulsen, A. Stochastic game dynamics under demographic fluctuations. Proc. Natl. Acad. Sci., 112(29), 9064–9069 (2015).
Suvinthra, M. & Balachandran, K. Large deviations for the stochastic predator-prey model with nonlinear functional response. J. Appl. Probab. 54(2), 507 (2017).
Google Scholar
Zou, X. & Wang, K. Optimal harvesting for a stochastic Lotka–Volterra predator-prey system with jumps and nonselective harvesting hypothesis. Optim. Control Appl. Methods 37(4), 641–662 (2016).
Google Scholar
Larsen, A. E. Modeling multiple nonconsumptive effects in simple food webs: a modified Lotka–Volterra approach. Behav. Ecol. 23(5), 1115–1125 (2012).
Google Scholar
Singh, A. Stochastic dynamics of consumer-resource interactions. bioRxiv (2021).
Bashkirtseva, I., Ryashko, L. & Tsvetkov, I. Analysis of stochastic phenomena in ricker-type population model with delay. In AIP Conference Proceedings, vol. 1895, p. 050003 (2017).
Halley, J. M. & Iwasa, Y. Extinction rate of a population under both demographic and environmental stochasticity. Theor. Popul. Biol. 53, 1–15 (1998).
Google Scholar
Hassell, M. P. (Oxford University Press, 2000).
Gurney, W. S. C. & Nisbet, R. M. Ecological Dynamics (Oxford University Press, 1998).
Murdoch, W. W., Briggs, C. J. & Nisbet, R. M. Consumer-Resouse Dynamics (Princeton University Press, 2003).
Kakehashi, N., Suzuki, Y. & Iwasa, Y. Niche overlap of parasitoids in host-parasitoid systems: its consequence to single versus multiple introduction controversy in biological control. J. Appl. Ecol. 21, 115–131 (1984).
Google Scholar
May, R. M. & Hassell, M. P. The dynamics of multiparasitoid-host interactions. Am. Nat. 117(3), 234–261 (1981).
Google Scholar
Hackett-Jones, E., Cobbold, C. & White, A. Coexistence of multiple parasitoids on a single host due to differences in parasitoid phenology. Theor. Ecol. 2(1), 19–31 (2009).
Google Scholar
van Velzen, E., Pérez-Vila, S. & Etienne, R. S. The role of within-host competition for coexistence in multiparasitoid-host systems. Am. Nat. 187(1), 48–59 (2016).
Google Scholar
Nicholson, A. & Bailey, V. A. The balance of animal populations. Part 1. Proc. Zool. Soc. Lond. 3, 551–598 (1935).
Google Scholar
Singh, A., Murdoch, W. W. & Nisbet, R. M. Skewed attacks, stability, and host suppression. Ecology 90(6), 1679–1686 (2009).
Google Scholar
Bešo, E., Kalabušić, S., Mujić, N. & Pilav, E. Stability of a certain class of a host-parasitoid models with a spatial refuge effect. J. Biol. Dyn. 14(1), 1–31 (2020).
Google Scholar
Taylor, A. D. Heterogeneity in host-parasitoid interactions: ‘aggregation of risk’ and the (cv^2>1) rule. Trends Ecol. Evolu. 8, 400–405 (1993).
Hassell, M. P., May, R. M., Pacala, S. W. & Chesson, P. L. The persistence of host-parasitoid associations in patchy environments. I. A general criterion. Am. Nat. 138, 568–583 (1991).
Google Scholar
Pacala, S. W. & Hassell, M. P. The persistence of host- parasitoid associations in patchy environments. II. Evaluation of field data. Am. Nat. 138, 584–605 (1991).
Google Scholar
Bernstein, C. Density dependence and the stability of host-parasitoid systems. Oikos 47, 176–180 (1986).
Google Scholar
Free, C., Beddington, J. & Lawton, J. On the inadequacy of simple models of mutual interference for parasitism and predation. J. Anim. Ecol. 46, 543–554 (1977).
Google Scholar
Rogers, D. & Hassell, M. General models for insect parasite and predator searching behaviour: interference. J. Anim. Ecol. 43, 239–253 (1974).
Google Scholar
Reeve, J. D., Cronin, J. T. & Strong, D. R. Parasitoid aggregation and the stabilization of a salt marsh host- parasitoid system. Ecology 75, 288–295 (1994).
Google Scholar
Rohani, P., Godfray, H. C. J. & Hassell, M. P. Aggregation and the dynamics of host-parasitoid systems: A discrete-generation model with within-generation redistribution. Am. Nat. 144(3), 491–509 (1994).
Google Scholar
May, R. M. Host-parasitoid systems in patchy environments: A phenomenological model. J. Anim. Ecol. 47, 833–844 (1978).
Google Scholar
Singh, A. & Nisbet, R. M. Semi-discrete host-parasitoid models. J. Theor. Biol. 247(4), 733–742 (2007).
Google Scholar
Singh, A. Population dynamics of multi-host communities attacked by a common parasitoid, bioRxiv (2021).
Singh, A. & Emerick, B. Hybrid systems framework for modeling host-parasitoid population dynamics. In 2020 59th IEEE Conference on Decision and Control (CDC), 4628–4633 (2020).
Lane, S. D., St, C. M. Mary, & Getz, W. M. Coexistence of attack-limited parasitoids sequentially exploiting the same resource and its implications for biological control. Ann. Zool. Fenn. 43, 17–34 (2006).
Pedersen, B. S. & Mills, N. J. Single vs. multiple introduction in biological control: the roles of parasitoid efficiency, antagonism and niche overlap. J. Appl. Ecol. 41(5), 973–984 (2004).
Google Scholar
Abram, P. K., Brodeur, J., Burte, V. & Boivin, G. Parasitoid-induced host egg abortion; an underappreciated component of biological control services provided by egg parasitoids. Biol. Control 98, 52–60 (2016).
Google Scholar
Jervis, M. A., Hawkin, B. A. & Kidd, N. A. C. The usefulness of destructive host-feeding parasitoids in classical biological control: Theory and observation conflict. Ecol. Entomol. 21(1), 41–46 (1996).
Google Scholar
Okuyama, T. Density-dependent distribution of parasitism risk among underground hosts. Bull. Entomol. Res. 109(4), 528–533 (2019).
Google Scholar
Cobbold, C. A., Roland, J. & Lewis, M. A. The impact of parasitoid emergence time on host-parastioid population dynamics. Theor. Popul. Biol. 75(2), 201–215 (2009).
Google Scholar
Liere, H., Jackson, D. & Vandermeer, J. Ecological complexity in a coffee agroecosystem: Spatial heterogeneity, popoulation persistence and biological control. PLoS One 7(9), e45508 (2012).
Zoroa, N., Lesigne, E., Fernandez-Saez, M.J., Zoroa, P. & Casas, J. The coupon collector urn model with unequal probabilities in ecology and evolution, J. R. Soc. Interface 14, 20160643 (2017).
Singh, A. & Emerick, B. Generalized stability conditions for host-parasitoid population dynamics: Implications for biological control. Ecol. Model. 456, 109656 (2021).
Ledder, G. Mathematics for the Life Sciences: Calculus, Modeling, Probability, and Dynamical Systems (Springer Science & Business Media, 2013).
Elaydi, S. An Introduction to Difference Equations (Springer, 1996).
Gajic, Z. & Qureshi, M. T. J. Lyapunov matrix equation in system stability and control. (Courier Corporation, 2008).
Singh, A. & Nisbet, R. M. Variation in risk in single-species discrete-time models. Math. Biosci. Eng. 5, 859–875 (2008).
Google Scholar
Emerick, B. K. & Singh, A. The effects of host-feeding on stability of discrete-time host-parasitoid population dynamic models. Math. Biosci. 272, 54–63 (2016).
Google Scholar
Pachepsky, E., Nisbet, R. M. & Murdoch, W. W. Between discrete and continuous: Consumer-resource dynamics with synchronized reproduction. Ecology 89(1), 280–288 (2007).
Google Scholar
Emerick, B. K., Singh, A & Chhetri, S. R. Global redistribution and local migration in semi-discrete host-parasitoid population dynamic models. Math. Biosci. 327, 108409 (2020).
Rogers, D. J. Random searching and incest population models. J. Anim. Ecol. 41, 369–383 (1972).
Google Scholar
Hassell, M. P. & Comins, H. N. Sigmoid functional responses and population stability. Theor. Popul. Biol. 14, 62–66 (1978).
Google Scholar
Fernández-arhex, V. & Corley, J. C. The functional response of parasitoids and its implications for biological control. Biocontrol Sci. Technol. 13(4), 403–413 (2003).
Google Scholar
Okuyama, T. Dilution effects enhance variation in parasitism risk among hosts and stabilize host-parasitoid population dynamics. Ecol. Model. 441, 109425 (2021).
