Effects of pollution on individual size of a single species. (English) Zbl 1461.92068
Summary: In this paper, we develop a single species evolutionary model with a continuous phenotypic trait in a pulsed pollution discharge environment and discuss the effects of pollution on the individual size of the species. The invasion fitness function of a monomorphic species is given, which involves the long-term average exponential growth rate of the species. Then the critical function analysis method is used to obtain the evolutionary dynamics of the system, which is related to interspecific competition intensity between mutant species and resident species and the curvature of the trade-off between individual size and the intrinsic growth rate. We conclude that the pollution affects the evolutionary traits and evolutionary dynamics. The worsening of the pollution can lead to rapid stable evolution toward a smaller individual size, while the opposite is more likely to generate evolutionary branching and promote species diversity. The adaptive dynamics of coevolution of dimorphic species is further analyzed when evolutionary branching occurs.
MSC:
| 92D15 | Problems related to evolution |
| 92D40 | Ecology |
| 34A38 | Hybrid systems of ordinary differential equations |
Keywords:
pulse pollution; invasion fitness function; evolutionary singulary strategy; evolutionary branching; coevolutionReferences:
| [1] | Metz, J. A., Nisbet, R. M. and Geritz, S. A. H., How should we define ‘fitness’ for general ecological scenarios?, Trends Ecol. Evol.7 (1992) 198-202. |
| [2] | Geritz, S. A. H.et al., Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree, Evol. Ecol.12 (1998) 35-37. |
| [3] | Dieckmann, U. and Law, R., The dynamical theory of coevolution: A derivation from stochastic ecological processes, J. Math. Biol.34 (1996) 579-612. · Zbl 0845.92013 |
| [4] | Kisdi, E., Evolutionary branching under asymmetric competition, J. Theoret. Biol.197 (1999) 149-162. |
| [5] | Hoyle, A. and Bowers, R. G., When is evolutionary branching in predator-prey systems possible with an explicit carrying capacity?, Math. Biosci.210 (2007) 1-16. · Zbl 1188.92037 |
| [6] | Geritz, S. A. H., Kisdi, E. and Yan, P., Evolutionary branching and long-term coexistence of cycling predators: Critical function analysis, Theoret. Popul. Biol.71 (2007) 424-435. · Zbl 1122.92053 |
| [7] | Svennungsen, T. O. and Kisdi, E., Evolutionary branching of virulence in a single infection model, J. Theoret. Biol.257 (2009) 408-418. · Zbl 1400.92541 |
| [8] | Zu, J., Mimura, M. and Takeuchi, Y., Adaptive evolution of foraging-related traits in a predator-prey community, J. Theoret. Biol.268 (2011) 14-29. · Zbl 1411.92227 |
| [9] | Zu, J. and Takeuchi, Y., Adaptive evolution of anti-predator ability promotes the diversity of prey species: Critical function analysis, BioSystems109 (2012) 192-202. |
| [10] | Zu, J. and Wang, J., Adaptive evolution of attack ability promotes the evolutionary branching of predator species, Theoret. Popul. Biol.89 (2013) 12-23. · Zbl 1302.92120 |
| [11] | Zu, J., Wang, J. and Du, J., Adaptive evolution of defense ability leads to diversification of prey species, Acta Biotheor.62 (2014) 207-234. |
| [12] | Doebeli, M. and Ispolatov, I., Symmetric competition as a general model for single-species adaptive dynamics, J. Math. Biol.67 (2013) 169-184. · Zbl 1402.92309 |
| [13] | Wang, X., Fan, M. and Hao, L. N., Adaptive evolution of foraging-related trait in intraguild predation system, Math. Biosci.274 (2016) 1-11. · Zbl 1365.92111 |
| [14] | Meng, X. Z. and Zhang, L., Evolutionary dynamics in a Lotka-Volterra competition model with impulsive periodic disturbance, Math. Methods Appl. Sci.39 (2016) 177-188. · Zbl 1342.92192 |
| [15] | Cushing, J. M., Difference equations as models of evolutionary population dynamics, J. Biol. Dyn.13 (2019) 103-127. · Zbl 1447.92333 |
| [16] | Meng, X. Z., Liu, R. and Zhang, T. H., Adaptive dynamics for a non-autonomous Lotka-Volterra model with size-selective disturbance, Nonlinear Anal. Real World Appl.16 (2014) 202-213. · Zbl 1325.92074 |
| [17] | Boldin, B. and Kisdi, E., Evolutionary suicide through a non-catastrophic bifurcation: Adaptive dynamics of pathogens with frequency-dependent transmission, J. Math. Biol.72 (2016) 1101-1124. · Zbl 1365.92073 |
| [18] | Fritsch, C., Campillo, F. and Ovaskainen, O., A numerical approach to determine mutant invasion fitness and evolutionary singular strategies, Theoret. Popul. Biol.115 (2017) 89-99. · Zbl 1381.92062 |
| [19] | Lenka, P., Regime shifts caused by adaptive dynamics in prey-predator models and their relationship with intraspecific competition, Ecol. Complex.36 (2018) 48-56. |
| [20] | Koehnke, M. C., Invasion dynamics in an intraguild predation system with predator-induced defense, Bull. Math. Biol.81 (2019) 3754-3777. · Zbl 1427.92077 |
| [21] | Liu, L. D., Meng, X. Z. and Zhang, T. H., Computing numerical simulations and evolutionary dynamics of a population model in a polluted environment, in Int. Conf. Computer and Communications (Chengdu, , 2016), pp. 50-54. |
| [22] | Dubey, B. and Hussain, J., Modelling the survival of species dependent on a resource in a polluted environment, Nonlinear Anal. Real World Appl.76 (2006) 187-210. · Zbl 1088.92054 |
| [23] | Liu, B., Chen, L. S. and Zhang, Y. Y., The effects of impulsive toxicant input on a population in a polluted environment, J. Biol. Syst.11 (2003) 265-274. · Zbl 1041.92044 |
| [24] | Liu, B., Teng, Z. D. and Chen, L. S., The effects of impulsive toxicant input on two-species Lotka-Volterra competition system, Int. J. Syst. Sci.1 (2005) 208-220. · Zbl 1097.34040 |
| [25] | Zhao, Z., Chen, L. S. and Song, X. Y., Extinction and permanence of chemostat model with pulsed input in a polluted environment, Commun. Nonlinear Sci. Numer. Simul.14 (2009) 1737-1745. · Zbl 1221.37209 |
| [26] | Jia, J. W. and Lv, T. T., Study of two-nutrient and two-micro-organism chemostat model with pulsed input in a polluted environment, Int. J. Biomath.8 (2015) 1550042. · Zbl 1327.34087 |
| [27] | Jiao, J. J., Cai, S. H. and Zhang, Y. J., Dynamics of a stage-structured single population system with winter hibernation and impulsive effect in polluted environment, Int. J. Biomath.9 (2016) 1650084. · Zbl 1342.92179 |
| [28] | Liu, M. and Wang, K., Survival analysis of a stochastic single-species population model with jumps in a polluted environment, Int. J. Biomath.9 (2016) 1650011. · Zbl 1334.60121 |
| [29] | Ackleh, A., Hossain, M. I., Veprauskas, A. and Zhang, A. J., Persistence and stability analysis of discrete-time predator-prey models: A study of population and evolutionary dynamics, J. Difference Equ. Appl.25 (2019) 1568-1603. · Zbl 1430.92063 |
| [30] | de Mazancourt, C. and Dieckmann, U., Trade-off geometries and frequency-dependent selection, Am. Nat.164 (2004) 765-778. |
| [31] | Werner, E. E. and Anholt, B. R., Ecological consequences of the trade-off between growth and mortality rates mediated by foraging activity, Am. Nat.142 (1993) 242-272. |
| [32] | Blomquist, G. E., Trade-off between age of first reproduction and survival in a female primate, Biol. Lett.5 (2009) 339-342. |
| [33] | de Oliveiraa, V. M., Amadob, A. and Campos, P. R. A., The interplay of tradeoffs within the framework of a resource-based modelling, Ecol. Model.384 (2018) 249-260. |
| [34] | Amado, A. and Campos, P. R. A., Ecological specialization under multidimensional trade-offs, Evol. Ecol.33 (2019) 769-789. |
| [35] | Ahmad, S. and Alan, C. L., Necessary and sufficient average growth in a Lotka-Volterra system, Nonlinear. Anal. Theory Methods Appl.34 (1998) 191-228. · Zbl 0934.34037 |
| [36] | Ahmad, S. and Lazer, A. C., Average growth and extinction in a competitive Lotka-Volterra system, Nonlinear. Anal. Theory Methods Appl.62 (2005) 545-557. · Zbl 1088.34047 |
| [37] | Leimar, O., Multidimensional convergence stability, Evol. Ecol. Res.11 (2009) 191-208. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
