Turing patterns in a predator-prey model with seasonality

Journal of Mathematical Biology
Xiaoying Wang, Frithjof Lutscher

Abstract

Many ecological systems show striking non-homogeneous population distributions. Diffusion-driven instabilities are commonly studied as mechanisms of pattern formation in many fields of biology but only rarely in ecology, in part because some of the conditions seem quite restrictive for ecological systems. Seasonal variation is ubiquitous in temperate ecosystems, yet its effect on pattern formation has not yet been explored. We formulate and analyze an impulsive reaction-diffusion system for a resource and its consumer in a two-season environment. While the resource grows throughout the 'summer' season, the consumer reproduces only once per year. We derive conditions for diffusion-driven instability in the system, and we show that pattern formation is possible with a Beddington-DeAngelis functional response. More importantly, we find that a low overwinter survival probability for the resource enhances the propensity for pattern formation: diffusion-driven instability occurs even when the diffusion rates of prey and predator are comparable (although not when they are equal).

References

Dec 7, 1978·Journal of Theoretical Biology·M Mimura, J D Murray
Apr 20, 2004·Journal of Theoretical Biology·Stefan A H Geritz, Eva Kisdi
Jul 12, 2005·Journal of Theoretical Biology·Andrew MorozovBai-Lian Li
Feb 8, 2008·Trends in Ecology & Evolution·Max Rietkerk, Johan van de Koppel
Aug 16, 2012·Bulletin of Mathematical Biology·Mark A Lewis, Bingtuan Li
Sep 13, 2012·Journal of Theoretical Biology·Stefan Geritz, Mats Gyllenberg
Sep 18, 2015·Journal of Mathematical Biology·Olga VasilyevaMark Lewis
Apr 19, 2018·Journal of Mathematical Biology·Lukas Eigentler, Jonathan A Sherratt

❮ Previous
Next ❯

Citations

Sep 6, 2020·Journal of Mathematical Biology·Lukas Eigentler, Jonathan A Sherratt
Apr 14, 2020·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·A P KolinichenkoL B Ryashko
Jul 18, 2021·Physical Review. E·Srilena KunduM Lakshmanan
Sep 23, 2021·Journal of Mathematical Biology·Yunfeng Geng, Frithjof Lutscher

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.