Bulletin of Mathematical Biology

, Volume 81, Issue 11, pp 4726–4742 | Cite as

Genotypic Selection in Spatially Heterogeneous Producer-Grazer Systems Subject to Stoichiometric Constraints

  • Chandani Dissanayake
  • Lourdes JuanEmail author
  • Kevin R. Long
  • Angela Peace
  • Md Masud Rana
Special Issue: Modelling Biological Evolution: Developing Novel Approaches


Various environmental conditions may exert selection pressures leading to adaptation of stoichiometrically important traits, such as organismal nutritional content or growth rate. We use theoretical approaches to explore the connections between genotypic selection and ecological stoichiometry in spatially heterogeneous environments. We present models of a producer and two grazing genotypes with different stoichiometric phosphorus/carbon ratios under spatially homogenous and heterogeneous conditions. Numerical experiments predict that selection of a single genotype, co-persistence of both genotypes, and extinction are possible outcomes depending on environmental conditions. Our results indicated that in spatially homogenous settings, co-persistence of both genotypes can occur when population dynamics oscillate on limit cycles near a key stoichiometric threshold on food quality. Under spatially heterogeneous settings, dynamics are more complex, where co-persistence is observed on limit cycles, as well as stable equilibria.


Genotypic selection Ecological stoichiometry Diffusion Population dynamics 

Mathematics Subject Classification

92D15 92D25 


Supplementary material

Supplementary material 1 (mp4 10700 KB)

Supplementary material 2 (mp4 10237 KB)

Supplementary material 3 (mp4 11373 KB)

Supplementary material 4 (mp4 9422 KB)

Supplementary material 5 (mp4 11295 KB)

Supplementary material 6 (mp4 6742 KB)


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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA
  2. 2.Sri Lanka Technological CampusColomboSri Lanka

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