Modeling effects of matrix heterogeneity on population persistence at the patch-level

Nalin Fonseka; Jerome Goddard Ⅱ; Alketa Henderson; Dustin Nichols; Ratnasingham Shivaji; Nalin Fonseka; Jerome Goddard Ⅱ; Alketa Henderson; Dustin Nichols; Ratnasingham Shivaji

doi:10.3934/mbe.2022638

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 13675-13709. doi: 10.3934/mbe.2022638

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Research article

Modeling effects of matrix heterogeneity on population persistence at the patch-level

1.
School of Arts and Sciences, Carolina University, Winston-Salem, NC 27101, USA
2.
Department of Mathematics, Auburn University Montgomery, Montgomery, AL 36124, USA
3.
Department of Mathematics and Statistics, University of North Carolina Greensboro, Greensboro, NC 27412, USA
Academic editor: Yang Kuang

Received: 08 June 2022 Revised: 01 August 2022 Accepted: 01 September 2022 Published: 19 September 2022

Habitat loss and fragmentation is the largest contributing factor to species extinction and declining biodiversity. Landscapes are becoming highly spatially heterogeneous with varying degrees of human modification. Much theoretical study of habitat fragmentation has historically focused on a simple theoretical landscape with patches of habitat surrounded by a spatially homogeneous hostile matrix. However, terrestrial habitat patches are often surrounded by complex mosaics of many different land cover types, which are rarely ecologically neutral or completely inhospitable environments. We employ an extension of a reaction diffusion model to explore effects of heterogeneity in the matrix immediately surrounding a patch in a one-dimensional theoretical landscape. Exact dynamics of a population exhibiting logistic growth, an unbiased random walk in the patch and matrix, habitat preference at the patch/matrix interface, and two functionally different matrix types for the one-dimensional landscape is obtained. These results show existence of a minimum patch size (MPS), below which population persistence is not possible. This MPS can be estimated via empirically derived estimates of patch intrinsic growth rate and diffusion rate, habitat preference, and matrix death and diffusion rates. We conclude that local matrix heterogeneity can greatly change model predictions, and argue that conservation strategies should not only consider patch size, configuration, and quality, but also quality and spatial structure of the surrounding matrix.
- heterogeneous landscape,
- locally heterogeneous matrix,
- reaction diffusion models,
- habitat preference,
- exact bifurcation diagrams,
- habitat fragmentation,
- logistic growth
Citation: Nalin Fonseka, Jerome Goddard Ⅱ, Alketa Henderson, Dustin Nichols, Ratnasingham Shivaji. Modeling effects of matrix heterogeneity on population persistence at the patch-level[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 13675-13709. doi: 10.3934/mbe.2022638

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Abstract

Habitat loss and fragmentation is the largest contributing factor to species extinction and declining biodiversity. Landscapes are becoming highly spatially heterogeneous with varying degrees of human modification. Much theoretical study of habitat fragmentation has historically focused on a simple theoretical landscape with patches of habitat surrounded by a spatially homogeneous hostile matrix. However, terrestrial habitat patches are often surrounded by complex mosaics of many different land cover types, which are rarely ecologically neutral or completely inhospitable environments. We employ an extension of a reaction diffusion model to explore effects of heterogeneity in the matrix immediately surrounding a patch in a one-dimensional theoretical landscape. Exact dynamics of a population exhibiting logistic growth, an unbiased random walk in the patch and matrix, habitat preference at the patch/matrix interface, and two functionally different matrix types for the one-dimensional landscape is obtained. These results show existence of a minimum patch size (MPS), below which population persistence is not possible. This MPS can be estimated via empirically derived estimates of patch intrinsic growth rate and diffusion rate, habitat preference, and matrix death and diffusion rates. We conclude that local matrix heterogeneity can greatly change model predictions, and argue that conservation strategies should not only consider patch size, configuration, and quality, but also quality and spatial structure of the surrounding matrix.

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