Spatial Dynamics and Spread of Ecosystem Engineers: Two Patch Analysis
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Spatial Dynamics and Spread of Ecosystem Engineers: Two Patch Analysis Jorge Arroyo-Esquivel1
· Alan Hastings2,3
Received: 28 May 2020 / Accepted: 2 November 2020 / Published online: 19 November 2020 © Society for Mathematical Biology 2020
Abstract Ecosystem engineers are organisms characterized by interacting with other organisms thorough physical modifications or modifying their habitat. Examples of ecosystem engineers include Spartina alterniflora cordgrass or the zebra mussel Dreissena polymorpha. For both of these, the effect of modifying the environment can be nonlocal, affecting other regions farther away from the region populated by the ecosystem engineer. This shows the importance of understanding the population dynamics of ecosystem engineers in a spatial context. To do this, we have developed an extension of the ecosystem engineer population model of Cuddington et al. (Am Natur, 2009. https://doi.org/10.1086/597216) to the simplest spatial model, incorporating two local populations. We use this model to understand the relationship between dispersal and engineering effects, both at local and regional scales. Our main result is that the delayed Allee effect induced in the nonspatial model is extended to the spatial model, so the spread dynamics of an ecosystem engineer can be similar to the Allee case. However, there are more complex possibilities due to the two components of the dynamics. We also find quantitative guidelines that explain the interaction between spread of the environment modification and organism spread. Keywords Ecosystem engineers · Allee effect · Spatial dynamics · Ecological spread Mathematics Subject Classification 92D25 · 34E10
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Jorge Arroyo-Esquivel [email protected]
1
Department of Mathematics, University of California Davis, Davis, CA, USA
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Department of Environmental Science and Policy, University of California Davis, Davis, CA, USA
3
Santa Fe Institute, Santa Fe, NM, USA
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J. Arroyo-Esquivel, A. Hastings
1 Introduction At a community scale, nontrophic interactions between organisms and their environment are important factors to consider when understanding biodiversity and ecosystem functions present in these environments (Goudard and Loreau 2008). However, mathematical models usually focus on biotic interactions and do not account for the former (Hastings et al. 2007), which are only implicitly considered in the parameters of the model. The concept of ecosystem engineers, introduced by Jones et al. (1994), presents certain populations as having nontrophic interactions that significantly modify the ecosystem structure. Thus, when modeling populations of ecosystem engineers, this type of interactions should be addressed. Previous models have considered this relationship between ecosystem engineers and their environment before (Gurney and Lawton 1996; Cuddington and Hastings 2004; Wright et al. 2004; Cuddington et al. 2009; Franco and Fontanari 2017). However, the question of what conditions allow for the spread of an ecosystem engineer and
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