American Institute of Mathematical Sciences

Advanced
2005, 2(4): 833-868. doi: 10.3934/mbe.2005.2.833

Edge-linked dynamics and the scale-dependence of competitive

Robert Stephen Cantrell 1, , Chris Cosner 1, and  William F. Fagan 2,

1. 

Department of Mathematics, University of Miami, P. O . Box 249085, Coral Gables, FL 33124-4250, United States
2. 

Department of Biology, University of Maryland, College Park, MD 20742, United States

Received  April 2005 Revised  October 2005 Published  October 2005

Empirical data for several ecological systems suggest that how resource availability scales with patch geometry may influence the outcome of species interactions. To study this process, we assume a pseudoequilibrium to reduce the dimensionality of a two-consumer-two-resource model in which different resources are available in the interior of a patch versus at the edge. We analyze the resulting two species competition model to understand how the outcome of competition between consumers changes as the size of the patch changes, paying particular attention to the differential scaling of interior and edge-linked allochthonous resources as a function of patch size. We characterize conditions on patch size and parameters under which competitive exclusion, coexistence, and a reversal in competitive dominance occur. We find that the degree of exclusivity in the use of edge versus interior habitats influences the potential for transitions in competitive outcomes, but that differences in resource quality between interior and edge habitats can, depending on the scenario, have either qualitative or quantitative influences on the transitions. The work highlights the importance of patch size to understanding species interactions and demonstrates that competitive dominance can be a scale- dependent trait.
Keywords: allochthonous resources, habitat fragmentation, metapopulation dynamics, habitat edges, patch size, edge e®ects, spatial subsidies., domain size.
Mathematics Subject Classification: 92D40, 34D2.
Citation: Robert Stephen Cantrell, Chris Cosner, William F. Fagan. Edge-linked dynamics and the scale-dependence of competitive. Mathematical Biosciences & Engineering, 2005, 2 (4) : 833-868. doi: 10.3934/mbe.2005.2.833
[1]

Peixuan Weng, Xiao-Qiang Zhao. Spatial dynamics of a nonlocal and delayed population model in a periodic habitat. Discrete & Continuous Dynamical Systems - A, 2011, 29 (1) : 343-366. doi: 10.3934/dcds.2011.29.343
[2]

Yueding Yuan, Yang Wang, Xingfu Zou. Spatial dynamics of a Lotka-Volterra model with a shifting habitat. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5633-5671. doi: 10.3934/dcdsb.2019076
[3]

Jacek Banasiak, Wilson Lamb. Coagulation, fragmentation and growth processes in a size structured population. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 563-585. doi: 10.3934/dcdsb.2009.11.563
[4]

J. J. P. Veerman, B. D. Stošić, A. Olvera. Spatial instabilities and size limitations of flocks. Networks & Heterogeneous Media, 2007, 2 (4) : 647-660. doi: 10.3934/nhm.2007.2.647
[5]

Pierre Degond, Maximilian Engel. Numerical approximation of a coagulation-fragmentation model for animal group size statistics. Networks & Heterogeneous Media, 2017, 12 (2) : 217-243. doi: 10.3934/nhm.2017009
[6]

Wilson Lamb, Adam McBride, Louise Smith. Coagulation and fragmentation processes with evolving size and shape profiles: A semigroup approach. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5177-5187. doi: 10.3934/dcds.2013.33.5177
[7]

Igor Nazarov, Bai-Lian Li. Maximal sustainable yield in a multipatch habitat. Conference Publications, 2005, 2005 (Special) : 682-691. doi: 10.3934/proc.2005.2005.682
[8]

Junfan Lu, Hong Gu, Bendong Lou. Expanding speed of the habitat for a species in an advective environment. Discrete & Continuous Dynamical Systems - B, 2017, 22 (2) : 483-490. doi: 10.3934/dcdsb.2017023
[9]

Qiaoling Chen, Fengquan Li, Feng Wang. A diffusive logistic problem with a free boundary in time-periodic environment: Favorable habitat or unfavorable habitat. Discrete & Continuous Dynamical Systems - B, 2016, 21 (1) : 13-35. doi: 10.3934/dcdsb.2016.21.13
[10]

L. M. Abia, O. Angulo, J.C. López-Marcos. Size-structured population dynamics models and their numerical solutions. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 1203-1222. doi: 10.3934/dcdsb.2004.4.1203
[11]

Thomas Lorenz. Nonlocal hyperbolic population models structured by size and spatial position: Well-posedness. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 4547-4628. doi: 10.3934/dcdsb.2019156
[12]

Linlin Su, Thomas Nagylaki. Clines with directional selection and partial panmixia in an unbounded unidimensional habitat. Discrete & Continuous Dynamical Systems - A, 2015, 35 (4) : 1697-1741. doi: 10.3934/dcds.2015.35.1697
[13]

Alexander V. Budyansky, Kurt Frischmuth, Vyacheslav G. Tsybulin. Cosymmetry approach and mathematical modeling of species coexistence in a heterogeneous habitat. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 547-561. doi: 10.3934/dcdsb.2018196
[14]

Feng-Bin Wang, Junping Shi, Xingfu Zou. Dynamics of a host-pathogen system on a bounded spatial domain. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2535-2560. doi: 10.3934/cpaa.2015.14.2535
[15]

Dan Zhang, Xiaochun Cai, Lin Wang. Complex dynamics in a discrete-time size-structured chemostat model with inhibitory kinetics. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3439-3451. doi: 10.3934/dcdsb.2018327
[16]

Qun Liu, Daqing Jiang. Dynamics of a multigroup SIRS epidemic model with random perturbations and varying total population size. Communications on Pure & Applied Analysis, 2020, 19 (2) : 1089-1110. doi: 10.3934/cpaa.2020050
[17]

Sebastian Aniţa, Ana-Maria Moşsneagu. Optimal harvesting for age-structured population dynamics with size-dependent control. Mathematical Control & Related Fields, 2019, 9 (4) : 607-621. doi: 10.3934/mcrf.2019043
[18]

Ondrej Budáč, Michael Herrmann, Barbara Niethammer, Andrej Spielmann. On a model for mass aggregation with maximal size. Kinetic & Related Models, 2011, 4 (2) : 427-439. doi: 10.3934/krm.2011.4.427
[19]

Maxim Arnold, Walter Craig. On the size of the Navier - Stokes singular set. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 1165-1178. doi: 10.3934/dcds.2010.28.1165
[20]

Julien Arino, Fred Brauer, P. van den Driessche, James Watmough, Jianhong Wu. A final size relation for epidemic models. Mathematical Biosciences & Engineering, 2007, 4 (2) : 159-175. doi: 10.3934/mbe.2007.4.159

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (12)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences