American Institute of Mathematical Sciences

Advanced
doi: 10.3934/dcds.2020038

Simulation of post-hurricane impact on invasive species with biological control management

Linhao Xu 1, , Marya Claire Zdechlik 2, , Melissa C. Smith 3, , Min B. Rayamajhi 3, , Don L. DeAngelis 4, and  Bo Zhang 5,,

1. 

Co-Innovation Center for Sustainable Forestry in Southern China, Jiangsu Province Key Laboratory of Soil and, Water Conservation and Ecological Restoration, Nanjing 210037, China
2. 

Department of Biology, University of Miami, Coral Gables, Florida 33124, USA
3. 

USDA-ARS Invasive Plant Research Lab, 3225 College Avenue, Fort Lauderdale, Florida 33314, USA
4. 

US Geological Survey, Wetlands and Aquatic Research Center, Davie, Florida 33314, USA
5. 

Department of Environmental Science and Policy, University of California, Davis, Davis, California 95616, USA

* Corresponding author: Bo Zhang, bozhangophelia@gmail.com; Tel. 001-786-863-6669

Received  February 2019 Revised  June 2019 Published  October 2019

Fund Project: This project was supported by USGS EMA Invasive Species FY18 Cyclical Fund

Understanding the effects of hurricanes and other large storms on ecological communities and the post-event recovery in these communities can guide management and ecosystem restoration. This is particularly important for communities impacted by invasive species, as the hurricane may affect control efforts. Here we consider the effect of a hurricane on tree communities in southern Florida that has been invaded by Melaleuca quinquevervia (melaleuca), an invasive Australian tree. Biological control agents were introduced starting in the 1990s and are reducing melaleuca in habitats where they are established. We used size-structured matrix modeling as a tool to project the continued possible additional effects of a hurricane on a pure stand of melaleuca that already had some level of biological control. The model results indicate that biological control could suppress or eliminate melaleuca within decades. A hurricane that does severe damage to the stand may accelerate the trend toward elimination of melaleuca with both strong and moderate biological control. However, if the biological control is weak, the stand is resilient to all but extremely severe hurricane damage. Although only a pure melaleuca stand was simulated in this study, other plants, such as natives, are likely to accelerate the decline of melaleuca due to competition. Our model provides a new tool to simulate post-hurricanes effect on invasive species and highlights the essential role that biological control has played on invasive species management.

Keywords: Invasive plant species management, stand structure, size-structured matrix model, post-hurricane recovery, biocontrol effect.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Linhao Xu, Marya Claire Zdechlik, Melissa C. Smith, Min B. Rayamajhi, Don L. DeAngelis, Bo Zhang. Simulation of post-hurricane impact on invasive species with biological control management. Discrete & Continuous Dynamical Systems - A, doi: 10.3934/dcds.2020038
References:
[1]

P. J. Bellingham, E. V. J. Tanner and J. R. Healey, Hurricane disturbance accelerates invasion by the alien tree Pittosporum undulatum in Jamaican montane rain forests, Journal of Vegetation Science, 16 (2005), 675-684.   Google Scholar

[2]

P. J. Bellingham, E. V. J. Tanner, P. H. Martin, J. R. Healey and O. R. Burge, Endemic trees in a tropical biodiversity hotspot imperilled by an invasive tree, Biological Conservation, 217 (2018), 47-53.  doi: 10.1016/j.biocon.2017.10.028.  Google Scholar

[3]

K. K. Bohn, P. J. Minogue and E. C. Pietersen, Control of invasive Japanese climbing fern (Lygodium japonicum) and response of native ground cover during restoration of a disturbed longleaf pine ecosystem, Ecological Restoration, 29 (2011), 346-356.   Google Scholar

[4]

H. Bugmann, A review of forest gap models, Climate Change, 51 (2001), 259-305.   Google Scholar

[5]

T. D. Center, P. D. Pratt, P. W. Tipping, M. B. Rayamajhi, T. K. Van and S. A. Wineriter, et al., Field colonization, population growth, and dispersal of Boreioglycaspis melaleucae Moore, a biological control agent of the invasive tree Melaleuca quinquenervia (Cav.) Blake, Biological Control, 39 (2006), 363–374. Google Scholar

[6]

T. D. Center, M. F. Purcell, P. D. Pratt, M. B. Rayamajhi, P. W. Tipping, S. A. Wright, et al., Biological control of Melaleuca quinquenervia: An Everglades invader, Biocontrol, 57 (2012), 151–165. Google Scholar

[7]

T. D. Center, T. K. Van, M. Rayachhetry, G. R. Buckingham, F. A. Dray and S. A. Wineriter, et al., Field colonization of the melaleuca snout beetle (Oxyops vitiosa) in south Florida, Biological Control, 19 (2000), 112–123. Google Scholar

[8]

C. M. D'Antonio, N. E. Jackson, C. C. Horvitz and R. Hedberg, Invasive plants in wildland ecosystems: Merging the study of invasion processes with management needs, Frontiers in Ecology and the Environment, 10 (2004), 513-521.   Google Scholar

[9]

J. W. Day, D. F. Boesch, E. J. Clairain, G. P. Kemp, S. B. Laska and W. J. Mitsch, et al., Restoration of the mississippi delta: Lessons from hurricanes katrina and rita, Science, 315 (2007), 1679–1684. doi: 10.1126/science.1137030.  Google Scholar

[10]

D. B. Flynn, M. Uriarte, T. Crk, J. B. Pascarella, J. K. Zimmerman and T. M. Aide, et al, Hurricane disturbance alters secondary forest recovery in puerto rico, Biotropica, 42 (2010), 149–157. doi: 10.1111/j.1744-7429.2009.00581.x.  Google Scholar

[11]

T. K. Henkel, J. Q. Chambers and D. A. Baker, Delayed tree mortality and Chinese tallow (Triadica sebifera) population explosion in a Louisiana bottomland hardwood forest following Hurricane Katrina, Forest Ecology and Management, 378 (2017), 222-232.   Google Scholar

[12]

C. C. Horvitz, J. B. Pascarella, S. McMann, A. Freedman and R. H. Hoffstetter, Functional roles of invasive non-indigenous plants in hurricane-affected subtropical hardwood forests, Ecological Applications, 8 (1998), 947-974.   Google Scholar

[13]

N. Ishshalom, L. D. L. Sternberg, M. Ross, J. O'brien and L. Flynn, Water Utilization of Tropical Hardwood Hammocks of the Lower Florida Keys, Oecologia, 92 (1992), 108-112.   Google Scholar

[14]

D. M. Lieurance, Biomass allocation of the invasive tree Acacia auriculiformis and refoliation following hurricane-force winds, Journal of the Torrey Botanical Society, 134 (2007), 389-397.   Google Scholar

[15]

S. M. Louda, Negative ecological effects of the musk thistle biological control agent, Rhinocyllus conicus, Nontarget Effects of Biological Control, Springer, 2000,215–243. Google Scholar

[16]

L. McAlpine and S. Porder, Evaluation of a large-scale invasive plant species herbicide control program in the Berkshire Taconic Plateau, Massachusetts, USA, Conservation Evidence, 6 (2006), 117-123.   Google Scholar

[17]

P. D. Pratt, M. B. Rayamajhi, T. K. Van, T. D. Center and P. W. Tipping, Herbivory alters resource allocation and compensation in the invasive tree Melaleuca quinquenervia, Ecological Entomology, 30 (2005), 316-326.   Google Scholar

[18]

M. B. Rayamajhi, P. D. Pratt, T. D. Center, P. W. Tipping and T. K. Van, A review of forest gap models, Climate Change, 51 (2001), 259-305.   Google Scholar

[19]

M. B. Rayamajhi, T. K. Van, P. D. Pratt, T. D. Center and P. W. Tipping, Melaleuca quinquenervia dominated forests in Florida: Analyses of natural-enemy impacts on stand dynamics, Plant Ecology, 192 (2007), 119-132.   Google Scholar

[20]

L. Sevillano, The Effects of Biological Control Agents on Population Growth and Spread of Melaleuca Quinquenervia, Ph.D thesis, University of Miami, 2010. Google Scholar

[21]

L. Sevillano, C. C. Horvitz and P. D. Pratt, Natural enemy density and soil type influence growth and survival of Melaleuca quinquenervia seedlings, Biol Control., 53 (2010), 168-177.  doi: 10.1016/j.biocontrol.2010.01.006.  Google Scholar

[22]

A. A. Sher, H. El Waer, E. Gonzalez, R. Anderson, A. L. Henry and R. Bierdon, et al., Native species recovery after reduction of an invasive tree by biological control with and without active removal, Ecological Engineering, 111 (2018), 167–175. doi: 10.1016/j.ecoleng.2017.11.018.  Google Scholar

[23]

J. Snitzer, D. Boucher and K. Kyde, Response of exotic invasive plant species to forest damage caused by Hurricane Isabel. Hurricane Isabel in perspective, Chesapeake Research Consortium Publication, 1 (2005), 5-160.   Google Scholar

[24]

J. Thompson, A. E. Lugo and J. Thomlinson, Land use history, hurricane disturbance, and the fate of introduced species in a subtropical wet forest in Puerto Rico, Plant Ecology, 192 (2007), 289-301.  doi: 10.1007/s11258-007-9318-5.  Google Scholar

[25]

P. W. Tipping, M. R. Martin, K. R. Nimmo, R. M. Pierce, M. D. Smart and E. White, et al., Invasion of a West Everglades wetland by Melaleuca quinquenervia countered by classical biological control, Biological Control, 48 (2009), 73–78. Google Scholar

[26]

P. W. Tipping, M. R. Martin, P. D. Pratt, T. D. Center and M. B. Rayamajhi, Suppression of growth and reproduction of an exotic invasive tree by two introduced insects, Biological Control, 44 (2008), 235-241.  doi: 10.1016/j.biocontrol.2007.08.011.  Google Scholar

[27]

A. Wright and L. Skilling (eds), Herbicide Toxicity and Biological Control Agents, Proceedings of the Eighth Australian Weeds Conference, Sydney, New South Wales, Australia, 21-25 September, 1987, Weed Society of New South Wales, Australia, 1987. Google Scholar

[28]

W. M. Xi, R. K. Peet and D. L. Urban, Changes in forest structure, species diversity and spatial pattern following hurricane disturbance in a Piedmont North Carolina forest, USA, Journal of Plant Ecology, 1 (2008), 43-57.  doi: 10.1093/jpe/rtm003.  Google Scholar

[29]

B. Zhang, D. L. DeAngelis, M. B. Rayamajhi and D. Botkin, Modeling the long-term effects of introduced herbivores on the spread of an invasive tree, Landscape Ecology, 32 (2017), 1147-1161.  doi: 10.1007/s10980-017-0519-6.  Google Scholar

[30]

B. Zhang, X. Liu, D. L. DeAngelis, L. Zhai, M. B. Rayamajhi and S. Ju, Modeling the compensatory response of an invasive tree to specialist insect herbivory, Biological Control, 117 (2018), 128-136.  doi: 10.1016/j.biocontrol.2017.11.002.  Google Scholar

[31]

J. K. Zimmerman, W. M. Pulliam, D. J. Lodge, V. Quinonesorfila, N. Fetcher and S. Guzmangrajales, et al., Nitrogen immobilization by decomposing woody debris and the recovery of tropical wet forest from hurricane damage, Oikos, 72 (1995), 314–322. doi: 10.2307/3546116.  Google Scholar

[32]

F. A. Dray, Jr, B. C. Bennett, and T. D. Center, Invasion history of Melaleuca quinquenervia (Cav.) S.T. Blake in Florida, Castanea, 71 (2006), 210–225. doi: 10.2179/05-27.1.  Google Scholar

show all references

References:
[1]

P. J. Bellingham, E. V. J. Tanner and J. R. Healey, Hurricane disturbance accelerates invasion by the alien tree Pittosporum undulatum in Jamaican montane rain forests, Journal of Vegetation Science, 16 (2005), 675-684.   Google Scholar

[2]

P. J. Bellingham, E. V. J. Tanner, P. H. Martin, J. R. Healey and O. R. Burge, Endemic trees in a tropical biodiversity hotspot imperilled by an invasive tree, Biological Conservation, 217 (2018), 47-53.  doi: 10.1016/j.biocon.2017.10.028.  Google Scholar

[3]

K. K. Bohn, P. J. Minogue and E. C. Pietersen, Control of invasive Japanese climbing fern (Lygodium japonicum) and response of native ground cover during restoration of a disturbed longleaf pine ecosystem, Ecological Restoration, 29 (2011), 346-356.   Google Scholar

[4]

H. Bugmann, A review of forest gap models, Climate Change, 51 (2001), 259-305.   Google Scholar

[5]

T. D. Center, P. D. Pratt, P. W. Tipping, M. B. Rayamajhi, T. K. Van and S. A. Wineriter, et al., Field colonization, population growth, and dispersal of Boreioglycaspis melaleucae Moore, a biological control agent of the invasive tree Melaleuca quinquenervia (Cav.) Blake, Biological Control, 39 (2006), 363–374. Google Scholar

[6]

T. D. Center, M. F. Purcell, P. D. Pratt, M. B. Rayamajhi, P. W. Tipping, S. A. Wright, et al., Biological control of Melaleuca quinquenervia: An Everglades invader, Biocontrol, 57 (2012), 151–165. Google Scholar

[7]

T. D. Center, T. K. Van, M. Rayachhetry, G. R. Buckingham, F. A. Dray and S. A. Wineriter, et al., Field colonization of the melaleuca snout beetle (Oxyops vitiosa) in south Florida, Biological Control, 19 (2000), 112–123. Google Scholar

[8]

C. M. D'Antonio, N. E. Jackson, C. C. Horvitz and R. Hedberg, Invasive plants in wildland ecosystems: Merging the study of invasion processes with management needs, Frontiers in Ecology and the Environment, 10 (2004), 513-521.   Google Scholar

[9]

J. W. Day, D. F. Boesch, E. J. Clairain, G. P. Kemp, S. B. Laska and W. J. Mitsch, et al., Restoration of the mississippi delta: Lessons from hurricanes katrina and rita, Science, 315 (2007), 1679–1684. doi: 10.1126/science.1137030.  Google Scholar

[10]

D. B. Flynn, M. Uriarte, T. Crk, J. B. Pascarella, J. K. Zimmerman and T. M. Aide, et al, Hurricane disturbance alters secondary forest recovery in puerto rico, Biotropica, 42 (2010), 149–157. doi: 10.1111/j.1744-7429.2009.00581.x.  Google Scholar

[11]

T. K. Henkel, J. Q. Chambers and D. A. Baker, Delayed tree mortality and Chinese tallow (Triadica sebifera) population explosion in a Louisiana bottomland hardwood forest following Hurricane Katrina, Forest Ecology and Management, 378 (2017), 222-232.   Google Scholar

[12]

C. C. Horvitz, J. B. Pascarella, S. McMann, A. Freedman and R. H. Hoffstetter, Functional roles of invasive non-indigenous plants in hurricane-affected subtropical hardwood forests, Ecological Applications, 8 (1998), 947-974.   Google Scholar

[13]

N. Ishshalom, L. D. L. Sternberg, M. Ross, J. O'brien and L. Flynn, Water Utilization of Tropical Hardwood Hammocks of the Lower Florida Keys, Oecologia, 92 (1992), 108-112.   Google Scholar

[14]

D. M. Lieurance, Biomass allocation of the invasive tree Acacia auriculiformis and refoliation following hurricane-force winds, Journal of the Torrey Botanical Society, 134 (2007), 389-397.   Google Scholar

[15]

S. M. Louda, Negative ecological effects of the musk thistle biological control agent, Rhinocyllus conicus, Nontarget Effects of Biological Control, Springer, 2000,215–243. Google Scholar

[16]

L. McAlpine and S. Porder, Evaluation of a large-scale invasive plant species herbicide control program in the Berkshire Taconic Plateau, Massachusetts, USA, Conservation Evidence, 6 (2006), 117-123.   Google Scholar

[17]

P. D. Pratt, M. B. Rayamajhi, T. K. Van, T. D. Center and P. W. Tipping, Herbivory alters resource allocation and compensation in the invasive tree Melaleuca quinquenervia, Ecological Entomology, 30 (2005), 316-326.   Google Scholar

[18]

M. B. Rayamajhi, P. D. Pratt, T. D. Center, P. W. Tipping and T. K. Van, A review of forest gap models, Climate Change, 51 (2001), 259-305.   Google Scholar

[19]

M. B. Rayamajhi, T. K. Van, P. D. Pratt, T. D. Center and P. W. Tipping, Melaleuca quinquenervia dominated forests in Florida: Analyses of natural-enemy impacts on stand dynamics, Plant Ecology, 192 (2007), 119-132.   Google Scholar

[20]

L. Sevillano, The Effects of Biological Control Agents on Population Growth and Spread of Melaleuca Quinquenervia, Ph.D thesis, University of Miami, 2010. Google Scholar

[21]

L. Sevillano, C. C. Horvitz and P. D. Pratt, Natural enemy density and soil type influence growth and survival of Melaleuca quinquenervia seedlings, Biol Control., 53 (2010), 168-177.  doi: 10.1016/j.biocontrol.2010.01.006.  Google Scholar

[22]

A. A. Sher, H. El Waer, E. Gonzalez, R. Anderson, A. L. Henry and R. Bierdon, et al., Native species recovery after reduction of an invasive tree by biological control with and without active removal, Ecological Engineering, 111 (2018), 167–175. doi: 10.1016/j.ecoleng.2017.11.018.  Google Scholar

[23]

J. Snitzer, D. Boucher and K. Kyde, Response of exotic invasive plant species to forest damage caused by Hurricane Isabel. Hurricane Isabel in perspective, Chesapeake Research Consortium Publication, 1 (2005), 5-160.   Google Scholar

[24]

J. Thompson, A. E. Lugo and J. Thomlinson, Land use history, hurricane disturbance, and the fate of introduced species in a subtropical wet forest in Puerto Rico, Plant Ecology, 192 (2007), 289-301.  doi: 10.1007/s11258-007-9318-5.  Google Scholar

[25]

P. W. Tipping, M. R. Martin, K. R. Nimmo, R. M. Pierce, M. D. Smart and E. White, et al., Invasion of a West Everglades wetland by Melaleuca quinquenervia countered by classical biological control, Biological Control, 48 (2009), 73–78. Google Scholar

[26]

P. W. Tipping, M. R. Martin, P. D. Pratt, T. D. Center and M. B. Rayamajhi, Suppression of growth and reproduction of an exotic invasive tree by two introduced insects, Biological Control, 44 (2008), 235-241.  doi: 10.1016/j.biocontrol.2007.08.011.  Google Scholar

[27]

A. Wright and L. Skilling (eds), Herbicide Toxicity and Biological Control Agents, Proceedings of the Eighth Australian Weeds Conference, Sydney, New South Wales, Australia, 21-25 September, 1987, Weed Society of New South Wales, Australia, 1987. Google Scholar

[28]

W. M. Xi, R. K. Peet and D. L. Urban, Changes in forest structure, species diversity and spatial pattern following hurricane disturbance in a Piedmont North Carolina forest, USA, Journal of Plant Ecology, 1 (2008), 43-57.  doi: 10.1093/jpe/rtm003.  Google Scholar

[29]

B. Zhang, D. L. DeAngelis, M. B. Rayamajhi and D. Botkin, Modeling the long-term effects of introduced herbivores on the spread of an invasive tree, Landscape Ecology, 32 (2017), 1147-1161.  doi: 10.1007/s10980-017-0519-6.  Google Scholar

[30]

B. Zhang, X. Liu, D. L. DeAngelis, L. Zhai, M. B. Rayamajhi and S. Ju, Modeling the compensatory response of an invasive tree to specialist insect herbivory, Biological Control, 117 (2018), 128-136.  doi: 10.1016/j.biocontrol.2017.11.002.  Google Scholar

[31]

J. K. Zimmerman, W. M. Pulliam, D. J. Lodge, V. Quinonesorfila, N. Fetcher and S. Guzmangrajales, et al., Nitrogen immobilization by decomposing woody debris and the recovery of tropical wet forest from hurricane damage, Oikos, 72 (1995), 314–322. doi: 10.2307/3546116.  Google Scholar

[32]

F. A. Dray, Jr, B. C. Bennett, and T. D. Center, Invasion history of Melaleuca quinquenervia (Cav.) S.T. Blake in Florida, Castanea, 71 (2006), 210–225. doi: 10.2179/05-27.1.  Google Scholar

Figure 1.  a) Simulated basal area of 0.1 ha melaleuca stand at year 200. b)Simulated size structure near steady state of 0.01 ha melaleuca at year 200 of simulation
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2.  a-d. Simulated size structure near steady state of 0.01 ha melaleuca 4, 8, 16 and 32 years after application of strong biological control
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3.  a) Simulated decline in basal area of melaleuca stand after start of strong biological control in year 200 of simulation. b) Simulated decline in basal area of melaleuca stand after start of strong biological control in year 200 with moderate hurricane in year 216 of simulation
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 4.  a-d. Simulated size structure near steady state of 0.01 ha melaleuca 4, 8, 16 and 32 years after application of moderate biological control
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 5.  a) Simulated decline in basal area of melaleuca stand after start of moderate biological control in year 200 of simulation. b) Simulated decline in basal area of melaleuca stand after start of moderate biological control in year 200 with moderate hurricane in year 2016
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 6.  a) Application of weak biological control decreases steady state values of total basal area of melaleuca stand to a lower level. b) Application of weak biological control decreases steady state values of total basal area of melaleuca stand to a lower level. The stand recovers from a moderate hurricane at year 400. c) Application of weak biological control decreases steady state values of total basal area of melaleuca stand to a lower level. The stand recovers only slowly from a strong hurricane at year 400. d) Effect of strong hurricane at year 400 on basal area of melaleuca stand when there is no biological control being applied. Although the effect on basal area is severe, recovery is faster than in the case where there is weak biocontrol
Figure Options

Download full-size image

Download as PowerPoint slide

[1]

Andrew J. Whittle, Suzanne Lenhart, Louis J. Gross. Optimal control for management of an invasive plant species. Mathematical Biosciences & Engineering, 2007, 4 (1) : 101-112. doi: 10.3934/mbe.2007.4.101
[2]

H. L. Smith, X. Q. Zhao. Competitive exclusion in a discrete-time, size-structured chemostat model. Discrete & Continuous Dynamical Systems - B, 2001, 1 (2) : 183-191. doi: 10.3934/dcdsb.2001.1.183
[3]

Dongxue Yan, Xianlong Fu. Asymptotic behavior of a hierarchical size-structured population model. Evolution Equations & Control Theory, 2018, 7 (2) : 293-316. doi: 10.3934/eect.2018015
[4]

Xianlong Fu, Dongmei Zhu. Stability analysis for a size-structured juvenile-adult population model. Discrete & Continuous Dynamical Systems - B, 2014, 19 (2) : 391-417. doi: 10.3934/dcdsb.2014.19.391
[5]

Xianlong Fu, Dongmei Zhu. Stability results for a size-structured population model with delayed birth process. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 109-131. doi: 10.3934/dcdsb.2013.18.109
[6]

Jixun Chu, Pierre Magal. Hopf bifurcation for a size-structured model with resting phase. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 4891-4921. doi: 10.3934/dcds.2013.33.4891
[7]

Keng Deng, Yixiang Wu. Extinction and uniform strong persistence of a size-structured population model. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 831-840. doi: 10.3934/dcdsb.2017041
[8]

József Z. Farkas, Thomas Hagen. Asymptotic analysis of a size-structured cannibalism model with infinite dimensional environmental feedback. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1825-1839. doi: 10.3934/cpaa.2009.8.1825
[9]

Dongxue Yan, Xianlong Fu. Asymptotic analysis of a spatially and size-structured population model with delayed birth process. Communications on Pure & Applied Analysis, 2016, 15 (2) : 637-655. doi: 10.3934/cpaa.2016.15.637
[10]

Qihua Huang, Hao Wang. A toxin-mediated size-structured population model: Finite difference approximation and well-posedness. Mathematical Biosciences & Engineering, 2016, 13 (4) : 697-722. doi: 10.3934/mbe.2016015
[11]

Dongxue Yan, Yu Cao, Xianlong Fu. Asymptotic analysis of a size-structured cannibalism population model with delayed birth process. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 1975-1998. doi: 10.3934/dcdsb.2016032
[12]

Azmy S. Ackleh, Vinodh K. Chellamuthu, Kazufumi Ito. Finite difference approximations for measure-valued solutions of a hierarchically size-structured population model. Mathematical Biosciences & Engineering, 2015, 12 (2) : 233-258. doi: 10.3934/mbe.2015.12.233
[13]

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
[14]

Azmy S. Ackleh, H.T. Banks, Keng Deng, Shuhua Hu. Parameter Estimation in a Coupled System of Nonlinear Size-Structured Populations. Mathematical Biosciences & Engineering, 2005, 2 (2) : 289-315. doi: 10.3934/mbe.2005.2.289
[15]

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
[16]

Keith E. Howard. A size structured model of cell dwarfism. Discrete & Continuous Dynamical Systems - B, 2001, 1 (4) : 471-484. doi: 10.3934/dcdsb.2001.1.471
[17]

Blaise Faugeras, Olivier Maury. An advection-diffusion-reaction size-structured fish population dynamics model combined with a statistical parameter estimation procedure: Application to the Indian Ocean skipjack tuna fishery. Mathematical Biosciences & Engineering, 2005, 2 (4) : 719-741. doi: 10.3934/mbe.2005.2.719
[18]

József Z. Farkas, Thomas Hagen. Asymptotic behavior of size-structured populations via juvenile-adult interaction. Discrete & Continuous Dynamical Systems - B, 2008, 9 (2) : 249-266. doi: 10.3934/dcdsb.2008.9.249
[19]

Jun Zhou. Bifurcation analysis of a diffusive plant-wrack model with tide effect on the wrack. Mathematical Biosciences & Engineering, 2016, 13 (4) : 857-885. doi: 10.3934/mbe.2016021
[20]

Ryszard Rudnicki, Radosław Wieczorek. On a nonlinear age-structured model of semelparous species. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2641-2656. doi: 10.3934/dcdsb.2014.19.2641

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (28)
  • HTML views (52)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences