Lure 2009 summer program john Alford Sam Houston State University Mathematics and Biology



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LURE 2009 SUMMER PROGRAM John Alford Sam Houston State University

Mathematics and Biology

  • Biology has inspired mathematics for hundreds of years
    • Thomas Malthus, An Essay on the Principle of Populations (1798)
      • population growth
    • Gregor Mendel, Experiments in Plant Hybridization (1865)
      • genetic variation

Mathematical Biology Classic Papers

  • Volterra, V.
  • Kermack, W.O. and McKendrick, A.G.
    • Contributions to the mathematical theory of epidemics, Proc. Roy. Soc. (1927)
  • Fisher, R.A.
    • The wave of advance of advantageous genes, Ann. Eugenics (1937)

Mathematical Biology Classic Papers

  • Turing, A.M.
    • The chemical basis of morphogenesis, Phil. Trans. Roy. Soc. Lond. (1952)
  • Hodgkin, A.L. and Huxley, A.F.
    • A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiology (1952)
  • Rosenzweig, M.L. and MacArthur, R.H.
    • Graphical representation and stability conditions of predator-prey interactions, American Naturalist (1963)

Mathematics and Biology

  • Increases in computing power and decreases in computing costs has revolutionized the biological, medical, and environmental sciences
    • gene sequencing data
    • GPS data
    • etc.
  • More data has resulted in a greater need for mathematical and statistical models to interpret it.

Invasive Species

Invasive Species

  • zebra mussels

Invasive Species

  • http://www.invasivespeciesinfo.gov/
  • Definition: plants, animals, pathogens and other organisms that are non-native to an ecosystem, and which may cause economic or environmental harm or adversely affect human health.

Invasive Species

  • http://www.invasivespeciesinfo.gov/
  • Impact adversely upon biodiversity, including decline or elimination of native species - through competition, predation, or transmission of pathogens - and the disruption of local ecosystems and ecosystem functions

Invasive Species

  • http://www.invasivespeciesinfo.gov/
  • Since the 17th century, invasive species have contributed to nearly 40% of all animal extinctions for which the cause is known

Invasive Species Control

  • www.invasivespeciesinfo.gov
    • The National Invasive Species Information Center (NISIC)
  • www.texasinvasives.org/
    • Pulling Together Initiative, a Texas-sized partnership to manage non-native invasive plants
  • www.aquatics.org/
    • AERF (aquatic ecosystem restoration foundation)
  • http://el.erdc.usace.army.mil/aqua/
    • Aquatic Plant Control Research Program (APCRP) US Army Corps of Engineers (see APIS link for simulation software)

Invasive Species

  • Invasion Stages
    • arrival
      • natural or human transportation of a species to a new area
    • establishment
      • the forming of a self-sustaining population in the new area
    • integration
      • invading species forms ecological links with other species in the region
    • Vermeij, G.J., An agenda for invasion biology, Biological Conservation, Biological Conservation, 1996

Invasive Species Control

    • Fire ant being attacked by a phorid fly

Invasive Species Control

  • Parasitic flies turn fire ants into zombies
  • By Bill Hanna, Fort Worth Star-Telegram Bill Hanna, Fort Worth Star-telegram – Tue May 12, 2:09 pm ET
  • It sounds like something out of science fiction: zombie fire ants. But it's all too real. Fire ants wander aimlessly away from the mound. Eventually their heads fall off, and they die. "It's a tool — they're not going to completely wipe out the fire ant, but it's a way to control their population," said Scott Ludwig , an integrated pest management specialist with the AgriLife Extension Service in Overton , in East Texas .
  • The tool is the tiny phorid fly, native to a region of South America where the fire ants in Texas originated. Researchers have learned that there are as many as 23 phorid species along with pathogens that attack fire ants to keep their population and movements under control.
  • The flies "dive-bomb" the fire ants and lay eggs. The maggot that hatches inside the ant eats away at the brain, and the ant starts exhibiting what some might say is zombie-like behavior.

Invasive Species Control

Invasive Species Control

  • Once arrival has occurred, the control options include
    • eradication
    • suppresion (reducing invading population densities)
    • slowing the spread

Invasive Aquatic Weeds

  • Invasive aquatic weeds
    • Hydrilla verticillata
      • submersed
    • water hyacinth
      • floating
    • giant salvinia
      • free-floating fern
    • many, many more

Invasive Aquatic Weed: Hydrilla

Invasive Aquatic Weed: Water Hyacinth

Invasive Aquatic Weed: Giant Salvinia

  • The photo on the right was taken 41 days after the photo on the left

Invasive Aquatic Weeds

  • Negative impacts
    • drinking water quality
    • flood control
    • recreational boating
    • habitats for other (native) plants
    • fish and wildlife habitat
    • etc.

Invasive Aquatic Weeds: Control

  • $100,000,000+ per year spent to control aquatic weeds*
  • Common methods of control
    • mechanical
    • chemical
    • biological
  • *Rockwell, H.W., Summary of the literature on the economic impact of aquatic weeds (2003)

Invasive Aquatic Weeds: Biological Control

  • Suppression: classical biological control of invasive plants
    • collect natural enemies (parasites, predators, or pathogens) of an invasive plant from its country of origin
    • release natural enemies into regions of infestation
    • suppress the population density of the invading plant

Invasive Aquatic Weeds: Biological Control

  • Examples of Biological Control Agents
    • herbivores
      • leaf-mining flies
      • weevils
      • grass carp
    • pathogens
      • fungi

Invasive Aquatic Weeds: Biological Control

  • Four host-specific insect biocontrol agents have been introduced in North America to Hydrilla
  • The leaf mining fly H. pakistanae has been the most successful of the four
  • (Doyle et. al., 2002)

Invasive Aquatic Weeds: Biological Control

  • H. pakistanae (species of leaf mining fly)

Invasive Aquatic Weeds: Biological Control

  • H. pakistanae (species of leaf mining fly)
    • small (2 mm in length)
    • Not strong flyers (appear to hop from one leaf to another)
    • lays eggs on a plant (each female produces several hundred eggs during her reproductive period)
    • eggs hatch in 3-4 days and larvae tunnel or mine plant leaves (9 to 12 leaves during 3 larval stages)
    • www.invasive.org/eastern/biocontrol

Invasive Aquatic Weeds: Biological Control

  • H. pakistanae (species of leaf mining fly)
    • pupae are formed within a puparium (pupal stage lasts 6-15 days) and attach to stems
    • adult flies emerge from the puparium and float to the surface in an air bubble
    • total development time is 20-35 days (depends on temperature and nutritional content of the plant)
    • total number of generations per growing season is variable (as high as 7)
    • www.invasive.org/eastern/biocontrol

Invasive Aquatic Weeds: Biological Control

  • H. pakistanae (species of leaf mining fly)
    • Hydrilla plants that are damaged by H. pakistanae appear brown
    • total photosynthetic area of the plant is reduced which reduces growth and vigor
    • damaged hydrilla are less competitive with other plants
    • www.invasive.org/eastern/biocontrol

Invasive Aquatic Weeds: Biological Control

  • 3,000,000+ flies have been released in US (including Lake Conroe and Huntsville state park lake) and have established at most of the release sites (Doyle et. al., 2002)

Invasive Aquatic Weeds: Biological Control

  • In general, there are a number of factors which may suppress the density of a biological control agent such as H. pakistanae
    • abiotic: cold winters, heavy rainfall
    • biotic: natural enemies, poor plant quality
  • This is an active area of research in ecology
  • (Wheeler G.S. and Center T.D., 2001)

Invasive Aquatic Weeds: Biological Control

The LURE Project

  • Generally
  • (more on these later)

The LURE Project

  • Specifically
    • Formulate a dynamical systems model (or models) for the biological control of aquatic weeds by insect herbivory
    • Analyze the model (or models) to investigate how biotic and/or abiotic factors influence success or failure of the biocontrol agent

The LURE Project

  • Problem
    • Formulate and analyze a mathematical model to describe the population dynamics of an aquatic weed and an insect herbivore

The LURE Project

The LURE Project

  • Problem
    • Formulate and analyze a mathematical model to describe the population dynamics of two aquatic weeds competing for resources and an insect herbivore which selectively eats one type of weed but not the other

The LURE Project

  • Problem
    • Increasing plant quality by manipulating nutrient content (fertilizer) may also increase the level of control (damage to plant) by the insect; but there exists a point of diminishing return for which too much fertilizer results in the plants outgrowing the damage from the insects (Cuda, 2008; Coetzee, 2007). Determine if there is an optimal amount of fertilizer that will promote insect herbivory but not decreases in insect density.

The LURE Project

  • Problem
    • Investigate the role that temperature has in the population dynamics of aquatic weeds and insect herbivores.

The LURE Project

  • Reading List (Journal Articles)
    • Coetzee J.A. et. al., Impact of nutrients and herbivory by Eccritotarsus catarinensis on the biological control of water haycinth, Eichhornia crassipes, Aquatic Botany, 2007
    • Cuda, J.P. et. al., Recent advances in biological control of submersed aquatic weeds, Journal of Aquatic Plant Management, 2008
    • Doyle R. et. al., Impact of herbivory by H. pakistanae on growth and photosynthetic potential of Hydrilla, Biological Control, 2002

The LURE Project

  • Reading List (Journal Articles)
    • Doyle R. et. al., Separate and interactive effects of competition and herbivory on the growth, expansion, and tuber formation of Hydrilla verticillata, Biological Control, 2007
    • Wheeler G.S. and Center T.D., The influence of hydrilla leaf quality on larval growth and development of the biological control agent Hydrellia pakistanae, Biological Control, 1996
    • Van, T.K. et. Al., Competitive interactions between Hydrilla and Vallisneria as influenced by insect herbivory, Biological Control, 1998

The LURE Project

  • Reading List (Journal Articles)
    • Wilson, J.R. et. al., Determinants and patterns of population growth in water hyacinth, Aquatic Botany, 2005
    • Shukla V.P., Modeling the dyamics of wetland macrophytes: Keoladeo National Park wetland, India, Ecological Modelling, 1998

The LURE Project

  • Reading List (Journal Articles)
    • Edelstein-Keshet L. and Rausher M.D., The effects of inducible plant defenses on herbivore populations 1. mobile herbivores in continuous time, The American Naturalist, 1989
    • Lewis M.A., Spatial coupling of plant and herbivore dynamics: the contribution of herbivore dispersal to transient and persistent waves of damage, Theoretical Population Biology, 1992
    • Noy-Meir I., Stability of grazing systems: an application of predator-prey graphs, Journal of Ecology, 1975


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