lure 2009 summer program john alford sam houston state university

LURE 2009 SUMMER PROGRAMLURE 2009 SUMMER PROGRAMJohn AlfordJohn Alford

Sam Houston State UniversitySam Houston State University

Mathematics and BiologyMathematics and Biology

Biology has inspired mathematics for Biology has inspired mathematics for hundreds of yearshundreds of years– Thomas Malthus, Thomas Malthus, An Essay on the An Essay on the

Principle of PopulationsPrinciple of Populations (1798) (1798)population growthpopulation growth

– Gregor Mendel, Gregor Mendel, Experiments in Plant Experiments in Plant HybridizationHybridization (1865) (1865)genetic variationgenetic variation

Mathematical Biology Classic PapersMathematical Biology Classic Papers

Volterra, V.Volterra, V.– Fluctuation in the abundance of a species Fluctuation in the abundance of a species

considered mathematicallyconsidered mathematically, , NatureNature (1926) (1926) Kermack, W.O. and McKendrick, A.G.Kermack, W.O. and McKendrick, A.G.

– Contributions to the mathematical theory of Contributions to the mathematical theory of epidemicsepidemics, , Proc. Roy. Soc.Proc. Roy. Soc. (1927) (1927)

Fisher, R.A.Fisher, R.A.– The wave of advance of advantageous genesThe wave of advance of advantageous genes, ,

Ann. EugenicsAnn. Eugenics (1937) (1937)

Turing, A.M.Turing, A.M.– The chemical basis of morphogenesisThe chemical basis of morphogenesis, , Phil. Phil.

Trans. Roy. Soc. Lond.Trans. Roy. Soc. Lond. (1952) (1952) Hodgkin, A.L. and Huxley, A.F.Hodgkin, A.L. and Huxley, A.F.

– A quantitative description of membrane A quantitative description of membrane current and its application to conduction and current and its application to conduction and excitation in nerveexcitation in nerve, , J. PhysiologyJ. Physiology (1952) (1952)

Rosenzweig, M.L. and MacArthur, R.H.Rosenzweig, M.L. and MacArthur, R.H.– Graphical representation and stability Graphical representation and stability

conditions of predator-prey interactionsconditions of predator-prey interactions, , American NaturalistAmerican Naturalist (1963) (1963)

Mathematical Biology Classic PapersMathematical Biology Classic Papers

Mathematics and BiologyMathematics and Biology

Increases in computing power and Increases in computing power and decreases in computing costs has decreases in computing costs has revolutionized the biological, medical, and revolutionized the biological, medical, and environmental sciences environmental sciences – gene sequencing datagene sequencing data– GPS dataGPS data– etc.etc.

More data has resulted in a greater need More data has resulted in a greater need for mathematical and statistical models to for mathematical and statistical models to interpret it.interpret it.

Invasive Species Invasive Species

red imported fire ant red imported fire ant


zebra mussels zebra mussels


http://www.invasivespeciesinfo.gov/http://www.invasivespeciesinfo.gov/

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



Impact adversely upon biodiversity, Impact adversely upon biodiversity, including decline or elimination of native including decline or elimination of native species - through competition, predation, or species - through competition, predation, or transmission of pathogens - and the transmission of pathogens - and the disruption of local ecosystems and disruption of local ecosystems and ecosystem functions ecosystem functions



Since the 17th century, invasive species Since the 17th century, invasive species have contributed to nearly 40% of all have contributed to nearly 40% of all animal extinctions for which the cause is animal extinctions for which the cause is known known

Invasive Species ControlInvasive Species Control

www.invasivespeciesinfo.govwww.invasivespeciesinfo.gov – The National Invasive Species Information Center (NISIC) The National Invasive Species Information Center (NISIC)

www.texasinvasives.orgwww.texasinvasives.org// – Pulling Together Initiative, a Texas-sized partnership to Pulling Together Initiative, a Texas-sized partnership to

manage non-native invasive plants manage non-native invasive plants www.aquatics.org/www.aquatics.org/

– AERF (aquatic ecosystem restoration foundation) AERF (aquatic ecosystem restoration foundation) http://http://el.erdc.usace.army.milel.erdc.usace.army.mil/aqua//aqua/

– Aquatic Plant Control Research Program (APCRP) US Aquatic Plant Control Research Program (APCRP) US Army Corps of Engineers (see APIS link for simulation Army Corps of Engineers (see APIS link for simulation software)software)

Invasive SpeciesInvasive Species

Invasion StagesInvasion Stages– arrivalarrival

natural or human transportation of a species to a new natural or human transportation of a species to a new areaarea

– establishmentestablishment the forming of a self-sustaining population in the new the forming of a self-sustaining population in the new

areaarea– integrationintegration

invading species forms ecological links with other invading species forms ecological links with other species in the regionspecies in the region

Vermeij, G.J., Vermeij, G.J., An agenda for invasion biology, An agenda for invasion biology, Biological Conservation, Biological Conservation, Biological Biological Conservation, 1996Conservation, 1996


Fire ant being attacked by a phorid flyFire ant being attacked by a phorid fly

Invasive Species ControlInvasive Species ControlParasitic 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 ETIt 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.


Stop the arrival (Stop the arrival (educateeducate the public) the public)– The Ballad of Aquatic Invasive SpeciesThe Ballad of Aquatic Invasive Species

by Scott Gatzkeby Scott Gatzke

Ballad_of_AIV.mp3


Once arrival has occurred, the Once arrival has occurred, the control options includecontrol options include– eradicationeradication– suppresion (reducing invading suppresion (reducing invading

population densities)population densities)– slowing the spreadslowing the spread

Invasive Aquatic WeedsInvasive Aquatic Weeds

Invasive aquatic weedsInvasive aquatic weeds– Hydrilla verticillataHydrilla verticillata

submersed submersed

– water hyacinthwater hyacinth floatingfloating

– giant salviniagiant salvinia free-floating fernfree-floating fern

– many, many moremany, many more

Invasive Aquatic Weed: Invasive Aquatic Weed: HydrillaHydrilla

Invasive Aquatic Weed: Invasive Aquatic Weed: Water HyacinthWater Hyacinth

Invasive Aquatic Weed: Invasive Aquatic Weed: Giant SalviniaGiant Salvinia

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

Invasive Aquatic WeedsInvasive Aquatic Weeds

Negative impactsNegative impacts– drinking water qualitydrinking water quality– flood controlflood control– recreational boatingrecreational boating– habitats for other (native) plantshabitats for other (native) plants– fish and wildlife habitatfish and wildlife habitat– etc.etc.

Invasive Aquatic Weeds: ControlInvasive Aquatic Weeds: Control

$100,000,000+ per year spent to control $100,000,000+ per year spent to control aquatic weeds*aquatic weeds*

Common methods of control Common methods of control – mechanicalmechanical– chemicalchemical– biologicalbiological

*Rockwell, H.W., *Rockwell, H.W., Summary of the literature on the Summary of the literature on the economic impact of aquatic weedseconomic impact of aquatic weeds (2003) (2003)

Invasive Aquatic Weeds: Biological ControlInvasive Aquatic Weeds: Biological Control

Suppression: classical biological Suppression: classical biological control of invasive plantscontrol of invasive plants– collect natural enemies (parasites, collect natural enemies (parasites,

predators, or pathogens) of an invasive predators, or pathogens) of an invasive plant from its country of originplant from its country of origin

– release natural enemies into regions of release natural enemies into regions of infestationinfestation

– suppress the population density of the suppress the population density of the invading plantinvading plant


Examples of Biological Control AgentsExamples of Biological Control Agents– herbivoresherbivores

leaf-mining fliesleaf-mining flies weevilsweevils grass carpgrass carp

– pathogenspathogens fungifungi


Four host-specific insect biocontrol Four host-specific insect biocontrol agents have been introduced in agents have been introduced in North America to HydrillaNorth America to Hydrilla

The leaf mining fly The leaf mining fly H. pakistanaeH. pakistanae has has been the most successful of the fourbeen the most successful of the four

((Doyle et. al., 2002)Doyle et. al., 2002)


H. pakistanaeH. pakistanae (species of leaf mining fly) (species of leaf mining fly)


H. pakistanaeH. pakistanae (species of leaf mining fly) (species of leaf mining fly)– small (2 mm in length)small (2 mm in length)– Not strong flyers (appear to hop from one leaf Not strong flyers (appear to hop from one leaf

to another)to another)– lays eggs on a plant (each female produces lays eggs on a plant (each female produces

several hundred eggs during her reproductive several hundred eggs during her reproductive period)period)

– eggs hatch in 3-4 days and larvae tunnel or eggs hatch in 3-4 days and larvae tunnel or mine plant leaves (9 to 12 leaves during 3 mine plant leaves (9 to 12 leaves during 3 larval stages)larval stages)

www.invasive.org/eastern/biocontrolwww.invasive.org/eastern/biocontrol


H. pakistanaeH. pakistanae (species of leaf mining fly) (species of leaf mining fly)– pupae are formed within a puparium (pupal pupae are formed within a puparium (pupal

stage lasts 6-15 days) and attach to stemsstage lasts 6-15 days) and attach to stems– adult flies emerge from the puparium and float adult flies emerge from the puparium and float

to the surface in an air bubbleto the surface in an air bubble– total development time is 20-35 days (depends total development time is 20-35 days (depends

on temperature and nutritional content of the on temperature and nutritional content of the plant)plant)

– total number of generations per growing total number of generations per growing season is variable (as high as 7)season is variable (as high as 7)



H. pakistanaeH. pakistanae (species of leaf mining fly) (species of leaf mining fly)– Hydrilla plants that are damaged by Hydrilla plants that are damaged by H. H.

pakistanaepakistanae appear brown appear brown– total photosynthetic area of the plant is total photosynthetic area of the plant is

reduced which reduces growth and vigorreduced which reduces growth and vigor– damaged hydrilla are less competitive damaged hydrilla are less competitive

with other plantswith other plants



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


In general, there are a number of In general, there are a number of factors which may suppress the factors which may suppress the density of a biological control agent density of a biological control agent such as such as H. pakistanae H. pakistanae – abiotic: cold winters, heavy rainfallabiotic: cold winters, heavy rainfall– biotic: natural enemies, poor plant biotic: natural enemies, poor plant

qualityquality This is an active area of research in This is an active area of research in

ecology ecology

(Wheeler G.S. and Center T.D., 2001)(Wheeler G.S. and Center T.D., 2001)

The LURE ProjectThe LURE Project

GenerallyGenerally– Learn some fundamental principles of Learn some fundamental principles of

nonlinear dynamical systemnonlinear dynamical system – Learn some fundamental principles of Learn some fundamental principles of

mathematical ecologymathematical ecology

(more on these later)(more on these later)


SpecificallySpecifically– Formulate a dynamical systems model Formulate a dynamical systems model

(or models) for the biological control of (or models) for the biological control of aquatic weeds by insect herbivoryaquatic weeds by insect herbivory

– Analyze the model (or models) to Analyze the model (or models) to investigate how biotic and/or abiotic investigate how biotic and/or abiotic factors influence success or failure of factors influence success or failure of the biocontrol agentthe biocontrol agent


ProblemProblem– Formulate and analyze a Formulate and analyze a

mathematical model to mathematical model to describe the population describe the population dynamics of an aquatic weed dynamics of an aquatic weed and an insect herbivoreand an insect herbivore


ProblemProblem

– Formulate and analyze a Formulate and analyze a mathematical model to mathematical model to describe the population describe the population dynamics of two aquatic weeds dynamics of two aquatic weeds competing for resourcescompeting for resources


ProblemProblem– Formulate and analyze a Formulate and analyze a

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


ProblemProblem– Increasing plant quality by manipulating Increasing plant quality by manipulating

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


ProblemProblem– Investigate the role that temperature Investigate the role that temperature

has in the population dynamics of has in the population dynamics of aquatic weeds and insect herbivores.aquatic weeds and insect herbivores.


Reading List (Journal Articles)Reading List (Journal Articles)– Coetzee J.A. et. al., Coetzee J.A. et. al., Impact of nutrients and Impact of nutrients and

herbivory by Eccritotarsus catarinensis on the herbivory by Eccritotarsus catarinensis on the biological control of water haycinth, Eichhornia biological control of water haycinth, Eichhornia crassipes, crassipes, Aquatic Botany, 2007Aquatic Botany, 2007

– Cuda, J.P. et. al., Cuda, J.P. et. al., Recent advances in biological Recent advances in biological control of submersed aquatic weeds, control of submersed aquatic weeds, Journal of Journal of Aquatic Plant ManagementAquatic Plant Management, 2008, 2008

– Doyle R. et. al., Doyle R. et. al., Impact of herbivory by H. Impact of herbivory by H. pakistanae on growth and photosynthetic pakistanae on growth and photosynthetic potential of Hydrilla, potential of Hydrilla, Biological Control, 2002Biological Control, 2002


Reading List (Journal Articles)Reading List (Journal Articles)– Doyle R. et. al.,Doyle R. et. al., Separate and interactive Separate and interactive

effects of competition and herbivory on the effects of competition and herbivory on the growth, expansion, and tuber formation of growth, expansion, and tuber formation of Hydrilla verticillata, Hydrilla verticillata, Biological Control, 2007Biological Control, 2007

– Wheeler G.S. and Center T.D., Wheeler G.S. and Center T.D., The influence of The influence of hydrilla leaf quality on larval growth and hydrilla leaf quality on larval growth and development of the biological control agent development of the biological control agent Hydrellia pakistanaeHydrellia pakistanae, Biological Control, 1996, Biological Control, 1996

– Van, T.K. et. Al., Van, T.K. et. Al., Competitive interactions Competitive interactions between Hydrilla and Vallisneria as influenced between Hydrilla and Vallisneria as influenced by insect herbivoryby insect herbivory, Biological Control, 1998, Biological Control, 1998


Reading List (Journal Articles)Reading List (Journal Articles)– Wilson, J.R. et. al.,Wilson, J.R. et. al., Determinants and Determinants and

patterns of population growth in water patterns of population growth in water hyacinth, Aquatic Botany, 2005hyacinth, Aquatic Botany, 2005

– Shukla V.P.,Shukla V.P., Modeling the dyamics of Modeling the dyamics of wetland macrophytes: Keoladeo wetland macrophytes: Keoladeo National Park wetland, India, Ecological National Park wetland, India, Ecological Modelling, 1998Modelling, 1998


Reading List (Journal Articles)Reading List (Journal Articles)

– Edelstein-Keshet L. and Rausher M.D., Edelstein-Keshet L. and Rausher M.D., The effects of The effects of inducible plant defenses on herbivore populations 1. inducible plant defenses on herbivore populations 1. mobile herbivores in continuous time, mobile herbivores in continuous time, The American The American NaturalistNaturalist, , 19891989

– Lewis M.A., Lewis M.A., Spatial coupling of plant and herbivore Spatial coupling of plant and herbivore dynamics: the contribution of herbivore dispersal to dynamics: the contribution of herbivore dispersal to transient and persistent waves of damage, transient and persistent waves of damage, Theoretical Theoretical Population Biology, 1992Population Biology, 1992

– Noy-Meir I., Noy-Meir I., Stability of grazing systems: an application of Stability of grazing systems: an application of predator-prey graphspredator-prey graphs, Journal of Ecology, 1975, Journal of Ecology, 1975

lure 2009 summer program john alford sam houston state university

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