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外国数学建模一篇
TheInterdisciplinaryContestinModeling2001Problem
CopyrightCOMAP2001
Pleasenotethatwhilelinksareindicatedthedataisprovidedonthepagesfollowingthe
problem.
2001InterdisciplinaryContestinModeling
ICM2001Problem
Zebramussels,Dreissenapolymorpha,aresmall,fingernail-sized,
freshwatermollusksunintentionallyintroducedtoNorthAmericavia
ballastwaterfromatransoceanicvessel.Sincetheirintroductioninthe
mid1980s,theyhavespreadthroughalloftheGreatLakesandtoan
increasingnumberofinlandwaterwaysintheUnitedStatesandCanada.
Zebramusselscolonizeonvarioussurfaces,suchasdocks,boathulls,
commercialfishingnets,waterintakepipesandvalves,nativemollusks
andotherzebramussels.Theironlyknownpredators,somedivingducks,
freshwaterdrum,carp,andsturgeon,arenotnumerousenoughtohavea
significanteffectonthem.Zebramusselshavesignificantlyimpactedthe
GreatLakesecosystemandeconomy.Manycommunitiesaretryingto
controloreliminatetheseaquaticpests.SOURCE:
GreatLakesSeaGrant
Networkhttp:
//www.sgnis.org/.
Researchersareattemptingtoidentifytheenvironmentalvariables
relatedtothezebramusselinfestationinNorthAmericanwaterways.
Therelevantfactorsthatmaylimitorpreventthespreadofthezebra
musselareuncertain.Youwillhaveaccesstosomereferencedatato
ildlitiflhildbtithtt
OurWaterways-AnUncertainFuture
TheInterdisciplinaryContestinModeling2001Problem
CopyrightCOMAP2001
includelistingsofseveralchemicalsandsubstancesinthewatersystem
thatmayaffectthespreadofthezebramusselthroughoutwaterways.
Additionally,youcanassumeindividualzebramusselsgrowatarateof
15millimetersperyearwithalifespanbetween4-6years.Thetypical
musselcanfilter1literofwatereachday.
RequirementA:
Discussenvironmentalfactorsthatcouldinfluencethe
spreadofzebramussels.
RequirementB:
Utilizingthechemicaldataprovidedat:
ap/undergraduate/contests/icm/imagesdata/LakeAChem1.xls,
andthemusselpopulationdataprovidedat:
ap/undergraduate/contests/icm/imagesdata/LakeAPopulation1.xls
modelthepopulationgrowthofzebramusselsinLakeA.Besureto
reviewtheInformationaboutthecollectionofthezebramussel
data.
RequirementC:
UtilizingadditionaldataonLakeAfromanotherscientist
providedat:
ap/undergraduate/contests/icm/imagesdata/LakeAChem2.xls
andadditionalmusselpopulationdataprovidedat:
ap/undergraduate/contests/icm/imagesdata/LakeAPopulation2.xls
corroboratethereasonablenessofyourmodelfromRequirementB.Asa
resultofthisadditionaldata,adjustyourearliermodel.Analyzethe
performanceofyourmodel.Discussthesensitivityofyourmodel.
RequirementD:
UtilizingtheChemicaldatafromtwolakes（LakeBand
LakeC）intheUnitedStatesprovidedat
ap/undergraduate/contests/icm/imagesdata/LakeB.xls
and
ap/undergraduate/contests/icm/imagesdata/LakeC.xls
determineiftheselakesarevulnerabletothespreadofzebramussels.
Discussyourprediction.
RequirementE:
ThecommunityinthevicinityofLakeB（inrequirement
D）isconsideringspecificpoliciesforthede-icingofroadwaysnearthe
lakeduringthewinterseason.Provideguidancetothelocalgovernment
officialsregardingapolicyon.de-icingagents..Inyourguidanceinclude
predictionsonthelong-termimpactofde-icingonthezebramussel
population.
TheInterdisciplinaryContestinModeling2001Problem
CopyrightCOMAP2001
pp
RequirementF:
Ithasbeenrecommendedbyalocalcommunityinthe
UnitedStatestointroduceroundgobyfish.Zebramusselsarenotoften
eatenbynativefishspeciessotheyrepresentadeadendecologically.
However,roundgobiesgreaterthan100mmfeedalmostexclusivelyon
zebramussels.Ironically,becauseofhabitatdestruction,thegobyis
endangeredinitsnativehabitatoftheBlackandCaspianSeasinRussia.
Inadditiontoyourtechnicalreport,includeacarefullycraftedreport（3-
pagemaximum）writtenexplicitlyforthelocalcommunityleadersthat
respondstotheirrecommendationtointroducetheroundgoby.Also
suggestwaystohelpreducethegrowthofthemusselwithinandamong
waterways.
Informationaboutthecollectionofthezebramusseldata
ThedevelopmentalstateoftheZebramusseliscategorizedbythreestages:
veligers（larvae）,settlingjuveniles,andadults.Veligers（microscopiczebramussel
larvae）arefree-swimming,suspendedinthewaterforonetothreeweeks,after
whichtheybeginsearchingforahardsurfacetoattachtoandbegintheiradultlife.
Lookingforzebramusselveligersisdifficultbecausetheyarenoteasilyvisibleby
thenakedeye.Settledjuvenilezebramusselscanbefeltonsmoothsurfaceslike
boatsandmotors.Anadvancedzebramusselinfestationcancoverasurface,even
formingthickmatssometimesreachingveryhighdensities.Thedensityofjuveniles
wasdeterminedalongthelakeusingthree15X15cmsettlingplates.Thetopplate
remainedinthewaterfortheentiresamplingseason（S-seasonal）toestimate
seasonalaccumulation.Themiddleandbottomplatesarecollectedafterspecific
periods（A.alternating）oftimedenotedby.LakeDays.inthedatafiles.
Thesettlingplatesareplacedunderthemicroscopeandalljuvenilesonthe
undersidesoftheplatearecountedanddensitiesarereportedasjuveniles/m2.
TheInterdisciplinaryContestinModeling2001Problem
Belowischemicaldatathatwascollectedbetween1992and1999onLakeAat10differentsites.
Thesitesrangefromsouthernlocations（site1）tonorthernlocations（site10）.
Thezebramusselwasfirstintroducedinthesouthernportionofthelake.
LakeLocationTestMinimum
Value
25th
Percentile
Population
Median
75th
Percentile
Maximum
Value
1Alk63.881.686.891.9104.5
1Ca23.224.826.827.227.5
1Chl-a0.694.136.279.4515.55
1Cl9.313.115.317.927
1Fe301381501595963
1K11.21.21.32.3
1Mg5.15.76.66.76.7
1Na6.89.411.412.612.9
1pH6.587.547.687.838.58
1Secchi0.20.60.91.11.8
1Temp8.516.120.221.724.2
LakeLocationTestMinimum
Value
25th
Percentile
Population
Median
75th
Percentile
Maximum
Value
2Alk51.766.372.476.388.9
2Ca1821.622.322.723.2
2Chl-a1.413.845.527.6222.94
2Cl9.613.214.918.231.8
2Fe5083143539709
2K1.31.41.51.52
2Mg4.55.15.25.46.2
2Na9.310.613.415.620.6
2pH6.837.7988.258.68
Chloride
Iron
Potassium
Magnesium
LakeTest
Alkalinity
Calcium
Chlorophyll
Mg
pH
SecchiDisk
Tranparency
Temperature
Sodiummg/L
Temp
Abbreviation
Alk
Ca
Chl-a
Cl
Fe
K
Na
mg/L
ug/L
mg/L
mg/L
UNITS
mg/LasCaCO3
mg/L
ug/L
pH
meters
oC
Secchi
pH
Belowyoufindzebramusselpopulationdatathatwascollectedat10differentsitesonLakeA.
Thesitesrangefromsouthernlocations（site1）tonorthernlocations（site10）.
ThezebramusselwasfirstintroducedinthesouthernportionoftheLakeA.
SeeFile:
Collectionforinformationoncollectioningzebramusseldata
LakeTestAbbreviationUnits
TypeofPlateQAA-Alternating
S-Seasonal
DaysintheWaterLakeDaysDays
DensityofjuvenilesDensityjuveniles/m2
LakeLocationDateQALakeDaysDensity
17/12/1994A31133
17/18/1994A370
19/2/1994A46133
19/21/1994A65133
111/2/1994A82578
111/2/1994S1542,089
17/12/1995A28222
17/25/1995A13178
18/22/1995A283,378
19/12/1995A21694,000
110/18/1995S98498,000
110/18/1995S98354,000
110/18/1995A36604,000
16/24/1996A190
19/3/1996A14116,000
19/17/1996A28440,000
19/30/1996A2722,978
111/4/1996A482,311
111/4/1996A354,400
111/4/1996S105386,000
16/4/1997A300
16/18/1997A2780,000
17/2/1997A2842,000
17/17/1997A292,622
18/1/1997A301,778
18/18/1997A3252,000
19/4/1997A34398,000
19/19/1997A32318,000
110/8/1997S156146,489
110/8/1997A3446,000
110/8/1997A1911,200
15/29/1998A304,267
16/17/1998A3410,889
17/7/1998A395,600
17/20/1998A3323,467
18/3/1998A2713,378
18/20/1998A3180,000
LakeAChem2--ThischemicaldataonLakeAwasprovidedbyanotherresearcher
LakeLocationDateStratumTDPCaMgTNTempChl-a
15/13/1992U0.030.010.58
15/26/1992U0.050.020.7015.80
16/11/1992U0.050.020.6921.3010.18
16/23/1992U0.060.020.5120.004.69
17/15/1992U0.060.010.7321.90
17/28/1992U0.050.010.6722.40
18/11/1992U0.050.010.7322.50
18/25/1992U0.050.010.5421.506.43
19/17/1992U0.060.020.5720.407.50
110/6/1992U0.060.010.6312.20
110/30/1992U0.060.020.57
15/4/1993U0.010.010.4214.10
16/1/1993U0.040.010.3917.30
16/8/1993U0.040.010.4017.50
16/30/1993U0.050.010.49
17/14/1993U0.090.020.79
18/5/1993U0.080.010.57
18/13/1993U0.060.010.36
18/19/1993U0.050.010.48
18/26/1993U0.060.01
19/2/1993U0.080.010.4423.50
19/22/1993U0.070.010.5416.10
110/6/1993U0.050.010.45
ug/L
mg/L
ug/L
mg/L
oC
UNITS
Samplesareobtainedfromboth
theEpilimnion（E）,（thetopmost
andwarmestlayerofwater）,and
theHypolimnion（H）（thecold
deepwaterlayer）and
Unstratified（U）.
mg/L
mg/L
Chlorophyll
Abbreviation
U/E/H
TP
DP
TN
Temp
Chl-a
Ca
Mg
Calcium
Magnesium
TotalNitrogen
Temperature
LakeTest
Stratum
TotalPhosphorus
DissolvedPhosphorus
LakeAPopulation2--NewResearcherInformation
Belowyoufindzebramusselpopulationdatathatwascollectedat10differentsitesonLakeA.
Thesitesrangefromsouthernlocations
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