《生态学》课程PPT教学课件（生态学原理与应用）04 population Growth

POPULATONGROWTH

POPULATION GROWTH

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bLakeplankiomadiatomsand(b)copepodFIGURE9.1

ECOLOGYCONHPZSANDAPPLICATIOASPOPULATIONGROWIRIn the presence of abundantresources,populations cangrowatgeometric or exponential rates

❖ In the presence of abundant resources, populations can grow at geometric or exponential rates

ECOLOGYCONCEPZSANDAPPLICAZIONSPOPULATIONGROWIHGeometric Growth

➢ Geometric Growth

The geometric rateofincreaseX,is theratio of numbers ataNumberslatertime,Nttito numbers atat lateran earliertime.Nrime, t+1Geometric population growthPhlox drummondii(Leverich and Levin,1979Annual plant, insects......N,=Noat(N-No2, N,-N,a=Noaa......)Numbersatearliert+11Latertime,tEarlicrTimetimetimeFIGURE8.IOThegeometricrateofincrease

Geometric population growth Phlox drummondii(Leverich and Levin,1979) Annual plant, insects. Nt = N0 λ t (N1=N0 λ, N2=N1 λ= N0 λ λ. )

Numberatsomeinitialtimetimes2raisedto thepowertN,=NoatN,=NoatNumberof timeintervals,in hours.days, years, ete.AveragenumberofNumber atoffspring leftbyansome timetindividual during onetime intervalFIGURE 9.2 Anatomy of the equationfor geometric populationgrowth

Nt = N0λ t

Growing geometrically,the number ofphlox at any point in time can be2.4177xdetermined using N, = No2' or by480.924=multiplying the previous population1.162.730sizeby2=2.4177.1,200.000N-1162.7301.000,000iooin800.000600.000400.000N=480.924200,0002N=198.9182.4177x0198.918=1024480.9246810YearsFICURE9.3Geometric growth by a hypothetical population of Phloxdrummondii

ECOLOGYCONCEPZSANDAPPLICAZIONSPOPULATIONGROWIRExponential Growth

➢ Exponential Growth

KONOPUSONGAOWTExponentialpopulationgrowthContinuous population growth in an unlimited environment can bemodeled as..dNN- No= rNr(%) = -dtNr>0:r<0:N, = No: ertr=0:

Exponential population growth Continuous population growth in an unlimited environment can be modeled as. = rN dN dt r(%) = Nt - N0 N0 Nt = N0 · ert r > 0 : r < 0 : r = 0 :