1、Chapter 6Population Growth生態學的分科：生態學的分科：以生物組織水準來分以生物組織水準來分 個體生態學個體生態學AutecologyAutecology 種群（族群）生態學種群（族群）生態學Population ecologyPopulation ecology 群體（群落）生態學群體（群落）生態學SynecologySynecology:community ecologycommunity ecology 生態系統生態學生態系統生態學Ecosystem ecologyEcosystem ecologyOutline Tabulating changes in pop
2、ulation age structure through time Time-specific life tables Age-specific life tablesOutline Fecundity schedules and female fecundity,and estimating future population growth Population growth models Deterministic models Geometric modelsOutline Population growth models(cont.).Logistic models Stochast
3、ic modelsDemography and Population Demography and Population GrowthGrowthDemography Demography 族群統計學、人口統計學族群統計學、人口統計學The quantitative description of a The quantitative description of a populationpopulationPopulation Population 族群族群A group ofA group of conspecifics conspecifics inhabits a inhabits a
4、specific place at a specific time.specific place at a specific time.The demographic and genetic populations.The demographic and genetic populations are not necessarily the same.are not necessarily the same.Demographic distinction and genetic.Demographic distinction and genetic difference are not nec
5、essarily difference are not necessarily corresponding.corresponding.Demography and Population Demography and Population GrowthGrowth.Population characteristicsPopulation characteristics.Quantitative parameters.Quantitative parameters.Population difference:density,age.Population difference:density,ag
6、e distributiondistribution.Population growth and quantitative.Population growth and quantitative methodsmethods.Population determination factors.Population determination factors.Offspring production and energy invest.Offspring production and energy invest.Population genetics variation.Population gen
7、etics variation.Intrapopulation Intrapopulation behavior behaviorPopulation density Population density 族群密族群密度度.abundant abundant 豐富的豐富的.common common 普遍普遍.rare rare 稀有稀有.endangered endangered 瀕危瀕危(絕絕)的的.extinct extinct 絕滅的絕滅的egeg.Zacco pachycephalusZacco pachycephalus 粗首獵粗首獵(溪哥溪哥)endemic to Taiwan,
8、but common in endemic to Taiwan,but common in west coastswest coastsSampling methods:Sampling methods:.Traps Traps 陷阱陷阱.Fecal pellets Fecal pellets 糞便糞便.Vacuolization frequencies Vacuolization frequencies 鳴叫頻度鳴叫頻度.pelt records pelt records 生皮記錄生皮記錄.Catch per unit effort(CPUE)Catch per unit effort(CP
9、UE)單位努力漁獲單位努力漁獲量量.Percentage ground cover Percentage ground cover 遮蔽度遮蔽度.Frequency of abundance along Frequency of abundance along transects or in quadrants of known area.transects or in quadrants of known area.穿越線或四分區豐度。穿越線或四分區豐度。.Feeding damage Feeding damage 食害程度。食害程度。.Roadside spotting in a stan
10、dard Roadside spotting in a standard distance distance 單位長度內視察的記錄。單位長度內視察的記錄。Estimates of absolute Estimates of absolute density-1density-1.Proportion of population marked=Proportion of population marked=(no.of animals marked at t1)/(total(no.of animals marked at t1)/(total no,of animals in populati
11、on)no,of animals in population).Proportion of sample marked=(no.Proportion of sample marked=(no.of marked animals captured at t2)/of marked animals captured at t2)/(total no.of animals captured at t2)(total no.of animals captured at t2)Estimates of absolute Estimates of absolute density-2density-2If
12、 random sampling,If random sampling,Proportion of population marked=Proportion of population marked=proportion of sample markedproportion of sample markedt1t1標示個體標示個體/族群數量族群數量 t2t2再捕獲標示個體數再捕獲標示個體數/t2t2捕獲數捕獲數（已知數）（未知數）（已知數）（未知數）（已知數）（已知數）（已知數）（已知數）Assumptions:Assumptions:1.1.標記不會對於個體有增加死亡率的危險標記不會對於個體
13、有增加死亡率的危險2.2.標記不會影響再捕捉的機率（記憶與學習）標記不會影響再捕捉的機率（記憶與學習）3.3.實驗期間族群內個體沒有移入或移出的問題實驗期間族群內個體沒有移入或移出的問題4.4.實驗期間沒有死亡或新生的變化實驗期間沒有死亡或新生的變化櫻花鉤吻鮭櫻花鉤吻鮭#13Chapt.06Salmon WatchSkin Diving#14Chapt.06Salmon Watch Skin Diving and Salmon Watch Skin Diving and CountingCounting1800180010901090660660113611366066069419416166
14、1695995925325394394327827856556512271227171817183463464084083428342849449478278272872879679618541854788788115511558578576376372495249518701870638638679679679679050010001500200025003000350040001987S1988S1989S1990S1991S1992S1993S1994S1995S1996S1997S1998S1999S2000S2001S2002S普查時間（：春季；：冬季）數量（尾）瑞伯颱風、芭比絲颱風
15、碧莉絲颱風、象神颱風溫泥颱風賀伯颱風枯水期八月大雨六月大雨九月洪水九月乾旱琳恩颱風韋恩颱風桃芝颱風、納莉颱風七家灣溪流域櫻花鉤吻鮭歷年族群變化圖重大天災以紅色圖說紅色圖說標於圖中歷年最高數量3428尾2000秋繁殖季節遭逢象神颱風1994年以來最低族群數量346尾頭前溪毛蟹頭前溪毛蟹DispersionDispersion分散情形分散情形.random distribution:random distribution:闊葉林中的樹闊葉林中的樹.aggregated:aggregated:草地上的韓國薊草地上的韓國薊.hyperdispersedhyperdispersed,regular in
16、,regular in dispersion:dispersion:繁殖區的海鳥繁殖區的海鳥雪山冷杉林Statistical methods:-1Statistical methods:-1.Poisson distributionPoisson distributionPxPx=a=ax xe e-a-a/x!/x!P=Poisson probability P=Poisson probability x=No.of occurrencesx=No.of occurrencesa=The mean number of occurrencesa=The mean number of occur
17、rencese=The base of the natural loge=The base of the natural log蘭嶼熱帶森林Statistical methods:-2Statistical methods:-2方差方差/平均數比率指標平均數比率指標If sIf s2 2/x/x (mean/variance)1 (mean/variance)1 hyperdispersionhyperdispersionIf sIf s2 2/x/x (mean/variance)1 (mean/variance)1;population is increasing Ro 1;populat
18、ion is decreasing Table 6.3 Reproductive Rate Variation in formula for plants Age-specific fecundity(m )is calculated differently Fx=total number of eggs,seeds,or young deposited nx=total number of reproducing individuals mx=Fx/nx Figure 6.5x Reproductive Rate Variation in formula for plants(cont.).
19、Table 6.4 Reproductive Rate Variation in formula for plants(cont.).Figure 6.6Deterministic Models:Geometric Growth Predicting population growth Need to know;Ro Initial population size Population size at time t Population size of females at next generation=Nt+1=RoNtDeterministic Models:Geometric Grow
20、th Population size(cont.).Ro=net reproductive rate Nt=population size of females at this generationDeterministic Models:Geometric Growth Dependency of Ro Ro 1;population increases Even a fraction above one,population will increase rapidlyoDeterministic Models:Geometric Growth Ro 1;population increas
21、es(cont.).Characteristic“J”shaped curve Geometric growth Figure 6.7100200300400500Population in size(N)0Generations30R =1.20 0R =1.15 0R =1.10 0R =1.05 01020N+1=R N t 0 tDeterministic Models:Geometric Growth Ro 1;population increases(cont.).Something(e.g.,resources)will eventually limit growth Popul
22、ation crash Figure 6.8a19101920193019401950Number of reindeer2000150010005000YearDeterministic Models:Geometric Growth Ro 1;population increases(cont.).Figure 6.8bDeterministic Models:Geometric Growth Ro 1;population increases(cont.).Figure 6.8cDeterministic Models:Geometric Growth Human population
23、growth Prior to agriculture and domestication of animals(10,000 B.C.)Average annual rate of growth:0.0001%Deterministic Models:Geometric Growth After the establishment of agriculture 300 million people by 1 A.D.800 million by 1750 Average annual rate of growth:0.1%Deterministic Models:Geometric Grow
24、th Period of rapid population growth Began 1750 From 1750 to 1900 Average annual rate of growth:0.5%From 1900 to 1950 Average annual rate of growth:0.8%From 1950 to 2000 Average annual rate of growth:1.7%Deterministic Models:Geometric Growth Period of rapid population growth Reasons for rapid growth
25、 Advances in medicine Advances in nutrition Trends in growth(Figure 6.9)1830193019601975198719982009202020332046210001234567891011131214Billions of people2-5 millionYears ago7,000BC6,000BC5,000BC4,000BC3,000BC2,000BC1,000BC1AD1,000AD2,000AD3,000ADYear4,000ADDeterministic Models:Geometric Growth Huma
26、n population statistics Population is increasing at a rate of 3 people every second Current population:over 6 billion UN predicts population will stabilize at 11.5 billion by 2150 Developed countries Average annual rate of growth from 1960-1965:1.19%Deterministic Models:Geometric Growth Human popula
27、tion statistics(cont.).Average annual rate of growth from 1990-1995:0.48%Developing countries Average annual rate of growth from 1960-1965:2.35%Deterministic Models:Geometric Growth Human population statistics(cont.).Developing countries Average annual rate of growth from 1990-1995:2.38%Deterministi
28、c Models:Geometric Growth Fertility rates Average number of live births typically borne by a woman during her lifetime(Table 6.6)Deterministic Models:Geometric Growth Fertility rates(cont.).Theoretic replacement rate:2.0 Actual replacement rate:2.1 Decline in fertility rate 1960-1965:5.0 1990:3.3Det
29、erministic Models:Geometric Growth Overlapping generations Many species in warm climates reproduce continually and generations overlap.Deterministic Models:Geometric Growth Overlapping generations(cont.).Rate of increase is described by a differential equationdN/dt=rN=(b d)N N=population size t=time
30、 r=per capita rate of population growthDeterministic Models:Geometric Growth Overlapping generations(cont.).Rate of increase is described by a differential equationdN/dt=rN=(b d)N b=instantaneous birth rate d=instantaneous death rate dN=the rate of change in numbersDeterministic Models:Geometric Gro
31、wth Rate of increase is described by a differential equation(cont.).dN/dt=the rate of population increase Produces a“J”shaped curve Plot with the natural logarithm,produces a straight line(Figure 6.8)01234520406080100r=0.02r=0.01r=0(equilibrium)Time(t)In(N)Deterministic Models:Geometric Growth r is
32、analogous to Ro In a stable population R=(ln Ro)/Tc Logistic Growth Occurs in populations where resources are or can be limiting Logistic growth equationsTc generation timeDeterministic Models:Geometric Growth Logistic growth equations dN/dt=rN(K-N)/K;ordN/dt=rN1-(N/K)dN/dt=Rate of population change
33、 r=per capita rate of population growth N=population size K=carrying capacity Deterministic Models:Geometric Growth(K-N)/K=unused resources remaining S-Shaped Curve:Figure 6.11As N gets larger,the amount of resources remaining gets smallerWhen N=K,zero growth will occurPopulation sizeKTimeDeterminis
34、tic Models:Geometric Growth Logistic growth assumptions Relation between density and rate of increase is linear Effect of density on rate of increase is instantaneous Environment(and thus K)is constant All individuals reproduce equally No immigration and emigrationDeterministic Models:Geometric Grow
35、th Testing assumptions Early laboratory cultures Pearl 1927 Figure 6.12150300450600750Amount of yeastK=66502468101214161820Time(hrs)Deterministic Models:Geometric Growth Complex studies and temporal effects(cont.).Figure 6.13200400600800TimeNNumber per 12 grams of wheatLogistic curve predicted by th
36、eoryTime(weeks)50100180Callandra oryzaeRhizopertha dominicaDeterministic Models:Geometric Growth Difficulty in meeting assumptions in nature Each individual added to the population probably does not cause an incremental decrease to r Time lags,especially with species with complex life cycles K may v
37、ary seasonally and/or with climateDeterministic Models:Geometric Growth Difficulty in meeting assumptions in nature(cont.).Often a few individuals command many matings Few barriers to prevent dispersal Effect of time lags Robert May(1976)Deterministic Models:Geometric Growth Effect of time lags(cont
38、.).Incorporated time lags into logistic equationdN/dt=rN1-(Nt-t t/K)dN/dt=Rate of population change r=per capita rate of population growth N=population size K=carrying capacityDeterministic Models:Geometric Growth dN/dt=rN1-(N t-t t/K)(cont.).Nt-t t=time lag between the change in population size and
39、 its effect on population growth,then the population growth at time t is controlled by its size at some time in the past,t-t t Nt-t t=population size in the past Ex.r=1.1,K=1000 and N=900 No time lag,new population sizeDeterministic Models:Geometric Growth No time lag,new population size(cont.).dN/d
40、t=1.1 x 900(1 900/1000)=99New population size=900+99=999Deterministic Models:Geometric Growth No time lag,new population size(cont.).With time lag,where a population is 900,although the effects of crowding are being felt as though the population was 800 Still below KdN/dt=1.1 x 900(1 800/1000)=198Ne
41、w population size=900+198=1098Possible for a population to exceed KDeterministic Models:Geometric Growth Effect of response time i.Inversely proportional to r=(1/r)Ratio of time lag(t t)to response time(1/r)or rt t controls population growthrt t is small(0.368)Population increases smoothly to carryi
42、ng capacity(Figure 6.14)KTime(t)Smooth responseKTime(t)Number of individuals(N)KTime(t)Damped oscillationsperiodamplitudeStable limit cycler small(0.368,1.75)Number of individuals(N)Number of individuals(N)Deterministic Models:Geometric Growth rt t is large(1.57)Population enters into a stable oscil
43、lation called a limit cycle Rising and falling around K Never reaching equilibrium rt t is intermediate(0.368 and 2.570)Deterministic Models:Geometric Growth Species with discrete generations Logistic equation(cont.).r is larger than 2.57 Limit cycles breakdown Population grows in a complex,non-repe
44、ating patterns,know as chaosStochastic Models Models are based on probability theory Figure 6.1600.100.200.30Proportion of observations68101214Population sizeStochastic Models Stochastic models of geometric growthdN/dt=rN=(b d)N If b=0.5,d=0,and N0=10,integral form of equationStochastic Models Stoch
45、astic models of integral form of equation Nt=N0ert So for the above example,Nt=10 x 1.649=16.49Stochastic Models Stochastic models of geometric growth(cont.).Path of population growth Figure 6.17Population densityTimeExtinctionPossible stochastic pathStochastic Models Probability of extinction=(d/b)
46、N0 The larger the initial population size The greater the value of b d The more resistant a population is to extinctionStochastic Models Introduce biological variation into calculations of population growth More representative of nature More complicated mathematicsApplied Ecology 1992 Johns Hopkins
47、study Developed countries 70%of couples use contraceptives Developing countries 45%of couples use contraceptives Africa,14%Applied Ecology Developing countries(cont.).Asia,50%Latin America,57%Applied Ecology 1992 Johns Hopkins study(cont.).China 1950s and 1960s Fertility was six children per woman 1
48、970s Government planning and incentives to reduce population growthApplied Ecology China(cont.).1990 75%use birth control Fertility rate dropped to 2.2 Other governments 1976,only 97 governments supported family planningApplied Ecology Other governments(cont.).1988,125 governments supported family p
49、lanning As of 1989,in 31 countries,couples have no access to family planningApplied Ecology Women Women in developing countries want fewer children In virtually every country outside of Saharan Africa,the desireds number of children is below 3Applied Ecology Countries concerned about low growth rate
50、s Some Western European countries and other developed countries Total fertility has dropped below the replacement level of 2.1Applied Ecology Countries concerned about low growth rates(cont.).Reduced populations concerns Affect political strength Economic structureSummary Life tables provide informa
