chap. 4 demography and population growth 鄭先祐生態主張者 ayo dall mountain sheep in...

Chap. 4 Demography and Chap. 4 Demography and population growthpopulation growth

鄭先祐生態主張者

Ayo

Dall mountain sheep in Alaska

Population Ecology 20012

Chap. 4 Demography and Chap. 4 Demography and population growthpopulation growth

Demography– Defining

populations– Population density– Dispersion – Age structure– Sex ratio

Population Growth– Exponential growth – Sigmoid growth– Transition matrices

Environmental application

•Human demography


Ecologists ask questionsEcologists ask questions ：：1. 族群的特徵？可測定的參項？族群間於密度、年齡分布、等項目，有何差異？2. 族群是如何的成長？族群的成長有何類型？物種間有何差異？有何參項可以測定？3. 族群的個體數量是如何的調控？什麼因素限制族群的數量？有何過程 ( 機制 ) 是可以穩定族群數量？4. 個體的能量如何的分配至其子代？應該要產生多少個子代？ How often? 每次要投入多少能量？5. 族群內的個體變異是如何產生和維持的？6. 族群內個體間的行為是如何的互動？


The applications of Population The applications of Population ecologyecology

If we are to protect species from anthropogenic extinction, we must understand populations and the processes by which they are regulated.

Human also rely on many wild species for food and recreation.

We try to control crop pests, weeds, parasites, and disease agents.


DemographyDemography

Demography is the quantitative description of a population.

Vital statistics of a population ： size, age and sex composition, spatial distribution.

A population is a group of conspecifics inhabiting a specific place at a specific time.

Definition of a population implies to define both its physical and its temporal boundaries.


Physical boundary Physical boundary

The physical boundary of a population is not always so clear-cut.

The number of individuals is not uniformly distributed across the landscape.

There is great spatial variation in bird abundance. Such as frequency distributions of abundance for

four species of passerine birds on breeding bird survey routes (Fig. 4.1)


Scissor-tailed flycatcher Carolina wren

Carolina chickadee Redeyed vireoFig. 4.1


IInhabits a complex region of nhabits a complex region of forest, agricultural fields, and forest, agricultural fields, and

small forest patches.small forest patches.


於 old-growth forest ，族群維持較為穩定。

於 successional forest ，每年冬季都會絕跡。

於 small forest patch ，族群密度可達到非常高。

於 large patch forest ，與 old-growth forest 型況相似。


Populations of Populations of PeromyscusPeromyscus mice mice How should we define a population of white-

footed mice in this landscape? How do we know what part of this landscape is

demographically independent? Do the inhabitants of each region constitute a

separate population? Each has a physical or ecological boundary, Or

should we consider all the mice in the entire region a population?


Physical boundaryPhysical boundaryWe must define the population rationally and

objectively.If we define too narrowly, we neglect the

important influences of other nearby regions.If we define too broadly, we lump together

units that may have separate regulatory mechanisms and effects.

This is a classic problem of scaling.


生態的生態的 vs. vs. 基因的基因的 The idea of a population is an arbitrary construct –

a concept ecologists have invented to designate an ecologically discrete group of individuals.

Ecologically and genetically defined populations do not necessarily coincide. (Fig. 4.2 and Fig. 4.4)

A deme is a local genetically defined population characterized by random mating within the group.

Within a deme, mating occurs within the genetic neighborhood.

Population Ecology 200113 灌木叢


13 年蟬的粒腺體基因型有兩型。


Population DensityPopulation DensityCrude densityEcological density

1


族群密度的估計，是族群變動研究的族群密度的估計，是族群變動研究的重點項目。重點項目。mark-recapture methods ( 標記 - 再捕捉方法 )§ assumptions

– 1. 研究期間內 , 標記永久性 , 且再捕獲時可正確記錄。– 2. 加標記處理後 , 再被捕之機率 , 不變。– 3. 加標記處理後 , 死亡率和遷移率 , 不受影響。– 4. 加標記處理後 , 此個体與其它個体的混合 ( 隨機 , 不會影響其被捕獲率。– 5. 取樣時間相對於調查期間 , 是短的。估計時是 quasi-continuous 實際上是 continuous– 6. (Petersen): no births, no immigrations no deaths, no emigrations

補充


§§ 調查方法與公式調查方法與公式( 一 ) Petersen estimate (1896): Lincoln index (1930) 最簡單，只有一次釋放，一次再捉。 n: total size of recapture m: no of individuals marked (x) r: marked individuals released (M) N: 當時之 population size r n r (n+1)N = ── or N = ──── (Bailey, 1950) m (m+1) r (n+1)(n-m) SE = ─────── (m+1) (m+2) 補充


(( 二二 ) ) Weighted mean Weighted mean 的方法的方法 : : 類似類似 Lincoln Lincoln indexindex

( Mini) (48+52+105) N = ───── = ────── = 34.2 ( mi)+1 (1+2+2)+1

1 2 6 SE = N ──── + ───── + ───── mi + 1 ( mi + 1) ( mi + 1) 例 : Apodemus sylvaticus ( 鼠 ) day i 1 2 3 4 number ni - 6 4 7 marked mi - 1 2 2 release ri 8 6 4 - 全部 Marked Mi - 8 13 15 Mini 48 52 105 補充


( 三 ) Jackson's positive method( 四 ) The triple catch method day 1: marked r1, released. day 2: m21 are marked, all r2 marked and released. day 3: m31 only day 1 mark, m32 include all day 2 mark. 例 : females of the grasshopper.day 1 2 3捕捉 50(n2) 38(n3)day 1-marked 11(m21) 5(m31)day 2-marked 9(m32) 釋放 42(r1) 50(r2) 補充


(( 四四 ) ) The triple catch methodThe triple catch method

m31(r2 + 1) 5 x 51 M21 = ────── + m21 M21 = ──── + 11 =36.5 (m32 + 1) 10

(n2 + 1) M21 51 x 36.5 N2 = ─────── N2 = ───── = 155.1 (m21 + 1) 12

M21 36.5 Φ1 = ─── Φ1 = ─── = 0.87 r1 42

(m31 + 1) n2 6 x 50 b2 = 1 - ────── b2 = 1 - ──── = 0.30 (n3 + 1) m21 39 x 11

SE(N2) = 64.7 SE(Φ1) = 0.32 補充


§§ 調查方法與公式調查方法與公式( 五 ) Jackson's negative method( 六 ) Fisher-Ford method

( 七 ) Jolly's stochastic method-- the most recent mark is noted, all previous marks are ignored.

補充


──────────────────────── Day 捕釋 Time of release of markds, j i ni ri 1 2 3 4 5 6 7 8 9 10 11 12 ────────── recaptured marks, mij ───── 1 - 54 2 146 143 10 3 169 164 3 34 4 209 202 5 18 33 5 220 214 2 8 13 30 6 209 207 2 4 8 20 43 7 250 243 1 6 5 10 34 56 8 176 175 0 4 0 3 14 19 46 9 172 169 0 2 4 2 11 12 28 51 10 127 126 0 0 1 2 3 5 17 22 34 11 123 120 1 2 3 1 0 4 8 12 16 30 12 120 120 0 1 3 1 1 2 7 4 11 16 26 13 142 - - 1 - 2 3 3 2 10 9 12 18 35 ────────────────────────

m6

y6 z6

補充


─────────── Day 釋 i ri mi yi zi ─────────── 1 54 - 24 - m6=2+4+8+20+43=77 2 143 10 80 14 3 164 37 70 57 y6=56+19+12+5+4+2+3=101 4 202 56 71 71 5 214 53 109 89 z6=1+6+5+10+34+0+...+1+0+1+0+2+3=121 6 207 77 101 121 7 243 112 108 110 8 175 86 99 132 9 169 110 70 121 10 126 84 58 107 11 120 77 44 88 12 120 72 35 60 13 - 95 - - ───────────

補充


ziri 121x207 Mi= mi + ─── m6= 77 + ──── = 324.99 yi 101

110 x 243 m7=112 + ───── = 359.50 108

Mi(ni + 1) 324.99 x 210 Ni=────── N6= ────── = 874.97 (mi + 1) 78

359.50 x 251 N7= ────── = 798.54 113 Mi + 1 359.5 Φi = ────── Φ6 = ─────── = 0.79 Mi - mi + ri 325 - 77 +207

Bi = Ni+1 - ΦiNi B6 = 798.5 - 0.79 x 875.0 =107.3 SE(N6) = 94 SE(Φ6) = 0.068 SE(B6) = 75 補充


§§ 處理的方法處理的方法 1. capture -- insects, Southwood (1966) -- freshwater, Lagler (1971) -- amphibians and reptiles, Woodbury (1956) -- mammals, Twigg (1975) -- birds and mammals, Taber and Cowan (1969) 原則 : (1) equal chance of being caught (2) sufficient data

補充


§§ 處理的方法處理的方法2. Handling -- Insects, chloroform, ether, NO2, N2,

CO2

-- fish, MS-222 -- mammals, bag -- birds, darkness 原則：不要受傷害補充


§§ 處理的方法處理的方法3. Marking ( 對象 ) -- insects, Southwood (1966) -- fish, Stott (1977) -- amphibians and reptiles, Woodbury (1956) -- mammals, Twigg (1975) -- mammals and birds, Taber and Cowan

(1969) 補充


4. Marking ( 工具 ) (1) paints: insects--dots color fish-- injecting color dyes (2) dusts: insects (3) mutilation ( 切斷 ) (4) tags and bands (5) radioactive labels 5. Release -- capture, mark and release, during the same period at the same site.

補充


§§ 參考文獻參考文獻 Begon, M. (1979) Investigating animal abundance:

capture-recapture for ecologists. Edward Arnold Limited, London.

Bishop, J. A. and D. J. Hartley (1976) The size and age structure of rural populations of Rattus norvegicus containing individuals resistant to the anti-coagulant poison warfarin. J. Anim. Ecol. 45:623-646.

Lagler, K. F. (1971) Capture, sampling and examination of fishes. In: Methods for Assessment of Fish Production in Fresh Waters. Ricker, W. E. (ed.), Blackwell, Oxford.

Southwood, T. R. E. (1966) Ecological methods. Methuen, London. 補充


Stott, B. (1971) Marking and tagging. In: Methods of Assessment of Fish Production in Fresh Waters. Ricker, W. E. (ed.), Blackwell, Oxford.

Taber, R. D. and Cowan, I. M. (1969) Capturing and marking wild animals. In: Wildlife Management Techniques. Giles, R. H., Jr. (ed.), The Wildlife Society, Washington.

Twigg, G. I. (1975a) Catching mammals. Mammal Rev. 5:83-100.

Twigg, G. I. (1975b) Marking mammals. Mammal Rev. 5:101-116.

Woodbury, A. A. (1956) Uses of marking animals in ecological studies: marking amphibians and reptiles. Ecology 37:670-674.

補充


旅鼠造出旅鼠造出來的通道來的通道


Dispersion Dispersion

Fig. 4.7 The three possible population dispersion patterns.

2


Poisson distributionPoisson distributionPoisson distribution, a mathematical

description of infrequent, random events.We can calculate the Poisson probability (P)

of any given number of occurrences by the formula Px = (ax e-a)/x!

x is the number of occurrencesa is the mean number of occurrencese is the base of the natural logarithms.


蚊子的幼蟲分布於 25 個小池塘。總共有 37 隻幼蟲，平均每個池塘有 1.5 隻幼蟲。

The assumptions of the Poisson distribution are small mean occurrence and that the mean number of occurrences equals the variance in the number of occurrences.


Fig. 4.8 Fig. 4.8 蚊子的幼虫於小池塘蚊子的幼虫於小池塘的分佈的分佈Px = (ax e-a)/x!The expected frequency of pools with two

larvae is P2 = (1.52 e-1.5)/2! = 0.251因為有 25 個小池塘，所以預期會有 0.25

1 x 25 = 6.28 個小池塘有 2 隻幼虫。實際觀察到的是有 4 個池塘有 2 隻幼虫。Ref. Table 4.1


Table 4.1Table 4.1

• The distribution is not random.


Dumped or hyperdispersionDumped or hyperdispersion (n-1)s2/x n is the number of pools s2 is the variance x is the mean number of larvae per pool (n-1)s2/x = (24)(2.68)/1.48 = 43.5 45.5 (df=24) ，顯著性高達 0.05 因為 x/s2 = 1.48/2.68 <1 ，所以 distribution is

dumped. 假若 x/s2 >1 ， diatribution is hyperdispersion.

( 每個小池塘內的幼蟲數目大致相同 ) 。


The effect of quadrate size The effect of quadrate size

Fig. 4.9 The effect of quadrate size on the analysis of dispersion.

(a) 實際分布 (b) 大區塊的樣區，結果呈現是 clumped © 小區塊的樣區，結果呈現的是 random


Coarse-Coarse-grained grained or fine-or fine-grained grained habitat habitat

陸棲蝸牛

老鷹


Fig Clematis 植物的地理分佈之不同層次。從大區域至小地點。這種植物局限於石灰岩 (limestone) 的特殊土壤地區。


Fig. 冠羽雲雀於繁殖季節的地理分佈情況。多層次的類型。


Age structureAge structure

Fig. 4.11 patterns of tooth wear in deer.

3


樹木可用年輪。樹木可用年輪。羊角可以半定年齡。羊角可以半定年齡。鹿可以牙齒的磨損。鹿可以牙齒的磨損。魚類可用魚鱗。魚類可用魚鱗。鳥類的幼鳥可以容易判鳥類的幼鳥可以容易判定。定。


8585 年的研究年的研究saguaro cacti saguaro cacti

in Arizonain Arizona


lxlx ，，存活率存活率dxdx ，，死亡個體數死亡個體數

ll22 = 487/608 = 487/608 =0.801=0.801

ll33 =480/608 =480/608 =0.789=0.789

ll1010 =268/608 =268/608 =0.441=0.441


mx, the number of live births for individuals of each age.

1000qx ，每千人的死亡率。


ex is the age-specific life expectancy.


lx dx 1000qx exlx dx 1000qx ex

Table 4.4 Live Table for U.S. Males (1929-1931)


LLxx = (n = (nxx +n +nx+1x+1)/2)/2 L L22 = (32 + 16)/2 = 24 = (32 + 16)/2 = 24

TTxx = = LLxx TT22 = 24 + 10 + 2 = 36 = 24 + 10 + 2 = 36

eexx = T = Txx/n/nxx e e22 = 36/32 = 1.13 = 36/32 = 1.13

36.0

Population Ecology 200152 一年生植物的 cohort life table


The drawbacks of life tablesThe drawbacks of life tables

The patterns of mortality remain relatively constant over the period of time included in each table.

Any biases in collecting the individuals can skew the life table.

If the year in which the cohort was born turns out to be unusual, or if mortality is abnormally high or low in a subsequent time period, the life table will not accurately reflect the patterns of mortality.


Survivorship curveSurvivorship curve ，， lxlx

Fig. 4.13 Survivorship curves for the data tabulated in Tables 4.2- 4.4. (a) Dall sheep (Table 4.2) (b) female thar (Table 4.3)


Fig. 4.14 Survivorship curves for black-tailed deer Fig. 4.14 Survivorship curves for black-tailed deer (a) and roebuck deer (b).(a) and roebuck deer (b).


Fig. 4.15 Bird survivorship Fig. 4.15 Bird survivorship curvescurves

(a) Survivorships curves for three species of Turdus.

(b) lapwing


Sex RatioSex Ratio

Primary (1o) sex ratio: sex ratio at fertilizationSecondary (2o)sex ratio: sex ratio at birth or

hatchingTertiary (3o)sex ratio: sex ratio at sexual

maturityQuaternary (4o)sex ratio: sex ratio of adult

population

4


Table 4.7 Terms used to describe the presence Table 4.7 Terms used to describe the presence of male and /or female flower partsof male and /or female flower parts


受植被的覆受植被的覆蓋度影響蓋度影響


受到日期先後受到日期先後的影響的影響Early bird Early bird

hypothesishypothesis


R. A. Fisher (1930)R. A. Fisher (1930)

A general theory of the evolution If the two sexes experience the same mortality

rates at birth, the sex ratio should be equal. If one sex experiences higher mortality or requires

parents to invest more energy, then the sex ratio may be skewed.

譬如：雄幼鳥需要較高的親代投資，男性的比率將會偏低。


Population growthPopulation growth

Exponential growth Nt = R0

tN0

– R0 is the net reproductive rate

– R0 = lx mx

dN/dt = rN r =b0 –d0

Nt=N0ert

– r is the intrinsic rate of increase


Nt=N0ert


A population has constant birth and death rates


Stable age distribution


Sigmoid growthSigmoid growth

dN/dt = rNdN/dt = rN (K-N) / KK is the carrying capacity, the maximum

population size the habitat can support.


dN/dt = rN (K-N) / K


Transition matricesTransition matrices-- Leslie matrix-- Leslie matrix


Linear recurrence equationsLinear recurrence equations

N0t+1 = (N0t x b0) + (N1t x b1) + (N2t x b2) + (N3t x b3)

N0t+1 = (N0t x l0)N2t+1 = (N1t x l1)N3t+1 = (N2t x l2)


A population of 660 A population of 660 individualsindividuals

Age(x) Nx bx lx 0 500 0 0.2 1 100 2 0.5 2 50 6 0.3 3 10 8 0.0


Transition matricesTransition matrices

0 2 6 8 500 580 0.2 0 0 0 100 100

0 0.5 0 0 X 50 = 500 0 0.2 0 10 10


Transition matricesTransition matrices

b0 b1 b2 … . bn-1 bn N0t N0t+1

L0 0 0 ….. 0 0 N1t N1t+1

0 l1 0 …… 0 0 N2t N2t+1

. X = .0 0 0 l n-1 0 Nnt Nnt+1


Environmental ApplicationEnvironmental Application

Human DemographyHuman Demography

Fertility rate, age structure and life expectancyFertility rates

– general fertility rate, the number of offspring produced per 1,000 adult females.

– Total fertility rate(TFR), the total number of children a female is expected to bear in her lifetime.

– TFR = 2.0 ，新生子代剛好取代父母– TFR > 2.0 ，新生子代多於父母兩人


Fig. 4B.1 Population age structure diagrams for Fig. 4B.1 Population age structure diagrams for countries with rapid, slow, zero, and negative countries with rapid, slow, zero, and negative

population growth rates.population growth rates.


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chap. 4 demography and population growth 鄭先祐 生態主張者 ayo dall mountain sheep in...

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chap. 4 demography and population growth 鄭先祐生態主張者 ayo dall mountain sheep in...