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 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
Population Ecology 20013
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?
Population Ecology 20014
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.
Population Ecology 20015
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.
Population Ecology 20016
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)
Population Ecology 20017
Scissor-tailed flycatcher Carolina wren
Carolina chickadee Redeyed vireoFig. 4.1
Population Ecology 20018
IInhabits a complex region of nhabits a complex region of forest, agricultural fields, and forest, agricultural fields, and
small forest patches.small forest patches.
Population Ecology 20019
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。
Population Ecology 200110
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?
Population Ecology 200111
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.
Population Ecology 200112
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
Population Ecology 200114
13 年蟬的粒腺體基因型有兩型。
Population Ecology 200115
Population DensityPopulation DensityCrude densityEcological density
1
Population Ecology 200116
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
Population Ecology 200117
§§ 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
Population Ecology 200118
(( 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
Population Ecology 200119
( 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
Population Ecology 200120
(( 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
Population Ecology 200121
§§ 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
Population Ecology 200122
──────────────────────── 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
Population Ecology 200123
─────────── 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
Population Ecology 200124
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
Population Ecology 200125
§§ 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
Population Ecology 200126
§§ 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
Population Ecology 200127
§§ 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
Population Ecology 200128
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
Population Ecology 200129
§§ 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
Population Ecology 200130
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
Population Ecology 200131
旅鼠造出旅鼠造出來的通道來的通道
Population Ecology 200132
Dispersion Dispersion
Fig. 4.7 The three possible population dispersion patterns.
2
Population Ecology 200133
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.
Population Ecology 200134
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.
Population Ecology 200135
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
Population Ecology 200136
Table 4.1Table 4.1
• The distribution is not random.
Population Ecology 200137
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 ) 。
Population Ecology 200138
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
Population Ecology 200139
Coarse-Coarse-grained grained or fine-or fine-grained grained habitat habitat
陸棲蝸牛
老鷹
Population Ecology 200140
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。
Population Ecology 200141
Fig. 冠羽雲雀於繁殖季節的地理分佈情況。多層次的類型。
Population Ecology 200142
Age structureAge structure
Fig. 4.11 patterns of tooth wear in deer.
3
Population Ecology 200143
Population Ecology 200144
Population Ecology 200145
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。
Population Ecology 200146
8585 年的研究年的研究saguaro cacti saguaro cacti
in Arizonain Arizona
Population Ecology 200147
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
Population Ecology 200148
mx, the number of live births for individuals of each age.
1000qx ,每千人的死亡率。
Population Ecology 200149
ex is the age-specific life expectancy.
Population Ecology 200150
lx dx 1000qx exlx dx 1000qx ex
Table 4.4 Live Table for U.S. Males (1929-1931)
Population Ecology 200151
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
Population Ecology 200153
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.
Population Ecology 200154
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)
Population Ecology 200155
Population Ecology 200156
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).
Population Ecology 200157
Fig. 4.15 Bird survivorship Fig. 4.15 Bird survivorship curvescurves
(a) Survivorships curves for three species of Turdus.
(b) lapwing
Population Ecology 200158
Population Ecology 200159
Population Ecology 200160
Population Ecology 200161
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
Population Ecology 200162
Population Ecology 200163
Population Ecology 200164
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
Population Ecology 200165
受植被的覆受植被的覆蓋度影響蓋度影響
Population Ecology 200166
受到日期先後受到日期先後的影響的影響Early bird Early bird
hypothesishypothesis
Population Ecology 200167
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 Ecology 200168
Population Ecology 200169
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
Population Ecology 200170
Nt=N0ert
Population Ecology 200171
Population Ecology 200172
A population has constant birth and death rates
Population Ecology 200173
Stable age distribution
Population Ecology 200174
Sigmoid growthSigmoid growth
dN/dt = rNdN/dt = rN (K-N) / KK is the carrying capacity, the maximum
population size the habitat can support.
Population Ecology 200175
dN/dt = rN (K-N) / K
Population Ecology 200176
Population Ecology 200177
Transition matricesTransition matrices-- Leslie matrix-- Leslie matrix
Population Ecology 200178
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)
Population Ecology 200179
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
Population Ecology 200180
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
Population Ecology 200181
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
Population Ecology 200182
Population Ecology 200183
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
Population Ecology 200184
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.
Population Ecology 200185
問題與討論!
ayo@faculty.pccu.edu.tw
Ayo 文化站 http://faculty.pccu.edu.tw/~ayo
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