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1、Lecture 10: Population Growth,http:/ 起重机 立体停车设备 电动葫芦 http:/ 衬塑复合管 涂塑复合管 钢塑复合管 消防涂覆钢管,World population,Population growth,Definition: how the number of individuals in a population increases or decreases with time Growth is controlled by rates of birth, immigration and death and emigration. Open or clo
2、sed population: no immigration and emigration, or immig.=emig. In closed population, growth is determined by birth rate and death rate.,10.1 Population growth reflects the difference between rates of birth and death,Model development A population of freshwater hydra growing in an aquarium in the lab
3、oratory. Population size N(t) when time is t. This is a closed population. Population size change is related to birth rate (b) and death rate (d) dN/dt=(b-d)N=rN The difference between birth rate and death rate is the intrinsic growth rate (r) (instantaneous per capita rate of growth). r=b-d,In a cl
4、osed population, population size change is related to birth rate (b) and death rate (d) The difference between birth rate and death rate is the intrinsic growth rate (r) (instantaneous per capita rate of growth). r=b-d Population growth is related to this intrinsic growth rate (r).,Exponential popul
5、ation growth,Equations: 1) dN/dt=rN (differential equation form) 2) N(t)=N(0) exp(rt) (exponential growth model) Conditions: Initial population is small No food or resource limitation,An example,Reindeer, St. Paul, Alaska.,Started in 1910 with only 4 males and 22 females In 1940, there were nearly 2
6、000,Whooping crane, an endangered species recovered from near extinction in 1941,How to calculate r? Software, Excel (trendline),Aransas National Wildlife Refuge,Properties of exponential growth,r determines the shape of the growth. r=0, no change in population size r0, increase in population size.,
7、Properties of exponential growth,Widely used in biology,N(t)=N(0)Exp(rt) Give a time t, we can predict the population size. An Example: Deer population: N(0)=300, r=0.5, after 5 years, whats the population size? N(5)=N(0)Exp(rt)=300*exp(0.5*5)=3655 (495, 815, 1344, 2216, 3655) t=10, ?,Prediction of
8、population growth,44524,10.2 Life table,Life table is an age-specific account of mortality. Purpose of life table: to provide a clear and systematic picture of mortality and survival within a population,How to construct a life table?,1. start with a cohort: a group of individuals born in the same pe
9、riod of time; 2. Add a column of lx as the probability at birth of surviving to any given age;,How to construct a life table (cont.)?,3. calculate dx, a measure of age-specific mortality 4. Calculate age-specific mortality rate, qx,10.3 Different types of life table,Two types Cohort or dynamic life
10、table as the above gray squirrel Time-specific life table,Elf opine,10.4 Life tables provide data for mortality and survivorship curves,Table is better than words, but a graph is worth one thousand words. Mortality curve and survivorship curve.,Mortality curves,Survivorship curves,Log scale for Y ax
11、is,Three basic types of survivorship,Type I (convex) Humans and other mammals and some plants (k-selection) Type II (survival rates do not vary with age) Adult birds, rodent, and reptiles, perennial plants Type III. Concave Mortality rate high in the beginning (r-selection) Oysters, Fish, many plant
12、 species (most trees),10.5 Birthrate is age-specific,Crude birthrate (demographers): # of birth over a period of time divided by population size at the beginning of the period*1000 Age-specific birthrates, bx Mean # of females birth to a female in each age group. (Only females give birth; birth rate
13、s vary with ages) Gross reproduction rate: sum of the bx values across all age classes, provides an estimate of average offspring born to a female over her lifetime.,10.6 Birth rate and survivorship determine net reproductive rate,Fecundity table: take survivorship column, lx, from life table and ad
14、d age-specific birthrate, bx. Net reproduction rate, R0: number of female offspring a female at birth can produce (or average # of females that will be produced (left) during a lifetime by a newborn females.),R0: depends on survivorship and fecundity R0=1, 1 or 1,10.7 Project population growth,Given
15、 a population with age structure and some other information (age-specific mortality rates and birthrates), we can project future changes of the population size. For example, a population of squirrel with 10 adults (1-yr) and 20 juveniles females, what would happen in the next 10 years?,What do we ne
16、ed to project future population size change?,Calculate age-specific survivor rate: sx=1-qx bx is age-specific birthrate,How to construct a population projection table?,How to construct a population projection table?,Population size (N) increases every year. Lambda (finite multiplication rate): =N(t+
17、1)/N(t).,Age distribution,Stable age distribution: by year 7, the proportion of each age group remain the same year after year. Population is still growing.,Geometric growth vs exponential growth,N(t)=N(0) t N(t)=N(0)exp(rt) =exp(r) or r=ln() These models are used to describe dynamics of populations
18、. Geometric growth is used for population generations not overlap (discrete time interval), exponential growth model is for continuous population.,Fig. 11.3,10.8 Stochastic processes can influence population dynamics,Whats stochastic process? Deterministic process: Given a set of initial conditions
19、(N(0), r), the exponential growth will predict only one exact outcome. But the age-specific mortality rates, birth rates represent probability and averages derived from the cohort or population under study (bx=2? 0,1,2,3).,Stochasticity,Demographic stochasticity: stochastic (or random) variations in
20、 birth and death rates that occur in populations from year to year. (Cause change in r). Environmental stochasticity: Random variation in the environment, such as annul variation in climate and natural disasters can have a direct influence on average birth and death rates within the population.,10.9
21、 Population extinction,If r becomes negative (birth rate death rate), population declines and will go extinction. Factors: Extreme environmental events (droughts, floods, cold or heat etc), loss of habitat (human). Small populations are susceptible to extinction,Allee effect, genetic drift, inbreedi
22、ng (mating between relatives),Overgraze, only 8 in 1950,Hackney and McGraw (West Virginia University) examined the reproductive limitations by small population size on American ginseng (Panax quinquefolius) Fruit production per plant declined with decreasing population size due to reduced visitation
23、 by pollination,Small population size may result in the breakdown of social structures that are integral to successful cooperative behaviors (mating, foraging, defense) The Allee effect is the decline in reproduction or survival under conditions of low population density There is less genetic variat
24、ion in a small population and this may affect the populations ability to adapt to environmental change,END,Geometric Growth,When generations do not overlap, growth can be modeled geometrically. Nt = Not Nt = Number of individuals at time t. No = Initial number of individuals. = Geometric rate of increase. t = Number of time intervals or generations.,Exponential Growth,Continuous population growth in an unlimited environment can be modeled exponentially. Appropriate for populations with overlapping generations. As population size increases, rate of population increase gets larger.,