世界人口分布分析

Lecture 10: Population GrowthWorld populationPopulation 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 closed 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 inthe laboratory.⏹Population size N(t) when time is t.⏹This is a closed population.⏹Population size change is related to birth rate (b) and deathrate (d)⏹dN/dt=(b-d)N=rN⏹The difference between birth rate and death rate is theintrinsic growth rate (r) (instantaneous per capita rate of growth).r=b-d⏹In a closed 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 population growth⏹Equations:❿1) dN/dt=rN (differential equation form)❿2) N(t)=N(0) exp(rt) (exponential growth model)⏹Conditions:❿Initial population is small❿No food or resource limitationAn exampleReindeer, St. Paul, Alaska. Started in 1910 with only 4 males and 22 femalesIn 1940, there were nearly 2000Whooping crane, anendangered speciesrecovered from nearextinction in 1941How to calculate r?Software, Excel (trendline) Aransas National Wildlife RefugeProperties of exponential growthr determines the shape of the growth.r=0, no change in population size r<0, decrease in population size; r>0, increase in population size.Properties of exponential growthWidely used in biologyN(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, what’s the population size?N(5)=N(0)Exp(rt)=300*exp(0.5*5)=3655(495, 815, 1344, 2216, 3655) t=10, ?Prediction of population growth 4452410.2 Life table⏹Life table is anage-specificaccount ofmortality.⏹Purpose of lifetable: to provide aclear andsystematic pictureof mortality andsurvival within apopulationHow to construct a life table?⏹1. start with acohort: a group ofindividuals born inthe same period oftime;⏹2. Add a column ofl x as the probabilityat birth ofsurviving to anygiven age;How to construct a life table (cont.)?⏹3. calculate d x, ameasure of age-specific mortality⏹4. Calculate age-specific mortalityrate, q x10.3 Different types of life table⏹Two types❿Cohort or dynamic life table⏹as the above gray squirrel❿Time-specific life tableElf opine10.4 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 curvesSurvivorship curves Log scale for Y axisThree basic types of survivorshipType I (convex)Humans and othermammals and someplants (k-selection)Type II (survival rates donot vary with age)Adult birds, rodent, andreptiles, perennial plantsType III. ConcaveMortality rate high in thebeginning (r-selection)Oysters, Fish,many plant species (mosttrees)10.5 Birthrate is age-specificCrude birthrate(demographers): # of birthover a period of time dividedby population size at thebeginning of the period*1000Age-specific birthrates, b xMean # of females birth to a female ineach age group.(Only females give birth; birth ratesvary with ages)Gross reproduction rate: sumof the bx values across allage classes, provides anestimate of average offspringborn to a female over herlifetime.10.6 Birth rate and survivorship determine net reproductive rate ⏹Fecundity table: take survivorship column, l x , from life table and add age-specific birthrate, b x .⏹Net reproduction rate, R 0: 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.)⏹R 0: depends on survivorship and fecundity ⏹R0=1, >1 or <110.7 Project population growth⏹Given 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 with10 adults (1-yr) and 20 juveniles females, what would happen in the next 10 years?What do we need to project future population size change?Calculate age-specific survivor rate: sx=1-qxbx is age-specific birthrateprojection table?projection table?Population size (N) increases every year.Lambda (finite multiplication rate): =N(t+1)/N(t).Age distributionStable age distribution: by year 7, the proportion of each age group remain the same year after year.Population is still growing.Geometric growth vs exponentialgrowth⏹N(t)=N(0) λt⏹N(t)=N(0)exp(rt)⏹λ=exp(r) or r=ln(λ)⏹These models are used to describe dynamics of populations. Geometric growth is used for population generations not overlap (discrete time interval), exponential growth model is for continuous population.Fig. 11.310.8 Stochastic processes caninfluence population dynamics ⏹What’s stochastic process?⏹Deterministic process: Given a set of initial conditions (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 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 Population extinction⏹If r becomes negative(birth rate < deathrate), populationdeclines and will goextinction.⏹Factors: Extremeenvironmental events (droughts, floods, coldor heat etc), loss ofhabitat (human).⏹Small populations are susceptible to extinction Allee effect, genetic drift, inbreeding (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)❿Fruit production per plant declined withdecreasing population size due toreduced visitation 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 variation in a small population and this may affect the population’s ability to adapt to environmental changeENDGeometric Growth⏹When generations do not overlap, growth can be modeled geometrically.N t = N o t❿N t= Number of individuals at time t.❿N o= Initial number of individuals.❿= Geometric rate of increase.❿t = Number of time intervals orgenerations.Exponential Growth⏹Continuous population growth in an unlimited environment can be modeled exponentially.⏹Appropriate for populations with overlapping generations.❿As population size increases, rate ofpopulation increase gets larger.。