Presentation on theme: "Properties of Populations"— Presentation transcript:
1 Properties of Populations Age structureDensityFertility
2 What is a population?A group of organisms of the same species that occupy a well defined geographicregion and exhibit reproductive continuity from generation to generation; ecologicaland reproductive interactions are more frequent among these individuals than withmembers of other populations of the same species.Population 1Population 2
3 Real populations are messy Geographic distribution of P. ponderosaBroken up into populationsBut divisions are not entirely clear
4 In the real world, defining populations isn’t simple Populations often do not have clear boundariesEven in cases with clear boundaries, movement may be commonHabitat 2Habitat 1
5 An extreme example…Ensatina salamanders Not only are populations continuous, but so are species!
6 Metapopulations make things even more complicated Occur in fragmented habitatsConnected by limited migrationCharacterized by extinctionand recolonization populations are transient
7 Glanville Fritillary in the Åland Islands The glanville fritillaryRed dots indicate occupied habitat andwhite dots empty habitat in Picture by Timo Pakkala
8 Some Important Properties of Populations 1) Density – The number of organisms per unit area2) Genetic structure – The spatial distribution of genotypes3) Age structure – The ratio of one age class to another4) Growth rate – (Births + Immigration) – (Deaths + Emigration)
9 Describing populations I – Population density United States at nightPopulation density of the Carolina wrenPopulation density shapes:Strength of competition within speciesSpread of diseaseStrength of interactions between speciesRate of evolution
10 Population density and disease, Trypanasoma cruzi (Chagas disease) Trypanasoma cruzi (protozoan)Currently infects between16,000,000 and 18,000,000 people andkills about 50,000 people each year“Assassin bug” (vector)
11 Population density and disease, Trypanasoma cruzi A case study from the Brazilian AmazonSince 1950, human population has increased ≈ 7 foldSince 1950, the number of infections has increased ≈ 30 foldSuggests that rates of infection are increasing with human densityAntonio R.L. Teixeira, et. al., 2000.Emerging infectious diseases. 7:
12 Describing populations II – Genetic structure Imagine a case with 2 alleles: A and a, with frequencies pi and qi, respectivelyaaAAAAaaAAaaAaAAaaAAAAaaAAAaAaaaaaAaAAaap1 = .9p2 = .1Population 1Population 2p1 = 18/20 = .9q1 = 2/20 = .1 = 1-p1p2 = 2/20 = .1q2 = 18/20 = .9 = 1-p2These populations exhibit genetic structure!
13 Sickled cells and malaria resistance Malaria in red blood cellsGenotypePhenotypeAANormal red blood cells, malaria susceptibleAaMostly normal red blood cells, malaria resistantaaMostly sickled cells, very sickA ‘sickled’ red blood cell
14 Global distribution of Malaria and the Sickle cell gene Recently colonizedby malaria;low frequency of sickle alleleHistorical rangeof malaria; high frequency of sickle alleleThe frequency of the sickle cell gene is higher in populations where Malaria has beenprevalent historically
16 What determines a population’s age structure? Probability of death for various age classesProbability of reproducing for various age classesThese probabilities are summarized using life tables
17 Mortality schedules: the probability of surviving to age x Parental careNumber surviving (Log scale)Little parental careAgeWe can quantify mortality schedules using life table
18 Quantifying mortality using life tables Numberalive at age xProportion survivingto age xAgeclassxNxlx110001.0002916.9163897.89745747.7476426.4267208.2088150.150920.020How could you collect this data in a natural population?Now let’s work through calculating the entries
19 Calculating entries of the life table: lx The proportion surviving to age class x = The probability of surviving to age class xlx = Nx/N0Follow a single ‘cohort’xNxlx110001.0002916= N2/N1 = 916/1000 = .9163897= N3/N1 = 897/1000 = .8974= N4/N1 = 897/1000 = .8975747= N5/N1 = 747/1000 = .7476426= N6/N1 = 426/1000 = .4267208= N7/N1 = 208/1000 = .2088150= N8/N1 = 150/1000 = .150920= N9/N1 = 20/1000 = .020
20 What determines a population’s age structure? Probability of death for various age classes# of offspring produced by various age classesThese probabilities are summarized using life tables
21 Fecundity schedules: # of offspring produced at age x mx = The expected number of daughters produced by mothers of age xMany mammalsmxLong lived plantsAgeFecundity can also be summarized using life tables
22 Summarizing fecundity using a life table xlxmx18.104.22.168.45.2This entry designates the EXPECTED # of offspring produced by an individual of age 4.In other words, this is the AVERAGE # of offspring produced by individuals of age 4
23 If lx and mx do not change, populations reach a stable age distribution Population starting with all four year oldsHigh juvenile but low adult mortalityPopulation starting with all one year oldsLow juvenile but high adult mortalityAs long as lx and mx remain constant, these distributions would never change!
24 Describing populations IV – Growth rate Negative growthPositive growthZero growthA population’s growth rate can be readily estimated*** if a stable age distribution has been reached ***
26 Using life tables to calculate population growth rate xlxmxlxmx1= 1*0 = 02.75= .75*0 = 03.5= .5*1 = .504.25= .25*4 = 1The first step is to calculate R0:R0 = ∑ lx mxThis number, R0, tells us the expected number ofoffspring produced by an individual over its lifetime.If R0 < 1, the population size is decreasingIf R0 = 1, the population size is steadyIf R0 > 1, the population size is increasingR0 = ∑ lx mx = 1* *0 + .5* *4 = 1.5
27 Using life tables to calculate population growth rate xlxmxlxmx12.753.5.504.25The second step is to calculate GThis number, G, is a measure of the generation time of the population, or more specifically, the expected (average) age of reproduction
28 Using life tables to calculate population growth rate The last step is to calculate rThis number, r, is a measure of the population growth rate.Specifically, r is the probability that an individual gives birth per unit time minus the probability that an individual dies per unit time. Population growth rate depends on two things:1. Generation time, G2. The number of offspring produced by each individual over its lifetime, R0
29 The importance of generation time Imagine two different populations, each with the same R0:Population 1Population 2xlxmxlxmx12.753.5.504.25xlxmxlxmx12.75.667.534.25R0,1 = 1.5R0,2 = 1.5G1 = 3.67G2 = 1.33r1 = .110r2 = .305The growth rate of population 2 is almost three times greater, even though individuals in the two populations have identical numbers of offspring!
30 Using r to predict the future size of a population The change in population size, N, per unit time, t, is given by this differential equation:Using basic calculusGives us an equation that predicts the population size at any time t, Nt, for a current population of size N0:One of the most influential equations in the history of biology
31 What are the consequences of this result? For population size to remain the same, the following must be true:This is the concept of an equilibriumThis can only be true if ???
32 What are the consequences of this result? If r is anything other than 0 (R0 is anything other than 1), the population goes extinct or becomes infinitely larger = -.1r = 0r = .1Population size, NGenerationGenerationGeneration
33 A real example of exponential population growth… From : Human population increases by ≈ 1.0 billionFrom : Human population increases by ≈ 10.0 billionThis observation had important historical consequences…
34 Using life tables: A practice question A team of conservation biologists is interested in determining the optimum environment for raising an endangered species of flowering plant in captivity. For their purposes, the optimum environment is the one that maximizes the growth rate of the captive population allowing more individuals to be released into the wild in each generation. To this end, they estimated life table data for two cohorts (each of size 100) of captive plants, each raised under a different set of environmental conditions. Using the data in the hypothetical life tables below, answer the following questions:Population 1(in environment 1)Population 2(in environment 2)xNxlxmx11001.0250.50325.258410.10A. Using the data from the hypothetical life tables above, calculate the expected number of offspring produced by each individual plant over its life, R0, for each of the populations.B. Using the data in the life tables above, calculate the generation time for each of the populations.C. Using your calculations in A and B, estimate the population growth rate, r, of the two populations. Which population is growing faster? Why?D. Assuming the populations both initially contain 100 individuals, estimate the size of each population in five years.E. If the sole goal of the conservation biologists was to maximize the growth rate of the captive population, which conditions (those experienced by population 1 or 2) should they use for their future programs?*** We will work through this problem during the next class. Be prepared***
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