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UIC BIOS 101 - DEMOGRAPHY

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DEMOGRAPHYReadingCatastrophesAge of IndividualsAge of individuals effects survivorship and fecundityCohortAgeS(x) & D(x)Proportionate survival =SurvivorshipSurvivorship valuesType II survivorshipSurvivorship CurvesFecundity, age specificNet Reproductive RateR0 and population growthA life tablePopulation projection 1Population projection 2Population projection 3Population growth is more dependent on numbers in certain age classes than total numberPer Capita Growth RateNumber of HumansLife tables can be applied to stagesProblemVocabularyExam 3 lecture #5 UIC BioS 101 Nyberg 1DEMOGRAPHYThe number of individuals in each age or stage group leads to improved population projection (compared to just knowing N).Exam 3 #5 UIC BioS 101 Nyberg 2Reading• Read section 52.1 Demography.• Box 52.1 on life tables & growth• Read p. 1050-53 on age structure.• Study Figures 52.13 & 52.14.• Life Tables Lab in labbook.Exam 3 #5 UIC BioS 101 Nyberg 3Catastrophes• Extreme conditions which kill many individuals in a population is an event known as a catastrophe.• Typically a catastrophe results in differential (unequal) mortality among age groups (classes).• Some populations have not able to recover after dramatic reductions.Exam 3 #5 UIC BioS 101 Nyberg 4Age of Individuals• Previous models have treated all individuals in the population as equivalent or equal.• The probability of reproductive success in real populations is dependent on the age, genotype, geographic location and other characteristics.Exam 3 #5 UIC BioS 101 Nyberg 5Age of individuals effects survivorship and fecundity• Individuals progress through stages of life (immature to mature) as they age.• Knowing the age of an individual is probably the most useful character to predict survival or reproductive status in humans and other mammals.• Age is irreversible, that is, one always gets older.Exam 3 #5 UIC BioS 101 Nyberg 6Cohort• To study change with age we can follow a ‘cohort’ of individuals born at same time from birth to death (longitudinal study).• More commonly we study individuals of different ages at one time (cross-sectional study)Exam 3 #5 UIC BioS 101 Nyberg 7Age• These models divide age into intervals given integer values, 0, 1, 2, ….• The length of the interval might be 1 year for dogs. For humans it is usually 5 years.• The symbol x is used for AGE.Exam 3 lecture #5 UIC BioS 101 Nyberg 8S(x) & D(x)• S(0) is the number of new borns in the cohort.• S(1) is the number of individuals in the cohort that survive to age 1.• The difference S(0) –S(1) = number that died between birth and age 1 = D(0)• S(x+1) = S(x) – D(x)• S(some large age) = 0, all dieExam 3 #5 UIC BioS 101 Nyberg 9Proportionate survival =Survivorship• Survivorship is the probability of a new born surviving to age X.• The symbol for survivorship is l(x).• l(x) = S(x)/S(0) where S(0) is the number of new borns in the cohort and S(x) is number of new borns in cohort that survive to age X.Exam 3 #5 UIC BioS 101 Nyberg 10Survivorship values• l(0) =1 as S(0)/S(0) = 1 • l(>>x) =0 as S(>>x)/S(0) = 0 as eventually all individuals die.• Mammals have high survivorship at young ages and then steep declines at old age. This is known as a type I curve.Exam 3 #5 UIC BioS 101 Nyberg 11Type II survivorship• If survivorship declines exponentially with age then survivorship curve is described as type II. • Type II survivorship implies that the probability of dying does NOT change with age, i.e., is constant.Survivorship CurvesExam 3 #5 UIC BioS 101 Nyberg 12Exam 3 #5 UIC BioS 101 Nyberg 13Fecundity, age specific• The number of female offspring produced by a female of age X in next year is called m(x) = fecundity at age X.• m(x) starts out at zero and then increases. In mammals it declines with advanced age.• Maturnity is origin of variable name, m.Exam 3 lecture #5 UIC BioS 101 Nyberg 14Net Reproductive Rate• R0 is the symbol for net reproductive rate = average number of female offspring produced by average new born female. • R0 = Σl(x)m(x) from x=0 until age all newborns are dead.Exam 3 #5 UIC BioS 101 Nyberg 15R0 and population growth• If R0 is > 1 then population is increasing in size.• If R0 is less than 1 then the population will decrease in total number of individuals.• The model assumes survivorship and fecundity don’t change with time.Exam 3 #5 UIC BioS 101 Nyberg 16A life tableAGE, xProportionSurviving to age xDaughters born per female of age xl(x)m(x)l(x)•m(x)Exam 3 #5 UIC BioS 101 Nyberg 17Population projection 1Projection of population assumes l(x) and m(x) are parameters, i.e., constants for particular species.Exam 3 #5 UIC BioS 101 Nyberg 18Population projection 2Exam 3 #5 UIC BioS 101 Nyberg 19Population projection 3Exam 3 #5 UIC BioS 101 Nyberg 20Population growth is more dependent on numbers in certain age classes than total numberDeclining or stable populationGrowing populationExam 3 lecture #5 UIC BioS 101 Nyberg 21Per Capita Growth Rate• The per capita growth rate of a population is the increase in number (ΔN) per individual (N) per time period (t), but if only some age classes reproduce, then the per capita growth rate is lowered by individuals in post-reproductive ages.Exam 3 #5 UIC BioS 101 Nyberg 22Number of HumansThe doubling time of the human population has been decreasing, that is our rate of growth is faster, not slower as expected in logistic model.Exam 3 #5 UIC BioS 101 Nyberg 23Life tables can be applied to stagesTwo important differences from human life tables are illustrated:1) Life tables can be used with stages (not just age),2) Survivorship and fecundity are sensitive to environmental conditions –in this case the amount of light available near the ground.Exam 3 #5 UIC BioS 101 Nyberg 24Problem• Calculate R0 for this life table.• Is this population increasing or decreasing?Age, x Survivorship Fecundity0 1.0 01 0.8 02 0.6 03 0.4 1.54 0.2 15 0Exam 3 lecture #5 UIC BioS 101 Nyberg 25Vocabulary• Population projection• Catastrophe• Population recovery• Census• Age• Net Reproductive Rate• Attribute• l(x), m(x), l(x)•m(x), R0• Survivorship• Fecundity• Stage vs


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