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# Life Tables Biol 28600

Purdue

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This 48 page Class Notes was uploaded by Sierra on Thursday February 11, 2016. The Class Notes belongs to Biol 28600 at Purdue University taught by Joshua Springer in Spring 2016. Since its upload, it has received 17 views. For similar materials see Introduction to Ecology and Evolution in Biology at Purdue University.

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Date Created: 02/11/16

Exam I Locations for Monday 15 February 8:00—10:00pm Last/Surname begins with O—Z Go to WTHR 200 PLUS those with accommodations that are NOT going to the DRC to take the test Last/Surname begins with A—N Go to EE 129 You MUST show your student ID when you turn in your exam! Bring a Calculator (You may NOT use your phone) Bring a pencil! Population Growth Individuals are added to a population through births and immigration Individuals leave the population through deaths and emigration An open population has immigration and emigration A closed population does not have or has a very low level of immigration and emigration that doesn’t influence population growth Immigration Emigration Birth Death Population size Population Growth Reflects the Difference between Rates of Birth and Death We can create simple mathematical models to describe how a population changes with time. Example: Hydra in an aquarium Closed population (no aquarium escapes!) most reproduction is asexual by budding Assume all reproduce asexually and all have one offspring at a time How will the population size change over time? Genetically diverse? Population Growth Reflects the Difference between Rates of Birth and Death Hydra --> bud iClicker New stems are formed from the root of an individual. These genets are genetically distinguished by the parent plant in that they are simply unique ramets. Separate stems connected by the same roots are still different genets. Is this statement correct? A) Yes B) No Population Growth Reflects the Difference between Rates of Birth and Death N number of individuals in the population t time N(t) number of individuals in the population at a given time We read this “N of t”, short for “N is a function of t” This is “function notation”, not multiplication. Assume the initial population size is 100 at time zero (here day zero) N(0) 100 Assume this population size is much lower than the available food and resource supply in the aquarium Population Growth Reflects the Difference between Rates of Birth and Death This population is closed No immigration or emigration are possible Budding will produce new Hydra – births Some Hydra will die these processes are continuous, not synchronized B number of new Hydra produced each day D number of Hydra that die each day For this population B 40, D 10 How do you calculate the size of the population at the end of day one? Population Growth Reflects the Difference between Rates of Birth and Death To calculate the new population size, add the births and subtract the deaths N(0) B D N(1) 100 40 10 130 Now, how do you calculate the population size at the end of day two? Can you use the same values for births and deaths? No. Population Growth Reflects the Difference between Rates of Birth and Death Obviously, the actual number of births and deaths depends on population size An estimate that is independent of population size can be expressed as a rate, rather than an absolute number To determine the per capita birthrate, b b B/N(0) 40/100 0.4 Similarly, death rate d D/N(0) 10/100 0.1 Population Growth Reflects the Difference between Rates of Birth and Death If we assume that b and d are constant, they can be used to predict the growth of a population over time regardless of population size Population Growth Reflects the Difference between Rates of Birth and Death Therefore, the population on a given day can be represented by the equation: N(t 1) N(t) bN(t) dN(t) How would you determined the size of the Hydra population after one day? After two days? Population Growth Reflects the Difference between Rates of Birth and Death The size of the hydra population after one day N(1) 100 0.4(100) 0.1(100) 130 The size of the hydra population after two days N(2) 130 0.4(130) 0.1(130) 169 This represents a geometric population growth pattern Population Growth Reflects the Difference between Rates of Birth and Death Then plug'n'chug. N(t 1) N(t) (b d)N(t) For the first day N(1) N(0) (0.4 0.1)100 30 For the second day N(2) N(1) (0.4 0.1)130 39 In this equation, the term on the left side represents a change in population size over a period of time Figure 9.4 7000 6000 r 0 )] (5000 N 4000 3000 Population size [ 1000 r 0 r 0 0 10 20 30 40 50 Time (t ) Population Growth Reflects the Difference between Rates of Birth and Death In 1911, the United States government introduced 25 reindeer (4 males and 21 females) onto the island of St. Paul in the Pribilof Islands, Alaska The purpose of the introduction was to provide fresh meat for the native residents Within 30 years, the population grew to more than 2000 individuals Figure 9.5 2000 1500 1000 Num500 of reindeer 0 1910 1920 1930 1940 Year Life Tables Provide a Schedule of Age- Specific Mortality and Survival A life table is an age-specific account of mortality Ecologists use life tables to examine systematic patterns of mortality and survivorship within populations Life tables can follow a cohort, a group of individuals in a population born in the same period of time Insurance companies use these types on data on us also! How much to charge us for premiums. Life Tables Provide a Schedule of Age- Specific Mortality and Survival A cohort life table followed 530 gray squirrels until all individuals died within six years after the study began (none survived to age six) Column x age classes (in years, for this example) Column n number of individuals from the cohort x that are alive at age x x n x 0 530 1 159 2 80 3 48 4 21 5 5 Section 9.2 Life Tables Provide a Schedule of Age-Specific Mortality and Survival Survivorship, l , is the number of individuals x surviving to a given age (x) as a proportion of the original cohort size (n /n ) x 0 For age 0, l 0n /n 0 500/530 1.0 For age 2, l n /n 80/530 0.15 2 2 0 x nx lx x starts as 1.0 for the first timepoint x, 0 530 1.00 because none of the 1 159 0.30 organisms you're counting is dead. 2 80 0.15 3 48 0.09 4 21 0.04 5 5 0.01 Figure 9.8a Survivorship (l ) of these x squirrels over time. 1.0 scale) 100.1 (log l 0.01 0 1 2 3 4 5 Age (years) (a) Life Tables Provide a Schedule of Age- Specific Mortality and Survival Age-specific mortality, d , is thx difference between the number of individuals alive for any age class (n ) x and the next older age class (n ) x 1 Dying from age 0 to 1, d n n 530 159 371 0 0 1 Dying from age 3 to 4, d n n 48 21 27 3 3 4 x nx dx 0 530 371 1 159 79 2 80 32 3 48 27 4 21 16 5 5 5 Life Tables Provide a Schedule of Age- Specific Mortality and Survival Age-specific mortality rate, q , is deterxined by the number of individuals dying during a given time interval (d ) divided by the number alive at the x beginning of that interval (n ) x For age 0, x n d q q0 d /0 071/530 0.70 x x x For age 4, 0 530 371 0.70 q d /n 16/21 0.75 1 159 79 0.50 4 4 4 2 80 32 0.40 3 48 27 0.55 4 21 16 0.75 All the animals die at the end of their lifespan, so thexlast q is 1.0 . 5 5 1.0 Life Tables Provide Data for Mortality and Survivorship Curves A mortality curve plots mortality rates (q ) against x age For the gray squirrel example, the graph shows that there are two distinct parts in the life history a juvenile phase when mortality is high a post juvenile phase when mortality rate decreases with age to a point, then increases again Mortality rate (q ) of xhese squirrels over time 1.0 )0.8 q 0.6 0.4 Mortality rate ( 0.2 0 0 1 2 3 4 5 Age (years) (a) Life Tables Provide a Schedule of Age- Specific Mortality and Survival A complete cohort life table for gray squirrels Different Types of Life Tables Reflect Different Approaches to Defining Cohorts and Age Structure A cohort, or dynamic, life table shows the fate of a single group of individuals born at a given time (the cohort) from birth to death a dynamic composite life table is constructed from individuals born over several time periods, not one A time-specific (static) life table is constructed by sampling a population in a way that obtains a distribution of age classes during a single period this is easier to construct than a cohort life table what assumptions must be made? Different Types of Life Tables Reflect Different Approaches to Defining Cohorts and Age Structure The assumptions for a time-specific life table: each age class sampled in proportion to its numbers in the population age-specific birthrates are constant over time age-specific mortality rates are constant over time Different Types of Life Tables Reflect Different Approaches to Defining Cohorts and Age Structure Life-tables for long-lived vertebrates almost always have overlapping generations Some animals, especially insects, live only one breeding season so generations do not overlap all individuals belong to the same age class to obtain the value of nxfor these species, observe a natural population over several annual seasons, estimating population at each time for many insects, n xan be obtained by estimating the number surviving from egg to adult Life Tables Provide Data for Mortality and Survivorship Curves Three general types of curves Type I (strongly convex) – survival rate is high throughout the life span, with most mortality at the end humans and other mammals, some plants Type II (straight) – survival rates do not vary much with age adult birds, rodents, reptiles, many perennial plants Type III (concave) – mortality is very high early in life oysters, fish, many invertebrates, many plants Figure 9.10 1.0 I scale) 10 II (log lx III .01 Age Figure 9.8a Survivorship (l ) of these x squirrels over time. 1.0 scale) 100.1 (xog l More or less a Type II curve. 0.01 0 1 2 3 4 5 Age (years) (a) Figure 9.11 1000 500 (a) 100 50 (b) (c) (d) 10 Numbe5 of individuals surviving 0 2 4 6 8 10 12 14 16 18 Age (years) Age-Specific Mortality and Birthrates Can Be Used to Project Population Growth Age-specific mortality rates (q x and age-specific birthrates (bx) can be combined to project future changes in the population How is a population projection table constructed? Why are only females followed in constructing the table? What assumptions does this approach require? Age-Specific Mortality and Birthrates Can Be Used to Project Population Growth A population projection table projects the growth of a population using information from a life table and fecundity table Uses a new term s is age-specific survival (the proportion of the x population that survives to the next age class) and is calculated using the age-specific mortality information s x 1 q x Age-Specific Mortality and Birthrates Can Be Used to Project Population Growth For a hypothetical population of gray squirrels introduced into an unoccupied oak forest Only females are followed – females form the reproductive units of the population Must assume that the q vaxues in the life table are the same for both males and females This population is established in year 0 N(0) 30 the population consists of 20 juveniles (age 0) and 10 adults (age 1) Age-Specific Mortality and Birthrates Can Be Used to Project Population Growth To project the fate of the initial population of 30 squirrels For those in year 0, s 0.00 (surviving to year 1) 20 0.30 6 For those in year 1, s 0.10 (surviving to year 2) 10 0.50 5 x b s Year 0 Year 1 x x 0 0.0 0.30 20 1 2.0 0.50 10 6 2 3.0 0.60 5 3 3.0 0.45 4 2.0 0.25 5 0.0 0.0 Total 30 Age-Specific Mortality and Birthrates Can Be Used to Project Population Growth Now calculate recruitment into age class 0 during year 1 For those in age class 1, b 2.0 1birthrate in year 1) 2.0 6 12 For those in age class 2, b 3.0 2birthrate in year 1) 3.0 5 15 Then add. 12 + 15 = 27 new squirrels x bx sx Year 0 Year 1 0 0.0 0.30 20 27 1 2.0 0.50 10 6 2 3.0 0.60 5 3 3.0 0.45 4 2.0 0.25 5 0.0 0.0 Total 30 38 Age-Specific Mortality and Birthrates Can Be Used to Project Population Growth Survivorship and fecundity are determined in the same way for each successive year This population is estimated to grow from 30 squirrels in year 0 to about 211 in year 10 Age-Specific Mortality and Birthrates Can Be Used to Project Population Growth An age distribution, the proportion of individuals in each age class for any one year, can be calculated from a population projection table divide the number in each age class (x) by the total population size for that year, N(t) In the gray squirrel population, from year 7 on, a stable age distribution, with the proportion of each age class the same in the population, is reached. Note that age ratios remain fixed after the 7-year point in this example. Age-Specific Mortality and Birthrates Can Be Used to Project Population Growth The population projection table also provides an estimate of population growth The finite multiplication rate N(t 1)/N(t) Initially varies from one year to the next, but once a stable age distribution is reached, is constant What does it mean when 1.0? Table 9.6 Section 9.7 Age-Specific Mortality and Birthrates Can Be Used to Project Population Growth If 1.0 the population size is constant If 1.0 the population is growing If 1.0 the population is declining How can be used to project population size into the future? Figure 9.12 1200 1000 800 ) ( N 600 400 200 0 5 10 15 20 Time (t) Stochastic Processes Can Influence Population Dynamics Environmental stochasticity is the random variation in the environment that can influence birthrates and death rates in a population. This variation can be the result of annual variations in climate temperature precipitation natural disasters fire flood drought iClicker Can we assume that all metapopulations of a species act in the same way? A) Yes, they’re subsets of the population as a whole B) No, they’re actually different species C) No, each has different dynamics D) Metapopulation is a made up term used to confuse students.

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