3-1 Population ecology Lab 3: Population life tables I. Intoduction to ecological populations, life tables, and population gowth models This week we begin a new unit on population ecology. A population is a set of individuals of the same species living in a given egion o habitat. Populations ae examples of ecological systems. As such, they exhibit both stuctual and functional popeties. The total numbe of individuals in a population, the age distibution of those individuals, the sex atio of adults, pobabilities of suvival (o motality), and ates of ae key taits of population stuctue. Ecologists employ a vaiety of methods to study the stuctue of populations. Life histoy tables, o life tables, ae a method of quantifying population stuctue that addesses all of the above population taits. Life tables povide age-specific infomation on suvival and ates fo a paticula population. An ecologist can collect two vey diffeent types of life histoy data fo individuals in a population, which can lead to two kinds of life tables. Hoizontal (dynamic o cohot) life tables equie ecologists to follow all the individuals of a single cohot in a population fom bith to death. Constuction of hoizontal life tables fequently depends on the ecaptue of maked individuals fo mobile species o epeated, epesentative samples of sessile species. Since individuals must be followed fom bith to death, the hoizontal life table technique is not well suited fo the study of long-lived individuals. Vetical (static o time-specific) life tables consist of data on individuals of all ages in a population fom a single point in time. In vetical life table studies, it is impotant to wok with a lage, andom sample of individuals to ensue that the data is epesentative of the entie population. Fo example, the age distibution of you sample of individuals should eflect the age distibution of the whole population. Non-destuctive sampling methods ae paticulaly useful fo the constuction of vetical life tables as they minimize the impact of lage sampling effots on population dynamics. Both dynamic and static obsevations of population stuctue can be used 1) to quantify the age stuctue of a population; 2) to estimate an optimal age of sexual matuity; and 3) to pedict population gowth ates. Population gowth pojections ae based on mathematical models such as the exponential gowth model: N t = N 0 (e t ). In the exponential gowth model, the numbe of individuals at any time (t) can be pedicted using the numbe of individuals at the stating time (N 0 ), the base of the natual logaithm (e = 2.7182818), the intinsic ate of population gowth (), and the time (t) since N 0. The intinsic ate of population gowth () is a diect consequence of the age stuctue of a population. Envionmental conditions, seasonal effects, and population densities also shape population gowth ates. In geneal, populations only exhibit exponential gowth when esouces ae not limited. Theefoe, ecologists developed density-dependent gowth models to simulate the effects of envionmental stess on population gowth. Othe population gowth model altenatives include the Leslie matix and Lotka-Voltea model.
3-2 II. Anatomy of life tables A life histoy table contains infomation on age classes (x), the total numbe of individuals in each age class (n(x)), suvival ates fo each age class (l(x)), ates fo each age class (b(x)), and the numbe of offsping poduced pe individual at each age class (l(x)*b(x) and l(x)*b(x)*x). The following is an example of a hoizontal life table: Example 1: Hoizontal Life Table Age class (months) Numbe/ age class Suvival ate Fecundity Offsping/ind x n(x) l(x) b(x) l(x)*b(x) l(x)*b(x)*x 0 134 1.000 0.00 0.00 0.00 1 117 0.873 0.00 0.00 0.00 2 82 0.612 6.28 3.84 7.69 3 64 0.478 9.60 4.59 13.76 4 52 0.388 12.10 4.70 18.78 5 43 0.321 13.60 4.36 21.82 6 23 0.172 17.40 2.99 17.92 7 13 0.097 14.50 1.41 9.85 8 3 0.022 15.00 0.34 2.69 9 2 0.015 0.00 0.00 0.00 10 1 0.007 8.30 0.06 0.62 11 0 0.000 5.00 0.00 0.00 Sum 22.28 93.12 fo sexual matuity 22.28 offsping 4.18 months 0.74 ind/month 5 months You will be povided with ates (b(x)) and pe-detemined age classes (x) fo life tables in this lab. Calculation of the othe paametes depends on the type of life table you ae constucting. The impotant diffeences between hoizontal and vetical life tables elate to thei espective sampling appoaches (descibed above) and calculations of suvivoship. Hoizontal (dynamic o cohot) life tables When using cohot infomation, calculate the suvival ate fo an age class (l(x)) as the numbe of individuals in that age class (n(x)) divided by the numbe of individuals alive in the fist age class (n(0)). In the above table, suvival at age class 0 (l(0)) is n(0)/n(0) o 134/134 = 1.000. At age class 1, l(1) = n(1)/n(0) o 117/134 = 0.873. Next, use the povided data to calculate the offsping poduced pe individual in each age class (l(x)*b(x)) and the age-weighted numbe of offsping fo each age class (l(x)*b(x)*x). Once the hoizontal life table is completed, you can calculate the net
3-3 epoductive ate ( ), mean geneation time (), and intinsic gowth ate () of the population. Net epoductive ate ( ) is the sum of the l(x)*b(x) column. It epesents the expected numbe of offsping an individual will poduce ove its lifetime in the population. If > 1, then population size inceases. If < 1, then population size deceases, and if = 1, then population size does not change. In the population descibed by the hoizontal life table above, an individual is expected to poduce 22.28 offsping ove its lifetime. Mean geneation time () is the sum of the l(x)*b(x)*x column divided by the net epoductive ate ( ). The intinsic gowth ate () is an estimate of population gowth; it is equal to the natual log of the net epoductive ( ) divided by the mean geneation time (): = ln ( ) /. The optimal age fo sexual matuity in the population coesponds to the age class with the geatest age-weighted (l(x)*b(x)*x). Vetical (static o time-specific) life table When using time-specific infomation, you need to count all of the individuals you sampled. Fist, ecod the numbe of individuals at each age class in you sample (s(x)). See the following vetical life table example. Example 2: Vetical Life Table fo a ambusia holbooki population Age class Sample/ Numbe/ Suvival Fecundity Offsping/ind (days) age class age class ate x s(x) n(x) L(x) b(x) l(x)*b(x) l(x)*b(x)*x 0 130 759 1.000 0.00 0.00 0.00 30 190 629 0.829 0.00 0.00 0.00 60 240 439 0.578 0.00 0.00 0.00 90 120 199 0.262 24.00 6.29 566.32 120 60 79 0.104 0.00 0.00 0.00 150 15 19 0.025 29.00 0.73 108.89 180 3 4 0.005 32.00 0.17 30.36 210 1 1 0.001 0.00 0.00 0.00 240 0 0 0.000 0.00 0.00 0.00 Sum 759 7.19 705.57 fo sexual matuity 7.19 offsping 98.17 days 0.02 ind/day 90 days
3-4 Next, you must detemine how many individuals ae alive in each age class (n(x)) using data you collect at a single time in the field. The assumption stands that each individual you sampled was alive in the fist age class (x = 0). Fo example, if you sample 759 individuals, all of them had to have been alive at the fist age class (x = 0). So, n(0) = 759 o the sum of the s(x) column (see the above vetical life table example). If 130 of the individuals in you total sample wee between 0 and 29 days old (age class 0), then 629 individuals in you sample wee alive at the second age class (x = 30). Once you have calculated the numbe alive at each age class (n(x)), you can detemine the suvival ate (l(x)) fo each age class. Suvival ate fo a specific age class (l(x)) is the numbe alive in that age class (n(x)) divided by the numbe alive in the fist age class (n(0)), o l(x) = n(x) / n(0). In the above vetical life table example, the suvival ate at age class 0 (l(0)) = 759/759 = 1.000, l(30) = 629/759 = 0.829, and so on. All othe calculations fo vetical life tables ae the same as descibed above fo hoizontal life tables. III. Objectives The field potion of today s lab will involve collecting data on mosquitofish (ambusia) populations in 3 campus ponds. ambusia holbooki is a small, live-beaing fish found thoughout south Floida, including the Eveglades. In this lab execise, you will also analyze peviously published data on the stuctue of clam (Musculium) populations. Musculium patumeium is a feshwate clam fom Viginia. The objectives of Lab 3 ae: 1) To geneate life histoy tables fo ambusia and Musculium. 2) To compae and contast the life histoy tables you geneate fo both oganisms. IV. Instuctions Befoe setting out to sample mosquitofish, complete the following pe-field instuctions: 1) eneate seveal hypotheses as a class that you can test with today s execise. 2) Discuss how to keep tack of the population data. Set up field data sheets fo ambusia sampling. 3) Divide into goups and wok as teams in the field. Wok should be divided up so that all team membes get to expeience each aspect of the execise. 4) Be sue you have all the field sampling equipment that you will need. 5) Each team should paticipate in sampling. You will pool data fom all teams to geneate a lage dataset. Use the complete dataset fo you analysis.
3-5 Field Instuctions: We will wok in 3 ponds on campus whee we will collect sample specimens of. holbooki. Fo each collected specimen, we will non-destuctively measue its standad length (in mm) and then elease it (handle the fish caefully). You TA will detemine the numbe of fish to be collected at each pond by each goup. Calculations: The age of each fish (in days) will be calculated using the elationship: Age = 8*(Standad Length)-68 [ 2 =0.702, P=0.001] Fish smalle than 9 mm will have ages < 0 days in the above fomula. Theefoe, exclude all fish with standad lengths < 9 mm. Use the values povided in Example 2 above to complete a vetical life table fo the mosquitofish population that we study. Honbach and Childes (1986) collected data on a Musculium patumeium population in a steam nea the Univesity of Viginia campus in the ealy 1980s. They collected age-specific data on 4 cohots of the feshwate clam ove 16 months. Population and data fo two of these cohots, one beginning in the fall of 1981 and the othe in the sping of 1982, ae povided in the tables that follow. Use these two incomplete tables to geneate a hoizontal life histoy table fo each cohot.
3-6 Hoizontal life table fo Musculium patumeium (Fall 1981) Age class Numbe/age Suvival ate Fecundity Offsping/ind (months) class x n(x) l(x) b(x) l(x)*b(x) l(x)*b(x)*x 1 313 0.00 2 310 0.00 3 293 0.00 4 146 0.00 5 111 0.00 6 101 20.80 7 27 9.70 8 26 15.40 9 25 8.00 10 1 9.00 11 1 27.00 12 0 0.00 Sum fo sexual matuity Hoizontal life table fo Musculium patumeium (Sping 1982) Age class Numbe/age Suvival ate Fecundity Offsping/ind (months) class x n(x) l(x) b(x) l(x)*b(x) l(x)*b(x)*x 1 134 0.00 2 117 0.00 3 82 6.28 4 64 9.60 5 52 12.10 6 43 13.60 7 23 17.40 8 13 14.50 9 3 15.00 10 2 0.00 11 1 8.30 12 0 5.00 Sum fo sexual matuity
3-7 Liteatue Cited Honbach, D. J., and D. L. Childes. 1986. Life histoy vaiation in a steam population of Musculium patumeium (Bivalvia: Pisidiidae). Jounal of the Noth Ameican Benthological Society 5:263-271. Futhe Reading Caswell, H., R. Lensink, M.. Neubet. 2003. Demogaphy and dispesal: Life table esponse expeiments fo invasion speed. Ecology 84(8):1968-1978. Stolen, M, K., and J. Balow. 2003. A model life table fo bottlenose dolphins (Tusiops tuncatus) fom the Indian Rive Lagoon system, Floida, U.S.A. Maine Mammal Science 19(4):630-649. Floate,. J., and M. P. Zalucki. 1999. Life tables of the pocessionay catepilla Ochogaste lunife Heich-Schaeffe (Lepidoptea: Thaumetopoeidae) at local and egional scales. Austalian Jounal of Entomology 38(4):330-339.