21/51/120, Bio Exercise #3 Due: 10 October 2006
Name:_________________________________________
Mortality and natality data for a cohort of B elding's ground squirrel, Citellus beldingi (after Zammuto and Sherman 198 6, Ca n. J. Zo ol. 64 602 -605 ). Squirrels were censused once per year in mid -summ er, shortly after wea ning; m x is the average number of female young just weaned by a female of age x. ____________________________________________________________________________________________
Age class Num ber alive An nu al Survival Cum ulative survival Expected life Fec und ity Realized fecu ndity Reprod uctive value Cohort size at SAD
x _____
Nx _____
Sx _____
lx _____
ex _____
mx _____
lxm x _____
Vx _____
Cx _____
0 1 2 3 4 5 6
238 93 49 18 12 6 0
0.0 1.7 2.1 2.4 3.0 2.1
_______________________________________________________________________________________ 1. 2. Fill in the life table. What proportion of squirrels live to be 2 years old?
3.
Of those squirrels that live to be 1 year old, what proportion survive to the 2nd year?
4.
W hat is the ex pected future lifespan of a 1 year old squirrel?
5.
Calculate R 0. Write it with the correct units. If there are 100 squirrels in mid-summer this year, how many would you expect to find in mid-summer next year? How many the year after?
6.
W rite the correct general equation for calculating reproductive value V x for a post-bre eding mod el.
7.
If you were managing this population of squirrels and a users group wanted to harvest as many squirrels as possible on a sustained yield basis, which age class would you recommend that they exploit? Explain.
BIO 21/51/120: EXAM PLE OF LIFE TABLE CALCULATIONS
Coho rt life table for little brow n bat Myotis lucifugus (based on annual pre-breeding censuses*)
x Nx
1 2 3 4 5
* *
Sx
0.4 0.7 0.5 0
lx
1 0.4 0.28 0.14 0
ex
0.82 1.05 0.5 0
mx
0 1 1.5 2
lxmx Vx
0 0.4 0.42 0.28 0 1.1 2.75 2.5 2
Cx
0.563 0.218 0.148 0.071 0
8 -xlx
0.968 0.375 0.254 0.123 0
lxmxx vx vx+1 vx+2 vx+3 vx+4
0 0.80 1.26 1.12 0 0 1 1.5 2 0.4 0.42 0.28 1.05 0.7 0 1 0 0 0
320 128 90 45 0
3 1.10 1.000 1.718 3.18 The value of x in the first row of the table is the approximate age at the time of sampling of the youngest individuals that are recognized (with a pre-breeding census, the table starts with x = 1; with a post-breeding census, the table starts with x = 0). Nx Sx = = = = = = = = = = = = = Number in cohort surviving to age x (measured; e.g., from marked individuals). Annual probability of survival Probability that an individual of age x will survive to age x+1. Nx+1 Nx / eq. 1 128 / 320 Cumulative Survivorship Proportion of individuals in age class 0 that survive to age class x. Note that l0 = 1.0 by definition. lx-1 S x-1; eq. 2 1 0.4 0.4 0.7 i.e., l1 = l0 P0
0.40
lx
0.4 0.28
ex
Expected life Expectation of future life given survival to age x. eq. 3
1.05
= =
(0.28 + 0.14) / 0.4 Fecundity at age x (average number of female offspring produced during the next year that survive to the time of the next census; e.g., average number of female bats produced last summer that survived to the next spring; measured in nature). Note that this is sometimes denoted as bx in life table models. Note that we define mx differently in a post-breeding model. Realized fecundity lx m x eq. 4 Probability of survival to age x @ Fecundity given survival. Female offspring in year x per initial female of age 1 0.28 1.5 females / female Net reproductive rate (per capita progeny / lifetime, individuals individual-1 lifetime-1) Average number of offspring produced by an average newborn offspring during its entire lifetime. Also equals the reproductive value for age class 0 (RV0). eq. 5 1.10
mx
lxm x
= = = = = = =
0.42
R0
= =
G
= = .
Generation time (units = time step of life table; in this case, years) Average difference between the birth of an individual and the birth of its own progeny eq. 6
2.89
= = . . = = =
3.18 / 1.10 . Intrinsic rate of increase (individuals individual -1 year-1) eq. 7 An exact solution requires iteration with Eulers equation. ln1.10 / 2.89 Finite rate of increase . (p...