WLF 448: Fish & Wildlife Population Ecology
Lab Notes 8b, Fall 2006

In-class Exercise \ Life Tables

A life table provides a nice summary of the pattern of survivorship of a population. This pattern of survival rates underlays most age-structured models of populations. When expanded to include age-specific reproductive rates (i.e., fecundity data), the expanded life table can be used to predict the rate of increase of a population and its stable age distribution. Today we will build an Excel worksheet to perform these calculations for a cohort of swans from which we have a sample of ages at death (i.e., Method #1 or Method #3).

  1. Start Microsoft Excel found under the Start menu:Lab software:Spreadsheets. .

  2. The following data were collected from female trumpeter swans banded as cygnets at Red Rocks Lake NWR. Enter these values into the dx column of the life table. WHY dx?:

Age 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Band Returns 242 12 5 6 5 8 7 8 6 11 10 14 16 11 9 17 11 16 10 12 8 5 3 6 4

Age 0 = cygnets

Calculating nx, lx, Sx, qx, and kx

  1. Create a life table using the spread sheet and the formulas provided in the lab notes.

Adding a Fecundity Schedule

Use the following age-specific reproductive rates to complete the extended life table for trumpeter swans at Red Rocks Lakes.

Age Female cygnets fledged per female
0 to 5 years 0
6 years 0.18
7+ years 0.23

Calculating Population "Growth" Rates

  1. Calculate population growth rates Ro, lamba, and r.

  2. Obtain r exactly, you must proceed by trial and error using Euler's equation. That is, you must make the quantity sum[e-rxl(x)m(x)], where r is the unknown, equal exactly 1.

  3. Is the population increasing, decreasing, or stationary? How can you tell? What is the intrinsic rate of increase (r), net reproductive rate per generation (Ro), and the finite rate of increase (lambda) tell us? What do these population-growth parameters really mean?

Survival and Mortality

  1. Plot the survivorship and mortality curve for this population. Do these graphs tell you anything that might help you manage this population?

  2. Calculate the finite survival rate for the period from birth to 3-years of age (i.e., age classes 0 to 3). Hint: multiply S0, S1, and S2.

Stable Age Distribution

  1. Calculate the stable age distribution in the last two columns of your life table.

  2. What is the stable age structure for this population? Why is this important?

Save Your New Worksheet

  1. Don't forget to save your completed worksheet.

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Revised: 25 August 2011