Population demographics

Population Dynamics - Quantitative Approach

Population Parameters: mortality, natality

1. Life Tables - Mortality rates

         a. Age-specific mortality; usually in cohort individuals

         b. Parameters:

                     x = age interval

                     nx = # indiv. at start age interval x

                     lx = proportion of org. surviving at start interval x

                     dx = # dying during age interval x to x+1

                     qx = rate of mortality during age interval x to x+1

         c. Cohort Life Table

         d. Nothing new for lx, dx, qx only measure nx

         e. Plot survivorship curves; demographers interested rates

         f. Log Scale based on 1000 indiv. thus per capita rate change

         g. Raymond Pearl 1921; 3-types of survivorship curves

         h. How do get data for life tables? Two Approaches:

                     i. Static life tables

                     ii. Cohort Life Table

                     iii. Compare two- if environment same

         i. Ecologists working with animals besides humans difficult

                     Three types data available

                     i. Directly Observed

                     ii. Age at death Observed

                     iii. Age structure Observed

2. Reproductive Rate- Balance mortality rate population

         a. Net population change = mortality rate + reprod. rate

         b. Intrinsic capacity of population increase:

                     i. Mean longevity or survival rate

                     ii. Mean natality or birth rate

                     ii. Mean growth rate

         c. These function:

                     i. Environmental conditions

                     ii. Genetic

         d. Age-specific reproductive rate or birth rate

                     i. Survivorship table and Fertility table (lx & bx)

                     ii. Calculate net reproduction rate (Ro)

                     iii. Frequency distribution of offspring

3. Stable Age Distribution-

         a. Intuitively; know 3 things calculate birth & death rate

                     i. age-specific survival rates (lx)

                     ii. age-specific birth rates (bx)

                     iii. age distribution

         b. Lotka 1922 - Contrary results do not need know age distribution

                     i. If birth and death rates are constant

                     ii. population reach fixed or stable age distribution

                     iii. Then only have to know birth-death = r

         c. Intrinsic capacity for increase or r

         d. This capacity is still a function of total population #

4. Geometric rate of increase - determines stable age distribution

         a. Model population; parthenogenic animal (no sex; divides)

         b. net reproduction rate Ro

         c. generation time G

         d. r = instantaneous increase population (based on no overlapping generations)

         e. Run through several iterations define actual r (See Box 10.2 text)

         f. Use the instantaneous rate to get finite rate of population increase lambda (λ)

5. Use understanding of r as way determine pop. increase

         a. Change function of Environmental variables

         b. Compare between species

         c. May not reflect the abundance or distribution in field

         d. Spp. with high r not always common/ low r not always rare

6. Three factors increase r:

         a. Decrease in age at first reproduction

         b. Increase in reproduction of progeny

         c. Increase in reproductive events

7. In nature: oversimplification of r

         a. Do not find:

                     i. Stable age distributions- pop. rarely long in unlimited fashion

                     ii. Age-specific rates survival & fertility b/c rarely in stationary phase

         b. r >complex; but provides model to compare rates in nature

8. In nature: life table & fertility tables

         a. Diagnostic tools environmental variables

9. Age composition clues status population