Population Ecology Notes

Population Ecology

Reminders

  • Continue Population Growth (chapter 9).
  • Lecture assignment 5 is posted and due Friday.
  • Lab reminders: Pre-lab quiz.

Top Hat Question: Population Growth Rate

  • A population has a birth rate of 0.10 and a death rate of 0.10.
  • What is the value of r (population growth rate) and how is the population changing?
  • Correct answer: r = 0, no change in population size.
  • Explanation:
    • r=birth rate−death rater = birth\,rate - death\,rate
    • r=0.10−0.10=0r = 0.10 - 0.10 = 0
    • When r = 0, the population size is not changing.

Exponential Population Growth (Figure 9.4)

  • Characteristic of populations in newly colonized areas where environmental conditions are favorable.
  • Population size [N(t)] increases rapidly over time when r > 0.
  • When r = 0, population size remains constant.
  • When r < 0, population size decreases.
  • Example: Reindeer population
    • Rapid population growth was seen, increasing from approximately 0 to 1500 between 1910 and 1940.
    • This is an example of exponential growth in a new environment with favorable conditions.

Life Tables

  • What if the death rate isn’t the same for everyone?
  • Life table: An age-specific account of mortality.
  • Cohort: A group of individuals born at the same time.
  • Key variables:
    • x = time period (e.g., year 0, year 1, year 2).
    • nxn_x = number of living individuals from cohort x.
    • l<em>xl<em>x = survivorship, proportion of original cohort still alive (probability of surviving to a certain age x). Calculated as l</em>x=n<em>xn</em>0l</em>x = \frac{n<em>x}{n</em>0}.
    • d<em>xd<em>x = deaths at a given time (x). Calculated as d</em>x=n<em>x–n</em>x+1d</em>x = n<em>x – n</em>{x+1}.
    • q<em>xq<em>x = age-specific mortality rate, probability of dying at that age. Calculated as q</em>x=d<em>xn</em>xq</em>x = \frac{d<em>x}{n</em>x}.
Example Life Table
xnxn_xlxl_xdxd_xqxq_x
0530530 / 530 = 1.00530 – 159 = 371371 / 530 = 0.70
1159159 / 530 = 0.30159 – 80 = 7979 / 159 = 0.50
28080 / 530 = 0.1580 – 48 = 3232 / 80 = 0.40
34848 / 530 = 0.0948 – 21 = 2727 / 48 = 0.55
42121 / 530 = 0.0421 – 5 = 1616 / 21 = 0.76
555 / 530 = 0.015 – 0 = 55 / 5 = 1.00

Top Hat Question: Calculating lxl_x

  • Given a life table, calculate the missing lxl_x value.
  • Correct approach: l<em>x=n</em>xn0l<em>x = \frac{n</em>x}{n_0}

Top Hat Question: Calculating qxq_x

  • Given a life table, calculate the missing qxq_x value.
  • Correct approach: q<em>x=d</em>xnxq<em>x = \frac{d</em>x}{n_x}

Mortality and Survivorship Curves

  • Mortality curve: Plots qxq_x (age-specific mortality rate) with age.
  • Survivorship curve: Plots lxl_x (survivorship) with age.

Types of Survivorship Curves

  • Survivorship curves plot the number of individuals still alive at each age in the maximum life span.
  • Using a percentage scale instead of actual ages on the x-axis allows comparison of species with widely varying life spans.
  • Type I: High survivorship throughout life until old age, when mortality increases (e.g., humans).
  • Type II: Constant mortality rate throughout life (e.g., some birds).
  • Type III: High mortality rate early in life, followed by high survivorship for the remaining lifespan (e.g., many plants and invertebrates).

Top Hat Question: Identifying Survivorship Curve Patterns

  • Selection of the curve that best represents a Type I survivorship pattern.

Obtaining Data for Life Tables

  • Three main methods:
    1. Follow one cohort until death (cohort table or dynamic life table).
    2. Follow multiple cohorts until death (dynamic composite life table).
    3. Sample the whole population at one time (time-specific life table).