14.2 Applications and skills

14.2.5 Lab: Modelling population growth

  • Do populations show logistic or exponential growth?
  • What are ideal conditions for growth?

Use these two techniques to investigate.

Technique 1: Counting yeast with a haemocytometer

Yeast, Saccharomyces cerevisiae, is a eukaryotic microorganism. You can monitor the growth of populations of yeast over a period of days or weeks by taking population samples using serial dilutions and a haemocytometer, which is a specialised tool for counting cells under a microscope.

You will need:

  • One packet dry brewers’ yeast
  • Erlenmeyer flask
  • Haemocytometer (and specialised cover slips)
  • 0.1ml pipette
  • Distilled water
  • Test tubes
  • 10ml graduated cylinder


  1. Activate the yeast according to the package instructions (usually 15g in 100g water at 37°C and 1g sugar is enough). This is your original population.
  2. Once yeast is activated, after about 10 minutes, dilute a sample of the suspension with distilled water.
  3. Add 0.1ml of the suspension into 9.9ml of distilled water in a test tube. Repeat the dilution two more times as shown in Figure 14.2.5a. You have just performed a serial dilution with a dilution factor of 10-6.

    serial dilution

    Figure 14.2.5a – Serial dilution
    The number of yeast cells in the original population is too large to count. Serial dilutions are a very useful technique to learn for biological analysis.

  4. Take a sample of the last dilution and mount it on the haemocytometer. First, place the cover slip over the counting grid area. Then drop the sample at the edge of the cover slip, allowing it to move by capillary action into the counting chamber.

    haemocytometerFigure 14.2.5b – Side view of a haemocytometer
    The sample is loaded at the end of the cover slip and pulled into the counting chamber by capillary action. The cover slip is 0.1mm in height from the counting surface, so that the concentration of cells can be calculated accurately.

  5. Mount the slide under high power and count the number of yeast cells that are visible within 10 randomly selected boxes. This will give you the population from a total volume of 0.25mm3.

    counting gridFigure 14.2.5c – Counting grid 
    Counting is normally done in the smallest boxes (shown in blue), in the central area of the grid. Each of the boxes is 0.5 x 0.5 x 0.1mm (height from coverslip).

  6. Calculate the concentration of yeast in your original sample using the formula:

    begin mathsize 12px style C o n c e n t r a t i o n space o f space s a m p l e space equals fraction numerator N u m b e r space o f space c e l l s space c o u n t e d over denominator V o l u m e space o f space s q u a r e s space c o u n t e d space x space D i l u t i o n space f a c t o r end fraction end style

    where the volume of squares counted is 0.25 mm3, and the dilution factor is 10-6. The population should be expressed as number of cells/mm3.

  7. Keeping your original population at room temperature, repeat steps 3–6 every day for two weeks. Graph your results.

Technique 2: Modelling population growth in duckweed

Unlike most plant species, duckweed (Lemna sp.) grows continuously. It reproduces asexually by producing thalli which break loose from the parent plant when its roots are large enough to support itself. Thalli are easy to count.


Figure 14.2.5d – Duckweeds are small freshwater autotrophs that consist of thalli (leaves) and long roots

You will need:

  • Glass beaker
  • Healthy Lemna
  • Lamp or other continuous light source
  • Forceps
  • Pond water (or dechlorinated tap water with added nutrient salts)


  1. Place two healthy plants in a beaker with a set volume of pond water (e.g. 200ml). Count and record the number of thalli on both plants.
  2. Continue to count thalli every other day for 3–4 weeks. Make sure to replenish any volume of pondwater lost to evaporation. Graph your results.

Variation: Compare the rates of population growth when the starting population in the same-volume beaker is much higher.

In the lab

  • Make sure your 0.1ml pipette is not contaminated when you do your serial dilutions.
  • More data is usually more reliable. Why not pool class data?
  • Yeast: How many times more concentrated is your original suspension compared with your diluted sample?
  • Duckweed: Tap water can be dechlorinated by leaving it in a shallow pan overnight.
  • Duckweed: Make sure you specify a minimum size for counting thalli.

micrographFigure 14.2.6e – Micrograph
Counting yeast is tricky! Take your time. Use a tally sheet or a handheld tally counter (below) so you don’t have to look away from the microscope.

tally counterFigure 14.2.6f – Handheld tally counter 


  • Do yeast and duckweed populations grow exponentially or logistically? Discuss the shape of the graphs.
  • Suggest variations to the main method that would (i) increase the rate of population growth, (ii) decrease the rate of population growth and (iii) change the carrying capacity.

IA: Exploration

Does competitive exclusion occur when two microorganisms are cultured together?

spectrophotometerFigure 14.2.6g – A spectrophotometer as lab variation
You can also use a spectrophotometer to estimate population sizes in your samples of yeast (above). A sample dilution is placed in a small cuvette and the optical density is read (below). Darker samples have more yeast.

optical density principleFigure 14.2.5h – Optical density principle

duckweed pondFigure 14.2.5i – Duckweed pond
Duckweeds are food for frogs and ducks and respond quickly to eutrophication.