C4.1.8 Modelling of the sigmoid population growth curve Notes

Modelling the Sigmoid Population Growth Curve

1. Populations do not grow indefinitely. Instead, they follow an S-shaped (sigmoid) growth curve under natural conditions, which reflects the impact of resource availability, competition, and environmental limitations.
2. This curve shows how populations increase rapidly at first, slow as resources become limited, and eventually stabilize near the carrying capacity.

The Sigmoid Growth Curve: Three Phases

1. Exponential Growth Phase – Rapid population increase due to:
   1. Abundant resources (e.g., food, space, nutrients).
   2. Minimal limiting factors like predators or competition.
2. Transitional Phase – Growth slows as:
   1. Competition for resources intensifies (e.g., food shortages, lack of space).
   2. Waste accumulation increases environmental stress.
   3. Predation and disease start having a larger impact.
3. Plateau Phase – Population stabilizes because:
   1. Birth and death rates equalize.
   2. Carrying capacity (K) is reached, the environment can no longer support further growth.
   3. Competition and predation prevent unchecked expansion.

Modelling Duckweed Growth

Duckweed (Lemna spp.) is a floating aquatic plant, that reproduces rapidly and is ideal for observing population dynamics in a controlled environment.

Steps to Model Duckweed Growth:

1. Set Up the Experiment:
   1. Fill a container (e.g., a tank or jar) with water and add nutrients like fertilizer to support duckweed growth.
   2. Introduce a small number of duckweed fronds into the container.

2. Monitor Growth:

1. Count the number of fronds at regular intervals (e.g., daily or every two days).
2. Record data on population size over time.

3. Analyze the Data:

1. Plot a graph with time on the x-axis and population size on the y-axis.
2. Identify the three phases of the sigmoid growth curve.

Modelling Yeast Growth

Yeast (Saccharomyces cerevisiae) is a single-celled fungus, that reproduces quickly in nutrient-rich solutions, making it ideal for population studies.

Steps to Model Yeast Growth

1. Prepare the Environment:
   1. Dissolve sugar (e.g., glucose) in water to create a nutrient solution.
   2. Add a small amount of yeast to the solution.
2. Monitor Growth:
   1. Use a microscope or spectrophotometer to measure yeast density at regular intervals.
   2. Record population size at each time point.
3. Analyze the Data:
   1. Plot the data on a graph to observe the sigmoid growth curve.
   2. Highlight the exponential, transitional, and plateau phases.

Applications and Implications

1. Predicting Population Dynamics:
   1. The sigmoid growth curve helps ecologists predict how populations respond to resource changes or the introduction of predators.
2. Managing Resources: Understanding carrying capacity (K) allows resource managers and conservationists to:
   1. Maintain sustainable ecosystems.
   2. Prevent overpopulation and depletion of natural resources.
   3. Develop effective wildlife and fisheries management plans.