Identify the lag, exponential (log), stationary and death phases in the sigmoid curve of population growth for a population growing in an environment with limited resources

The sigmoid curve of population growth, also known as the logistic growth curve, illustrates how a population grows in an environment with limited resources. This curve is characterized by four distinct phases: lag phase, exponential (log) phase, stationary phase, and death phase. Here’s a detailed explanation of each phase:

1. Lag Phase

• Description: The lag phase is the initial stage of population growth where the growth rate is slow. During this period, individuals are adapting to their new environment.
• Characteristics:
  • Few reproductive individuals are present, leading to minimal reproduction.
  • Organisms are metabolically active, increasing in size and preparing for reproduction.
  • Environmental conditions are being assessed, and necessary adaptations are occurring.

2. Exponential (Log) Phase

• Description: Following the lag phase, the population enters the exponential growth phase, characterized by rapid population increase.
• Characteristics:
  • Resources (such as food and space) are abundant, allowing for high rates of reproduction.
  • The number of individuals increases logarithmically, leading to a steep upward slope on the graph.
  • Mortality rates are low due to favorable conditions, resulting in a high net growth rate as natality significantly exceeds mortality.

3. Stationary Phase

• Description: As resources become limited and competition increases, the population enters the stationary phase where growth stabilizes.
• Characteristics:
  • The birth rate declines as resources become scarce, while mortality rates may rise due to increased competition and limited food supply.
  • The population size levels off as natality equals mortality, resulting in a plateau on the graph.
  • This phase reflects the carrying capacity ($K$) of the environment, where the population oscillates around a stable size.

4. Death Phase

• Description: In some contexts, particularly in microbial studies, a death phase may be identified following the stationary phase.
• Characteristics:
  • The death rate exceeds the birth rate due to factors such as resource depletion and accumulation of waste products.
  • Population size begins to decline as individuals die off faster than new individuals can be born.
  • This phase highlights the consequences of prolonged resource limitation and environmental stress