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Q3(c):
Describe briefly: (c) Sigmoid growth curve

Solution :

Theoretical Basis of the Sigmoid Growth Curve

The sigmoid growth curve, or S-shaped curve, represents the growth pattern of a living organism or population in a natural environment where resources are finite. It illustrates the progression of growth over time, characterized by an initial slow phase, a rapid exponential phase, and a final plateau due to environmental limitations [Per the principles of population ecology and plant physiology].

Mathematical Formulation

The growth $W$ at time $t$ is expressed by the following equation:

$W_1 = W_0 e^{rt}$

Where:

  • $W_1$ = Final size (weight, height, number).
  • $W_0$ = Initial size at the beginning of the period.
  • $r$ = Growth rate.
  • $t$ = Time of growth.
  • $e$ = Base of natural logarithms.

Steps of the Sigmoid Curve Development

  1. Lag Phase: The initial stage where growth is extremely slow. The organism is adapting to the environment, synthesizing enzymes, and preparing for metabolic acceleration [Biological justification: High metabolic activity with low net increase in biomass].
  2. Log (Exponential) Phase: The period of maximum growth rate. Cells divide rapidly, and the organism increases in size geometrically. This occurs when nutrients and space are abundant [Mathematical justification: Derivative of growth rate $dW/dt$ is at its maximum].
  3. Stationary Phase: As resources (nutrients, light, space) become limited, growth slows down. The birth/production rate equals the death/loss rate, leading to a plateau [Ecological justification: Reaching the 'Carrying Capacity' ($K$) of the environment].
Time (t) Size (W) Lag Log Stationary

Comparative Analysis of Growth Phases

Phase Growth Rate Primary Condition
Lag Minimal Acclimatization
Log Maximum Abundant Resources
Stationary Zero Resource Depletion

Final Solution: The sigmoid growth curve is an S-shaped trajectory depicting growth under limited environmental conditions, characterized by an initial lag phase, a steep log phase representing exponential growth, and a final stationary phase where growth ceases due to nutrient scarcity or space limitations.


More Questions from Class 11 Biology Plant Growth and Development EXERCISES


CBSE Solutions for Class 11 Biology Plant Growth and Development


Chapters in CBSE - Class 11 Biology


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