Problem 193 - Objective Biology for NEET

Question

Assertion: A sigmoid curve is a characterstic of living organism growing in a natural environment. Reason: Sigmoid curve is an S shaped curve.

Step-by-Step Solution

Answer

Yes, the assertion is correct. The sigmoid curve which is S-shaped is a characteristic of living organism growing in a natural environment. The stages represented by the sigmoid curve; initial slow growth, a period of rapid growth, and finally population stabilisation, accurately characterise the growth of organisms in a natural environment.

Step 1: Understand the Sigmoid Curve

Sigmoid curve, also known as an S-curve, is a mathematical concept often used to model the natural life cycle of many things, including population growth of organisms. It is named that way due to its S shape. The sigmoid curve generally starts off with a slow growth, and as resources become more available, the growth will speed up. Finally, as resources become saturated, the population growth rate will slow down and eventually stabilize, which represents the upper portion of the S-curve.

Step 2: Relate the Sigmoid Curve to Organism Growth

In the context of organism growth in a natural environment, the sigmoid curve plays a crucial role. It begins with a slow growth rate, as the population is small and breeding pairs are not abundant. As more offspring are produced, the population begins to grow more quickly - representing the exponential growth phase of the sigmoid curve. As the carrying capacity, or maximum sustainable population, of the environment is approached, competition for resources leads to the growth of the organism slowing down and population stabilizing - representing the plateau of the sigmoid curve.

Step 3: Conclusion

Hence, the sigmoid (S-shaped) curve is indeed a characteristic of a living organism growing in a natural environment, signifying initial slow growth, followed by a period of rapid growth, and finally stabilizing at the system's carrying capacity. This is not merely because of its S shape, but because of the stages of growth it represents.

Key Concepts

Population Growth

Population growth in biology refers to the increase in the number of individuals in a population. It is a dynamic process that can be influenced by numerous factors such as birth rates, death rates, immigration, and emigration. Understanding population growth is crucial for predicting how species will adapt to their environments and for managing ecosystems sustainably.

Populations do not grow indefinitely. Initially, when there is less competition for resources, growth tends to be slower while the population size is small. This slow growth is known as the lag phase, and populations use this time to adapt to their surroundings and establish themselves.

As conditions become favorable, like increased availability of food and mates, the growth rate accelerates. This leads to the exponential growth phase, where population size increases rapidly. During this phase, resources are plentiful, and populations can exhibit their maximum potential growth rate, often described by the formula \(dN/dt = rN\), where \N\ is the population size, \r\ is the intrinsic rate of increase, and \t\ is time.

However, exponential growth is not sustainable in the long term, as resources become limited and environmental pressures increase. This results in the deceleration of growth and leads to the sigmoid (S-shaped) curve where the population stabilizes at the carrying capacity of its environment.

Carrying Capacity

The carrying capacity of an environment is the maximum number of individuals of a particular species that can be sustainably supported in a given area over time. It represents the limit to population growth imposed by the availability of resources, such as food, water, and shelter, as well as other environmental conditions.

When a population nears its carrying capacity, resources become scarcer, and the growth rate begins to slow down. This is due to factors like increased competition, predation, disease, and waste accumulation. Carrying capacity is not a fixed value and can change with the alteration of environmental conditions and the adaptive characteristics of the population.

Understanding carrying capacity is vital for the management of wildlife reserves, fisheries, and agriculture. It helps inform policies on sustainable harvest levels and habitat conservation. In the context of the S-curve, the carrying capacity is represented by the plateau at the top of the curve, where the size of the population stabilizes. It is essential to note that if a population exceeds its carrying capacity, it can lead to environmental degradation and population crashes.

Exponential Growth Phase

The exponential growth phase is a period where a population grows at an increasingly rapid rate due to the abundance of resources and minimal limiting factors. During this phase, each individual or pair has the potential to reproduce at an optimum level, leading to a doubling effect on the population size over each time period.

The formula \(dN/dt = rN\) best describes exponential growth, where population growth rate \(dN/dt\) depends on the current population size \(N\) and the intrinsic rate of increase \(r\). In the absence of limiting factors, \(r\) remains constant, and the population grows exponentially.

This phase can be observed in nature after a disturbance—like a forest fire—where an environment temporarily has a surplus of resources. It is also evident in species that have been introduced to a new habitat without natural predators. However, this phase is typically transient as environmental resistance such as decreased resources or increased waste, diseases, and predation rates eventually slow population growth and lead to the sigmoid growth pattern.