Population Attributes and Population Growth: Quick Revision

A brief note on Population Attributes and Population Growth. Read it before a test. Try each question at the end before you open its answer.

Attributes

• Population: the same species, one area, shared resources, able to breed together.
• Four processes: natality (B) and immigration (I) add. Mortality (D) and emigration (E) take away.
• Change: $N_{t+1} = N_t + (B + I) - (D + E)$.
• Rates: birth rate $= B/N$ and death rate $= D/N$ for each individual in a stated time.
• Density: a number, a biomass or a percent cover. Tigers are estimated from pug marks and fecal pellets.
• Sex ratio: males to females. Age groups: pre-reproductive, reproductive and post-reproductive.
• Age pyramid: triangle is expanding, bell is stable, urn is declining.

Growth

• Exponential: $dN/dt = rN$ and $N_t = N_0 e^{rt}$. J shaped. Unlimited resources.
• Logistic: $dN/dt = rN(K - N)/K$. S shaped. Lag, acceleration, deceleration and asymptote.
• r: the intrinsic rate of natural increase, $b - d$. K: the carrying capacity.
• Largest logistic rate: $rK/4$ at $N = K/2$. It is zero at 0 and at K.
• Life history (not in the NEET syllabus): salmon and bamboo breed once. Oysters have many small offspring. Birds and mammals have few large ones.

A worked example

A population of 100 has 20 births and 10 deaths in a year. No individual enters or leaves. What is the birth rate?

1. The birth rate is the births divided by the population.
2. $20 \div 100 = 0.2$ for each individual in a year.

Practice with new numbers

A program to try

The program finds the population at the end of a year.

Mistakes to avoid

• Saying that r is the birth rate. It is the birth rate minus the death rate.
• Mixing up the pyramid shapes. Triangle is expanding, bell is stable, urn is declining.
• Putting the fastest logistic growth at K. It is at K/2, and the rate is zero at K.
• Forgetting immigration and emigration. They change the density too.

Check yourself

1. What is the carrying capacity?

2. What shape is the logistic curve?

3. Which pyramid shape shows a declining population?

4. What is the largest growth rate of a logistic population?

Sources

• NCERT (2023). Biology, Textbook for Class XII, chapter 11.
• OpenStax Biology 2e (2018), chapter 45, Population and Community Ecology.
• Campbell Biology, 12th edition (2021), Pearson, chapter 53, Population Ecology.