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 ) N_{t+1} = N_t + (B + I) - (D + E) N t + 1 = N t + ( B + I ) − ( D + E ) . Rates: birth rate = B / N = B/N = B / N and death rate = D / N = D/N = 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: d N / d t = r N dN/dt = rN d N / d t = r N and N t = N 0 e r t N_t = N_0 e^{rt} N t = N 0 e r t . J shaped. Unlimited resources. Logistic: d N / d t = r N ( K − N ) / K dN/dt = rN(K - N)/K d N / d t = r N ( K − N ) / K . S shaped. Lag, acceleration, deceleration and asymptote. r: the intrinsic rate of natural increase, b − d b - d b − d . K: the carrying capacity. Largest logistic rate: r K / 4 rK/4 r K /4 at N = K / 2 N = K/2 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?
The birth rate is the births divided by the population. 20 ÷ 100 = 0.2 20 \div 100 = 0.2 20 ÷ 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.
Run it. Does the population rise or fall?
1. Change emigrants to 0. What do you expect?
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 What is the carrying capacity? Stuck? Show a hint Show the answerWhat shape is the logistic curve? Stuck? Show a hint Show the answerWhich pyramid shape shows a declining population? Stuck? Show a hint Show the answerWhat is the largest growth rate of a logistic population? Stuck? Show a hint Show the answerSources 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.