The accompanying figure shows logistic population growth for two species in the same habitat. Which of the following conclusions hold true? (i) Species 1 has higher intrinsic growth rate 
(ii) Species 2 has higher intrinsic growth rate
(iii) Carrying capacity for Species 1 is higher
(iv) Carrying capacity for Species 2 is higher
The question asks us to analyze logistic population growth for two species and determine which statements about their growth and carrying capacities are true. Below is the step-by-step reasoning:
- The logistic growth curve is characterized by a rapid growth rate initially, followed by a plateau when the population reaches carrying capacity.
- We can observe the following from the curves:
- Intrinsic Growth Rate: The initial steepness of the curve indicates the intrinsic growth rate. Species 1 reaches its asymptote more quickly, but Species 2 has a steeper initial curve, indicating a higher intrinsic growth rate for Species 2. Therefore, statement (ii) is incorrect, and statement (i) is correct.
- Carrying Capacity: The plateau of the curve represents the carrying capacity. The plateau level for Species 2 is higher than for Species 1, meaning Species 2 has a higher carrying capacity. This confirms that statement (iv) is correct, and statement (iii) is incorrect.
- Based on the above analysis:
- Option "Both (i) and (iv)" is correct as Species 1 has a higher intrinsic growth rate and Species 2 has a higher carrying capacity.
Important Questions from Population growth curves
The population of whirligig beetles in a lake grows or declines exponentially i.e.
$N(t) = N(0)e^{rt}$
where $N(t)$ is the population size at time $t$, $N(0)$ is the initial population size and $r$ is the per capita rate of population change, occurring only due to birth and death.
A researcher tracks population sizes for a year and finds the following:Time interval Number of beetles at start Number of beetles at end January - March 1000 150 April – June 150 3013 July – September 3013 100 October - December 100 2009 Assuming that the individual birth rates remain constant throughout the year and only death rates are affected, which one or more of the following statements is/are true?
(In your calculations, round off the birth and date rates to two decimal places)- The population size at which net recruitment is the highest is also when the greatest amount can be harvested, while ensuring the long-term survival of the population. The amount harvested at this population size is known as
The graphs shown represent the relationship between population size ($N$) and population growth rate ($\frac{dN}{dt}$). Which one of the following growth curves represents a density-dependent population that experiences a strong Allee effect?
Overfishing reduced food availability for sea lions in California, causing a decline in their population size. In 1972, under the US Endangered Species Act, fishing was banned from sea lion foraging areas. Subsequently, the population of sea lions increased in a logistic form as shown in the figure.
The per capita growth rate is highest in the interval __________ and the population growth rate is highest in the interval __________
Consider the logistic population growth model, given by $$ \frac{dn}{dt} = rn \left(1 - \frac{n}{k}\right) $$ where $r$ is the intrinsic growth rate, $n$ is the population size and $k$ is the carrying capacity. Which one or more of the following is/are assumption(s) of the model?
