A population of unicorns is growing over time, but its rate of growth is declining. Which of the following graphs best represents this pattern of growth?
The question asks us to identify which graph best represents the growth pattern of a population where the growth rate is slowing down. This indicates that the population is still growing, but at a decreasing rate over time.
To solve this, let's analyze each graph:
- Option (i): The graph shows a curve that is increasing but the slope is gradually flattening out. This indicates that while the population continues to grow, the rate of growth decreases over time. This is typical of logistic growth, where initial growth is rapid but slows over time due to factors like resource limitations.
- Option (ii): This graph shows a straight line with a negative slope, representing a consistent decrease in population size over time, which doesn't match the description.
- Option (iii): The curve here is continuously steep, showing an increasing growth rate, which contradicts the description of a declining growth rate.
- Option (iv): This graph represents steady, linear growth with a constant positive slope, indicating no change in the growth rate, which also doesn't fit the scenario described.
Since the correct description involves growth with a declining rate, Option (i) is the most accurate representation.
In conclusion, as the population grows, external factors such as resource limitations and increased competition typically cause a reduction in the growth rate, which is best illustrated by the flattening curve in Option (i).
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?
