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Difficulty: HardPopulation Dynamics and Ecological Sampling

An ecologist used a 2 m×2 m2\text{ m} \times 2\text{ m} quadrat frame thrown randomly 15 times across a 1.2 hectare1.2\text{ hectare} (12,000 m212,000\text{ m}^2) savanna habitat in Yankari Game Reserve to estimate the population size of the variegated grasshopper (*Zonocerus variegatus*). A total of 180 grasshoppers were counted across all 15 quadrat throws. What is the estimated total population of *Zonocerus variegatus* in the entire 1.2 hectare1.2\text{ hectare} study area?

Answer: 36000 grasshoppers

Answer

The estimated total population of *Zonocerus variegatus* in the entire study area is 36,000 grasshoppers.
To estimate total population, first calculate total sampled area (15×4 m2=60 m215 \times 4\text{ m}^2 = 60\text{ m}^2). Dividing total individuals counted (180180) by total sampled area (60 m260\text{ m}^2) yields a mean density of 3 grasshoppers/m23\text{ grasshoppers/m}^2. Extrapolating this density across the total study area (12,000 m212,000\text{ m}^2) gives 3×12,000=36,0003 \times 12,000 = 36,000 grasshoppers.

Step-by-Step Solution

1
Calculate the surface area of one quadrat frame
2 m×2 m=4 m22\text{ m} \times 2\text{ m} = 4\text{ m}^2
Establishing the individual quadrat area is required to find the total sampling footprint.
2
Determine the total area sampled across all 15 quadrat throws
15×4 m2=60 m215 \times 4\text{ m}^2 = 60\text{ m}^2
Multiplying single quadrat area by total throws gives the aggregate area sampled.
3
Compute the mean population density per square meter
180 grasshoppers60 m2=3 grasshoppers/m2\frac{180\text{ grasshoppers}}{60\text{ m}^2} = 3\text{ grasshoppers/m}^2
Population density is defined as the total number of organisms counted divided by total sampled area.
4
Extrapolate population density to the total study area
3 grasshoppers/m2×12,000 m2=36,000 grasshoppers3\text{ grasshoppers/m}^2 \times 12,000\text{ m}^2 = 36,000\text{ grasshoppers}
Multiplying density by the full area of the ecosystem section yields the total estimated population.

Key Concept

Quadrat Sampling and Population Extrapolation
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Topics

Population Dynamics and Ecological Sampling

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