Population Dynamics and Ecological Sampling

21 questions

Question 1Question

An ecology student deployed a 1 m21\text{ m}^2 quadrat 10 times in a farmland ecosystem in Nigeria to estimate the population of a weed species. The total count of the weed recorded across all 10 quadrats was 50. What is the estimated population density of the weed per square metre?

Show answer & explanation

Answer: 5 weeds/m25\text{ weeds/m}^2

Answer

The population density of the weed is 5 weeds/m25\text{ weeds/m}^2.
Population density is computed by dividing the total number of individuals counted by the total sampled area. In this scenario, 50 weeds/(10×1 m2)=5 weeds/m250\text{ weeds} / (10 \times 1\text{ m}^2) = 5\text{ weeds/m}^2.

Step-by-Step Solution

1
Calculate the total surface area sampled by all quadrats.
Total Area = 10 quadrats×1 m2/quadrat=10 m210 \text{ quadrats} \times 1\text{ m}^2/\text{quadrat} = 10\text{ m}^2.
Population density calculation requires knowing the total area over which samples were taken.
2
Divide the total count of organisms by the total sampled area.
Density = 50 weeds10 m2=5 weeds/m2\frac{50\text{ weeds}}{10\text{ m}^2} = 5\text{ weeds/m}^2.
Population density is defined as the number of individuals of a species per unit area.

Key Concept

Quadrat Sampling and Population Density
Estimated Time:45s
Question 2Question

During an ecological survey of a savanna ecosystem in Nigeria, 40 grasshoppers were captured, marked with non-toxic paint, and released back into their habitat. A second sample of 50 grasshoppers captured two days later contained 10 marked individuals. What is the estimated total population size of grasshoppers in this habitat?

Show answer & explanation

Answer: 200

Answer

The estimated total population size of grasshoppers is 200.
Applying the Lincoln Index formula N=M×CRN = \frac{M \times C}{R} with M=40M = 40 marked initially, C=50C = 50 in the second capture, and R=10R = 10 recaptured marked individuals gives N=40×5010=200N = \frac{40 \times 50}{10} = 200 grasshoppers.

Step-by-Step Solution

1
Identify the values from the capture-recapture sampling data.
Initial marked individuals M=40M = 40, second sample size C=50C = 50, recaptured marked individuals R=10R = 10.
These parameters are required for the Lincoln Index population size estimation formula.
2
Calculate the population size using N=M×CRN = \frac{M \times C}{R}.
N=40×5010=200N = \frac{40 \times 50}{10} = 200.
Multiplying the size of the first sample by the size of the second sample and dividing by the number of recaptured marked individuals yields the total population estimate.

Key Concept

Lincoln Index (Capture-Mark-Recapture Method)
Question 3Question

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?

Show answer & explanation

Answer: 36000

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
Question 4Question

An ecology student investigated the population of *Tridax procumbens* in a cassava farmland in Ogun State using a 0.5 m×0.5 m0.5\text{ m} \times 0.5\text{ m} quadrat frame. Across 10 random quadrat throws, the total number of *Tridax procumbens* plants counted was 80. What is the estimated population density of *Tridax procumbens* per square metre (m2\text{m}^{-2}) in the farmland?

Show answer & explanation

Answer: 32 plants m232\text{ plants m}^{-2}

Answer

The population density of *Tridax procumbens* is 32 plants m232\text{ plants m}^{-2}.
The area of one quadrat frame is 0.5 m×0.5 m=0.25 m20.5\text{ m} \times 0.5\text{ m} = 0.25\text{ m}^2. Across 10 throws, the total area sampled is 10×0.25 m2=2.5 m210 \times 0.25\text{ m}^2 = 2.5\text{ m}^2. Dividing the total number of plants counted (80) by the total sampled area (2.5 m22.5\text{ m}^2) yields an accurate population density of 32 plants m232\text{ plants m}^{-2}.

Step-by-Step Solution

1
Calculate the area of a single quadrat frame.
Area of 1 quadrat=0.5 m×0.5 m=0.25 m2\text{Area of 1 quadrat} = 0.5\text{ m} \times 0.5\text{ m} = 0.25\text{ m}^2
Determines the spatial coverage of one quadrat throw.
2
Calculate the total area sampled across all quadrat throws.
Total sampled area=10×0.25 m2=2.5 m2\text{Total sampled area} = 10 \times 0.25\text{ m}^2 = 2.5\text{ m}^2
Accounting for all 10 sampling units used during field sampling.
3
Divide the total count of organisms by the total sampled area.
Population Density=80 plants2.5 m2=32 plants m2\text{Population Density} = \frac{80\text{ plants}}{2.5\text{ m}^2} = 32\text{ plants m}^{-2}
Population density is defined as the number of individuals of a species per unit area.

Key Concept

Quadrat Sampling and Population Density Calculation
Question 5Question

Match each ecological sampling instrument with its most appropriate application or target organism group during a field study in a Nigerian savanna ecosystem.

Click a left item, then click its matching right item

Items

Pooter
Pitfall trap
Quadrat frame
Sweep net

Matches

Show answer & explanation

Answer

Pooter matches Minute insects found on tree bark or foliage collected via suction; Pitfall trap matches Small crawling invertebrates on the soil surface and leaf litter; Quadrat frame matches Sessile or slow-moving organisms such as herbaceous weed plants; Sweep net matches Flying insects residing within tall grass canopy or shrubs.
Each equipment item is designed specifically for an organism's mobility level and habitat position: pooters extract tiny delicate insects via suction, pitfall traps collect ground-surface crawlers falling into sunken containers, quadrats quantify immobile plant species across defined area units, and sweep nets intercept active canopy insects.

Step-by-Step Solution

1
Identify the primary mechanism and target organism type for each sampling equipment.
Pooter uses suction for minute insects; pitfall trap targets ground crawlers; quadrat measures non-motile plants/animals in sample areas; sweep net catches flying foliage insects.
Different organism mobility, size, and micro-habitat dictate the appropriate ecological sampling tool.
2
Pair each instrument from the left column with its unique matching description from the right column.
Four correct matches established between instrument and ecological application.
Ensures complete alignment with ecological sampling standards.

Key Concept

Selection and Application of Ecological Sampling Instruments
Question 6Question

An ecology student investigated the population density of water hyacinth (*Eichhornia crassipes*) in a section of a freshwater creek in Bayelsa State. A quadrat frame measuring 0.5 m×0.5 m0.5\text{ m} \times 0.5\text{ m} was randomly thrown 2020 times across the sampling site. The cumulative count of water hyacinth plants recorded across all 2020 quadrat throws was 150150. What is the estimated population density of water hyacinth in plants/m2\text{plants/m}^2?

Show answer & explanation

Answer: 30 plants/m230\text{ plants/m}^2

Answer

The population density of water hyacinth is 30 plants/m230\text{ plants/m}^2.
To find population density, the total number of organisms observed (150150) must be divided by the total area sampled. Since one 0.5 m×0.5 m0.5\text{ m} \times 0.5\text{ m} quadrat has an area of 0.25 m20.25\text{ m}^2, twenty throws cover a total area of 20×0.25 m2=5.0 m220 \times 0.25\text{ m}^2 = 5.0\text{ m}^2. Dividing 150150 plants by 5.0 m25.0\text{ m}^2 yields 30 plants/m230\text{ plants/m}^2.

Step-by-Step Solution

1
Calculate the surface area of a single quadrat frame
Area of one quadrat=0.5 m×0.5 m=0.25 m2\text{Area of one quadrat} = 0.5\text{ m} \times 0.5\text{ m} = 0.25\text{ m}^2
Population density must be expressed in units of area, so the quadrat dimensions must first be converted into area.
2
Calculate the total area sampled across all throws
Total area sampled=20 throws×0.25 m2=5.0 m2\text{Total area sampled} = 20 \text{ throws} \times 0.25\text{ m}^2 = 5.0\text{ m}^2
The cumulative plant count represents the total organisms found across the entire combined sampled space.
3
Calculate the population density per square metre
Population Density=Total organism countTotal area sampled=150 plants5.0 m2=30 plants/m2\text{Population Density} = \frac{\text{Total organism count}}{\text{Total area sampled}} = \frac{150\text{ plants}}{5.0\text{ m}^2} = 30\text{ plants/m}^2
Population density is defined as the total number of individuals of a species per unit area.

Key Concept

Quadrat Population Density Calculation
Estimated Time:1m 30s
Question 7Question

During a field study of an intertidal mangrove swamp in Cross River State, a student used a 0.5 m×0.5 m0.5\text{ m} \times 0.5\text{ m} quadrat frame to sample the periwinkle (*Tympanotonus fuscatus*) population. Across 1010 randomly placed quadrat throws, a total count of 180180 periwinkles was recorded. What is the estimated population density of *Tympanotonus fuscatus* per square metre in this habitat?

Show answer & explanation

Answer: 72 periwinkles/m272\text{ periwinkles/m}^2

Answer

The estimated population density is 72 periwinkles/m272\text{ periwinkles/m}^2.
The correct option correctly evaluates population density by calculating the total sampled area (10×0.25 m2=2.5 m210 \times 0.25\text{ m}^2 = 2.5\text{ m}^2) and dividing the total counted organisms (180180) by that area, yielding 72 periwinkles/m272\text{ periwinkles/m}^2.

Step-by-Step Solution

1
Calculate the area of a single quadrat frame
Area of 1 quadrat = 0.5 m×0.5 m=0.25 m20.5\text{ m} \times 0.5\text{ m} = 0.25\text{ m}^2.
Determines the surface area enclosed by one sampling unit.
2
Determine the total area sampled across all throws
Total sampled area = 10 throws×0.25 m2=2.5 m210 \text{ throws} \times 0.25\text{ m}^2 = 2.5\text{ m}^2.
Accounts for the cumulative ground area surveyed during the 10 quadrat throws.
3
Calculate the population density per square metre
Population density = Total number of organismsTotal sampled area=1802.5 m2=72 periwinkles/m2\frac{\text{Total number of organisms}}{\text{Total sampled area}} = \frac{180}{2.5\text{ m}^2} = 72\text{ periwinkles/m}^2.
Population density is expressed as the total number of individuals per unit area.

Key Concept

Quadrat Population Density Calculation
Question 8Question

An ecologist conducted a survey in an abandoned oil palm plantation in Edo State to determine the density of Siam weed (*Chromolaena odorata*). Using a 1 m×1 m1\text{ m} \times 1\text{ m} quadrat frame thrown randomly 20 times across the field, a total of 160 Siam weed plants were counted. What is the estimated population density of Siam weed in this plantation?

Show answer & explanation

Answer: 8 plants/m28\text{ plants/m}^2

Answer

The estimated population density of Siam weed is 8 plants/m28\text{ plants/m}^2.
Population density is defined as the number of individuals of a species per unit area. To calculate this accurately using quadrats, the total number of organisms counted (160 plants) must be divided by the total area sampled. Since 20 quadrats of 1 m21\text{ m}^2 each were sampled, the total sampled area is 20 m220\text{ m}^2. Thus, 16020=8 plants/m2\frac{160}{20} = 8\text{ plants/m}^2.

Step-by-Step Solution

1
Calculate the area of a single quadrat frame
Area of 1 quadrat=1 m×1 m=1 m2\text{Area of 1 quadrat} = 1\text{ m} \times 1\text{ m} = 1\text{ m}^2
Determines the sampling area covered by one throw of the frame.
2
Calculate the total area sampled across all quadat throws
Total sampled area=20×1 m2=20 m2\text{Total sampled area} = 20 \times 1\text{ m}^2 = 20\text{ m}^2
Finds the combined area evaluated in the 20 random quadrat throws.
3
Calculate the population density per square metre
Population Density=Total number of individualsTotal sampled area=160 plants20 m2=8 plants/m2\text{Population Density} = \frac{\text{Total number of individuals}}{\text{Total sampled area}} = \frac{160\text{ plants}}{20\text{ m}^2} = 8\text{ plants/m}^2
Applies the standard ecological formula for population density using quadrat data.

Key Concept

Population Density Calculation using Quadrats
Estimated Time:1m 0s
Question 9Question

During an ecological study of an agricultural fish pond in Ibadan, Oyo State, a student employed the mark-release-recapture technique to estimate the population size of tilapia (*Oreochromis niloticus*). In the initial sampling, 120120 fish were captured, marked with harmless plastic tags, and released back into the pond. Two days later, a second sample of 150150 fish was netted, out of which 3030 individuals were found to be marked. What is the estimated total population size of tilapia fish in the pond?

Show answer & explanation

Answer: 600

Answer

The estimated total population size of tilapia fish in the pond is 600.
The correct answer is derived using the Lincoln index formula for population estimation: N=M×CRN = \frac{M \times C}{R}, where M=120M = 120 (initial marked sample), C=150C = 150 (total second sample), and R=30R = 30 (recaptured marked sample). Substituting these values yields N=120×15030=600N = \frac{120 \times 150}{30} = 600 fish.

Step-by-Step Solution

1
Identify the values for the Lincoln Index (Lincoln-Petersen estimator) parameters from the problem statement.
Number marked in first capture (MM) = 120120, total caught in second capture (CC) = 150150, recaptured marked individuals (RR) = 3030.
The capture-recapture method relies on the proportion of marked individuals in the second sample being equal to the proportion of marked individuals in the total population.
2
Apply the Lincoln Index formula N=M×CRN = \frac{M \times C}{R}.
N=120×15030N = \frac{120 \times 150}{30}.
Multiplying the initial sample size by the second sample size and dividing by the recaptured marked count yields the total estimated population.
3
Perform the division and multiplication to solve for NN.
N=600N = 600.
Simplifying 15030=5\frac{150}{30} = 5, then 120×5=600120 \times 5 = 600 fish.

Key Concept

Lincoln Index (Mark-Release-Recapture Method)
Question 10Question

An ecology student investigated the population of spear grass (*Imperata cylindrica*) on a 400 m2400\text{ m}^2 plot in Jos, Plateau State. A rectangular quadrat measuring 1.0 m×0.5 m1.0\text{ m} \times 0.5\text{ m} was thrown randomly 16 times across the plot, yielding a total count of 120 spear grass plants. What is the estimated population density of spear grass in plants/m2\text{plants/m}^2?

Show answer & explanation

Answer: 15.0 plants/m215.0\text{ plants/m}^2

Answer

15.0 plants/m215.0\text{ plants/m}^2
The population density is defined as the total number of individuals of a species per unit area sampled. The area of one quadrat is 1.0 m×0.5 m=0.5 m21.0\text{ m} \times 0.5\text{ m} = 0.5\text{ m}^2. Sampling 16 times gives a total sampled area of 16×0.5 m2=8.0 m216 \times 0.5\text{ m}^2 = 8.0\text{ m}^2. Dividing the total count of 120 plants by 8.0 m28.0\text{ m}^2 yields 15.0 plants/m215.0\text{ plants/m}^2.

Step-by-Step Solution

1
Calculate the area of a single quadrat frame
Area of 1 quadrat=1.0 m×0.5 m=0.5 m2\text{Area of 1 quadrat} = 1.0\text{ m} \times 0.5\text{ m} = 0.5\text{ m}^2
Determines the sampling surface area covered by one throw.
2
Calculate the total area sampled across all quadrat throws
Total sampled area=16 throws×0.5 m2=8.0 m2\text{Total sampled area} = 16 \text{ throws} \times 0.5\text{ m}^2 = 8.0\text{ m}^2
Finds the total ground space inspected during the field survey.
3
Calculate the population density of spear grass per square metre
Population Density=Total plant countTotal sampled area=120 plants8.0 m2=15.0 plants/m2\text{Population Density} = \frac{\text{Total plant count}}{\text{Total sampled area}} = \frac{120\text{ plants}}{8.0\text{ m}^2} = 15.0\text{ plants/m}^2
Determines average number of organisms per unit area.

Key Concept

Quadrat Population Density Calculation
Estimated Time:1m 30s
Question 11Question

Match each population ecology term on the left with its correct definition on the right.

Click a left item, then click its matching right item

Items

Carrying capacity
Environmental resistance
Biotic potential
Natality

Matches

Show answer & explanation

Answer

Carrying capacity matches the maximum population size sustained indefinitely by a habitat; Environmental resistance matches the sum of factors restricting growth; Biotic potential matches the maximum growth rate under ideal conditions; Natality matches the rate of adding new individuals through birth.
Each ecological term is matched to its precise definition: Carrying capacity represents the maximum population size an ecosystem can sustain; Environmental resistance includes all physical and biological limiting factors; Biotic potential is the maximum reproductive capability under ideal conditions; Natality is the birth rate of a population.

Step-by-Step Solution

1
Define carrying capacity
Carrying capacity matches the description of maximum sustainable population size.
Ecosystem resources like food and space place an upper bound on population size.
2
Define environmental resistance
Environmental resistance matches the sum of all factors restricting population growth.
Biotic and abiotic factors work together to curb unlimited population expansion.
3
Define biotic potential
Biotic potential matches the maximum theoretical reproductive rate under ideal conditions.
It represents physiological capability to reproduce without environmental constraints.
4
Define natality
Natality matches the birth rate of individuals added per unit time.
Natality specifically concerns reproductive additions to the population.

Key Concept

Population Dynamics Parameters
Estimated Time:1m 0s
Question 12Question

In population ecology studies across Nigerian savanna ecosystems, several factors govern population size and growth rate. Match each population dynamic concept on the left with its corresponding ecological description on the right.

Click a left item, then click its matching right item

Items

Density-dependent factor
Density-independent factor
Carrying capacity (KK)
Biotic potential (rmaxr_{max})

Matches

Show answer & explanation

Answer

Density-dependent factor matches with the environmental limiting factor whose impact intensifies as population density increases; Density-independent factor matches with the abiotic environmental event causing mortality regardless of population density; Carrying capacity (KK) matches with the maximum sustainable population size a habitat can support; Biotic potential (rmaxr_{max}) matches with the theoretical maximum rate of population growth under ideal conditions.
Density-dependent factors fluctuate in influence based on population numbers (such as intraspecific competition). Density-independent factors influence mortality uniformly regardless of population density (such as abiotic fire or drought). Carrying capacity (KK) represents the maximum equilibrium population size an ecosystem's resources can maintain. Biotic potential (rmaxr_{max}) defines the maximum theoretical reproductive rate under optimal, unrestricted environmental conditions.

Step-by-Step Solution

1
Identify the characteristic of density-dependent regulation.
Density-dependent factors operate proportionately to population density (e.g., competition for food, spread of infectious parasites).
As population density rises, individual survival and reproduction drop due to increased resource competition.
2
Distinguish density-independent regulation.
Density-independent factors are physical/climatic perturbations that kill a fixed percentage of organisms regardless of density.
Abiotic catastrophes like wildfires affect sparse and dense populations equally.
3
Define carrying capacity (KK) and biotic potential (rmaxr_{max}).
Carrying capacity (KK) is environmental sustainability bound, whereas biotic potential (rmaxr_{max}) is maximum intrinsic reproductive output under zero environmental resistance.
Recognizing these equilibrium and theoretical growth parameters clarifies population growth curves (SS-curve and JJ-curve).

Key Concept

Population Regulation and Dynamic Growth Parameters
Estimated Time:1m 30s
Question 13Question

An ecology student sampled the population of guinea grass (*Panicum maximum*) in a 600 m2600\text{ m}^2 pasture plot in Kaiama, Kwara State, using a 0.5 m×0.5 m0.5\text{ m} \times 0.5\text{ m} quadrat frame. The counts of grass clumps recorded from 10 randomly placed quadrats were 4, 6, 3, 7, 5, 2, 8, 4, 6, and 5. What is the estimated total population of guinea grass clumps in the entire pasture plot?

Show answer & explanation

Answer: 12000

Answer

The estimated total population of guinea grass clumps in the pasture plot is 12,000 clumps.
To estimate total population size from quadrat samples, first determine the total area sampled (10 quadrats×0.25 m2=2.5 m210 \text{ quadrats} \times 0.25\text{ m}^2 = 2.5\text{ m}^2). Dividing the total count of organisms (50 clumps50\text{ clumps}) by this sampled area yields a population density of 20 clumps/m220\text{ clumps/m}^2. Multiplying the density by the total area of the plot (600 m2600\text{ m}^2) gives the estimated total population of 12,000 clumps12,000\text{ clumps}.

Step-by-Step Solution

1
Determine the surface area of a single quadrat frame
Area of one quadrat = 0.5 m×0.5 m=0.25 m20.5\text{ m} \times 0.5\text{ m} = 0.25\text{ m}^2
Knowing the individual quadrat dimensions is necessary to calculate the sample area.
2
Calculate the total area sampled across all 10 quadrats
Total area sampled = 10×0.25 m2=2.5 m210 \times 0.25\text{ m}^2 = 2.5\text{ m}^2
Ten quadrats were placed, so the total sample area equals ten times the single quadrat area.
3
Find the total count of organisms recorded in all samples
Total count = 4+6+3+7+5+2+8+4+6+5=50 clumps4 + 6 + 3 + 7 + 5 + 2 + 8 + 4 + 6 + 5 = 50\text{ clumps}
Summing individual counts across all sampling frames gives the total sample size.
4
Compute the average population density per unit area
Population density = 50 clumps2.5 m2=20 clumps/m2\frac{50\text{ clumps}}{2.5\text{ m}^2} = 20\text{ clumps/m}^2
Density is defined as total count divided by total sampled area.
5
Extrapolate population density to the entire study area
Total estimated population = 20 clumps/m2×600 m2=12,000 clumps20\text{ clumps/m}^2 \times 600\text{ m}^2 = 12,000\text{ clumps}
Multiplying population density per square metre by total plot area gives the estimated overall population size.

Key Concept

Extrapolation of population size from sample quadrat density
Question 14Question

An ecological survey was conducted in the Borgu sector of Kainji Lake National Park to estimate the population size of grasscutters (*Thryonomys swinderianus*). In the initial phase, 8080 grasscutters were captured, marked with ear tags, and released back into the habitat. One week later, a second sample of 100100 grasscutters was captured, out of which 2020 individuals retained their mark. If post-marking field monitoring established that 10%10\% of all originally marked animals lost their tags during the interval, what is the estimated total population size of grasscutters in the study area?

Show answer & explanation

Answer: 360

Answer

The estimated total population size of grasscutters in the study area is 360.
Accounting for a 10% tag loss reduces the active marked population from 80 to 72 individuals. Applying the Lincoln-Petersen index formula (N=M×CRN = \frac{M \times C}{R}) with M=72M = 72, C=100C = 100, and R=20R = 20 gives an estimated total population size of 360 grasscutters.

Step-by-Step Solution

1
Calculate the effective number of marked individuals (MeffM_{eff}) in the population considering the 10% tag loss.
Meff=80×(10.10)=72M_{eff} = 80 \times (1 - 0.10) = 72 marked individuals.
Animals that lost their tags no longer register as marked upon recapture, effectively reducing the active marked proportion in the population.
2
Substitute Meff=72M_{eff} = 72, total recaptured C=100C = 100, and marked recaptured R=20R = 20 into the Lincoln-Petersen index formula N=Meff×CRN = \frac{M_{eff} \times C}{R}.
N=72×10020=360N = \frac{72 \times 100}{20} = 360.
The proportion of marked individuals in the recaptured sample equals the proportion of effective marked individuals in the total population.

Key Concept

Lincoln-Petersen Mark-Recapture Index with Sampling Bias Adjustment
Question 15Question

An ecological researcher investigated the population of freshwater snails (*Bulinus globosus*) in a stream marsh measuring 250 m2250\text{ m}^2 near Oguta Lake, Imo State. Using a quadrat frame of size 0.5 m20.5\text{ m}^2, the researcher randomly threw the quadrat 1010 times across the sampling site and recorded snail counts of 4,6,3,5,7,2,8,4,5,4, 6, 3, 5, 7, 2, 8, 4, 5, and 66. Based on these sample measurements, what is the estimated total population size of *Bulinus globosus* in the entire 250 m2250\text{ m}^2 marsh area?

Show answer & explanation

Answer: 2,500 snails2,500\text{ snails}

Answer

The estimated total population size of Bulinus globosus in the marsh plot is 2,500 snails.
To estimate total population size using quadrat sampling, calculate the total area sampled (10×0.5 m2=5 m210 \times 0.5\text{ m}^2 = 5\text{ m}^2). Divide the total count of organisms (50 snails50\text{ snails}) by the total sampled area (5 m25\text{ m}^2) to obtain a population density of 10 snails/m210\text{ snails/m}^2. Multiplying this density by the total marsh plot area (250 m2250\text{ m}^2) yields the correct total population estimate of 2,500 snails2,500\text{ snails}.

Step-by-Step Solution

1
Calculate the total number of organisms counted across all sampled quadrats
Sum of counts = 4+6+3+5+7+2+8+4+5+6=50 snails4 + 6 + 3 + 5 + 7 + 2 + 8 + 4 + 5 + 6 = 50\text{ snails}
Determines the total sample count obtained from field sampling.
2
Calculate the total surface area sampled by the quadrats
Total sampled area = Number of quadrats×Area of one quadrat=10×0.5 m2=5 m2\text{Number of quadrats} \times \text{Area of one quadrat} = 10 \times 0.5\text{ m}^2 = 5\text{ m}^2
Required to compute the population density per square metre.
3
Calculate the mean population density per unit area
Density = Total organism countTotal sampled area=50 snails5 m2=10 snails/m2\frac{\text{Total organism count}}{\text{Total sampled area}} = \frac{50\text{ snails}}{5\text{ m}^2} = 10\text{ snails/m}^2
Provides the average concentration of organisms per square metre.
4
Extrapolate the density to estimate the total population in the study area
Total population = Population density×Total study area=10 snails/m2×250 m2=2,500 snails\text{Population density} \times \text{Total study area} = 10\text{ snails/m}^2 \times 250\text{ m}^2 = 2,500\text{ snails}
Scales the sample density to the full size of the habitat plot.

Key Concept

Population Density and Quadrat Sampling Calculation
Question 16Question

An biology student placed a 1 m21\text{ m}^2 quadrat 10 times randomly in a grassland plot within Yankari Game Reserve to estimate the population density of wild marigold (*Tithonia diversifolia*). A total of 150 wild marigold plants were counted across all 10 quadrat samples. What is the population density of the wild marigold plants in organisms per square metre?

Show answer & explanation

Answer: 15

Answer

The population density of wild marigold plants is 15 plants/m215\text{ plants/m}^2.
Population density is calculated using the formula: Population Density=Total number of individuals countedTotal area sampled\text{Population Density} = \frac{\text{Total number of individuals counted}}{\text{Total area sampled}}. Since 10 quadrats of 1 m21\text{ m}^2 each were thrown, the total area sampled is 10 m210\text{ m}^2. Dividing 150 plants by 10 m210\text{ m}^2 yields 15 plants/m215\text{ plants/m}^2.

Step-by-Step Solution

1
Calculate total area sampled
Total area = 10 m210\text{ m}^2
The area of a single quadrat is 1 m21\text{ m}^2 and 10 quadrats were sampled in total.
2
Calculate population density
Density = 15 plants/m215\text{ plants/m}^2
Population density is determined by dividing the total count of organisms by the total sampled area.

Key Concept

Calculating population density using quadrat sampling data.
Question 17Question

An ecologist conducted a mark-release-recapture study to estimate the population size of fiddler crabs (*Uca tangeri*) in a mangrove swamp along the Bonny Estuary in Rivers State. During the first sampling session, 150150 crabs were captured, marked with non-toxic waterproof paint, and released back into the habitat. One week later, a second sample of 120120 crabs was captured from the same area, of which 4040 were found to be marked. What is the estimated total population size of fiddler crabs in this sampled area?

Show answer & explanation

Answer: 450

Answer

The estimated total population size of fiddler crabs in the sampled area is 450.
The estimated population size is calculated using the Lincoln-Petersen index formula N=M×CRN = \frac{M \times C}{R}, where M=150M = 150, C=120C = 120, and R=40R = 40. Substituting these values gives N=150×12040=450N = \frac{150 \times 120}{40} = 450 crabs.

Step-by-Step Solution

1
Extract the given values for the mark-release-recapture formula
Marked initially (MM) = 150150; Total captured in second sample (CC) = 120120; Marked recaptures (RR) = 4040.
These three quantitative metrics are required to calculate the population estimate.
2
Apply the Lincoln-Petersen Index formula: N=M×CRN = \frac{M \times C}{R}
N=150×12040N = \frac{150 \times 120}{40}
The index assumes that the proportion of marked individuals in the second sample equals the proportion of marked individuals in the total population.
3
Compute the final population estimate (NN)
N=450N = 450
Dividing 120120 by 4040 yields 33, and multiplying 150150 by 33 gives 450450 crabs.

Key Concept

Lincoln-Petersen Index for Animal Population Estimation
Estimated Time:1m 30s
Question 18Question

A biology researcher used a 0.5 m20.5\text{ m}^2 quadrat thrown 20 times at random to estimate the population of Mexican sunflower (*Tithonia diversifolia*) in a cashew orchard measuring 500 m2500\text{ m}^2 in Ilorin. If a total of 160 plants were counted across all quadrat throws, what is the estimated total population size of *Tithonia diversifolia* in the orchard?

Show answer & explanation

Answer: 8,000 plants

Answer

The estimated total population size of *Tithonia diversifolia* in the orchard is 8,000 plants.
To find the estimated population size, first calculate the total area sampled (20×0.5 m2=10 m220 \times 0.5\text{ m}^2 = 10\text{ m}^2). Next, calculate the population density (160 plants/10 m2=16 plants/m2160\text{ plants} / 10\text{ m}^2 = 16\text{ plants/m}^2). Finally, multiply the density by the total area of the orchard (16 plants/m2×500 m2=8,000 plants16\text{ plants/m}^2 \times 500\text{ m}^2 = 8,000\text{ plants}).

Step-by-Step Solution

1
Calculate the total area sampled by all quadrat throws.
Total sampled area = 20 throws×0.5 m2=10 m220 \text{ throws} \times 0.5\text{ m}^2 = 10\text{ m}^2.
Population density must be calculated relative to the total area examined, not just a single quadrat.
2
Calculate the average population density per square metre.
Population density = 160 plants10 m2=16 plants/m2\frac{160\text{ plants}}{10\text{ m}^2} = 16\text{ plants/m}^2.
Density is determined by dividing total organisms counted by total sampled area.
3
Extrapolate population density to the entire study area.
Estimated total population = 16 plants/m2×500 m2=8,000 plants16\text{ plants/m}^2 \times 500\text{ m}^2 = 8,000\text{ plants}.
Multiplying mean density per unit area by total habitat area yields the estimated total population size.

Key Concept

Population Density and Extrapolation using Quadrat Sampling
Estimated Time:1m 30s
Question 19Question

An ecology student placed a 0.5 m20.5\text{ m}^2 quadrat 1010 times at random within a plot in Okomu National Park to estimate the population of Siam weed (*Chromolaena odorata*). If a total count of 120120 Siam weed plants was recorded across all sample throws, what is the estimated population density of Siam weed in plants per square metre?

Show answer & explanation

Answer: 24 plants/m224\text{ plants/m}^2

Answer

The estimated population density of Siam weed is 24 plants/m224\text{ plants/m}^2.
To estimate population density per unit area using quadrat sampling, the total number of individuals counted (120120) must be divided by the total area of all quadrats combined (10×0.5 m2=5.0 m210 \times 0.5\text{ m}^2 = 5.0\text{ m}^2). Dividing 120120 by 5.0 m25.0\text{ m}^2 yields 24 plants/m224\text{ plants/m}^2.

Step-by-Step Solution

1
Calculate the total area sampled by the quadrat throws.
Total Sampled Area=Number of Throws×Area of One Quadrat=10×0.5 m2=5.0 m2\text{Total Sampled Area} = \text{Number of Throws} \times \text{Area of One Quadrat} = 10 \times 0.5\text{ m}^2 = 5.0\text{ m}^2
Population density must be calculated over the aggregate area covered by all sampling units combined.
2
Determine the population density per square metre.
Population Density=Total Number of OrganismsTotal Sampled Area=120 plants5.0 m2=24 plants/m2\text{Population Density} = \frac{\text{Total Number of Organisms}}{\text{Total Sampled Area}} = \frac{120\text{ plants}}{5.0\text{ m}^2} = 24\text{ plants/m}^2
Density measures the number of individuals per unit area.

Key Concept

Quadrat Population Density Calculation
Question 20Question

During a field study on population dynamics in a secondary forest plot in Ogun State, 8080 African giant land snails (*Archachatina marginata*) were captured, tagged, and released back into their habitat. A fortnight later, a second sample of 5050 snails was collected, revealing that 1616 of them bore the original tags. What is the estimated total population size of these snails in the forest plot using the Lincoln Index?

Show answer & explanation

Answer: 250

Answer

The estimated total population size of snails in the forest plot is 250.
The estimated total population size NN is calculated using the Lincoln Index formula N=M×CRN = \frac{M \times C}{R}, where M=80M = 80 (initially marked), C=50C = 50 (second capture total), and R=16R = 16 (recaptured marked). Substituting these values yields N=80×5016=250N = \frac{80 \times 50}{16} = 250 snails.

Step-by-Step Solution

1
Extract the given sample data for the Lincoln Index variables.
Initial marked count (MM) = 80, second sample total (CC) = 50, recaptured marked count (RR) = 16.
The mark-release-recapture method relies on the proportion of marked individuals recaptured in the second sample.
2
Set up the Lincoln Index equation.
N=M×CRN = \frac{M \times C}{R}
This formula assumes that marked and unmarked individuals mix randomly throughout the population and have equal probability of recapture.
3
Calculate the estimated population size (NN).
N=80×5016=400016=250N = \frac{80 \times 50}{16} = \frac{4000}{16} = 250
Performing the arithmetic yields the estimated total population size.

Key Concept

Population Estimation using Mark-Release-Recapture (Lincoln Index)
Page 1 / 2Next
Population Dynamics and Ecological Sampling Practice Questions — JAMB UTME | Examkin