Calculate Simpson's Diversity Index, Lincoln Index, and population growth. With visual charts, step-by-step solutions, and quadrat sampling analysis. Perfect for GCSE and A-Level Biology.
Simpson's Diversity Index — measure biodiversity from species counts
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Ecology is the study of interactions between organisms and their environment. It covers how populations grow and change, how species interact in communities, and how ecosystems function as a whole.
In GCSE and A-Level Biology, ecology involves fieldwork (quadrat sampling, transects, capture-recapture) and data analysis (diversity indices, population estimates, growth models). This calculator handles all the key calculations.
All organisms of the same species living in the same area at the same time
All the different species living and interacting in the same area
A community of organisms and their non-living environment (abiotic factors)
The variety of species in an area. Measured using indices like Simpson's D
Non-living factors that affect organisms: temperature, light, water, pH, soil
Living factors: predation, competition, disease, food availability
Studying a small area to estimate what the whole habitat is like. Must be random and representative
A square frame (e.g. 0.25 m²) placed on the ground to count organisms in a defined area
Simpson's Diversity Index is the most commonly used measure of biodiversity at GCSE and A-Level. It accounts for both the number of species (species richness) and the evenness of their distribution.
A pond survey finds: 10 dragonflies, 8 frogs, 5 newts.
N = 10 + 8 + 5 = 23
n(n-1): 10(9) = 90, 8(7) = 56, 5(4) = 20
Sum = 90 + 56 + 20 = 166
N(N-1) = 23 × 22 = 506
D = 1 - 166/506 = 1 - 0.328 = 0.672 (High diversity)
Practice with these GCSE and A-Level style ecology problems:
Q: A student counts 15 daisies, 8 buttercups, and 5 clover plants in a field. Calculate the Simpson's Diversity Index.
A: N = 15 + 8 + 5 = 28. n(n-1): 15(14) = 210, 8(7) = 56, 5(4) = 20. Sum = 286. N(N-1) = 28 × 27 = 756. D = 1 - 286/756 = 1 - 0.378 = 0.622 (Moderate-high diversity).
Exam Tip: Remember: it's n(n-1), NOT n². The formula is D = 1 - Sum/N(N-1).
Q: A student catches 20 woodlice, marks them with a dot of paint, and releases them. The next day, she catches 30 woodlice, 5 of which are marked. Estimate the total population.
A: M = 20, C = 30, R = 5. N = (M × C) / R = (20 × 30) / 5 = 600 / 5 = 120 woodlice.
Exam Tip: Always state assumptions: closed population, random mixing, marks do not affect survival.
Q: A bacterial colony starts with 100 cells and has a growth rate of r = 0.5 per hour. (a) After 10 hours with unlimited resources? (b) After 10 hours with K = 10000?
A: (a) Exponential: N = 100 × e^(0.5 × 10) = 100 × e^5 = 100 × 148.41 = 14,841 bacteria. (b) Logistic: N = 10000 / (1 + (9900/100) × e^(-5)) = 10000 / (1 + 99 × 0.00674) = 10000 / 1.667 = 5,997 bacteria (approaching but not yet at K).
Exam Tip: Exponential gives the J-curve. Logistic gives the S-curve with growth slowing near K.
Q: A student places 30 quadrats (each 0.25 m²) randomly in a meadow. Daisies are found in 24 quadrats, buttercups in 18. Calculate frequency and density for each.
A: Daisy frequency = (24/30) × 100 = 80%. Buttercup frequency = (18/30) × 100 = 60%. Total area = 30 × 0.25 = 7.5 m². Daisy density = 24/7.5 = 3.2 per m². Buttercup density = 18/7.5 = 2.4 per m².
Exam Tip: Frequency is a percentage. Density needs units (per m²). State that quadrats were placed randomly.
Q: A hedgehog population falls from 1200 to 840 over 5 years. Calculate the percentage change.
A: % change = (840 - 1200) / 1200 × 100 = -360/1200 × 100 = -30%. The population decreased by 30%.
Exam Tip: Always divide by the ORIGINAL value (1200), not the new value (840). This is the most common exam mistake.
Using n² instead of n(n-1)
Simpson's uses n(n-1), NOT n². This accounts for sampling without replacement.
Wrong N in Simpson's
N is the TOTAL organism count, not the number of species. Species count is 'species richness'.
Forgetting Lincoln Index assumptions
Always state: closed population, random mixing, marks unaffected, equal capture probability.
Non-random quadrat placement
Use random number coordinates to place quadrats. Deliberate placement introduces sampling bias.
Dividing by new value in % change
Always divide by the ORIGINAL value: (new - original) / original × 100.
Confusing exponential and logistic
Unlimited resources = exponential (J-curve). Carrying capacity present = logistic (S-curve).
Simpson's Diversity Index (D) measures biodiversity. It ranges from 0 (single species) to 1 (many equally abundant species). The formula is D = 1 - Sum of n(n-1) / N(N-1).
The Lincoln Index estimates total population size using capture-recapture data. It is used for mobile organisms like snails, fish, or insects that cannot be counted directly.
Use exponential growth when resources are unlimited (J-curve). Use logistic growth when there is a carrying capacity K — the maximum sustainable population (S-curve).
Carrying capacity is the maximum population size an environment can sustain. It is limited by food, water, space, and shelter. In the logistic model, growth slows as the population approaches K.
Population density = number of organisms / area. Units are typically organisms per m² (or per km² for larger areas). Always include the unit.
Random sampling prevents bias. If you choose where to sample, you might unconsciously select unusual areas. Random placement ensures results are representative of the whole habitat.
Frequency is the percentage of quadrats containing a species (presence/absence). Density is the number of organisms per unit area. A species can have high frequency but low density.
Yes! It covers all GCSE and A-Level ecology calculations: Simpson's Index, Lincoln Index, population growth, quadrat sampling, and percentage change with step-by-step solutions.
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