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First teaching 2023

First exams 2025

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Estimating Population Size (SL IB Biology)

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Naomi H

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Naomi H

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Random Sampling

  • Finding out about the abundance and distribution of populations can be achieved by counting all of the organisms present in a habitat
  • This is possible for areas that are very small or where the species involved is very large
  • For larger and more complex habitats it is not possible to find, identify, and count every organism that is present
  • When this is the case, sampling can be used to make an estimate for the total species numbers
    • Sampling involves measuring small samples of a population that act to represent the whole population

Sampling

  • Sampling is a method of investigating the abundance and distribution of populations
  • There are two different types of sampling
    • Random
    • Systematic
  • In random sampling the positions of the sampling points are selected at random
    • This method avoids bias by the person that is carrying out the sampling
    • Bias can affect the results, e.g.
      • A student might choose to carry out samples in a particular location because it looks interesting, and this might give the impression that the habitat contains more species than it really does
  • In systematic sampling the positions of the sampling points are located at fixed intervals throughout the sampling site
    • This avoids accidentally missing out sections of habitat due to chance
    • Systematic sampling allows researchers to investigate the effect of the presence of certain environmental features on species distribution, e.g. by taking samples along a line that extends away from an environmental feature such as a river
      • A line of this type is known as a transect
  • When a sampling area is reasonably uniform then random sampling is the best choice
  • Random sample sites can be selected by
    • Laying out a grid over the area to be studied
    • Generating random number co-ordinates 
    • Placing sample sites in the grid squares that match the random number co-ordinates

Random & systematic sampling diagram

Random and Systematic Sampling

Random sampling involves selecting sample sites at random while systematic sampling involves placing sample sites at regular intervals

NOS: Students should be aware that random sampling, instead of measuring an entire population, inevitably results in sampling error

  • A population estimate that is based on sampling makes the assumption that individuals are distributed evenly across the sample site, e.g.
    • Random sampling may happen to miss an area of a site in which no individuals are present; this will result in an overestimate of population size
    • Random sampling may happen to miss an area of a site where many individuals are present; this will result in an underestimate of population size
  • There are many factors that influence the distribution of a population, so an even distribution is very unlikely, and so the chance of sampling error occurring when calculating such an estimate is very high
    • A sampling error is the difference between an estimated population size and a true population size
    • This occurs when a sample is not truly representative of a whole population
  • Sampling error can be minimised by good investigation design, e.g. carrying out the right type of sampling and taking a large enough sample size
  • When scientists write about their findings they must include details of any experimental methods used; this allows their readers to evaluate any error that may be present in the results

Random Quadrat Sampling

Sampling using frame quadrats

  • A frame quadrat is a square frame that is placed within the area to be studied to provide a sample
    • Quadrats are used to study the distribution of sessile organisms
    • Quadrats can be different sizes depending on the species being studied
      • A 1 m² quadrat can be used to study small organisms such as herbaceous plants in a grassland or limpets on a rocky shore
      • A 400 m² quadrat can be used to study large organisms such as trees
        • Quadrats like this will usually be marked out with string rather than a frame!
  • Frame quadrats can be placed in a habitat randomly, e.g. using random co-ordinates, or systematically, e.g. along a transect

Frame quadrat diagram

Quadrat in use

A frame quadrat can be used to measure abundance and distribution

  • Scientists can record different types of data from a frame quadrat depending on the aim of a study and the species involved
    • Presence or absence of a species
    • Species frequency; how many individuals are in the quadrat
    • Species abundance; measured on a scale called the ACFOR scale on which species are recorded as being abundant, common, frequent, occasional, rare, or none
    • Percentage cover; the percentage of the quadrat covered by a species
      • Quadrats can be divided up into smaller squares to allow percentage cover to be assessed more easily

Recording percentage cover diagram

Percentage Cover in Quadrat

Abundance in a frame quadrat can be assessed by measuring percentage cover

Analysing results

  • Quantitative investigations of variation can involve the interpretation of mean values and their standard deviations
    • A mean value describes the average value of a data set
    • Standard deviation is a measure of the spread or dispersion of data around the mean
      • A small standard deviation indicates that the results lie close to the mean, so there is little variation
      • A large standard deviation indicates that the results are more spread out around the mean, so there is a lot of variation
  • In the quadrat study described here, a mean could be calculated for the number of individuals of a species found in each quadrat, and then the standard deviation could be calculated to find out how spread out the data points are around the mean
    • This would give an indication of how evenly distributed the population is across the habitat

Small vs large standard deviation graph

Graph showing a large and a small standard deviation

A small standard deviation shows that data are closely grouped around the mean while a large standard deviation shows that data are spread widely around the mean

Estimating Population Size: Motile Organisms

Capture-mark-release-recapture

  • The sampling methods described above are only useful for non-motile (sessile) organisms
  • Different methods are required for estimating the number of individuals in a population of motile organisms
    • The mark-release-recapture method can be used
  • The mark-release-recapture method is carried out as follows:
    • The first large sample is taken; as many individuals as possible are caught, counted and marked in a way that won’t affect their survival
      • e.g. if studying a species of beetle, a small amount of brightly coloured non-toxic paint can be applied to their wing cases
    • The marked individuals are returned to their habitat and allowed to randomly mix with the rest of the population
    • When a sufficient time period has passed another large sample is captured
    • The number of marked and unmarked individuals within the sample are counted
    • The proportion of marked to unmarked individuals is used to calculate an estimate of the population size using a statistical measure known as the Lincoln index

Population size = M × bold N over bold R

      • Where:
        • M = number of marked individuals in the first sample
        • N = total number of individuals in the second sample (marked and unmarked)
        • R = number of marked individuals recaptured in the second sample

Worked example

Scientists wanted to investigate the abundance of leafhoppers in a small grassy meadow.

They used nets to catch a large sample of leafhoppers. Each insect was marked on its underside with non-toxic, waterproof paint and then released back into the meadow.

The following week another large sample was caught using sweep nets.

Use the figures below to estimate the size of the leafhopper population in this meadow.

  • No. caught and marked in first sample  (M) = 236
  • No. caught in second sample (N) = 244
  • No. of marked individuals recaptured in the second sample (R)  = 71

Answer:

Step One: Write out the Lincoln index equation and substitute in the known values

N = M x straight N over straight R

N = 236 × 244 over 71

Step Two: Calculate the population size estimate (N)

N = 236 x 3.44

N = 811.84

= 812 (to the nearest whole organism)

  • The Lincoln index makes some assumptions about the population and the capture-mark-release-recapture method:
    • The marked individuals disperse and mix back in fully with the main population
    • The marking doesn't affect the survival rates of the marked individuals, e.g. doesn't make them more visible and therefore more likely to be predated
    • The marking remains visible throughout the sampling and doesn't rub off
    • The population stays the same size during the study period, i.e.
      • There are no significant changes in population size due to births and deaths
      • There are no migrations into or out of the main population

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Naomi H

Author: Naomi H

Expertise: Biology

Naomi graduated from the University of Oxford with a degree in Biological Sciences. She has 8 years of classroom experience teaching Key Stage 3 up to A-Level biology, and is currently a tutor and A-Level examiner. Naomi especially enjoys creating resources that enable students to build a solid understanding of subject content, while also connecting their knowledge with biology’s exciting, real-world applications.