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Scott Deken
COA Field Ecology & Natural History
Grasshopper Population Estimation
One of the most wide-spread sampling techniques used to estimate wildlife populations is the
mark and recapture technique, also known as the Peterson Index.
I begin this lab with giving the students a bag of M & M’s or Skittles or something small
with multiple colors. Using small sample sizes they are to figure out how many candy
individuals are in the bag. They should come to the conclusion that they can estimate the
number using ratios.
Population/Density of Grasshoppers in a particular area.
Time: Day 1 – about 90 minutes
Day 2 – about 45 minutes
Say you wanted to estimate the density of grasshoppers in a particular area. Students use a
butterfly net or their hands to catch as many grasshoppers they can. Each grasshopper is
painted with nail polish as a tag, counted, and then released into the same area. The
grasshoppers are painted on the pronotum (the large plate just in back of its head which looks
a little like a saddle). 24 to 48 hours later the students repeat the sampling process, capturing
both marked and unmarked grasshoppers. The proportion of marked to unmarked
individuals gives an estimate of the size of the entire population.
The following equation, known as the Peterson Index, gives an estimate of the number of
individuals in the population:
Total Marked on Day 1 – M
Total Captured on Day 2 – S
Total Marked & Recaptured on Day 2 – R
Estimate of Population Size – N
R = S
M
N
Scott Deken
COA Field Ecology & Natural History
Rearrangement of this equation:
N = SM
R
For example, say on Monday the students capture and paint 80 grasshoppers. On Tuesday,
they capture 60 grasshoppers in the same area. If 10 grasshoppers of this second catch were
grasshoppers with paint marks (recaptures) then the population estimate would be:
Total Population = (50 x 60) / 10 = 300 grasshoppers
If this work was done in an area of 200 sq. meters, then the density of grasshoppers can also
be determined.
Density = 300 grasshoppers / 200 m2
Or 1.5 grasshoppers per m2
The Peterson Index only gives a reasonable estimate of population size if both marked and
unmarked individuals have the same probability of being captured. This is not always a safe
assumption, however. Colored nail polish on the pronotum of the grasshopper could make
the grasshopper more obvious to predators and thus are eaten at a higher rate than unmarked
grasshoppers. If the nail polish is toxic, the grasshoppers might die at a higher rate than
unmarked grasshoppers. Marked grasshoppers might remember their previous days ordeal
and hide more rigorously from the students on the second day and be more difficult to
capture. If the organisms studied are caught in traps with food, they may deliberately return
to the trap for more food and thus be caught more frequently.
Extensions
Discuss their population distribution – Clumped, uniform, random – in this small area and
across the school property as a whole.
Discuss limits to the population - Density Dependent Factors & Density Independent Factors.
Identify the species of grasshoppers caught.
Update grasshopper populations yearly. What is the cause of the variation?
Discuss in terms of Hardy-Weinberg assumptions (gene frequencies stay the same if there
is random mating, a large population size, no sexual selection, no gene flow, no
mutations).
Construct a pyramid of numbers:
First trophic level – all autotrophs
Second trophic level – all herbivores (grasshoppers + others that would need to be
counted)
Third trophic level – all carnivores (birds, mice, frogs, etc)
Fourth trophic level (predatory birds, fox, etc.)