IB Biology: Nutrient Cycling
Understanding: The supply of inorganic nutrients is maintained by nutrient cycling.
Nutrients refer to the material required by an organism, and include elements such as carbon, nitrogen
and phosphorus.
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The supply of inorganic nutrients on Earth is finite – new elements cannot simply be created and
so are in limited supply
Hence chemical elements are constantly recycled after they are used:
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Autotrophs obtain inorganic nutrients from the air, water and soil and convert them into organic
compounds
Heterotrophs ingest these organic compounds and use them for growth and respiration, releasing
inorganic byproducts
When organisms die, saprotrophs decompose the remains and free inorganic materials into the
soil
The return of inorganic nutrients to the soil ensures the continual supply of raw materials for the
autotrophs
Nutrient Cycling
IB Biology: Chi-squared test
Skill: Testing for association between two species using the chi-squared test with data
obtained by quadrat sampling.
The presence of two species within a given environment will be dependent upon potential
interactions between them. If two species are typically found within the same habitat, they
show a positive association.
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Species that show a positive association include those that exhibit predator-prey or
symbiotic relationships
If two species tend not to occur within the same habitat, they show a negative association

Species will typically show a negative association if there is competition for the same
resources
o One species may utilize the resources more efficiently, precluding survival of the
other species (competitive exclusion)
o Both species may alter their use of the environment to avoid direct competition
(resource partitioning)
If two species do not interact, there will be no association between them and their distribution
will be independent of one another
Quadrat Sampling
The presence of two species within a given environment can be determined using quadrat
sampling
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A quadrat is a rectangular frame of known dimensions that can be used to establish
population densities
o Quadrats are placed inside a defined area in either a random arrangement or
according to a design (e.g. belted transect)
o The number of individuals of a given species is either counted or estimated via
percentage coverage
o The sampling process is repeated many times in order to gain a representative
data set
Quadrat sampling is not an effective method for counting motile organisms – it is used for
counting plants and sessile animals
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In each quadrat, the presence or absence of each species is identified
This allows for the number of quadrats where both species were present to be
compared against the total number of quadrats
Quadrat Sampling Method
Chi-Squared Tests
A chi-squared test can be applied to data generated from quadrat sampling to determine if
there is a statistically significant association between the distribution of two species
A chi-squared test can be completed by following five simple steps:
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Identify hypotheses (null versus alternative)
Construct a table of frequencies (observed versus expected)
Apply the chi-squared formula
Determine the degree of freedom (df)
Identify the p value (should be <0.05)
Skill: Recognizing and interpreting statistical significance
Example of Chi-Squared Test Application
The presence or absence of two species of scallop was recorded in fifty quadrats (1m 2) on a
rocky sea shore
The following distribution pattern was observed:

6 quadrats = both species ; 15 quadrats = king scallop only ; 20 quadrats = queen
scallop only ; 9 quadrats = neither species
Step 1: Identify hypotheses
A chi-squared test seeks to distinguish between two distinct possibilities and hence requires
two contrasting hypotheses:
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Null hypothesis (H0): There is no significant difference between the distribution of two
species (i.e. distribution is random)
Alternative hypothesis (H1): There is a significant difference between the distribution of
species (i.e. species are associated)
Step 2: Construct a table of frequencies
A table must be constructed that identifies expected distribution frequencies for each species
(for comparison against observed)
Expected frequencies are calculated according to the following formula:
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Expected frequency = (Row total × Column total) ÷ Grand total
Step 3: Apply the chi-squared formula
The formula used to calculate a statistical value for the chi-squared test is as follows:
Where: ∑ = Sum ; O = Observed frequency ; E = Expected frequency
These calculations can be broken down for each part of the distribution pattern to make the
final summation easier
Based on these results the statistical value calculated by the chi-squared test is as follows:
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𝝌2 = (2.20 + 2.38 + 1.59 + 1.73) = 7.90
Step 4: Determine the degree of freedom (df)
In order to determine if the chi-squared value is statistically significant a degree of freedom
must first be identified
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The degree of freedom is a mathematical restriction that designates what range of
values fall within each significance level
The degree of freedom is calculated from the table of frequencies according to the following
formula:
df = (m – 1) (n – 1)
Where:
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m = number of rows
;
n = number of columns
When the distribution patterns for two species are being compared, the degree of
freedom should always be 1
Step 5: Identify the p value
The final step is to apply the value generated to a chi-squared distribution table to determine if
results are statistically significant
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A value is considered significant if there is less than a 5% probability (p < 0.05) the
results are attributable to chance
When df = 1, a value of greater than 3.841 is required for results to be considered statistically
significant (p < 0.05)
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A value of 7.90 lies above a p value of 0.01, meaning there is less than a 1% probability
results are caused by chance
Hence, the difference between observed and expected frequencies are statistically
significant
As the results are statistically significant, the null hypothesis is rejected and the alternate
hypothesis accepted:
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Alternate hypothesis (H1): There is a significant difference between observed and
expected frequencies
Because the two species do not tend to be present in the same area, we can infer there
is a negative association between them
Practice Question
Two species of fir tree are found along the coast of Southern California.
These two tree species are the Grand Fir (Abies grandis) and the Noble Fir (Abies procera).
Their distribution patterns were establsihed via 150 quadrat samples, yielding the following results:
25 = both present ; 30 = Noble Fir only ; 45 = Grand Fir only ; 50 neither present
Activity: Use the chi-squared test to determine if these two plant species show association.
IB Biology: Chi-squared table
A chi-squared table shows the distribution of critical values according to each degree of freedom. This
allows for an assessment to be made as to whether the data is statistically significant (p<0.05) or not.
For accurate data, the following conditions should be met:
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All items in the group should be independent and collected on a random basis
No group should contain very few items (e.g. less than 10)
The total number of items should be large (e.g. more than 50)
Chi Squared Distribution Table