Transcript Laboratory 1: Nearest Neighbor

Substrate and Time of
Day Effects on Benthic
Organisms
Trawling Data


Both Day and Night Data in HeckShare Folder
Pool trawl data into per habitat for comparisons
between habitats, and between day/night for
sand and mud.
i.e. Day Trawling – Trawls 2,3 combine for shell
 Compare combined Day Trawls for mud with
combined Night Trawls for mud

Similarity Calculations

Compare similarity in fish/invert species
composition during day between:


Mud-Sand; Mud-Shell; Sand-Shell (Day and Night)
Use Jaccard similarity index:
J = C / (A+B-C)
 A = No. of spp. on substrate 1
 B = No. of spp. On substrate 2
 C = No. of spp. shared by both substrates


Value varies from 0 (no common spp.) to 1 (all
common)
Similarity Calculations
Mud Sand Shell
Mud 1
Sand
1
Shell
1
If Sand has 22 spp.
Mud has 20 spp.
10 spp. overlap
J = 10 / (22+20-10)
J = 0.3125
Euclidean Distance

Considers the distribution of individuals with
species in each collection:

DeltaJK = Sqrt [ Sum (Xif – Xik)2 ]
DeltaJK = Euclidean Distance
 Xif = Number indiv’s of species “i” in collection “j”
 Xij= Number indiv’s of species “i” in collection “k”
 n = Total number of species

Euclidean Distance

Compensate for fact that Euclidean Distance
increases with number of species in a sample by
calculating average distance:

djk = [ Sqrt ( Delta2jk) ] / (n)
djk = average Euclidean distance b/n sample j and k
 Deltajk = Euclidean Distance
 n = number of species in the samples being
compared

Euclidean Dist. Calculations
Site 1 Site 2 Site 3
Sp. 1 2000 1000 500
Sp. 2 20 10
5
Sp. 3 0
5
0
ED1,2 = sqrt [ (2000-1000)2 + (20-10)2 + (0-5)2 ]
ED1,3 = sqrt [ (2000-500)2 + (20-5)2 + (0-0)2 ]
ED2,3 = sqrt [ (1000-500)2 + (10-5)2 + (5-0)2 ]
Questions

Explain why you found the similarity values you
did, using material from lecture, notes, text,
observations

Discuss why Jaccard and Euclidean distances
showed different patterns (if they did)

Describe similarities and differences in body
shape, shell thickness, and general morphology
of the taxa inhabiting various substrates
Laboratory: Competition
and relating Habitat Size
to Number of Individuals
Number of mud crabs
Regression
35
30
25
20
15
10
5
0
y = 0.0396x + 0.8
R² = 0.608
0
100
200
300
400
500
600
700
Oyster colony volume (cm3)

m = 0.396; b = 0.8

For any oyster clump volume (x), one can
predict the expected number of mud crabs (y)
Number of mud crabs
Regression
35
30
25
20
15
10
5
0
P = 0.001
y = 0.0396x + 0.8
R² = 0.608
0
100
200
300
400
500
600
700
Oyster colony volume (cm3)

If linear relationship strong (R2 ~ 1; p<0.05), then
suggests clumps could be at or near carrying capacity K

If only one mature male present, indicates males
compete for space and for females
Questions

1. How strong is the relationship between oyster clump
volume and the number of mud crabs?

2. Use the results to design a means of testing whether
competition is responsible for the patterns observed.

3. Indicate how factors (e.g. presence of stone crabs or
predatory fish) may be involved in explaining your
results and how you would test their importance.
Predation Experiments
Methods

Every 24 hours, check tethered crabs
Record identity and size of consumed animals
 Replace lost animals each day so that original density
of 3 animals/tether maintained over next 2 trials


Any escapes or unconfirmed predation, do
not count them in analysis.

In raw data, identify any escaped crabs
Data Analysis

Compare % of mud crabs, hermits consumed on each
of the two habitats using Chi-Square
Also evaluate whether crab size or type of a hermit
crab’s shell was correlated with percentage of prey
taken by predators
% Eaten per 24 hours

100
90
80
70
60
50
40
30
20
10
0
1
2
3
4
5
Crab Size (CW or Shell Length)
6
7
Chi-Square

Compares theorized predictions vs. observed
data
Ho = no sig diff b/n theorized and exp. populations
 Ha = There is a sig diff b/n theorized and exp. Pops



Chi-Square (χ2) = [ Sum (#observed – #expected)2 ] /
[ #expected ]
Calculate χ2 value and compare to Table 2 at
p=0.05 (on page 55)
Chi-Square Contingency Tables

Take observations (f) and compare to theoretical
values (F) calculated from equation:

F = RC/n
Where, F = frequency of observations
 R = Row frequency
 C = Column frequency
 n = Total number of data in all positions of table

Chi-Square Contingency Tables


Obs’d for birds in different regions of forest:
Take Observed data to calculate theoretical:
F for birds in trees in spring = (59*43)/120
 F for birds in shrubs in autumn = (61*42)/120

In Trees In Shrubs On Ground Total
In Spring
30
20
9
59
In Autumn
13
22
26
61
Total
43
42
35
120
Chi-Square Contingency Tables

Create Theoretical Table to which one may
compare observations:
In Trees
In Shrubs
On Ground
Total
In Spring
21.14
20.65
17.21
59.00
In Autumn
21.86
21.35
17.79
61.00
Total
43.00
42.00
35.00
120.00
Chi-Square Contingency Tables

Chi-Square Value calculated as:

χ2 = ∑∑ [ (f – F)2 / F ]

Where ∑∑ indicates to sum values across all rows
and columns
Chi-Square Contingency Tables
In Trees
30
13
43
In Shrubs
20
22
42
On Ground
9
26
35
Total
59
61
120
In Trees
In Shrubs
On Ground
Total
In Spring
21.14
20.65
17.21
59.00
In Autumn
21.86
21.35
17.79
61.00
Total
43.00
42.00
35.00
120.00
In Spring
In Autumn
Total
χ2 = [(30-21.14)2 / 21.14] + [(20-20.65)2 / 20.65] +[(9-17.21)2 / 17.21] +
[(13-21.86)2/21.86] + [(22-21.35)2 / 21.35] + [(26-17.79)2 / 17.79]
χ2 = [3.713 + 0.020 + 3.917 + 3.591 + 0.020 + 3.789] = 15.050
Chi-Square Contingency Tables

Take value of 15.050 and compare to Critical
Value for χ2 at alpha = 0.05 and degrees of
freedom

DF = (no. of rows – 1) * (no. of columns – 1)
DF = (2-1) * (3-1) = 2


So, Critical value at alpha = 0.05 and DF = 2 is
5.991 (pg. 55), which is <15.050 and reject null
hypothesis – There is a difference
Questions




1. Are there sig. diff’s in predation rate among
habitats? Why do these exist?
2. Does prey size influence the results?
3. Does the kind of shell carried by hermit crabs
influence vulnerability to predation?
4. Is predation likely to be an important factor in
the ecology of the species studied?
Data Example
Date
Habitat CW Mud Crab Consumed? Size Hermit Crab Consumed?
6/23/2009 G
7
N
4
N
6/23/2009 G
8
Y
5
N
6/23/2009 G
9
Y
6
Y
6/23/2009
S
6
Y
5
Y
6/23/2009
S
7
N
5
N
6/23/2009
S
8
N
4
Y
6/24/2009
6/24/2009
6/24/2009
6/24/2009
6/24/2009
6/24/2009
G
G
G
S
S
S
7
6
4
5
7
8
Y
Y
N
N
Y
Y
4
5
7
8
5
3
Y
N
Y
Y
N
Y