# Statistics for ecology

UNIVERSITY OF SCIENCE
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FINAL EXAM

Subject: Statistics for Ecology
Topic: Analysis of presence or absence of species
Requirement:
The data to be analyzed is the data on the abundance of Faramea occidentalis (in
attached text file). Please explain the influence of precipitation, altitude, age and
geology parameters on the presence-absence of Faramea occidentalis species. The
calculation and the numerical results are required.

Full name:

Bui Thi Hao

Class:

K55 of Advanced Program of Environmental Science

Student’s code: 1000739

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Content:
Page

A. Load the data from external file..........................................................
B. Doing analysis.....................................................................................
I.
Explanation with single explanatory variable................................
a. Explain the influence of Age categories..............................
b. Explain the influence of elevation(i.e.altitude)...................
c. Explain the influence of Precipitation ...............................
d. Explain the influence of Geology ......................................
II.
Explanation with several explanatory variables..........................

SOLUTION
A. Load the data from external file

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B. Doing analysis

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Due to the more comprehensive analysis of frequencies, I prefer to use GLMgeneralized linear model (binomal or quasibinomal flexibly)
I.
Explanation with single explanatory variable
a. Explain the influence of Age on the presence-absence of species

From using Biodiversity.R, I got the result as above. The result shows the
coefficients of Age.categories (in logit value). However, more important, the deviance
residuals and Pr-value should be concerned. According to the above results, the variance
of presence/absence of Faramea occidentalis depending on age.categories explained only
3.0793 per 59.401 of null deviance (5.18%) (very small). Especially, that Pr-value ~

0.2508 in the ANOVA table is so high implies there is evidence so that coefficients of
categories equal zero. It means age categories have no effect on the presence/absence of
species.
In conclusion, the age categories in their own have no contribution on explaining
the presence/absence of Faramea occidentalis.

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b. Explain the influence of elevation(i.e.altitude) on the presence-absence of
species

From using Biodiversity.R, I got the result as above. The result shows the
coefficients of Elevation (in logit value), as well as, the deviance residuals and Pr-value.
According to the above results, the variance of presence/absence of Faramea
occidentalis depending on elevation explained only 9.9317 per 59.401 of null deviance
(16.72%) (so small). However, that Pr-value ~ 0.0357 is very low implies there is
evidence so that coefficients of elevation do not equal zero. It means, elevation still has
certain effect on the presence/absence of species.
In conclusion, the elevation in its own has contribution on explaining the
presence/absence of Faramea occidentalis (but not clear and strong due to small
explained deviance) according to the following link fuction:
Logit(µ)= 1.0595-0.00784x = y
Where µ: the mean of presence/absence value
x: the elevation value (should be the mean value of certain interval)
 µ= exp(y)/(1+exp(y))

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c. Explain the influence of Precipitation on the presence-absence of species

The above result shows the coefficients of precipitation (in logit value), as well as,
the deviance residuals and Pr-value. Accordingingly, the variance of presence/absence
of Faramea occidentalis depending on precipitation explained only 8.8406 per 59.401 of
null deviance (14.88%) (so small). However, that Pr-value ~ 0.0172 is very low implies
there is evidence so that coefficients of precipitation do not equal zero. It means,
precipitation still has certain effect on the presence/absence of species.
In conclusion, the precipitation in its own has contribution on explaining the
presence/absence of Faramea occidentalis ((but not clear and strong due to small
explained deviance) according to the following link fuction:
Logit(µ)= 6.9483-0.00272x = y
Where
µ: the mean of presence/absence value
 µ= exp(y)/(1+exp(y))
x: the precipitation value ((should be the mean value of certain interval)

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d. Explain the influence of Geology on the presence-absence of species

The above result shows the coefficients of geology (in logit value), as well as, the
deviance residuals and Pr-value. Accordingingly, the variance of presence/absence of
Faramea occidentalis depending on geology explained 25.548 per 59.401 of null
deviance (43%) (noticeable). Moreover, that Pr-value ~ 0.002027 in the ANOVA table
is very low implies there is evidence so that coefficients of geology do not equal zero. It
means, v has certain effect on the presence/absence of species.
In conclusion, the geology in its own has contribution on explaining the
presence/absence of Faramea occidentalis according to the following link fuction:
Logit(µ)= intercept + coefficient for geology category = y
Where µ: the mean of presence/absence value
 µ= exp(y)/(1+exp(y))
Example: For GeologyTc:
Logit(µ)= -2.0794+2.367 = 0.2876 => µ= 57.14 %
II.
Explanation with several explanatory variables

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Is there more complex pattern in relationship of explanory variables on
explaining response varible => Use binomal GLM on several explanatory
variables

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As we know, AIC (Akaike Information Criterion) is to provide us information about
combination of simplicity and explained deviance. A model with a lower AIC has a
better combination of simplicity and explained deviance, therefore be more prefered than
that with the higher AIC.
 It is better to use model with ( Precipitation + Precipitation^2 + Age. Cat +
Geology + Elevation^2) rather than (Precipitation + Precipitation^2 + Age. Cat +
Geology + Elevation+ Elevation^2), and than (Precipitation+ Age. Cat + Geology
+ Elevation) (since AIC respectively: 42.020 < 43.376 < 43.969)
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In conclusion, the best model is binomal GLM on Precipitation +
Precipitation^2 + Age. Cat + Geology + Elevation^2

As above result, this model can explain up to (59.401-18.020)/59.401= 69.66% of null
deviance of dataset (much higher than that off all the models with single explanatory
variable). Moreover, in the single term deletions, the deletion of any term will cause the
increase of AIC, i.e. the less combination of simplicity and explained deviance. That
means all of mentioned terms should be kept in the model, and the link function would
be:

Y= Logit(µ)= -8.830e + 8.031e^-2.x -1.765e^-5.x2+ y+z-6.407e^-5.k
Where:
µ: the mean of presence/absence value => µ= exp(Y)/(1+exp(Y))
x: the precipitation value

z: coefficient for age category

y: coefficient for geology category

k: the elevation value
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Conclusion:
Each explanatory variable (precipitation, altitude, age and geology) has its own influence
on response variable ( the presence/absence of Faramea occidentalis) at certain level
(even zero level-no influence). More obviously, however, the complex pattern in which
all explanatory variables are included is much better in explaining the presence/absence
of species, so such a model should be more prefered.

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