Relations between Depth, Morphology, and
Population Dynamics in Corals
Yuval Itan
Project advisor: Dr. N. Furman
Introduction
Ecology: interactions between living organisms and their environment.
Mathematics in Ecology• Formulate basic theories in ecology
• Prediction of ecological processes
• Allowing computer simulations
Modeling topics
• Topics for modeling: physiological ecology and population ecology
• physiological ecology: morphology
• Population ecology: population dynamics
Morphology
• Morphology: the form and structure
of an organism
Corals Morphology
• Equation for morphology in corals- Morphology change as a function of time:
dL = c(L) + b(L)L + (j-kL)
dtL – volume/surface area ratio.b – living tissue L dependant deterministic biomass.c – skeleton L dependant deterministic biomass.j,k – stochastic fluctuations of external noise.
Population dynamics
• Population dynamics: understand and predict behavior of populations
• Specifically: age-survivorship relations
Corals Population dynamics• Equations for population dynamics in
corals-
1. Von Bartalansky model for coral growth:
– coral’s length at a specific age (t). – coral’s maximal length.
-ktt mL = L (1 - e )
tLmL
k – species constant.
Corals Population dynamics2. Beverton & Holt model for Corals survivorship:
N – number of individuals.z – death rate.
-ztt 0N = N e
A birth of a hypothesis
• We are dealing with aquatic organisms models
• Surely (?) depth affects this guys’ morphology and population dynamics
Research goal
• Finding relations between:
Depth Population DynamicsDepth MorphologyMorphology Population Dynamics
Research location
• Performed at “The Interuniversity Institute for Marine Sciences at Eilat” (IUI)
Research organism
• Stylophora pistillata- a branching stony coral
• Measurements: maximum diameter: 35cm shape: usually symmetrical with branches
Collecting the information• Measuring at depths: 2m, 5m, 12m
• Area at each depth:
• Measuring for all corals: 1. Height, width, length 2. % of dead tissue
210m
Basic analysis
• Transferring all info to Excel tables
• Using Excel for basic summaries and means.
• Determining basic parameters for morphology and population dynamics
Morphology parameters• Make it simple (……)
• Describing “flatness”/”tallness” of the coral
2cm cm
cm
width length
indexheight
<1 taller
=1 symmetrical
>1 flatter
Dynamics parameters
• Population’s mortality- % dead tissue:
% Dead tissue =
Dead
Mass
V
V
DeadV ( * * )*(% )height width length dead=
MassV ( * * )height width length=
Dynamics parameters
• Approximate age index- simple again:
• Fits to supported coral’s age research articles
3
height width lengthage
SPSS analysis
• Trying to prove significance of: 1. Depth Population Dynamics 2. Depth Morphology 3. Morphology Population Dynamics
• Advanced further statistical analysis
Depth Population Dynamics
• Population dynamics: age, death
• Depth age distribution significance:Test Statisticsa,b
19.717
2
.000
Chi-Square
df
Asymp. Sig.
age_allslope
Kruskal Wallis Testa.
Grouping Variable: depth_slopeb.
PROVED
Morphology Dynamics
• Morphology death average significance shown graphically:
PROVED
Depth Morphology
• The last link to find
• SPSS analysis:Independent Samples Test
3.719 .056 1.077 126 .284 4.67908 4.34510 -3.91975 13.27792
1.433 94.126 .155 4.67908 3.26611 -1.80575 11.16392
Equal variancesassumed
Equal variancesnot assumed
deadpercent_2_5_12slope
F Sig.
Levene's Test forEquality of Variances
t df Sig. (2-tailed)Mean
DifferenceStd. ErrorDifference Lower Upper
95% ConfidenceInterval of the
Difference
t-test for Equality of Means
HYPOTHESIS REJECTED
There is still hope
• The relation between slope existence
and morphology was also checked:
PROVED
Independent Samples Test
6.075 .014 -7.073 243 .000 -.45934 .06495 -.58727 -.33141
-10.835 63.763 .000 -.45934 .04239 -.54404 -.37464
Equal variancesassumed
Equal variancesnot assumed
all_indexesF Sig.
Levene's Test forEquality of Variances
t df Sig. (2-tailed)Mean
DifferenceStd. ErrorDifference Lower Upper
95% ConfidenceInterval of the
Difference
t-test for Equality of Means
Mathematical analysis
• 2nd order polynomial interpolation to depth dependant age distribution and mortality:
Depth dependant death
0
5
10
15
20
2 4 6 8 10 12
Depth (-meters)
De
ad
tis
sue
(%
)
Depth dependant age average
0
2
4
6
8
10
12
14
2 4 6 8 10 12
Depth (-meter)
Ag
e a
ve
rag
e (
~ye
ars
)
Mathematical analysis
• A finite number of morphology states- 4th order interpolation:morphology dependant death
0
5
10
15
20
25
30
1 2 3 4 5 6
Morphology index (const.)
De
ad
tis
su
e (
%)
1 -tallest6- flattest
Conclusions
• The ideal depth for growth is 5m: low mortality rate and a young population
• There are “stable morphology states”- low mortality rate. Optional- sinus function
• Slope affects much more on morphology than depth (could not model it)
The End
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