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