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: L – 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. k – species constant.

Corals Population dynamics 2. Beverton & Holt model for Corals survivorship: N – number of individuals. z – death rate.

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 Dynamics Depth  Morphology Morphology  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

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 <1  taller =1  symmetrical >1  flatter

Dynamics parameters Population ’ s mortality- % dead tissue: % Dead tissue = = =

Dynamics parameters Approximate age index- simple again: Fits to supported coral ’ s age research articles

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:  PROVED 

Morphology  Dynamics Morphology  death average significance shown graphically:  PROVED 

Depth  Morphology The last link to find SPSS analysis:  HYPOTHESIS REJECTED 

There is still hope The relation between slope existence and morphology was also checked:  PROVED 

Mathematical analysis 2 nd order polynomial interpolation to depth dependant age distribution and mortality:

Mathematical analysis A finite number of morphology states- 4 th order interpolation: 1- tallest 6- 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