1. Relations between Depth, Morphology, and Population Dynamics in Corals Yuval Itan Project advisor: Dr. N. Furman

2. Introduction Ecology: interactions between living organisms and their environment.

3. Mathematics in Ecology Formulate basic theories in ecology Prediction of ecological processes Allowing computer simulations

4. Modeling topics Topics for modeling: physiological ecology and population ecology physiological ecology: morphology Population ecology: population dynamics

5. Morphology Morphology: the form and structure of an organism

6. 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.

7. Population dynamics Population dynamics: understand and predict behavior of populations Specifically: age-survivorship relations

8. 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.

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

10. A birth of a hypothesis We are dealing with aquatic organisms models Surely (?) depth affects this guys ’ morphology and population dynamics

11. Research goal Finding relations between: Depth  Population Dynamics Depth  Morphology Morphology  Population Dynamics

12. Research location Performed at “ The Interuniversity Institute for Marine Sciences at Eilat ” (IUI)

13. Research organism Stylophora pistillata- a branching stony coral Measurements: maximum diameter: 35cm shape: usually symmetrical with branches

14. 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

15. Basic analysis Transferring all info to Excel tables Using Excel for basic summaries and means. Determining basic parameters for morphology and population dynamics

16. Morphology parameters Make it simple ( …… ) Describing “ flatness ” / ” tallness ” of the coral <1  taller =1  symmetrical >1  flatter

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

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

19. SPSS analysis Trying to prove significance of: 1. Depth  Population Dynamics 2. Depth  Morphology 3. Morphology  Population Dynamics Advanced further statistical analysis

20. Depth  Population Dynamics Population dynamics: age, death Depth  age distribution significance:  PROVED 

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

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

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

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

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

26. 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)

27. The End