1. Joaquim Fort Univ. de Girona (Catalonia, Spain)
FEPRE workshop
26-27 March 2007
Future prospects
Joaquim Fort
Univ. de Girona (Catalonia, Spain)

2. FEPRE work by the Girona group
1. Time-ordered models → SUBMITTED 
2. Realistic dispersion kernels → FINISHED 
3. Non-isotropic models → PLANNED …
4. Genetic clines → PLANNED …
5. Non-homogeneous models → PLANNED …

3. Recall
<

4. Limitations of the HRD and Fisher Eqs.1 2

5. 1st example 1
100%
5 km 2
99%
1 km 1%
10 km

6. 2nd example 1
100%
5 km 2
75%
0 km
25%
10 km

7. x  We look for a model without using D R0 R0= reproduction
Probability distance 

8. Continuous space:
In 2 dims:

9. Invasion speed:
f(λ) v λ

10. “Random-walk“ simulations
How can we check these formulae?
“Random-walk“ simulations

11. “Random-walk“ simulations
Individuals jump on a lattice 1 2
t =T
t =2T 3
In this figure, all individuals jump the same . But the program allows for jumps with several values of 

12. “Random-walk” fortran program
2-dimensional grid with nodes separated e.g. 3 km E.g. jumps with the same probability and x,y up to e.g. ± 15km
1) probab=1/number of jumps 2) do j=1, t final 3) Dispersion do x=1, do y=1, do x = -15/3,15/3 do y = -15/3,15/ pp(x+ x ,y+ x ) = pp(x+ x ,y+ x ) + probab · p(x,y) 4) p(x ,y) = pp(x ,y ) pp(x,y) = 0 5) Reproduction do x=1, do y=1, p(x,y) = R0 p(x,y) 6) continue [ see 2) ]

13. Typical results from fortran simulations
We can find the speed

14. Fortran simulations versus formulae
Hypothetical example

15. Neolithic transition
70%

16. FEPRE work by the Girona group
1. Time-ordered models → SUBMITTED 
2. Realistic dispersion kernels → FINISHED 
3. Non-isotropic models → PLANNED …
4. Genetic clines → PLANNED …
5. Non-homogeneous models → PLANNED …

17. Realistic dispersion kernels
30%!

18. FEPRE work by the Girona group
1. Time-ordered models → SUBMITTED 
2. Realistic dispersion kernels → FINISHED 
3. Non-isotropic models → PLANNED …
4. Genetic clines → PLANNED …
5. Non-homogeneous models → PLANNED …

19. Non-isotropic models
Main purpose: comparison to observations without any free or adjustable parameters

20. FEPRE work by the Girona group
1. Time-ordered models → SUBMITTED 
2. Realistic dispersion kernels → FINISHED 
3. Non-isotropic models → PLANNED …
4. Genetic clines → PLANNED …
5. Non-homogeneous models → PLANNED …

21. Genetic clines 11,000 yr BP (uncal) Population AA aa Aa
Farmers % 0% %
Hunter-gatherers 0% 100% 0%

22. FEPRE work by the Girona group
1. Time-ordered models → SUBMITTED 
2. Realistic dispersion kernels → FINISHED 
3. Non-isotropic models → PLANNED …
4. Genetic clines → PLANNED …
5. Non-homogeneous models → Prof. T. Pujol