Figure legends for online supplemental information:
APPENDIX A1: Technical details of the optimization algorithm.
TABLE A1: Characteristics of the nine microsatellites analyzed.
TABLE A2: Cycling conditions for multiplex PCR.
TABLE A3: Proportions of Multiplex PCR.
TABLE A4: Probability values of a non-parametric one-tailed Kolmogorov-Smirnov Z
test for the difference between the highly inbred subpopulation and the other
subpopulations for several genetic parameters. Shading denotes non-significant
differences.
FIGURE A1: Population inbreeding coefficient and global coancestry for each
simulated replicate and management strategy.
1
APPENDIX A1: Technical details of the optimization algorithm.
Optimization algorithm
For isolated subpopulations (IS) and OMPG schemes, independent optimizations
were performed for each subpopulation every generation. Following Fernández et al.
(2001) the objective function was
 Nk Nk

min   f ij ci.c j .   
 i1 j 1

 Nkm N

   cij f ij  ,
 i1 j  N 1 
km


(1)
where Nk is the number of individuals belonging to subpopulation k (the first Nkm being
males and the rest females), cij is the number of offspring to be contributed by the
couple formed by male i and female j, ci. is the number of offspring to be contributed by
individual i with all its partners (in this case will be only one partner, as monogamy is
imposed), and  is a weighting factor to be given to the choice of the mating pair. The
number of variables c is equal to the number of all possible couples between males and
females, i.e., Nkm  Nkf. The first term of (1) represents the global coancestry of the
progeny ( f ) given the contributions from the parents, whereas the second term
represents the average coancestry of the progeny with the particular mating pairs
assumed. Because the objective was to apply minimum global coancestry contributions
and, only when two solutions have the same f , then apply minimum coancestry
between couples as a criterion, the optimal solution is giving a small value to . This
would produce a minimum coancestry mating scheme but maintaining the individual
contributions that yield the minimum global coancestry in the progeny (Fernández et al.
2001). The particular value used in the present experiment ( = 0.01) was determined by
preliminary computer simulations. First, several cases were run with  = 0 to find out
the optimum value for the global coancestry term. Then, the problems were re-run with
increasing values of  until the f of the final solution started to increase. With the
chosen value of the parameter we would exert the highest pressure on the mating
scheme but assuring the lowest global coancestry.
To impose solutions only compatible with monogamy, the following restrictions
were added to the algorithm,
N km
y
i 1
ij
1
j  N km  1,, N
(2)
2
Nk
y
1
ij
i  N km 1
j  1,, N km
(3)
where yij is a dichotomic dummy variable with a value of one if the couple ij produces
any offspring, and zero otherwise.
In the case of the Dynamic method (DM1 and DM2), the optimization protocol
was performed for the structured population as a whole. Because the maximization of
global diversity is the main objective of the experiment, the objective function was
NT NT
min
 f c
i 1 j 1
c ,
ij i .. j ..
(4)
where NT is the total number of individuals in the population (i.e. the sum of individuals
of all subpopulation), cijk is the number of offspring contributed by the couple formed
by male i and female j to subpopulation k, and ci.. is the global contribution of individual
i with any partner to any subpopulation. Due to the experimental design (mating could
only occur within subpopulations) the number of variables c is equal to the sum of the
products of the number of males and females in each subpopulation. Monogamy was
assured by including a set of restrictions similar to those explained above for the IS and
OMPG schemes.
The average inbreeding coefficient of the next generation ( F t 1 ) was controlled
by including the following restriction,
N km
n

N
 f c
ij ijk
i 1 j  N km 1
Nk n
k 1
 F t 1 ,
(5)
where n = 4 is the number of subpopulations. Note that, because the precise couples
were also determined jointly with the contributions of progeny, inbreeding levels were
not expected average values under random mating, but the true values of the offspring
which would be generated under that particular mating and contributions scheme.
Different values for the maximum level of inbreeding were applied to the two
implementations of the Dynamic method (DM1 and DM2), as specified in the previous
section.
Due to the particular optimization strategy implemented in the software
METAPOP, a simulated annealing algorithm, when the imposed restriction was too
severe to be met and, consequently, the problem was unfeasible, the program was still
able to yield a solution. In that situation the software provides the feasible solution
3
closest to the desired restriction. This is an advantage over other optimization methods
that simply crash when they can not fit the restrictions.
In order to make results from the OMPG design and the Dynamic method
comparable, the optimization protocol for the DM methods also included a restriction
for controlling the maximum number of migrants,
NT
n
 c
i 1 k l
i .k
 2nM ,
(6)
where l is the subpopulation of individual i, ci.k is the total contribution of individual i
with progeny to any subpopulation different from its own one, and M is the maximum
number of individuals allowed to move (on average) per generation from/to any
subpopulation. To allow a direct comparison with the OMPG scheme, M was set to 1
for DM1 and DM2 schemes.
4
TABLE A1: Characteristics of the nine microsatellites analyzed.
Bibliographic
Multiplex
PCR
1
2
3
Annealing
Temp. (ºC)
50.5
51
54
Locus
Repeat
Observed
Size
Range
No
Alleles
Size
Range
No
Alleles
Chrom.
Cytological
Position
Primer Forward
Primer Reverse
3L9222187ca
(CA)12
180-202
7
178-200
8
3L
67A
gcgattttcagtggctcaatg
tggctaatagatttcaacaac
3R1302339ga
(GA)10
101-125
7
103-119
4
3R
90A
catcagattcggcataag
aactggagcatgaaaaac
3R16177365gt
(GT)10
143-153
7
145-151
3
3R
92E
ttggttttactgaatggctgac
tcaagttgtagcaaagttagag
AC002446
(TC)18
144-188
14
150-172
9
2R
58B
tccttattcggtctacaaatct
atacacatgcacatccgtatag
AC004641
(CA)22
92-154
25
98-138
14
2R
53D
atcacaactggaccctctat
aatttcacaaccaacaacta
3R22473342gt
(GT)11
113-127
8
115-127
8
3R
97D
gagtgacaaatgaacgct
atctgcaaaaacggaaac
Dm1639-TC
(TC)12
102-120
8
110-118
5
2R
58A
gcctcgctccgtcccgttcc
cgattgtttccattgttcac
3R11178343ga
(GA)13
184-206
9
188-198
6
3R
88F
gctctcgctggctgagtc
gttcaaggacccgaagtg
3R24298455ca
(CA)13
162-174
7
160-170
6
3R
98D
ttcgtcgtggatgtgttg
ttcatggttgtggacttg
5
TABLE A2: Cycling conditions for multiplex PCR.
time (min)
temp. (ºC)
4
94
Denaturation
1
94
Annealing
1
Annealing
temp.
Extension
1
72
45
72
Denaturation
30 cycles
Final extension
6
TABLE A3: Proportions of Multiplex PCR.
Extracted genomic DNA
2 μl
Reaction buffer 10x
2 μl
MgCl2
2.5mM
Forward primer for each microsatellite
(Labelled with FAM, HEX, or NED)
0.0010 – 0.0015 mM
Reverse primer for each microsatellite
0.0010 – 0.0015 mM
dNPTs
Taq DNA polymerase
deionized water
0.5 mM
1U
up to a final volume of 20 μl
7
TABLE A4: Probability values of a non-parametric one-tailed Kolmogorov-Smirnov Z
test for the difference between the highly inbred subpopulation and the other
subpopulations for several genetic parameters. Shading denotes non-significant
differences.
Generation
0
1
2
3
4
5
6
7
8
9
10
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.018
0.005
0.005
0.032
0.018
0.227
0.018
0.005
0.005
0.018
0.018
0.300
0.227
0.482
0.482
0.355
0.227
DM2
0.005
0.002
0.005
0.105
0.045
0.205
0.227
0.355
0.482
0.355
IS
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
OMPG
0.005
0.002
0.005
0.005
0.005
0.005
0.002
0.005
0.105
0.118
0.005
0.005
0.005
0.018
0.077
0.482
0.482
0.227
0.300
0.200
DM2
0.005
0.005
0.005
0.005
0.005
0.061
0.045
0.355
0.473
0.118
IS
-
0.005
-
0.227
-
0.018
-
0.045
-
0.118
OMPG
-
0.005
-
0.118
-
0.118
-
0.482
-
0.118
-
0.118
-
0.482
-
0.355
-
0.118
-
0.227
DM2
-
0.355
-
0.482
-
0.227
-
0.227
-
0.227
IS
-
-
-
-
0.032
-
-
-
-
0.184
-
-
-
-
0.105
-
-
-
-
0.418
-
-
-
-
0.427
-
-
-
-
0.355
DM2
-
-
-
-
0.439
-
-
-
-
0.482
IS
-
-
-
-
0.018
-
-
-
-
0.355
OMPG
-
-
-
-
0.118
-
-
-
-
0.355
-
-
-
-
0.355
-
-
-
-
0.227
-
-
-
-
0.227
-
-
-
-
0.355
IS
F
f
W
Na
He
OMPG
DM1
DM1
DM1
OMPG
DM1
DM1
DM2
0.005
0.005
0.005
0.118
0.018
Non significant Kolmogorov-Smirnov Z Tests are shaded.
F – Inbreeding coefficient, f – Coancestry, W – Fitness,
Na – Average number of alleles, He – Expected heterozygosity,
IS – Isolated subpopulations, OMPG – One migrant per generation,
DM1 – Dynamic method 1, DM2 – Dynamic method 2
8
FIGURE A1: Population inbreeding coefficient and global coancestry for each
simulated replicate and management strategy.
Replicate
B
C
Average
Coancestry
Average
Inbreeding Coefficient
A
Generation
9