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 subpopulationsfor several genetic parameters. Shading denotes non-significant differences.
FIGURE A1: Population inbreeding coefficient and global coancestry for each simulated replicate and management strategy.
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
,(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., NkmNkf. The first term of (1) represents the global coancestry of the progeny () 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, 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 theof 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,
(2)
(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
,(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 () was controlled by including the following restriction,
,(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 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,
,(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.
TABLE A1: Characteristics of the nine microsatellites analyzed.
MultiplexPCR / Annealing
Temp. (ºC) / Locus / Repeat / Bibliographic / Observed / Chrom. / Cytological
Position / Primer Forward / Primer Reverse
Size
Range / No
Alleles / Size
Range / No
Alleles
1 / 50.5 / 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
2 / 51 / 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
3 / 54 / 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
TABLE A2: Cycling conditions for multiplex PCR.
time (min) / temp. (ºC)Denaturation / 4 / 94
30 cycles / Denaturation / 1 / 94
Annealing / 1 / Annealing temp.
Extension / 1 / 72
Final extension / 45 / 72
TABLE A3: Proportions of Multiplex PCR.
Extracted genomic DNA / 2 μlReaction 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 / 0.5 mM
Taq DNA polymerase / 1 U
deionized water / up to a final volume of 20 μl
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 subpopulationsfor several genetic parameters. Shading denotes non-significant differences.
Generation / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10F / IS / 0.005 / 0.005 / 0.005 / 0.005 / 0.005 / 0.005 / 0.005 / 0.005 / 0.005 / 0.005 / 0.005
OMPG / 0.005 / 0.005 / 0.005 / 0.018 / 0.005 / 0.005 / 0.032 / 0.018 / 0.227 / 0.018
DM1 / 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
f / IS / 0.005 / 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
DM1 / 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
W / IS / 0.005 / - / 0.005 / - / 0.227 / - / 0.018 / - / 0.045 / - / 0.118
OMPG / - / 0.005 / - / 0.118 / - / 0.118 / - / 0.482 / - / 0.118
DM1 / - / 0.118 / - / 0.482 / - / 0.355 / - / 0.118 / - / 0.227
DM2 / - / 0.355 / - / 0.482 / - / 0.227 / - / 0.227 / - / 0.227
Na / IS / 0.118 / - / - / - / - / 0.032 / - / - / - / - / 0.184
OMPG / - / - / - / - / 0.105 / - / - / - / - / 0.418
DM1 / - / - / - / - / 0.427 / - / - / - / - / 0.355
DM2 / - / - / - / - / 0.439 / - / - / - / - / 0.482
He / IS / 0.018 / - / - / - / - / 0.018 / - / - / - / - / 0.355
OMPG / - / - / - / - / 0.118 / - / - / - / - / 0.355
DM1 / - / - / - / - / 0.355 / - / - / - / - / 0.227
DM2 / - / - / - / - / 0.227 / - / - / - / - / 0.355
1
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
FIGURE A1: Population inbreeding coefficient and global coancestry for each simulated replicate and management strategy.
ReplicateA B C
Average
Inbreeding Coefficient /
Average
Coancestry /
Generation
1