Approximate Bayesian Computation (ABC) analysis
Methods
We tested several demographic scenarios by means of Approximate Bayesian Computation
(Beaumont et al. 2002). We analyzed mtDNA and nuclear genes separately, to account for the
different inheritance mode. We used a subsample of the whole dataset, namely 188 mtDNA
haplotypes and 66 haplotypes for the two nuclear genes: the Sweden and Latvian localities (1 and 2,
Table 1) were excluded by the analysis because they are outside the range of the inferred species
paleodistribution and they were covered by the ice sheet at LGM (see Fig. 3); for nuclear markers,
only individuals analysed at both genes were used. Generation time was set to three years, mutation
rate to 10-8 and 10-9 per site per year for mtDNA and the nuclear loci respectively. We explored a
total of nine models which differed in the number and location of glacial refugia as well as in the
persistence or not of the Northern population during the last glaciation. Hereafter, the description of
the nine models:
1) Model 1. We simulated a single glacial refugium extending throughout Southern Europe.
Therefore, we pooled Italians, Spanish, Balkans and Turkish populations in a single
panmictic population (localities 13-22, 12, 7, Table 1). After the Last Glacial Maximum
(LGM) the North (localities 3-6, 8-11, Table 1) was recolonized from a population diverging
from the Southern refugium. After divergence, no migration was allowed between the
Southern and Northern group. A post-glacial change in population size was simulated in
both populations.
2) Model 2. We simulated two southern refugia, the first including populations from Italy
+Balkans+Turkey, the second including Spain only. After the LGM the North was
recolonized from a population diverging from the Italy+Balkans+Turkey refugium. After
divergence, no migration was allowed among the three populations. A post-glacial change in
population size was simulated for all populations.
3) Model 3. We simulated two southern refugia, the first including populations from
Italy+Balkans+Turkey, the second including Spain only. After the LGM the North was
recolonized from a population diverging from Spain. After divergence, no migration was
allowed among the three populations. A post-glacial change in population size was
simulated for all populations.
4) Model 4. We simulated a single panmictic population of constant size, hence pooling Italy,
Balkans, Turkey, Spain and the Northern group.
5) Model 5. We simulated two southern refugia, the first including populations from
Italy+Balkans+Turkey, the second including Spain only. After the LGM the North was
recolonized from a population resulting from the admixture between the two refugia. After
divergence, no migration was allowed among the three populations. A post-glacial change in
population size was simulated for all populations.
6) Model 6. We simulated three refugia: Italy+Balkans+Turkey (localities 13-22, 7, Table 1),
Spain (locality 12, Table 1) and the Northern group (localities 3-6, 8-11, Table 1). In other
words, we simulated the persistence of the Northern populations also during the glaciation.
We assumed a star-like population tree and a symmetric migration matrix. All three refugia
were allowed to vary the effective population size after the LGM.
7) Model 7. We simulated three refugia: Italy+Balkans+Turkey, Spain and the Northern group.
In other words, we simulated the persistence of the Northern populations also during the
glaciation. We assumed a population tree based on the matrix of mtDNA pairwise Fst:
((Italy+Balkans+Turkey, Northern group), Spain). A symmetric migration matrix was
implemented after the LGM. All three refugia were allowed to vary the effective population
size after the LGM.
8) Model 8. We simulated three refugia: Italy+Balkans+Turkey, Spain and the Northern group.
In other words, we simulated the persistence of the Northern populations also during the
glaciation. We assumed a population tree based on the matrix of pairwise Fst:
((Italy+Balkans+Turkey, Northern group), Spain). A symmetric migration matrix was
implemented after the last population split (looking forward in time). All three refugia were
allowed to vary the effective population size after the LGM.
9) Model 9. We simulated a two refugia model: Spain+part of the Northern group (locality 12,
3, 8-11, Table 1), Italy+Balkans+Turkey +part of the Northern group (localities 13-22, 7, 46, Table 1) which exchange migrants after the LGM. Both refugia were allowed to vary the
effective population size after the LGM.
To compare the nine models we defined three sampling groups where to compute summary
statistics. These sampling groups corresponded to: 1) Italy+Balkans+Turkey; 2) Spain; 3) Northern
populations. Sample sizes of these three groups were 100, 15 and 74 haplotypes for the mtDNA and
22, 6 and 42 haplotypes for the two nuclear loci. For models where the sampling groups did not
correspond to the simulated populations (Model 1, 4, 9), the sampling groups were created a
posteriori. For example, in Model 4 we first simulated a single panmictic population and then
randomly select 100, 15 and 74 haplotypes (in the mtDNA dataset) to define the three sampling
groups.
Results and Discussion
Neither mtDNA nor the 2 nuclear genes strongly supported any of the tested models (see Table
below). Indeed, the results for the mtDNA and nuclear markers exhibited low probability values
(i.e. values did not exceed 21% and 18%, respectively) in a narrow range and were similar among
very different models (i.e. Model 1 and 5 for mtDNA). Mitochondrial and nuclear markers provided
major support to different models. For instance, three refugia model (i.e. with the persistence of the
northern population during the glacial period, Model 8) received the highest probability for nuclear
genes (P = 0.178), while the single southern refugium model with post-glacial recolonisation
(Model 1) received the highest probability (P = 0.216) for mtDNA markers. The parameter
estimates for the tested models are available on request.
Model 1
Model 2
Model 3
Model 4
Model 5
Model 6
Model 7
Model 8
Model 9
mtDNA
0,216
0,098
0,123
0,064
0,209
0,067
0,056
0,066
0,102
nuclear genes
0,0005
0,0917
0,0874
0,0696
0,1394
0,1468
0,1594
0,1779
0,1274
There may be several explanations for these results: (i) none of the tested models provided a good
approximation of the true demographic history of I. ricinus; (ii) the markers we used did not have
sufficient power to discriminate among the tested models; (iii) model selection with ABC
sometimes produces misleading results (Robert et al. 2011), but a proper evaluation of the
performance of this model under the specific settings used here being beyond the scope of this
work; and (iv) the predictions of (at least some) of these models are not sufficiently different and
could not be easily discriminated, even with more loci. The final point is of particular interest here.
Indeed, one of the main reasons that prompted us to apply the ABC algorithm was to test the
likelihood of the population persisting in the Northern area during the glacial period. However,
large effective population sizes were found in all models, in both the refugia and recolonised areas
at the present time and at the end of the last glaciation. This finding indicates that the last glaciation
did not cause any loss of diversity in the northern area. This phenomenon might be because of
population persistence or because the founding population after the glacial period was very large. It
is possible that a model with such a large founding population cannot be easily discriminated from a
model of population persistence; hence, ABC might not be useful in discriminating between these 2
hypotheses for this species. Therefore, for all these reasons, we did not include the ABC analysis in
the revised version of the paper.
References
Beaumont MA, Zhang W, Balding DJ (2002) Approximate Bayesian Computation in Population
Genetics. Genetics, 162, 2025–2035.
Robert CP, Cornuet JM, Marin JM, Pillai NS (2011) Lack of confidence in approximate Bayesian
computation model choice. Proceedings of the National Academy of Sciences of the USA, 108,
15112–15117.