Divergence time estimates obtained using two different methods based on Approximate Bayesian Computation (DIYABC) and an Isolation-with-migration model (IMa) led us to reject the hypothesis that divergence of HAL and MOS from the anadromous LIL population is natural and occurred several thousand years ago. Instead, divergence time coincided remarkably well with establishment of water mills and impassable dams in the Medieval from ca. 1200 to 1500. There was less congruence regarding the demographic impact of the establishment of dams, as DIYABC consistently provided higher estimates of effective population sizes than did IMa and estimates based on the linkage disequilibrium method (LDNE).
Bayesian cluster analysis showed that the two lake populations HAL and MOS were genetically distinct, whereas the anadromous trout populations showed a regional genetic structure, reflecting ongoing gene flow and isolation-by-distance, as documented in other studies
[32, 46]. Importantly, these results also showed a minimal genetic contribution by stocked trout to the focal populations LIL, MOS and HAL, which could otherwise complicate estimation of divergence time and demographic parameters.
In the following, we first discuss the reliability of the estimates provided by DIYABC and IMa, and subsequently the impact of the impassable dams on genetic population structure and adaptive divergence.
Reliability of estimates
The conclusion that the two lake populations diverged from anadromous trout due to habitat fragmentation during the Medieval relies on the results using the methods IMa
 and DIYABC
. In both cases we used wide and flat priors that should not strongly influence posterior distributions. The mutation rate assumed, however, is a factor of uncertainty. For the IMa analyses we assumed a rate of 3.0 × 10-4, estimated using DIYABC. This is quite close to estimates of mutation rate at dinucleotide loci in e.g. humans of 2.73 × 10-4
 and 5.56 × 10-4 in common carp (Cyprinus carpio)
. Hence, the mutation rate assumed must be considered realistic, and it would require a much lower mutation rate (2.01 × 10-5) to change the estimate of divergence time for LIL-HAL from 789 years to, say, 12,000 years, coinciding with the end of the last Glaciation.
Whereas the congruence of results from different replicated runs of IMa suggests good convergence, a potential problem consists in the simplified model assumed, where LIL exchanges migrants with either HAL or MOS. In reality, both populations could simultaneously contribute to gene flow, but even more importantly LIL would be subject to gene flow from other anadromous populations. We are unable to resolve the magnitude of this potential problem, but we note that the results obtained generally make sense. For both lake populations the estimate of gene flow from LIL was virtually zero, as would be expected given the problems of passing the dams upstream. In contrast, there was a signal of downstream gene flow into LIL from MOS. Gene flow in this direction is certainly a realistic possibility, as fish can pass the dams downstream by simply being flushed with the current.
estimates of HAL and MOS obtained using IMa were of the same order of magnitude, albeit higher than estimates obtained independently using LDNE. In contrast, estimates of N
in LIL obtained by IMa were more than 5 times times higher than those derived from LDNE. Although recent bottlenecks could explain this result, there was no evidence for this to have taken place. Alternatively, the result could reflect gene flow from other anadromous populations into LIL, thereby inflating historical N
estimates (as in IMa) compared to contemporary estimates (as in LDNE) that pertain to the current or only a few generations back in time. The complexities of estimating N
in populations showing some degree of geographical continuity are increasingly acknowledged
, and we tentatively suggest that the N
estimate in LIL based on IMa should be interpreted more broadly as encompassing LIL and neighboring populations contributing to gene flow.
The DIYABC analyses appeared robust towards the choice of summary statistics, as evidenced by similar outcomes of the different analyses. However, unlike IMa it is assumed that there is no gene flow following splitting of populations. In the present case, this is probably not a major problem, as IMa suggested low gene flow between LIL and HAL/MOS, and divergence time estimates were quite similar between methods. Effective population size estimates, however, differed strongly between IMa and DIYABC, with the latter providing 5–10 times higher estimates than IMa. In both cases the estimates are “historical”, i.e. encompassing many generations, although IMa estimates N
from the ancestral population prior to divergence and N
of the separate populations after divergence, the latter thereby giving more weight to the recent past (in the present case the centuries since establishment of dams). Most summary statistics applied in DIYABC, such as expected heterozygosity, F
and numbers of alleles should primarily reflect historical N
over a very long time scale
, with the exception of M
 which detects recent bottlenecks. Differences of the time scale over which N
is estimated could therefore explain the discrepancies of results. We emphasize the N
estimates obtained by IMa as being most realistic and relevant in a conservation context; they are generally congruent with estimates of contemporary N
obtained using LDNE and with estimates from Danish brown trout populations obtained using temporal methods, that for anadromous populations in Danish rivers generally range from ca. 250 to > 1,000 for large river systems
In total, we find the estimates of divergence time obtained by IMa and DIYABC to be robust, whereas N
estimates differ, probably reflecting the different time scales that they apply to.
Impact on genetic population structure and adaptive divergence
Our results suggest that the two lake populations HAL and MOS were previously part of a coherent anadromous trout population inhabiting the Gudenå River system. The Gudenå River is the largest watershed in Denmark, and the effective population size of the ancestral trout population prior to fragmentation has presumably been high; > 1,000, given the estimates obtained from the KON and RIB populations (see Table
). Gene flow has occurred to and from other such populations enabling introduction of new adaptive variation and potentially both enhancing and limiting local adaptation, depending on local selection regimes and migration-drift-selection equilibrium
[24, 25]. Following the establishment of water mills, HAL and MOS have been disconnected from these dynamics for several centuries.
What is the primary impact of this fragmentation? Contemporary N
was estimated to 153 and 252 for HAL and MOS, respectively. Although these values cannot be considered high, they should also not be cause for immediate conservation concern. Indeed, they are higher than several estimates of N
in undisturbed resident brown trout populations from Sweden
[75, 76] that have been isolated naturally presumably for even longer time spans that the MOS and HAL populations, and are in fact comparable to N
in some of the anadromous populations included in the study (Table
2). It should be considered, however, that several of these latter populations included for reference have likely declined recently, as documented by comparison of historical and contemporary samples from the populations
We suggest that the most important consequence of the dams concerns local adaptation and evolutionary potential. Even if trout ascend the dams downstream and migrate to sea, they will be unable to return to spawn. This could impose strong selection against anadromy, although the response to selection depends on heritability of the trait. There are few studies available that have estimated heritability of anadromy in salmonids. However, a study based on pedigreeing a wild brook trout (Salvelinus fontinalis) population found heritability of life-history tactics (anadromy versus residency) as high as 0.52-0.56
. If this is also the case in brown trout, then the 600–700 years since establishment of dams corresponding to 170–200 generations should have left ample opportunities for selective responses to occur. On the other side, a recent study of trout in HAL documented that 15% of individuals aged between 1 and 3 years and with a length exceeding 12 cm left the lake and would potentially undertake migration to the sea, whereas 40% migrated into the lake and 44% remained in the tributaries
. Hence, a potential for long-distance migration involving anadromy seems still to be present in the population, although it is unknown if a larger proportion of individuals would have left the lake prior to the establishment of dams.
The lack of immigration from other populations into the lakes should in the short term reduce influx of locally maladaptive alleles thereby shifting the migration-selection balance in favor of local adaptation. A common garden experiment including both LIL and HAL trout demonstrated significantly different temperature-related reaction norms for early life history traits, with HAL showing adaptation to higher incubation temperatures during winter owing to the spawning tributaries being fed by ground water
. Whereas this selection regime would have been similar prior to the establishment of dams, local adaptation would be expected to be reduced depending on the rate of immigration from other populations and their degree of maladaption
In the long term, it is expected that reproductive isolation of the lakes combined with the relatively low effective population sizes should impose limits to the response to selection, due to the fact that loss of potentially adaptive variation is not counteracted by introduction of new variation through migration. This is all the more serious, as anthropogenic pressure increases the need for populations to adapt to environmental change
[2, 4, 80], and specifically for brown trout it is predicted that its future distribution will become significantly reduced due to loss of suitable habitat
. The requirements for maintaining evolutionary potential have been expressed in the classical “500 rule”
 (but see also
 for discussion), stating that N
should be 500 or more for new mutations to balance loss of quantitative variation by drift. This criterion is not fulfilled in HAL and MOS. Assuming no mutation, the limit to response to selection, R(∞) should be given by the expression R(∞) = 2N
R(1), where R(1) denotes the initial response to selection. Moreover, the time until 50% of the response, t50% is roughly equal to 1.4N
. If we assume that HAL became isolated 700 years ago, corresponding to 200 generations and that N
is 153, then t50% is 214 generations, approximately equal to the number of generations that have elapsed since isolation of the population. Although this is based on simplified assumptions, it nevertheless suggests that there should still be adaptive potential within HAL and the presumably larger MOS population. Of course, different conclusions could apply to other anthropogenically isolated populations with much lower N