Laboratory strains of Port-en-Bessin (Por, Normandie, 49° 21' 00'' N 0° 45' 10'' W) and St. Jean-de-Luz (Jean, Basque Coast, 43° 24' 50'' N 1° 39' 45'' W) were established from copulae that were caught in the field during September 2007 (Por) and October 2007 (Jean) respectively. The laboratory strains were reared according to Neumann . Temperature in the climate chambers (Snijders Economic Premium) was at 20°C, relative humidity at 50% and the light dark cycle (LD) was 14:10 (lights on at 7 a.m.), with 5000 lux during the day and 45 minutes each of stepwise dusk and dawn (one step of 1250 lux every 15 min). Full moon was simulated with a standard incandescent torch light bulb (about 1 Lux) switched on all night for four successive nights every 30 days. All generations - parental strains, F1 and BC - were subject to two cycles of artificial moonlight pre-treatment before adult emergence started.
Since temperature and mechanical vibrations are known to act as zeitgeber for the lunar rhythm of Clunio marinus as well [25, 26], we recorded both parameters in our climate chambers. Temperature was recorded with a digital minimum-maximum thermometer (TFA 30.1017.10) and did not vary by more than ± 0.6 °C across the whole experiment in each of the climate chambers. Vibration data were recorded with a vibration data logger (irDAN®vibra_c from ESYS) for 545 hours in one minute intervals and analyzed with Chronos-Fit software  for periodicity. The Lomp-Scargle periodogram (also called power spectrum) identified periods above threshold significance at 968.9, 272.5, 141.4, 108.5, 88.1, 71.7 and 61.2 hours. None of these is close to a tidal period (12.42 hours) or a multiple of it, precluding that the lunar rhythm could have been entrained by another zeitgeber than artificial moonlight. Furthermore, none of the significant periods is close to a 24 hour period plus the daily shift in diurnal emergence time observed in the BC, excluding that emergence was directly triggered by changes in vibration intensity.
The newly established strains were kept under laboratory conditions for one generation before starting the crosses.
In order to allow for genetic and molecular analysis, crosses were carried out as single pair matings. We first produced hybrids of the two strains in both directions (Por × Jean, Jean × Por) and then performed backcrosses to the Jean strain in both directions (F1 × Jean, Jean × F1). This is in contrast to Neumann  who backcrossed to the Por parental strain. Notably, the patterns of inheritance of diurnal emergence time were intermediate in both experiments. To be able to cross the strains and hybrids we had to synchronize their emergence peaks, both lunar and diurnal, by keeping them in separate climate chambers that were running at a phase-shifted light-dark cycle and with different days of artificial full moon.
F1 and BC were also raised under standard moonlight treatment. In the BC, two families with 57 or 20 individuals respectively were raised singly for future molecular analysis, these two families representing reciprocal crosses for both the F1 and the BC. A possible difference between these two backcross families in the lunar and diurnal emergence times was tested by comparing the phenotype distributions in a Kolmogorov-Smirnov test. We could not find significant differences in emergence times, neither lunar (major peak: p = 0.22; minor peak: p = 0.17) nor diurnal (lunar peaks summed up: p = 0.66). The other BC clutches were reared in mass cultures.
Lunar phenotypes were recorded for all, and diurnal phenotypes for most individuals. The lunar phenotypes (in units of days) are recorded as the day of the artificial moonlight cycle when the individual emerged, "day 1" being the first day with artificial moonlight in the laboratory cycle of 30 days. The diurnal phenotypes (in units of hours) were recorded in reference to the phase of the light-dark cycle in the respective climate chamber. Following Neumann , the middle of the dark phase was defined as "hour 0", thus making the middle of the light phase "hour 12". For the parental generation and the F1 generation, diurnal emergence times were recorded continuously while performing the crosses and later grouped into 30 minute intervals. For the backcross progeny, diurnal emergence times were recorded by catching all emerged midges in 30 minute intervals for the two single families, or in 1 hour intervals for the mass crosses. Each BC family emerged over two lunar cycles. As recording of diurnal phenotypes was not possible throughout the full emergence period of more than 2 months, diurnal emergence times are not available for all individuals, explaining the reduced numbers of individuals in analyses requiring diurnal emergence times. Data were summed over lunar cycles for analysis.
Both crossing and recording took place partly during the dark phase. During that time we worked under red light, using an custom-made hand-held LED lamp emitting a wavelength of 650 nm. While the midges are attracted to white light, they did not respond behaviourally to the red LED. As a control we also treated standard cultures with this lamp. We did not observe a shift in diurnal emergence times in these cultures, and so concluded that the red light presented in the first hours of the dark phase during our manipulations did not shift the circadian clock of the individuals in our experiment.
Due to malfunctioning thermostats, the parental strains and most of the F1 families were unintentionally raised at 14°C instead of 20°C, while the single reared backcross families were reared at 22°C instead of 20°C. We made no adjustment to the observed diurnal emergence phenotypes due to this, because previous experiments on Clunio marinus have shown that the diurnal time of emergence is not affected by temperature . This is consistent with the well-known temperature compensation of endogenous circadian clocks [49, 50] and the previously-established role of the circadian clock in directly controlling diurnal emergence in Clunio [3, 48]. However, we did correct the lunar emergence phenotypes of the parental strains and the affected F1 progeny that were raised at 14°C by 1 day, because previous experiments on Clunio marinus have shown that reducing the temperature from 20°C to 14°C increases the pupal development interval by about 1 day . The temperature increase from 20°C to 22°C is not expected to have a major effect ; no correction was applied in this case. Neumann has shown [3, 51] that the developmental event controlled by the temperature-compensated lunar clock is not emergence from the pupa per se, but a certain stage in imaginal disk development in the early last larval instar. From this switching point larval develoment and thus timing of entry into the pupal stage are temperature compensated as well . However, from the time of pupation to emergence of adults, pupal development is not temperature-compensated, and lower temperatures lead to later lunar emergence times. The correction we applied assumes no genetic component to the temperature-dependence of pupal development rate. The adjustment would not affect conclusions about the correlation coefficient of lunar and diurnal emergence times among the backcross progeny, which measures the pattern of variation about the means and was calculated and analysed independently for the single rearing (22°C) and the mass rearing (20°C). It could affect the goodness-of-fit tests for the number of loci controlling lunar emergence time, but should do so independently of the number of loci assumed. To test this, we repeated the test with uncorrected data; in this case, all genetic models are rejected at the 0.05 significance level, but the pattern of p values still has the same relation, thus the model which is the most likely remains the same, unaffected by the use of the uncorrected data.
All graphs and statistics were calculated using the R  statistical programming environment.
To test for the number of genes involved in determining diurnal or lunar emergence time respectively, for the BC we calculated the expected distribution of phenotypes according to different numbers of genetic factors involved and tested the observed distribution of phenotypes against them. The expected distribution for one genetic factor was obtained by combining the observed distributions of the parents of the BC, i.e. the F1 and the Jean strain. For more genetic factors, we obtained the expected distribution by sampling 200,000 individuals from the observed distributions of the F1 and the Jean strain. For the process of sampling we divided the sample into the underlying genotypes according to Mendelian expectations, e.g. 1:2:1 for two genetic factors, 1:3:3:1 for three genetic factors and so on. The fraction of pure parental genotypes (F1, Jean) was sampled directly from the observed parental distributions. For mixed genotypes we sampled one phenotype each from the observed F1 and Jean distributions and averaged the values according to the ratio of genetic factors coming from F1 vs. Jean. The combined distribution of phenotypes of all genotypes was assumed to be the expected distribution for the respective number of genetic factors. The expected distribution was then scaled to the size of the original sample (67 for diurnal emergence times of the single families; 816 for diurnal emergence times in Neumann 1967; 487 for the lunar emergence times in the major peak of the BC) and compared to the observed distribution of the original sample in a Kolmogorov-Smirnov test, and in a G-test for independence referred to the Chi-square distribution with 18 degrees of freedom for the lunar data or 10 degrees of freedom for the circadian data respectively.
The correlation of diurnal and lunar emergence times was assessed by Pearson's product moment correlation. To test which degree of genetic linkage would be required to achieve a correlation of the given magnitude, we compiled matrices of all possible genotypes in the BC for all genetic models from 2-4 lunar and 2-4 circadian genes. Linkage models considered were of the following form: 0 linkages: all lunar genes unlinked to all circadian genes; 1 linkage: one lunar gene linked to one circadian gene; all others mutually unlinked; 2 linkages: same as 1 linkage but in addition a second lunar gene linked to a second circadian gene; etc. Depending on the pattern of genetic linkage assumed, we sampled genotypes for 62 individuals (number of individuals with known diurnal emergence time in the major BC peak of the single reared families) from the full matrix in case of freely recombining factors, or from the respective subsets of the matrix in the case of linkage. For these genotypes we then sampled phenotypes: For each gene coming from F1 or Jean strain we sampled a corresponding phenotype from the F1 or Jean distribution. Then these phenotypes were weighted according to the number of genes assumed to be involved in determining the respective trait, lunar or diurnal emergence time. The genes were assumed to have equal effects. The resulting lunar and diurnal phenotypes were grouped into classes according to those used in the observed BC and the correlation was assessed using Pearson's product moment correlation. We repeated this procedure 100.000 times for each genetic model. The fraction of p values smaller or equal to the p value of the observed BC distribution is the p value obtained, presamp. If a model with a certain degree of linkage was already rejected, we did not test the genetic models that would allow for more independence of the traits, e.g. if a model with 3 circadian genes, 2 lunar genes and 2 linkages was rejected, we did not test the model with 4 circadian genes, 2 lunar genes and 2 linkages, as this model would necessarily imply a higher degree of independence of the two traits.
The timing traits of the laboratory strains relative to artificial moonlight were taken from [3, 30, 53]. If mean values and standard deviations were not given, we calculated them from the graphs.
The data on the local tidal regimes were taken from tide tables for the year 1979. As there is no notable difference between years, the choice of year does not matter. The tide tables, as well as all data and calculations based on them, are in Central European Time (CET). To obtain the interval between the light stimulus and the spring tides in the field we had to obtain a measure for these two events. To estimate the time of the moonlight stimulus, the date of all days with a low tide between 11 p.m. and 1 a.m. was noted. Usually this condition is fulfilled for 2 or 3 days in a row. There are two periods in a lunar cycle when low tides occur around midnight, but for every lunar cycle only the period during the moonlit quarters (i.e. the one closer to full moon) was considered, as only during this period will the moon be in the sky during the midnight low tide and can act as a zeitgeber. The spring tides occur around full moon and new moon, but the exact spring tide day varies by one or two days from place to place and across the year. Therefore we used the days of full moon and the days of new moon as a universal approximation of the spring tide days for all places. Finally, the time between the light stimuli and new moon or full moon respectively was averaged for all months of the year 1979. The time of low tide on full moon day or new moon day respectively was averaged for the whole year of 1979 as well.