All procedures used in the study were approved by the Institutional Review Board of Kanton St. Gallen, Switzerland with a waiver of the requirement for informed consent of the participants given the fact that the study involved the analysis of publicly available data.

Race times on long courses for the annual top ten men and women in breaststroke and freestyle swimming recorded in the Swiss high score list between 1994 and 2011 were obtained per civil year from the website of the Swiss Swimming Federation 22 . The Swiss Swimming Federation records only the annual best swimming performance for each athlete, so no Swiss athlete was included more than once in the same year. Race times for the eight female and male finalists competing on international level in breaststroke and freestyle in the FINA (Fédération Internationale de Natation) World Swimming Championships between 1994 and 2011 were obtained from the website of the FINA 23 . Race times for athletes competing on national level were available annually for swimmers for both breaststroke and freestyle and all distances (i.e. 50 m, 100 m, and 200 m). For FINA finalists, race times were available from the World Championships in Rome (1994), Perth (1998) Fukuoka (2001), Barcelona (2003), Montreal (2005), Melbourne (2007), Rome (2009) and Shanghai (2011). The 50 m breaststroke was held for the first time in the 2001 World Championships.

Since races in breaststroke swimming were held for 50 m, 100 m and 200 m but freestyle races for 50 m, 100 m, 200 m, 400 m, 800 m and 1,500 m, we analysed freestyle swimming races only for 50 m, 100 m, and 200 m to compare with breaststroke swimming results. To allow a comparison of swimming performance for different styles and distances, race times were transformed to swimming speed by dividing race distance by time. To determine temporal trends, we compared the average annual swimming speed for each stroke and race distance, by the top ten Swiss men and top ten Swiss women, and by the eight men and eight women competing in the FINA finals. To analyse the maximum overall swimming performance, we averaged the fastest ten swimming speeds in each stroke for four groups: Swiss women, Swiss men, FINA women, and FINA men. Sex-related differences were calculated using the equation [(women swimming speed) – (men swimming speed)]/(men swimming speed) × 100. The calculation was performed for pairs of equally placed athletes during each year, e.g., the fastest women and men, the second fastest women and men, etc. The absolute value of the sex-related difference for each pair was used to calculate the annual mean and standard deviation.

Prior to statistical analyses, each data set was tested for normal distribution and homogeneity of variances. Normal distribution was tested using a D’Agostino and Pearson omnibus normality test. Homogeneity of variances was tested using a Levene’s test, in cases with two groups, and with a Bartlett’s test, in cases with more than two groups. A potential change in swimming speed across years was investigated using regression analyses. Since the change in sex difference in endurance is assumed to be non-linear 24 , we additionally calculated the non-linear regression model that fits the data best. For swimmers at national level, polynomial regressions from 2^nd to 17^th degree were calculated; for swimmers at international level, polynomial regressions from 2^nd to 7^th degree were calculated. Additionally, LOWESS (i.e. locally weighted scatterplot smoothing) and 64 further standard models were used. We compared the best-fit non-linear models to the linear models using Akaike’s Information Criteria (AIC) and F-test in order to show which model (i.e. linear versus non-linear) would be the most appropriate to explain the trend of the data. One-way analysis of variance (ANOVA) with subsequent Tukey-Kramer post-hoc tests were used to compare data for multiple groups. A two-way ANOVA with a Bonferroni post-hoc test was used to determine the significance of interactive effects of swimming style and sex on performance. Significance of all statistical tests was accepted at p < 0.05. Statistical analyses were performed using IBM SPSS Statistics (Version 19 and 20, IBM SPSS, Chicago, IL, USA) and GraphPad Prism (Version 5 and 6.01, GraphPad Software, La Jolla, CA, USA). Data are reported in the text and figures as mean ± standard deviation (SD).

Figure 1,2,3 and 4 present the changes in swimming speeds for breaststroke (Figure 1) and freestyle (Figure 2) in Swiss swimmers and for breaststroke (Figure 3) and freestyle (Figure 4) in FINA swimmers for 50 m (Panels A), 100 m (Panels B) and 200 m (Panels C). Swimming speed increased linearly for Swiss swimmers in breaststroke (Table 1) and freestyle (Table 2). In FINA finalists, swimming speed increased also linearly in breaststroke (Table 3) and freestyle (Table 4), with the exception of male FINA swimmers in the 50 m breaststroke (Figure 3A).

For all distances, the changes in swimming speed were linear.

For all distances, the changes were linear.

For all distances, the changes were linear.

The changes were linear for all distances.

In breaststroke, male Swiss swimmers increased their swimming speed by 0.008 m · s⁻¹, 0.004 m · s⁻¹, and 0.005 m · s⁻¹ per annum in 50 m, 100 m, and 200 m, respectively, and female swimmers by 0.006 m · s⁻¹, 0.004 m · s⁻¹, 0.004 m · s⁻¹ per annum, respectively. Male FINA swimmers increased swimming speed by 0.004 m · s⁻¹ per annum over 100 m and 200 m, respectively, and female swimmers by 0.005 m · s⁻¹, 0.004 m · s⁻¹, 0.003 m · s⁻¹ per annum in 50 m, 100 m, and 200 m, respectively. In freestyle, male Swiss swimmers increased swimming speed by 0.007 m · s⁻¹, 0.008 m · s⁻¹, and 0.005 m · s⁻¹ per annum in 50 m, 100 m, and 200 m, respectively, and female swimmers by 0.002 m · s⁻¹ per annum for all distances. Male FINA swimmers increased swimming speed by 0.006 m · s⁻¹, 0.005 m · s⁻¹, and 0.004 m · s⁻¹ per annum in 50 m, 100 m, and 200 m, respectively, and female swimmers by 0.006 m · s⁻¹, 0.004 m · s⁻¹, and 0.003 m · s⁻¹ per annum, respectively.

Men swam consistently faster than women for both strokes and all distances. In Swiss swimmers, swimming speed in breaststroke showed no changes across years (Figure 5 and Table 5). In freestyle, however, the sex difference in swimming speed increased linearly (Table 6) for all distances (Figure 6). In FINA finalists, the sex differences in swimming speed showed no significant trends over time (Table 6) for breaststroke (Figure 7) and for freestyle (Figure 8). Sex differences in both breaststroke and freestyle performance decreased significantly (p < 0.0001) with increasing race distance for both Swiss (Figure 9) and FINA swimmers (Figure 10) (i.e. for breaststroke at national level 50 m 11.8%, 100 m 11.4% and 200 m 10.5%; international level 50 m 11.2%, 100 m 10.6% and 200 m 9.9%; for freestyle at national level 50 m 12.0%, 100 m 11.3% and 200 m 9.3%, international level 50 m 11.3%, 100 m 10.6%, 200 m 9.4%, respectively).

The changes were linear for all distances.

The changes were all linear.

Based on the fastest breaststroke and freestyle swimmers, swimming style and sex had a significant interactive effect on swimming speed for both Swiss (F = 15.13, Dfn = 1, DFd = 2156, p = 0.0001) and FINA athletes (F = 6.77, Dfn = 1, DFd = 732, p = 0.0094) (Table 7). In Swiss swimmers, style accounted for 61.9% of the total variance of race time (F = 5753.7, Dfn = 1, DFd = 732, p < 0.0001) and sex for 14.7% of total variance (F = 1365.6, Dfn = 1, DFd = 2156, p < 0.0001), while the interaction accounted for 0.16% (F = 15.1, Dfn = 1, DFd = 2156, p = 0.0001). In the FINA swimmers, style accounted for 59.5% of the total variance of race time (F = 1691.3, Dfn = 1, DFd = 732, p < 0.0001), sex accounted for 14.5% (F = 412.2, Dfn = 1, DFd = 732, p < 0.0001), and the interaction accounted for 0.24% (F = 6.8, Dfn = 1, DFd = 732, p = 0.009).

All main effects of stroke and sex on swimming speed were highly significant (2-way ANOVA, p < 0.0001). A significant interactive effect of swim style x sex is indicated by *(p = 0.0001) and **(p = 0.009).

The increased swimming speed of women and men in freestyle and breaststroke swimming during the 1994–2011 period as well as the new world records during the 2012 Olympic Games 8 are partly attributable to technological advances. Deeper deck-level pools, more effective anti-wave lane ropes, and improved swimming suits reducing drag, improving buoyancy, and enhancing body compression, contributed to the enhanced swimming performance 3 25 . Full-body, polyurethane, technical swimsuits were most probably an important contributor to the unprecedented run of broken records from 1990 to 2009 26 . A full-body suit improves performance by 3.2 ± 2.4% and reduces drag by 6.2 ± 7.9% for distances from 25 m to 800 m leading to a reduction of energy costs 27 . Indeed, FINA’s release of new rules in 2010 limiting the types of technical swimsuits that could be worn by athletes was followed by a downward trend in performance 26 . However, since 2010, there were still world records in 50 m pools achieved. Especially, world records in breaststroke swimming were improved. For women, Katie Ledecky improved the world records in 800 m and 1,500 m freestyle in 2013, Missy Frankling in 2012 for 200 m backstroke, Ruta Meilutyte in 2013 for 50 m and 100 m breaststroke and Rikke Møller Pederson for 200 m breaststroke. For butterfly, Dana Vollmer improved the world record for 100 m in 2012. For men, Sun Yang improved the 1,500 m freestyle world record in 2012, Cameron van der Burgh in 2012 the world record in 100 m breaststroke, Akihiro Yamaguchi also in 2012 for 200 m breaststroke and Ryan Lochte in 2011 for 200 m individual medley 8 .

In addition to technological advances, swimming speed during the 1994–2011 period could have been affected by changes in anthropometric and physiological characteristics 28 , improvements in training 29 , competition psychology 30 31 , and sports nutrition 32 , as well as increased access to the sport by a larger number of athletes 4 . A study of 6–17 year-old children during 20^th century found an increase of 1–2 cm in body height and 0.5-1.5 kg in body weight per decade 33 , a trend which could have led to the improved performances observed in our study. Charles and Bejan 34 observed that the mean body height of champion swimmers in 100 m freestyle increased by 11.4 cm since 1912, and predicted that the fastest athletes would become heavier and taller in future. If available, anthropometric data for Swiss and FINA competitors during the 1994–2011 period could be used to test these assumptions. Due to the linear increase in swimming speed for both national and international swimmers for both breaststroke and freestyle, we may assume that the limits of performance have not reached yet a limit with the exception of the 50 m breaststroke in FINA finalists where the limit of performance may be been reached. However, the period of 1994–2011 might be too short to define whether the change was really linear. Nevill et al. 3 investigated the changes in swimming speeds in 100 m, 200 m, and 400 m freestyle world records from 1957 to 2006 and found that a flattened ‘S-shaped curve’ logistic curve best described the changes.

Results of previous studies reporting that the difference between men and women’s world freestyle records remained stable during the past 60 years 3 4 26 , were confirmed by results of the present study showing that sex-related differences in breaststroke - and in freestyle swimming by FINA athletes - remained relatively constant over time. The temporal increase in the sex-related difference in freestyle performance by Swiss swimmers is difficult to explain. Different levels of freestyle swimming performance by the variations of velocity, stroke rate, and especially stroke length were found in 100 m freestyle for male swimmers of differing skills (i.e. national versus international level) 35 . Additionally, international swimmers are able to maintain a higher energetic and biomechanical capacity than national swimmers 15 and high-speed swimmers have a higher and more stable stroke length and index of coordination than low-speed swimmers 36 .

Sex-related differences in performance are largely explained by sex-specific differences in body dimensions, swimming speed, buoyancy, stroke mechanics, stroke length, starts and turn time, basic and specific endurance, anaerobic power and capacity, muscle power, and flexibility 3 37 38 39 . Young male swimmers have a higher speed fluctuation, active drag, power needed to overcome and technique drag index than young female swimmers 40 . Male freestyle swimmers have also a greater stroke length than female swimmers 36 . Male athletes exhibit greater left ventricular end-diastolic volume than female athletes, resulting in higher stroke volume at rest and during exercise, and higher cardiac output in absolute and relative terms 41 . Men also have 5-10% higher haemoglobin content, which increases oxygen carrying capacity at sub-maximal oxygen uptake levels. These factors lead to greater peak aerobic power, accounting for sex-related differences in the contribution of aerobic energy to exercise 42 43 , a factor that is particularly relevant to longer race distances (i.e. 100 m-200 m). It has also been reported that pacing strategy differed between women and men 44 . Men applied a positive pacing strategy whereas women applied a negative pacing strategy in 200 m and 400 m medley between 2000 and 2011 for international races 44 . However, it is unlikely that these factors changed significantly during 1994–2011, especially as the change would have had to be greater in Swiss men than in Swiss women to explain the observed results. The gains in swimming speed during the early 21^st century following the introduction of new technological swim suits were greater for men than for women in freestyle swimming, while the gains in breaststroke was similar for the two sexes 45 . Although these technological effects might explain the increase in the sex-related difference in Swiss freestyle swimmers, the explanation is countered by the lack of a concomitant increase in FINA swimmers. Differential access to competitive swimming and/or improved training concepts might partly explain the increasing sex-related difference in Swiss freestyle swimming. However, participation in Swiss swimming competition showed a steady annual increase of 3% by both sexes, during 1994–2011 46 .

The stable sex difference at international level is in agreement with previous investigations 4 6 26 . In this highly competitive and demanding environment both men and women have the same access to state-of-the-art training and equipment. It remains to be explored, why at national level men showed a higher increase in swim speed compared to women. Although the sex difference in sport is closing, it remains due to biological differences affecting performance. However, the sex difference is also influenced by reduced opportunity and socio-political factors that influence full female participation across a range of sports around the world 47 .

There is also indirect evidence that the sex-related difference might be different in breaststroke compared to freestyle swimming. Active drag coefficient (C_d) as a measure of technique and performance was lower for faster swimmers 48 . Havriluk found that C_d was similar for men and women in freestyle swimming, but that women had a significantly lower C_d than men in breaststroke 49 . Therefore, the greater power of men, which allows them to outperform women in freestyle swimming, might not provide such a great advantage in breaststroke.

The results of the present study showed a decrease in sex-related difference with increasing distance for both breaststroke and freestyle swimming. These results confirm the conclusions of Tanaka and Seals 38 reporting a decrease in the sex-related difference in freestyle performance with increasing race distance from 50 m to 1,500 m. The decrease was attributed to the fact that women were swimming more efficiently than men, and so show relative improvement in performance as distance increases. The more efficient swimming of women is due to their greater fat percentage, shorter legs, and smaller body density, resulting in a more horizontal and streamlined position and smaller body size, which reduces body drag 50 51 .

Differences in upper body power might also play a role in the decreasing sex-related difference with increasing race distance 52 . It has been shown that swimming performance was associated with dry land strength of the upper body such as mean power of lat pull down back in elite male freestyle swimmers 53 . Freestyle swimming performance was positively correlated with upper body power in races from 50 m to 400 m 52 , but the correlation weakened with increasing race distance 52 . Thus, the greater muscle power of men might become less important with increasing swim distance 54 .

It has been assumed that women would be able to outrun men in ultra-marathon running and it was suggested that the sex difference in running would disappear with increasing running distance particularly in distances longer than the marathon 55 . However, a very recent study investigating the sex differences in ultra-marathon running from 50 km to 1,000 km showed that the sex differences in running speeds decreased non-linearly in 50 km and 100 km but remained unchanged in 200 km and 1,000 km 56 . Furthermore, the sex differences in running speeds showed no change with increasing length of the race distance 56 . The findings suggested that it would very unlikely that women will ever outrun men in ultra-marathons held from 50 km to 100 km 56 . For ultra-swimming, however, very recent studies showed that elite female open-water ultra-distance swimmers improved in 10 km but impaired in 25 km leading to a linear decrease in sex difference in 10 km and a linear increase in sex difference in 25 km 57 . The linear changes in sex differences suggest that women will improve in the near future in 10 km, but not in 25 km 57 . However, women might be able to beat men in longer ultra-distances. In the 36 km 'Maratona del Golfo Capri-Napoli' race held from 1954 to 2013, the sex difference in performance decreased linearly from ~38.2% in 1963 to ~6.0% in 2013 58 . The linear change in both race times and sex differences suggested that women might be able to achieve men's performance or even to outperform men in the near future in open-water ultra-distance swimming. Indeed, in the 46 km 'Manhattan Island Marathon Swim' held in water temperatures <20°C held between 1983 and 2013, the best women were ~12-14% faster than the best men 59 . Most probably the low water temperatures and the higher body fat enable women to beat men in ultra-distance swimming in cold water.

This study has three major limitations. First, we investigated the ten fastest swimmers competing at national level and the eight finalists in the World Championships. The mean of eight swimmers might give a different result compared to the mean of ten swimmers. The 10^th fastest woman is not comparable, in terms of level and performance, to the 10^th fastest man; this might have influenced the sex difference. Future studies might also normalize the performance (i.e. percent of the best performance of each year) which could actually show a better improvement in women’s performance. Second, we used swimming speed as variable to express swimming performance. However, in swimmers, performance could also be compared using FINA points 23 . The ‘FINA Points Table’ allows comparisons of results among different events. The FINA Points Table assigns point values to swimming performances, more points for world class performances typically 1000 or more and fewer points for slower performances 23 . For future studies, performance could be better compared using the ‘FINA Points Table’. Future studies should investigate temporal trends in other swimming styles to determine whether temporal improvement is a generalized phenomenon. Potentially influential factors such as anthropometric characteristics, training, motivation, and nutrition should be included to elucidate the mechanisms underlying temporal changes in athletic performance 16 . Third, we used a time frame of 18 years (1994 to 2011) and investigated the changes across years using linear and non-linear regression analyses. Interestingly, we found only linear changes for both swimming speed and sex difference. In contrast, Nevill et al. 3 and Stanula et al. 9 reported non-linear changes in freestyle swimming speeds. However, Nevill et al. 3 investigated a time period of 50 years (1957–2006) and Stanula et al. 9 of 113 years (1986–2008). The shorter time frame in our study most probably explains why we found linear trends and the other authors 3 9 in contrast non-linear trends. The investigation of longer time frames for breaststroke swimmers might show a non-linear trend in both swimming speed and sex difference in swimming speed.