Correction to: Scientific Reports https://doi.org/10.1038/s41598-020-76649-3, published online 12 November 2020
The original version of this Article contained errors due to the miscalculation of the winning rates.
Firstly, the data presented in Figure 2 was incorrect. As a result, in panel A, “R2 = 0.55” was corrected to “R2 = 0.72”; in panel B, “R2 = 0.57” was corrected to “R2 = 0.74”; and in panel C, “R2 = 0.41” was corrected to “R2 = 0.61” and “R2 = 0.64”.
In panel D, the Table:
Eye span | Body length | |
|---|---|---|
male-male | 0.55 | 0.35 |
female-female | 0.57 | 0.46 |
male–female | 0.41 | 0.29 |
female-male | 0.41 | 0.29 |
now reads:
Eye span | Body length | |
|---|---|---|
male-male | 0.72 | 0.49 |
female-female | 0.74 | 0.59 |
male–female | 0.64 | 0.48 |
female-male | 0.61 | 0.40 |
As a result, the legend of Figure 2,
“Flies with relatively long eye spans are likely to be winners in contests. Winning rates in 100 [(A) male vs. male], 140 [(B) female vs. female] and 88 [(C) male vs. female] contests including more than 10 games for pairs of randomly chosen individuals with different eye-span lengths were measured and analysed in regard to their relationship with the eye-span ratio (own eye span/opponent’s eye span). Because the rates of both the winner and loser in a contest are simultaneously shown in the same coordinate system, the scatter of the data points shows symmetry around the origin. Thus, to focus on only one player in all contests, ignore values less than 1.0 on the abscissa or less than 0.5 on the ordinate. Only one data point in (A), for which the eye-span ratio is 2.15, was excluded as an outlier. Solid lines were drawn by sigmoid approximation via the Gauss–Newton algorithm (Minitab 16, Minitab Inc.). R2 = 0.55 (A), 0.57 (B), 0.41 [males in (C)], and 0.41 [females in (C)]. Broken lines indicate 95% confidence intervals. The P values of the three approximation lines are all less than 0.001, indicating significant fits. The P value from the ANCOVA of the datum point distribution among the three kinds of sexual combinations was 0.9998, indicating a non-significant difference.”
now reads:
“Flies with relatively long eye spans are likely to be winners in contests. Winning rates in 100 (A, male vs. male), 140 (B, female vs. female) and 88 (C, male vs. female) contests including more than 10 games for pairs of randomly chosen individuals with different eye-span lengths were measured and analysed in regard to their relationship with the eye-span ratio (own eye span/opponent’s eye span). Each datum point represents one player’s outcome in a contest on one pair of flies with different eye spans. A single contest generates two data points: one for long-eyed fly and the other for short-eyed fly. Because all the winning rates included draws in the denominator, the mean values in each sexual combination are less than 0.5. Only one data point in A, for which the eye-span ratio is 2.15, was excluded as an outlier. Solid lines were drawn by sigmoid approximation via the Gauss-Newton algorithm (Minitab 16, Minitab Inc.). R2 = 0.72 (A), 0.74 (B), 0.64 (males in C), and 0.61 (females in C). Broken lines indicate 95% confidence intervals. The P values of the three approximation lines are all less than 0.001, indicating significant fits. The P value from the ANCOVA of the datum point distribution among the three kinds of sexual combinations was 0.9469, indicating a non-significant difference.”
The original Figure 2 and accompanying legend appear below.
Flies with relatively long eye spans are likely to be winners in contests. Winning rates in 100 [(A) male vs. male], 140 [(B) female vs. female] and 88 [(C) male vs. female] contests including more than 10 games for pairs of randomly chosen individuals with different eye-span lengths were measured and analysed in regard to their relationship with the eye-span ratio (own eye span/opponent’s eye span). Because the rates of both the winner and loser in a contest are simultaneously shown in the same coordinate system, the scatter of the data points shows symmetry around the origin. Thus, to focus on only one player in all contests, ignore values less than 1.0 on the abscissa or less than 0.5 on the ordinate. Only one data point in (A), for which the eye-span ratio is 2.15, was excluded as an outlier. Solid lines were drawn by sigmoid approximation via the Gauss–Newton algorithm (Minitab 16, Minitab Inc.). R2 = 0.55 (A), 0.57 (B), 0.41 [males in (C)], and 0.41 [females in (C)]. Broken lines indicate 95% confidence intervals. The P values of the three approximation lines are all less than 0.001, indicating significant fits. The P value from the ANCOVA of the datum point distribution among the three kinds of sexual combinations was 0.9998, indicating a non-significant difference.
Consequently, the values present in the Results section, under the subheading ‘Hypothesis 1: Eye span as an honest signal to inform opponents of fighting capacity’, were incorrect. As a result,
“The coefficient of determination representing the correlation was 0.55. Similar striking correlations were also found in contests between females (Fig. 2B) and in contests between males and females (Fig. 2C), with winning rates for longer-eyed individuals of 85% (P value = 6.3 × 10–18) in female-female contents and 78% (P value = 5.4 × 10–8) in male–female contents and coefficients of determination of sigmoid fitting curves of 0.57 and 0.41, respectively. In the contests between males and females, neither sex was more likely to win. The fitted curves for these three kinds of sexual combinations were very similar and indistinguishable by covariance analysis. Based on these results, it appears that this species participates in contests in which eye span acts as an honest signal of fighting capacity that informs the opponent similarly in all three kinds of sexual combinations. However, among the contests in which the difference between the eye spans of both individuals was small (less than 10%), the male-male contest displaying the winning rate of around 50% (more than 40% and less than 60%) showed a higher percentage than contests of other sexual combinations (32% in male-male contents, 16% in female-female contests, and 10% in male–female contests). This might suggest a tendency for males to not readily give up during a game.”
now reads:
“The coefficient of determination representing the correlation was 0.72. Similar striking correlations were also found in contests between females (Fig. 2B) and in contests between males and females (Fig. 2C), with winning rates for longer-eyed individuals of 85% (P value = 6.3 × 10–18) in female-female contents and 78% (P value = 5.4 × 10–8) in male–female contents and coefficients of determination of sigmoid fitting curves of 0.74 and 0.61–0.64, respectively. In the contests between males and females, neither sex was more likely to win. The fitted curves for these three kinds of sexual combinations were very similar and indistinguishable by covariance analysis. Based on these results, it appears that this species participates in contests in which eye span acts as an honest signal of fighting capacity that informs the opponent similarly in all three kinds of sexual combinations. However, among the contests in which the difference between the eye spans of both individuals was small (less than 10%), the male-male contest displaying the winning rate of around average 41.9% (more than 31.9% and less than 51.9%) showed a higher proportion than contests of other sexual combinations (26% in male-male contents, 13% in female-female contests, and 14% in male–female contests). This might suggest a tendency for males to not readily give up during a game.”
In addition, the data in Tables ‘Estimated values of parameters’ and ‘Coefficient of determination’, present in the Supplementary Information, Section 3: ‘Statistical method for fitting sigmoid curves to the relationship between winning rate and eye-span ratio between players’ was incorrect. The correct and incorrect values appear below. The original Supplementary Information is provided below.
Incorrect:
Estimated values of parameters:
Regression coefficient | Estimate | Standard error | 95% Confidence intervals | |
|---|---|---|---|---|
Male vs male | Theta1 | 0.752089 | 0.0297833 | (0.697686, 0.828404) |
Theta2 | 0.247911 | 0.0297833 | (0.171596, 0.302314) | |
Theta3 | − 0.000000 | 0.0254107 | (− 0.052998, 0.052998) | |
Theta4 | 0.083989 | 0.0234799 | (0.042551, 0.153038) | |
Female vs female | Theta1 | 0.769293 | 0.0257683 | (0.722399, 0.825377) |
Theta2 | 0.230707 | 0.0257683 | (0.174623, 0.277601) | |
Theta3 | 0.000000 | 0.0205945 | (− 0.041031, 0.041031) | |
Theta4 | 0.076302 | 0.0172004 | (0.047411, 0.116102) | |
Males in male vs female | Theta1 | 0.816198 | 0.0978977 | (*, 1.35182) |
Theta2 | 0.214554 | 0.0869185 | (‐0.146609, 0.34818) | |
Theta3 | 0.032999 | 0.0924641 | (− 0.168222, 0.33956) | |
Theta4 | 0.156657 | 0.0819604 | (0.056978, 0.57010) | |
Females in male vs female | Theta1 | 0.785446 | 0.0869185 | (0.651821, 1.14661) |
Theta2 | 0.183802 | 0.0978977 | (− 0.351816, *) | |
Theta3 | − 0.032999 | 0.0924640 | (− 0.339557, 0.16822) | |
Theta4 | 0.156657 | 0.0819603 | (0.056978, 0.57010) |
Coefficient of determination:
Factors | DF | Square sum | Mean square | F-value | p-value | |
|---|---|---|---|---|---|---|
Male vs male | Regression | 1 | 8.3362 | 8.3362 | 246.27 | < 0.001 |
Residual error | 198 | 6.7022 | 0.0338 | |||
Sum | 199 | 15.0384 | ||||
Coefficient of determination: 8.3362/15.0384 = 0.554 | ||||||
Female vs female | Regression | 1 | 13.971 | 13.971 | 372.46 | < 0.001 |
Residual error | 278 | 10.428 | 0.038 | |||
Sum | 279 | 24.399 | ||||
Coefficient of determination: 13.971/24.399 = 0.573 | ||||||
Males in male vs female | Regression | 1 | 7.111 | 3.9105 | 60.24 | < 0.001 |
Residual error | 86 | 4.056 | 0.0649 | |||
Sum | 87 | 11.167 | ||||
Coefficient of determination: 3.9105/9.4934 = 0.412 | ||||||
Females in male vs female | Regression | 1 | 3.9105 | 3.9105 | 60.24 | < 0.001 |
Residual error | 86 | 5.5828 | 0.0649 | |||
Sum | 87 | 9.4934 | ||||
Coefficient of determination: 3.9105/9.4934 = 0.412 | ||||||
Correct:
Estimated values of parameters:
Regression coefficient | Estimate | Standard error | 95% Confidence intervals | |
|---|---|---|---|---|
Male vs male | Theta1 | 0.740116 | 0.0220877 | (0.697420, 0.788496) |
Theta2 | 0.133642 | 0.0215938 | (0.087323, 0.175114) | |
Theta3 | 0.006398 | 0.0132290 | (− 0.019918, 0.033322) | |
Theta4 | 0.055613 | 0.0120333 | (0.032345, 0.087582) | |
Female vs female | Theta1 | 0.759356 | 0.0197601 | (0.721084, 0.801000) |
Theta2 | 0.107508 | 0.0190800 | (0.068658, 0.143590) | |
Theta3 | 0.009126 | 0.0114918 | (− 0.013435, 0.032022) | |
Theta4 | 0.052528 | 0.0093982 | (0.034393, 0.073573) | |
Males in male vs female | Theta1 | 0.801408 | 0.0611882 | (*, 0.943666) |
Theta2 | 0.089077 | 0.0542438 | (− 0.0277675, 0.183084) | |
Theta3 | 0.051497 | 0.0439795 | (− 0.0402507, 0.139824) | |
Theta4 | 0.106692 | 0.0368689 | (0.0566858, 0.188948) | |
Females in male vs female | Theta1 | 0.788780 | 0.0673040 | (*, 0.939862) |
Theta2 | 0.048852 | 0.0673549 | (− 0.123703, 0.161645) | |
Theta3 | − 0.008878 | 0.0525570 | (− 0.121066, 0.095168) | |
Theta4 | 0.127686 | 0.0439338 | (0.069573, 0.237555) |
Coefficient of determination:
Factors | DF | Square sum | Mean square | F-value | p-value | |
|---|---|---|---|---|---|---|
Male vs male | Regression | 1 | 14.079 | 14.0795 | 518.92 | < 0.001 |
Residual error | 198 | 5.372 | 0.0271 | |||
Sum | 199 | 19.452 | ||||
Coefficient of determination: 14.0795/19.452 = 0.724 | ||||||
Female vs female | Regression | 1 | 23.568 | 23.5684 | 777.13 | < 0.001 |
Residual error | 278 | 8.431 | 0.0303 | |||
Sum | 279 | 31.999 | ||||
Coefficient of determination: 23.5684/31.999 = 0.737 | ||||||
Males in male vs female | Regression | 1 | 7.111 | 7.11071 | 150.78 | < 0.001 |
Residual error | 86 | 4.056 | 0.04716 | |||
Sum | 87 | 11.167 | ||||
Coefficient of determination: 7.11071/11.167 = 0.637 | ||||||
Females in male vs female | Regression | 1 | 6.904 | 6.90449 | 136.56 | < 0.001 |
Residual error | 86 | 4.348 | 0.05056 | |||
Sum | 87 | 11.253 | ||||
Coefficient of determination: 6.90449/11.253 = 0.614 | ||||||
The original Article and accompanying Supplementary Information file have been corrected.
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Takeda, K., Furuta, T., Hamada, M. et al. Author Correction: Handicap theory is applied to females but not males in relation to mate choice in the stalk-eyed fly Sphyracephala detrahens. Sci Rep 13, 1463 (2023). https://doi.org/10.1038/s41598-023-28547-7
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DOI: https://doi.org/10.1038/s41598-023-28547-7
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