# «James Walker 1st year DPhil, Interdisciplinary Bioscience Doctoral Training Partnership Supervised by Prof Fritz Vollrath and Dr Beth Mortimer Oxford ...»

Gait synchronisation was measured by calculating the hind lag (HL), defined as the time lag between the right and left hind feet footfalls expressed as a percentage of the cycle duration. This parameter was calculated for a single spider for 100 steps across each leg treatment.

Synchronisation Co-ordination between hind legs HL Hind lag Statistical procedures All data processing, statistics and figure plotting were performed using MATLAB, RStudio (v.

0.98.1091) and Microsoft Excel (v. 2013). Hind lag was described using the median and interquartile range as the distributions were not normal. Mauchly's test for sphericity found the sphericity assumption (variances of the differences between all possible pairs of groups are equal) does not hold for the curvature data and therefore a non-parametric Freidman’s test was used. Linear regression was used to describe the relationship different parameters. Multiple regressions were performed only for variables with prior justification where an effect was suspected. The significance level for all statistical tests was set at p 0.05, with the false discovery rate, the expected proportion of erroneous rejections among all rejections, used to deal with the inflated risk of type I error arising from multiple testing, see Benjamini and Hochberg (1995). This exerts a less stringent control over false discovery in comparison to familywise error rate procedures such as the widely used Bonferroni correction resulting in increased statistical power at the cost of increasing the type I error rate.

## RESULTS

A total of 275 tracks were analysed with 5 repeat measurements across 5 leg treatments for 11 female Tegenaria domestica.Stepping pattern and gait compensation Gait analysis found that intact spider leg movement followed an alternating tetrapod gait where diagonally opposed legs are moved relatively synchronously (see Figure 2a). The contact sequences are similar to those described in previous works (Wilson, 1967, Biancardi et al., 2011) with 4231 being the dominant stepping sequence (legs labelled as in Figure 2b).

Following autotomy, substantial changes in leg synchronisation were observed along with relative changes in the stride length and duty factor of different legs (see Figure 2a for a comparison of 8 vs 5 legs). The stepping sequence described for intact spiders above remained dominant across all individuals on the non-autotomised side until the third leg from the autotomy side was lost resulting in a shift in the dominant foot patterning to 4312.

0.3 0.2 0.1 0.4

0 2.0 1.5 0.5 1.0

Figure 2 – (a) Example of contact sequences for 3 stepping cycles comparing an intact individual to the same individual after 3 legs have been removed from the same side. (b) Labelling of spider legs for gait analysis with legs numbered 1-4 from front to back, A on the side to which autotomy has been induced and U on the unaltered side.

Table 2 - Median Hind lag for different leg numbers indicates a change in gait as more legs are autotomised. A median value of 0.5 indicates a tendency to alternate and the interquartile range gives an indication of the strength of this anatagonism. Calculated for 100 steps on one individual T. domestica.

Figure 3 - Increase in average curvature with successive legs removed from the same side. Boxes represent the interquartile range with the black line showing the median value and bars showing range.

A repeated measures Freidman test found a statistically significant difference in average curvature between leg autotomy treatments, χ2(4) = 153, p 0.001. Post hoc analysis with Wilcoxon signed-rank tests was conducted using the false discovery rate. This found no significant difference between legs 7 and 8 or 5 and 4 but that all 18 other pairwise comparisons showed a significant difference.

Controlling for the effects of speed The average running speed for each spider and treatment was analysed using a Freidman test, showing a significant difference between groups, χ2(4) = 290, p 0.001. The more legs that were autotomised, the greater the reduction in speed with an average 78% reduction in speed between intact and 4 legged spiders.

The dependency between speed and curvature was examined for the fourth leg treatment where 5 intact legs remained. Mean speed (s) and mean curvature (k) were found to vary inversely according to the equation = −1.39 + 39.528 (R2 = 0.61, df = 10, p 0.05). Speed (s) is related to stride length (l) and stepping frequency (f) by the equation: s = l * f and therefore the relationship between speed and curvature can be further dissected using these variables. Both mean stride length (l) and mean stepping frequency (f) were found to increase proportionally with speed according to the following equations: = 14.4 + 0.14 (R2 = 0.71, df = 10, p 0.01) and = 28.37 + 4.43 (R2 = 0.41, df = 10, p = 0.10). This indicates that variation in speed is better explained by stepping frequency than stride length.

Given the dependency between these variables and curvature, it is necessary to control for the effect of stepping frequency in order to determine the effect of autotomy on track curvature. The results of an ordinary least squares multiple regression model fitted for all data with the number of legs and mean stepping frequency was found to strongly predict track curvature (R2 = 0.69, p = 0.0241), see Table below.

This analysis suggests that once legs have been autotomised, track curvature can be reduced if the spider increases stepping frequency across all legs. The inclusion of average duty factor across all legs and hind lag did not improve the fit of the model and so were not included in this analysis.

Duty factor compensation In addition to a change in the stepping pattern, the contact sequences in Figure 2a clearly show a change in duty factor (the ratio of the duration of a foot contact interval to the stride duration) between leg autotomy treatments. The average duty factor across all legs showed large variation across individuals and was found to be negatively correlated with the average speed (r = -0.6, p 0.05) which was also found to decrease with leg number (see above). Therefore, for each leg the percentage difference from the mean duty factor for each track was calculated in order to examine the relative increase or decrease in duty factor for different treatments. Figure 4 shows this difference averaged across all 11 spiders in order to demonstrate the mean relative duty factor for each leg when intact (8 legs) or after 3 legs from the same side have been autotomised (5 legs). The figure shows that the forelegs (A1 and U1) of intact spiders, and the remaining foreleg of treated spiders (U1) have a low duty factor relative to the other legs. As seen in Figure 2a above, the duty factor of the remaining hind leg (A4) after treatment is increased relative to the mean duty factor.

*

Figure 4 – Duty factor compensation for 8 vs 5 legs (N = 11). Bars marked with an asterisk indicate a significant difference in duty factor for a particular leg compared with the mean.

The error bars represent the standard error. Legs are labelled as in Figure 2b.

Stride length compensation The gap which is created by inducing the spider to autotomise legs from the same side was found to be compensated for by increasing stride length, the linear distance between footfalls of the same leg between strides. Stride length showed large variation across the 11 spiders examined in this study and is weakly correlated with speed and therefore the percentage difference from the mean stride length for each leg was analysed in order to make comparisons across all individuals. Figure 5 shows this comparison between 8 legged and 5 legged spiders for relative differences in stride length.

In intact spiders, the fore legs (A1 and U1) have a large stride length with increased variability relative to the other legs both for intact spiders and those with legs autotomised. Spiders with 5 legs remaining showed a large significant relative increase in stride length on the side from which legs had been autotomised (A4).

* * Percentage difference in stride length

-5

-10

-15

-20

Figure 5 - Stride length compensation for 8 vs 5 legs (N=11). Bars marked with an asterisk indicate a significant difference in duty factor for a particular compared with the mean. The error bars represent the standard error. Legs are labelled as in Figure 2b.

Learning After 4 legs had been lost from the same side for all 11 spiders no individual was found to have a curvature which correlated with 6 evenly space time points over a 2 week period ( -0.15 r 0.15 and p 0.05 for a regression of time against curvature for each individual). No effect of trial number on curvature within each treatment was found for any individual; however, a slight inverse effect of trial number was found on running speed for some individuals.

## DISCUSSION

The results of this study confirm the findings of previous work that the autotomy of legs in spiders comes at a cost. With subsequent legs lost in T. domestica the degree of curvature increased and in the direction of the autotomy side, presumably due to the introduction of asymmetry into an otherwise symmetrical system. As expected from previous studies, the running speed was found to decrease across treatments (Amaya et al., 2001, Apontes and Brown, 2005). However, these spiders did show a remarkable ability to control locomotion even when half of their legs had been lost demonstrating the robustness of this system. Previous studies of extreme loss in Nephila report a similar ability to compensate during web building consistently building functional webs with only 4 legs indicating impressive behavioural flexibility (Weissmann, 1987). The coefficient of variation for curvature in intact spiders was relatively low and probably represents bilateral asymmetry arising from genetic and developmental instability (Moller and Gorner, 1994). The higher coefficient of variation for curvature when 4 legs had been lost suggests that in addition to intraspecific variation in symmetry found in intact spiders, there is also variation in the response to autotomy treatments, which could be due to different abilities to compensate for loss of legs.The lack of improvement in curvature over time when 4 legs had been lost suggests that no learning has occurred. The absence of an effect of trial number on curvature over time suggests that the repeated trials on the same individual did not affect compensation; however, for some individuals the speed decreased throughout trials indicating some effect of fatigue influencing spider performance.

Attempts were made to train spiders to use a point light source as a visual cue to guide their trajectory, however no tendency to orientate either towards or away from the light was observed. This could be explained by the poor visual sensitivity found in T. domestica (Land, 1985) or could reflect a general tendency to rely to a greater extent on other forms of sensory information for orientation such as proprioception (Görner and Claas, 1985).

Curvature compensation model The curvature compensation analyses show that spiders compensate for lost legs through the adjustment of various parameters. My results indicate that in the event of leg loss, stepping frequency is the most important parameter across all legs available to running spiders in order to moderate speed and reduce track curvature. However, while these analyses have highlighted the relationship between these variables, it does not necessarily imply that spiders are adopting any particular strategy to reduce curvature using these variables in response to induced autotomy of legs. The stride-based analysis shows that when 3 legs are autotomised from the same side, the spider will respond by increasing stride length and duty factor for the remaining leg on the autotomy side. These changes are presumably to compensate for the increased mechanical load on autotomy side and to fill the gap created by leg removal. In order to validate these predictions it would be necessary to develop a computational model of spider walking and then adjust these parameters accordingly when different legs have been autotomised. These predictions could then prove useful in the design of robust compensation algorithms for legged robots when limbs are lost.

Peripheral control and morphological computing The results of gait analyses in this study indicate that inducing running spiders to autotomise 3 legs from the same side has a dramatic effect on the timing and stepping pattern of the remaining legs.

The hind legs, which in intact spiders show a strong tendency to alternate, began to move relatively synchronously and spiders adopted a stepping sequence only rarely adopted by intact spiders (Foelix, 2010). Whilst the loss of a single leg is common in natural populations, the extreme autotomy treatment used here is likely to be rare and as such it is unlikely that specific preprogrammed compensation strategies may have evolved and are stored in the CNS. Similar amputation studies in insects report correspondingly large changes in gait that was taken to mean that sensory input, or lack of input, causes changes of the behaviour that are not easily explained by assuming rigid preprogrammed central commands (Delcomyn, 1999). The role of proprioceptive reflexes is likely to be similar in spiders where much of the computation required for control is outsourced to their sensory morphology. Lyriform organs are thought to be the proprioreceptors critical to coordination during locomotion as they are typically located near joints where strain appears to be greatest there during walking (Seyfarth, 1985). It is likely that, similarly to insects, the control of walking in spiders is hierarchical whereby the brain determines direction and speed of walking whereas coordination is controlled locally in ganglia determining individual leg movements based on sensory feedback (Delcomyn, 1985).