Movement patterns of the grey field slug (Deroceras reticulatum) in an arable field

The nature of the slug movement data collected in our field experiment (i.e. position on or beneath the soil surface observed at discrete moments of time) makes it possible to analyse the slug locomotory track in terms of the discrete-time random movement framework^12,16,35,36. Within this framework, a curvilinear movement path is approximated by a broken line (see Fig. 2) and the movement of an individual slug is parameterized by the following frequency distributions:

1. 1.

   The distribution of the step sizes along the movement path (i.e. the distance between sequential pairs of recorded positions; Fig. 2) or the corresponding average speed

2. 2.

   The distribution of turning angle (the angle between the straight lines drawn between sequential pairs of recorded positions; Fig. 2).

Once all the information is available, it is possible to calculate the mean squared displacement as a function of time^12,37. Additionally, in case the movement consists of alternating periods of active movement and immobility (periods with no recorded displacement resulting from feeding or inactivity, hereafter referred to as“resting time”), one should also consider the distribution of the corresponding periods.

Speed, squared displacements and the straightness index

It is apparent from the data that slug movement is intermittent, with periods of locomotion interspersed between periods in which they remain motionless. Tables 1 and 2 show, for the sparse and dense releases respectively, the number of ‘active’ time intervals when the slugs were moving. Periods during which slugs were motionless are marked by the zeros in Tables 1 and 2, but all these individuals resumed their movement during the following hours, confirming that they were alive throughout the assessment period. We therefore retain the zeros in the data for the subsequent analysis.

The baseline discrete-time framework considers animal position at equidistant moments of time. However, in the field experiment (as described in the previous section), time taken to locate slugs at each assessment resulted in the time interval varying between measurements (sparse release treatment: 27–87 mins; dense release treatment: 20–103 mins). The step size, i.e. the displacement during one time interval, depends in part on the duration of that interval, hence risking bias in the results. We address this issue by scaling the step size by the duration of the corresponding time interval, i.e. by considering the average speed during the step:

where

is the displacement of the kth slug during the ith time interval, i.e. the distance between the two sequential positions in the field. Here N is the total number of steps made by the given slug during the full period of the experiment (in our field data, for all slugs (N=10)).

For each individual slug, we then calculate the mean speed over all steps along the movement path:

The results for the sparse and dense releases are shown in Tables 1 and 2, respectively; see also Fig. 3a.

The mean speed of slug movement, although being an important factor for slug dispersal, does not provide enough information about the rate at which the slug increases its linear distance from the point of release, because it does not provide information on the frequency of turning or the turning angle. In order to take that into account, we calculate the straightness index³⁵, i.e. the ratio of the total displacement (distance between the point of release and the final position at the end of the experiment) to the total distance travelled along the path:

where (t_0) is the time of slug release and (t_N) is the time of the final observation. The actual distance travelled is approximated by the length of the corresponding broken line (see the dark solid line in Fig. 2).

The straightness index quantifies the amount of turning (a combination of the frequency and angles of turns) along the whole movement path, i.e. over the whole observation time, but it says nothing about the rate of turning on the shorter time scale of a single ‘step’ along the movement path. To account for this, along with the mean speed we calculate the mean scaled squared displacement (SSD):

see Tables 1 and 2 and Fig. 3b. For the same value of mean speed, a larger value of the SSD corresponds to a straighter movement on the timescale of a single step, with a smaller turning rate.

An immediate observation from visual analysis of the data shown in Fig. 3 is that both slug speed and the SSD are smaller in the case of dense release than in the sparse release. Therefore, a preliminary conclusion can be drawn that average slug movement is slower in the dense release compared to the sparse release treatment.

Turning angles

We now proceed to analyse the distribution of turning angles. The histogram of different values of the angle is shown in Fig. 4. Let us consider first the case of sparse release (see Fig. 4a). We readily observe that the distribution is roughly symmetrical and has a clear maximum at (theta _T=0). The latter indicates that, on this timescale, slug movement is better described as the CRW than the standard diffusion^1,16. Indeed, the standard diffusion (also known as the simple random walk) assumes that there is no bias in the movement direction, in particular there is no correlation in the movement direction in the intervals before and after the recorded position, which means that the turning angle is uniformly distributed over the whole circle. On the contrary, in the case where a correlation between the movement directions exists (hence resulting in the CRW), the distribution of the turning angle becomes hump-shaped. This is in agreement with the results of previous studies on animal movement (in particular, invertebrates^12,38) as well as a general theoretical argument¹³.

In order to provide a more quantitative insight, we look for a functional description of the turning angle distribution using several distributions that are commonly used in movement ecology. The results are shown in Table 3. We establish that the turning angle data are best described by the exponential distribution. Somewhat unexpectedly, it outperforms the Von Mises distribution, although the latter is often regarded as a benchmark and its use has some theoretical justification¹. However, the exponential distribution of the turning angle has previously been observed in movement data on some other species, e.g. on swimming invertebrates³⁹.

The distribution of turning angle obtained in the case of dense release exhibit different features; see Fig. 4b. However, in this case, the distribution is not symmetric and has a clear bias towards positive values: the mean turning angle corresponding to the data shown in Fig. 4b is (langle theta _T rangle = 0.772approx pi /4). Since the slugs used in the dense release are from the same cohort as those used in the sparse release, we consider this bias as an effect of the slug density: the movement pattern of an individual slug is affected by the presence of con-specifics. We discuss possible specific mechanisms for the responsiveness to this factor in the Discussion.

An attempt to describe the turning angle data from the dense release by a symmetric distribution returns low values of (r^2) (see Suppl. Appendix A.1). However, the accuracy of data fitting comparable with the sparse release can be achieved by using an asymmetric distribution, i.e. where the corresponding function has different parameters for the positive and negative values of the angle. The results are shown in Table 4.

The turning angle data shown in Fig. 4 were obtained using all active steps along the movement paths. However, since periods of slug movement alternate with periods of resting, it may raise the question of the relevance of the turning angle at the locations where slugs remained motionless for some time. In order to check the robustness of our results, we now repeat the analysis to calculate the turning angle differently by omitting the segments adjoined with the rest position. The results are shown in Fig. 5. In this case, a reliable fit may not be possible due to there being insufficient data. However, a visual inspection of the corresponding histograms suggests that the main properties of the turning angle distribution agree with those observed above for the bigger data set. Namely, in both cases the distribution has a clear maximum at (theta _T=0) (this is seen particularly well in the case of sparse release). In the case of sparse release the distribution is approximately symmetric, while in the case of dense release there is a clear bias towards positive values. We therefore conclude that the properties of the turning angle distribution are robust with regard to the details of its definition.

Movement and resting times

Our field data shows that, while foraging, slugs do not move continuously but alternate periods of movement and rest; see the second column in Tables 1 and 2. Such behaviour is typical of many animal species^38,40. In this section, we analyse the proportion of time that slugs spend moving, in particular to reveal the differences, if any, between the sparse and dense release.

Figure 6 shows the corresponding data where for the convenience of analysis the slugs are renumbered in a hierarchical order, so that slug 1 spends the highest proportion of time moving, slug 2 has the second highest, etc. We readily observe that the sparse release slugs tend to move more frequently than those from the dense release treatment: slugs that move for more than half of the total observation time constitute about 50% of the group in the case of sparse release but less than 30% in the case of dense release.

In order to make a more quantitative insight, we endeavour to describe the data using several standard distributions; see Tables 5 and 6. We find that the normal distribution performs better than others both in sparse and dense release treatments. Importantly, however, the parameters of the distribution are significantly different between the two cases; in particular, the standard deviation appears to be approximately twice as large in the case of sparse release. Arguably, it confirms the above conclusion that slugs move more frequently or for longer in the case of sparse release. Slugs released as a group tend to spend considerably more time at rest compared to the slugs released individually.

To avoid a possible bias due to the different group size (17 slugs in the sparse release and 11 in the dense release), we now rearrange the data in terms of the proportion of the group that moves with a given frequency. The results are shown in Fig. 7. Although the amount of data in this case does not allow us to describe them using a particular function, the two cases clearly exhibit distributions with different properties. In particular, the average movement frequency is 0.467 for the sparse release and 0.264 for the dense release, and the corresponding variances are 0.090 and 0.065, respectively.

To further quantify the differences, Fig. 8 shows the number of slugs moving in each observation interval. Once again, we observe that the graph exhibits essentially different properties between the two releases. In particular, over the first interval, the majority of slugs (14 out of 17) move in the case of sparse release but none of the slugs move in the case of dense release. In the second half of the observation time (intervals 6–10) on average about 50% of slugs (8 out of 17) move in the case of sparse release but only about 25% of slugs (2–3 out of 11) move in the case of dense release.

Based on the differences between the two releases, we conclude that the presence of con-specifics is the factor that affects the distribution of slug movement time. Thus, along with the results of the previous sections, it suggests that slug movement is density dependent.

Source: Ecology - nature.com