Estimating Total Length of Partially Submerged Crocodylians from Drone Imagery

We generally found that the drone-based measurements are very accurate. Flight height (20, 30 and 40 m) resulting in slight differences of image resolution (0.51, 0.76 and 1.02 cm² per pixel) had no significant effect on the precision of the measurement, which remains on the order of ±1 cm (Table 2, Figure 2a). Similarly, the standard deviation of the difference was around 0.8 cm for all target sizes (Table 2, Figure 3b). There was no apparent effect of cloud cover or time of day. This precision of the measurement is largely enough for our purpose. In particular, the 40 m flight altitude, and its corresponding image resolution of 1.02 cm² per pixel, recommended for drone surveys of crocodiles [10] appears well adapted. Note that, as part of our previous work [10], we showed that C. suchus was not affected by drones at flight altitudes > 10 m, though [31] observed that C. porosus responded to drones at 30 m. We are not aware of any other studies on disturbances to crocodylians due to drones, and it is not yet known whether different drones with different power and/or sound profiles will have different impacts, nor could we presume to know the results of such tests for other crocodylian species. Although there is already some literature on the impact of drones on wildlife (birds: [3,9,52,53], mammals: [54,55,56], and reptiles and fish: [57]), disturbance tests should be performed before implementing any drone survey.

However, our results suggest several additional considerations. First, we found a clear bias in that TL tended to be systematically, although marginally (median difference ≈ 0.5 cm), overestimated (>75% of the measurements, Figure 3). This is probably mostly due to the pixelated nature of the image. At the tested image resolutions, the target size was quite small, making it difficult to decide between adjacent pixels when delimiting the end points. We tended to include the last pixel, which partly surpasses the end of the target. This may be related to a second source of imprecision, which is observer heterogeneity in choosing the measurement endpoints. From one measurement to the next three weeks later, we found a mean difference of ±0.43 cm (95% of the differences were between −1.09 cm and +1.80 cm) and a standard deviation of the variability of 0.76 cm (Figure S1b).

Finally, within a single photo or in reconstructed orthophotos, two targets could actually be at different distances from the drone camera due to micro-topological variation (e.g., crocodiles can rest on rocks or fallen trees, etc., resulting in uneven ground). However, we did not observe any significant effects. For example, when GSD was estimated automatically by Agisoft Metashape Pro, the inaccuracy (±0.070 cm/pixel at 40 m) was larger than the true difference in GSD (0.025 cm/pixel per meter; hence −0.05 cm/pixel at 38 m and +0.05 cm/pixel at 42 m) (Figure 3c). The topology effect is thus overshadowed by the GSD variation in the processing software and as long as the difference in level does not exceed ±2.8 m, then the error will be limited to 0.025 cm/pixel per meter. To maintain a constant altitude during the flight, elevation information can be used by Shuttle Radar Topography Mission (SRTM) to establish an automated flight plan wherein the drone maintains a constant altitude relative to terrain heterogeneity along the flight path, but this makes set-up more complex and more costly for virtually no benefit.

This level of imprecision (Table 2, Figure 3a) has very little, if any, impact on how these data are ultimately used in crocodylian monitoring programs. Crocodylians are usually categorized into size classes based on either broader life stage categories or estimated total length categories. The first method comprises subjective categories such as hatchlings (youngs of the year), juveniles, subadults, or adults, which are often defined by some ecological criteria (e.g., probability to disperse or ability to reproduce), differ from one species to another, and between males and females within a species [58,59,60]. The second method is based on visual estimation of total length and typically the observed animals are grouped into 25 or 50 cm classes [61,62,63,64]. In both cases, the groupings of individuals are quite coarse with length thresholds that far surpass 1 cm variation. Moreso, biologically, within and between species, sexes and geographical locations, there is notable variation in the size thresholds. Thus, the minor imprecision in measurements in drone-based methods will have no biologically meaningful effect on the outcomes.

Two prior studies included size class estimations of individuals from drone surveys, but only measured individuals fully visible on the banks [33,34]. Most crocodylians, however, spend most of their time at least partially submerged with only their heads visible [49]. Providing a population-level demographic classification based only on crocodiles basking on land would inevitably make the assessment biased towards larger size classes because smaller crocodiles are less likely to be fully emerged and visible on banks [10,65,66]. Thus, the ability to estimate the total body length (TL) of an individual crocodile from its head-length (HL) provides an alternative to measure the size of individuals that are partially submerged. For many crocodylian species, the typical HL:TL allometric relationship is about at 1:7 ratio [48,67], but the exact ratio differs between crocodylian species [48]. Moreover, even within the same species, the allometric ratio can also vary with the size, particularly for very large animals [68,69,70,71]. For example, the ratio of very large C. porosus seems to be closer to 1:8 [49]. Drone-captured images allow more accurate and repeatable measurements, thus, providing a great advantage over the traditional on-ground visual estimation approach, though still acknowledging that between and within-species variation may bias the estimated TL from HL measurements in the photos.

The simple HL:TL ratio calculated for the 17 different species varied from 1:5.6 to 1:7.3 (Table 1). These results are similar to previous studies estimating this relationship for some of these species [48,49,72,73,74,75,76], while for others this is the first time this information is being published (e.g., C. suchus, M. leptorhynchus). With the exception of C. palustris, in 16 of the 17 species, the slope of the allometric method was also very close to 1 in logarithmic scale reinforcing the usefulness of the ratio for both these species and for our sample (Table 1). If the allometry slope were strictly equal to 1, the two methods (ratio and allometric) would lead to the same estimation, but only the allometric method provides information on bias and precision (Figure 4). Deviation from 1 in the allometric method predicts an ontogenetic shift in the relationship with crocodile size (and thus age), where slope of 1 predicts that it increases more than proportionally (as observed by [77]). For C. porosus, we found a slope equal to 1.05 possibly driven by the HL:TL ratio which is closer to 1:8 (than 1:7 as in other species) for the larger individuals. In the allometric method, the intercept coefficients were quite variable between species (Table 1, Figure 4), again reinforcing the interspecific differences. The species for which the relationship was the least accurate was C. palustris (Figure S9), which is likely due to the small sample size for this species that came from two different populations with different size class distributions and for which the method of measurement was unknown. It should be emphasized that the residual analysis for each of the 17 regressions showed no particular problems, and that the R-squared are very close to 1. The worst of these is for C. palustris, equal to 0.94 (Table 1).

• Measurement bias: We accounted for the measurement imprecision in drone photos previously identified from the standard targets by using a Johnson’s SU-distribution, which better fit the data than a Gaussian distribution (Figure S1b). The Johnson’s SU-distribution was fitted on the logarithm of the relative measurement error and the value of its four parameters are: gamma = 0.0947, delta = 0.936, xi = 0.0209 and lambda = 0.0227.
• Head inclination: The drone objective is perpendicular to the ground, thus if the target is not horizontal its size can be underestimated (see Methods, Figure 1). This could be particularly problematic to measure crocodile head length because crocodylians often incline their head. We assessed this potential distortion by conservatively assuming that, on average, crocodiles have a head inclination of 5° and 99% of the population have a head inclination Figure S1a; pers. obs.). With this assumption, we calculated that we underestimate the true length in drone photos by 0.7% on average, and that the underestimate is less than 6% for 99% of the population. Randomly adding target inclination distortions in our model further confirmed that it results in limited relative imprecision (2.7% of total variability).
• Allometric variation: For all species, we observed a robust allometric relationship between HL and TL (See Table 1, Figure 5a and Figures S2a–S17a). Our data show that the absolute variation of the allometric relationship increases with the size of the individuals (i.e., more variance around the predicted values for bigger crocodylians), but with a fairly constant relative error (average ≃ 9.63%, range ≃5.8% for M. leptorhynchus to ≃15% for G. gangeticus, not including C. palustris, which we excluded because of the afore-explained data quality problems). As it was directly measured on real crocodiles, this variation comes from biological processes independent from the measuring method.

Overall, despite several sources of imprecision, we were able to design a reference allometric framework based on a statistical model to estimate TL from HL with a robust confidence interval for 17 different crocodylian species (See Figure 5a and Figures S2a–S17a, Tables S1–S17). The advantage of our method is that it offers an objective estimate with a defined error (half width of the 95% confidence interval ≃ 13% of the estimated length for C. suchus, and between ≃11% for M. leptorhynchus and ≃18% for G. gangeticus, also without including C. palustris), while traditional methods are based mostly on subjective estimates during on-ground visual evaluations. We evaluated the variance structure of the different sources of imprecision for all 17 species (Table 1, Figure 5b and Figures S2b–S17b). As an example, for C. suchus the variation distribution is fairly constant among individuals (Figure 5b) as follows: (i) head inclination, mean = 2.7% of the total variation; (ii) HL measurement errors (i.e., observer and hardware/software effects), mean = 46.8% of the total variation; (iii) natural allometric variability, mean = 47.8% of the total variation; (iv) allometry estimation (due to the number of observations from which the allometry coefficients are estimated), mean = 2.7% of the total variation (see Table 1 for the other species). The largest contribution to the imprecision came from natural allometric variability between individuals (i.e., within the species), which obviously cannot be reduced. The second largest contributor to imprecision is the accuracy of measurements from the photos, which in our case was limited by the camera resolution and, generally, had very little effect on the overall TL estimation (see above). This source of measurement imprecision, in addition to benefiting from a margin for improvement, is not constrained by the experience of the observer, which itself varies among species [47,48].

We then wanted to compare our framework’s estimates to actual crocodiles from natural populations. Ideally, we would have taken precise measurements by hand from captured individuals and then taken pictures of the same individuals with the drone. Unfortunately, due to COVID travel limitations, we were unable to access wild or captive crocodiles. Consequently, we tested our reference allometric framework with orthorectified drone photos of C. suchus previously collected in 2018 in Niger and Benin [10]. We measured and estimated both TL_p and TL_e, i.e., HL and TL measured directly from the drone photos (TL_p), and estimated TL estimated from our framework (TL_e) from TL_p. Most of the TL_p fell within the CI of our TL_e (n = 78 of 99), confirming the robustness of our predictions (Figure 6). The 21 TL_p outside of the TL_e CI were below the lower CI, which might suggest a tendency of the TL_p method to underestimate the true size. The largest discrepancy between TL_p and TL_e was only 17 cm, which is biologically negligible for demographic classification of most individuals detectable by drones, because most crocodiles detected this way are typically >1.5 m TL (see below and Figure 7). Thus, the magnitude of any underestimation likely has little to no bearing for management.

Any discrepancy is likely mostly explained by measurement errors resulting from measuring a crocodile that is not lying perfectly straight. It can also be difficult to clearly identify the exact end of the crocodile tail on the photos and/or parts of the tail are missing or deformed due to past injuries [78], which will be difficult to see in drone photos. These same uncertainties probably affected the TL measurements in previous drone studies [33,34]. Ultimately, only on-ground TL measurements compared to TL_e from drone-captured pictures of the same individuals will definitively confirm the robustness of our method. Regardless, our results already provide confidence in the framework, as most individuals fell within the CI (Figure 6). As a result, the size class distribution of a large sample would be only marginally affected and, with little to no bearing for population management or other demographic inferences, and access to demographic information from a greater portion of the population is worth this small trade-off.

Using [10] data from 2018, we measured HL for C. suchus individuals along a 2 km transect of the Tapoa River (W National Park, Niger) and in the Bali Pond (Pendjari National Park, Benin). In Niger, we detected 226 individuals, including 25 individuals for which only the head was measurable (11% of the detected individuals) and 67 individuals for which both the head and full body length were measurable (30% of the detected crocodiles). In Benin, we detected 253 individuals, including 64 individuals for which only the head was measurable (25% of the detected individuals) and 32 individuals for which both the HL and TL were measurable (13% of the detected crocodiles). At both sites, neither the HL nor the TL were fully visible/measurable for the remaining ± 60% of individuals. Compared to previous drone-based approaches that measured only fully visible individuals, our method allowed us to capture usable demographic data for an additional 37% (Niger) to 200% (Benin) of the individuals within the detected sample, resulting in a more representative view of the population size-class distribution than was previously possible (e.g., as in the work presented in [34] or [33]).

We used the results of the best replicates (for which the number of detected crocodiles were the highest) of each transect (from the work presented in [10]) to obtain size-class distributions for the study areas in Niger and Benin. Using our reference allometric framework, we assigned each detected crocodile to a 25 cm TL_e size class and obtained a fairly robust estimation of the population size-structure for individuals greater than 1.5 m TL, with a median in the 1.75–2.0 m size class (Figure 7). In Niger, only two individuals were larger than 2.75 m, with the largest estimated to be 3.97 m (First quartile: Q_inf = 349.19 cm; Mean = 397.17 cm; third quartile: Q_sup = 451.43 cm), which would be a very large contemporary individual for this species (M.H. Shirley, pers. obs.). A previous nocturnal spotlight survey in this area observed multiple large individuals (i.e., 2.5–3.0 m TL), as well as a balanced size class distribution including more than 46% of individuals juveniles (i.e., 79,80].

As has been previously documented [10,34], drone surveys almost completely miss the small individuals (approximately less than 100 cm). They are often hidden in vegetation or are simply too small to detect or reliably identify even in very high resolution drone photos [10]. They are also predominantly nocturnal compared to adults, mostly to avoid predation risk from diurnal predators (e.g., birds, fish, mammals, snakes, and bigger crocodiles), which is less of a risk with increasing crocodile size [81,82]. For the same reasons, small crocodylians can also be difficult to detect using traditional survey methods [17]. However, for most crocodylian populations, hatchlings and juveniles represent more than 50% of the individuals and only a fraction of them will survive until adulthood [20,83]. A high proportion of juvenile size classes can be a good indicator of healthy populations because it represents high female fecundity, high juvenile survival, and high recruitment potential [84,85,86,87]. Thus, our inability to fully describe the size class distribution of crocodile populations remains one of the most significant limitations of drone-based approaches (but it also affects the more traditional methods).