Scientific Papers

Analyzing tiger interaction and home range shifts using a time-geographic approach | Movement Ecology

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This section describes the results of our interaction analysis, organized based on different tiger dyads. Since the time interval of the tracking data is 1 h, the time lag of two spatially intersected PPAs equal to or shorter than 1 h is considered as a concurrent interaction, while the time lag longer than 1 h is regarded as a delayed interaction.

Duration of concurrent interaction

The duration of monthly concurrent interactions (time lag \(\le 1\) h) between the five tigers captured in the data are summarized in Fig. 5. The outcomes represent how long tigers potentially interacted (i.e. quantified as accumulative duration of continuous PPA intersection sequences) each month. In general, the results show only a few instances of relatively short concurrent intra-sexual interactions between adults. Total duration of monthly concurrent interaction between the adult male and the young tigers is less than 4 h. The neighbor female and the mother tiger only interact for a brief period (average 4 h) during the tracking period of September through December 2018.

Fig. 5
figure 5

The heat map of monthly duration of concurrent interactions among the five tigers in each month. Darker colors represent longer duration of monthly concurrent interactions for each dyad

Most of the mother–young concurrent interactions are detected during the pre-dispersal period (September 2019–January 2020, average monthly duration of \(257.0 \pm 116.2\) h), peaking in October 2019. However, the concurrent interaction detected in dispersal Stage 1 (February 2020–April 2020) between the mother and the young is significantly shorter (average monthly of \(24.3 \pm 27.3\) h), and even becomes less in dispersal Stage 2 (May 2020–August 2020, monthly average of \(2.9 \pm 2.9\) h).

Interestingly, as the duration of mother–young interaction decreases, the male–mother interaction increases. The male tiger and the mother interact concurrently for a total of 147 h in May 2020, and then the duration drops to an average of 31 h per month in the following months. The two young tigers show a notable interaction in January 2020, interacting for approximately 450 h, which appears to mark the onset of dispersal. Afterward, Stage 2 of dispersal starts in May 2020 when the male associates with the female from May 22 to May 29, 2020, as described below (Table 6).

Comparison between ORTEGA and proximity-based approach

A comparative analysis of ORTEGA and the existing proximity-based approach is conducted, exploring the impact of varying time lag parameter and spatial buffer (a threshold to define the close contact between two individuals) when quantifying the duration of potential concurrent interactions. As an illustrative example, we employ the tracking data of the mother tiger and the young-2 tiger, specifically during pre-dispersal, dispersal Stage 1, and dispersal Stage 2. Because of the lack of ground truth data, we assume that a greater number of interactions occur in the pre-dispersal stage when the mother tiger and her young stay together, and fewer interactions occur during the dispersal stages when the young become independent of their mother.

Since the tracking data is collected at a 60-min interval, to detect concurrent interactions, we apply three different time windows (0, 30, and 60 min) in both ORTEGA and the proximity-based approach. Additionally, four spatial buffer thresholds (200, 500, 1000, and 2000 ms) are considered for the proximity-based approach. The results are visualized as box plots in Fig. 6. The Mann–Whitney U Test (summarized in Table 7) indicates that the median duration of interaction computed using the two methods are significantly different, especially in pre-dispersal and dispersal Stage 1.

Fig. 6
figure 6

A comparative analysis of interaction duration for the mother tiger and young-2 as generated by ORTEGA and the proximity-based approach. Each subplot represents a stage, with interaction duration box-plotted at different time windows (0, 30, and 60 min) for the PPA or buffer intersections. Different colors distinguish between ORTEGA’s results in grey and proximity-based approach at various distances (200, 500, 1000, 2000 meter) in other colors. If a box plot does not appear for a particular method at a given time lag, it signifies that no interactions were detected using that method for the given time lag

The results suggest that ORTEGA better captures the potential interaction using PPA intersection, particularly noticeable during the pre-dispersal stage when the young stays together with the mother tiger. Conversely, the proximity-based approach fails to detect potential concurrent interactions using buffer intersection at this stage, especially when the time window is shorter than the temporal resolution of data, irrespective of the size of spatial buffers.

ORTEGA does not rely on a spatial buffer threshold. Therefore, its performance remains consistent. In contrast, the results of the proximity-based approach vary based on the size of the spatial buffer. In the pre-dispersal and dispersal Stage 1, the proximity-based approach captures more interactions when the buffer increases, with overall performance aligning with the results from ORTEGA results at the time window of 60 min. Moreover, the results of the proximity-based approach seems to overestimate the number of interactions especially with larger buffer sizes and temporal windows.

These experiments highlight the dependency of the proximity-based approach on simultaneous tracking and regular location updates to determine when individuals are in close proximity. As a result, larger time windows and spatial buffers may overestimate potential interactions, while smaller ones could underestimate them. That is, when tracking data are coarse or include gaps and the two animals are not observed at the same time, the proximity-based approach misses potential encounters. In contrast, since ORTEGA uses the PPA to consider the potential areas between the tracking points, it can better capture potential encounters in such cases. Furthermore, ORTEGA is capable of analyzing delayed interactions, while the common proximity-based approaches do not support this function.

Mother–young interaction

Mother tiger and young-1

The outcomes suggest that young-1 maintains a close relationship with his mother before dispersal, as indicated by the overlapping red and blue home ranges in Fig. 7a and the concurrent interactions captured in Fig. 8a during the pre-dispersal phase. The home range area of young-1 during the pre-dispersal phase is 43.7 km2 (Table 3), with an overlap of 43.5 km2 with the mother tiger, accounting for 99.6% of the young-1’s home range (Table 1). During this phase, the number of observed incidences of interactions between young-1 and his mother per month are: \(25 \pm 28.3\) incidences per month concurrently, \(6.0 \pm 2.8\) incidences per month with a lag of 1 day, and \(2.5 \pm 2.1\) incidences per month with a lag of 1 week. The longest monthly concurrent duration between the mother tiger and young-1 lasts around 256 h in January 2020.

Fig. 7
figure 7

Shifts in home ranges of the mother tiger (in red), young-1 (in blue), young-2 (in green), male tiger (in purple) as the young disperse

Fig. 8
figure 8

Frequency of concurrent and delayed interaction (for time lags of 1 day and 1 week) between mother tiger and a young-1 and b young-2 in pre-dispersal, dispersal Stage 1, and dispersal Stage 2. These frequencies represent how many times tigers come into a potential contact regardless of the duration of interaction

As young-1 matures, he moves northeastward. His home range overlap with his mother decrease to 35.2% during Stage 1 of dispersal, and further decreases to 10.0% during Stage 2 of dispersal (Table 1). Only one concurrent interaction between the mother tiger and young-1 is detected in Stage 2 of dispersal in June 2020 (Fig. 8a). The results indicate a low level of interaction between these two tigers during dispersal.

Mother tiger and young-2

Compared to young-1, young-2 shows a closer relationship with their mother, with a larger shared home range and a higher frequency of interactions before and during dispersal. The home range overlap between young-2 and the mother tiger is 99.6% of young-2’s home range (Table 1). In terms of monthly interaction, young-2 and the mother show \(45.2 \pm 12.1\) incidences of concurrent interactions before dispersal, \(4.7 \pm 4.2\) incidences with a time lag of 1 day, and \(1.8 \pm 1.3\) incidences per month with a time lag of 1 week (Fig. 8b). The monthly concurrent duration between the mother tiger and young-2 lasts 165 h in September 2019, 398 h in October 2019, 304 h in November 2019, 320 h in December 2019, and 334 h in January 2020 (Fig. 5). This indicates that young-2 stays close to the mother or follows her path and becomes independent of its mother more gradually.

The home range overlap between mother tiger and young-2 decreases to 61.0% during dispersal, and continued to decline to 26.2% in Stage 2 of dispersal (Table 1). Although there is a larger home range overlap, the frequency of concurrent interactions between the mother and young-2 drops to the similar level as young-1. A total of 14 concurrent interactions are detected during Stage 1 of dispersal, and 7 incidences are captured during Stage 2 of dispersal. The detected delayed interaction with a time lag of 1 day decreases from \(5.7 \pm 0.6\) incidences per month during Stage 1 of dispersal to \(3.5 \pm 1.9\) incidences per month during Stage 2 of dispersal (Fig. 8b). These results may indicate the awareness of the two tigers of the presence of one another, but less desire for concurrent interactions.

Female–male interaction between the mother tiger and the male tiger

Figure 9 summarizes the outcomes of interaction analysis between the male tiger and the mother tiger. The results indicate a higher level of interaction between the dyad in the month of May 2020, after the young’s dispersal. Although the home range of the male tiger covers 34.9% of the home range of the mother tiger before the young disperse (Table 1), the male tiger tends to avoid concurrent interactions with the mother tiger when the young are still in a close relationship with their mother (November 2019–Jan 2020). The young start to disperse when the male begins to interact with the mother. During Stage 1 of dispersal, he had 10 concurrent interaction and 10 delayed interactions at a time lag of 1 week with the mother tiger (Fig. 9). The proportion of home range overlap increases to 40.5% during dispersal of the young. During Stage 2 of dispersal, the coverage increases to 82.9%, which indicated that the male tiger home range includes most of the female tiger home range (purple-red dyad in Fig. 7c). The longest concurrent interaction between the male tiger and the mother tiger lasts 25 h from May 29 17:00 to May 30 18:00 (Table 6). The average frequency of the two dyad’s concurrent interaction after May 2020 decreases to 7.3 times per month on average, with an average duration of 31 h each month (Fig. 9).

Fig. 9
figure 9

A heat map of representing the frequencies of concurrent and delayed interactions between the mother tiger and the male tiger in each month at a time lag from 1 day to 3 weeks. Darker colors represent higher interaction frequencies

As mature tigers, both the mother and the male tiger have stable home ranges. The mother tiger’s home range of \(67.8 \pm 14.9\) km2 is nearly round-shape, while the male tiger maintains a larger home range of \(143.6 \pm 30.5\) km2, around 2–3 times the size of the mother tiger’s. The mother tiger shifts her western home range boundary toward the east after the young dispersal, as a result, more space is available to the neighbor tiger (red polygons in Fig. 7). This suggests that the male tiger avoids visiting the shared home range with the mother tiger prior to the young dispersal, and patrols more often post-dispersal.

Male–male interaction

We explore two types of male–male tiger interaction in this section: between subadult males (Fig. 10) and between subadults and adult males (Fig. 11).

Fig. 10
figure 10

The frequency of concurrent and delayed (time lags of 1 day and 1 week) interactions between young-1 and young-2 during the pre-dispersal, dispersal Stage 1, and dispersal Stage 2

Fig. 11
figure 11

A heat map representing the monthly frequency of concurrent and delayed interactions between the adult male tiger and a young-1, and b young-2 for a time lag from 1 day to 3 weeks. Darker colors represent higher interaction frequencies

Young-1 and young-2

Figure 10 suggests that the two young stay close together (concurrent interaction = 34.0 ± 31.1 per month with an average duration of 8.2 h) or follow each other (delayed interaction counts with a delay of 1 day = 5.0 ± 4.4 per month) before dispersal. In February 2020, the two young male tigers move north to establish their own territories, sharing the same territory but staying separated until April 2020 (Fig. 7). In the following 4 months (dispersal Stage 2), their interaction drops to \(6.8 \pm 6.8\) incidences per month concurrently with an average duration of 4.0 h. Their concurrent interaction frequency reaches a maximum of 16 incidences in June 2020 with a duration of 67 h. Their delayed interactions over a time lag of 1 day are \(4.3 \pm 1.0\) incidents per month during Stage 2 of dispersal and it reduces to no interaction after July 2020.

Both young male tigers shift their home ranges toward north, but still share a portion of their mother’s territory during Stage 1 of dispersal. By Stage 2 of dispersal the young males seem to try to establish their territories. Notably, young-2 shows more movement compared to young-1. Table 3 shows that the home range area of young-2 is larger than young-1 at all stages, which may be reflective of its more active movement patterns.

Male tiger and two young

The results underline the tendency of male tigers to avoid interaction, which is reflected in the smaller overlap in home range between the three male tigers compared to the overlap between the mother tiger and the adult male tigers. Prior to the young male’s dispersal, the home range overlap areas between the adult male and the two subadult tigers are 8.4 km2 and 23.7 km2, respectively (Tables 1 and 3). However, during their dispersal, the coverage decreases to none for the young-1 and 13.8 km2 for the young-2 (blue-purple dyad in Fig. 7b, Table 1). The adult male tiger starts to interact more with the mother tiger once the young leave her (Fig. 9).

The results suggest fewer concurrent interaction or delayed interactions with a time lag shorter than 1 week between the male tiger and the young, although their home range has a small overlap before the young dispersal. The number of first delayed interactions across different time lags (1 day to 3 weeks) is shown in Fig. 11. No interaction is detected between the male and young-1 during dispersal Stage 1.

With the increase in time lag, more delayed interactions are detected between young-2 and the male tiger during stage of dispersal. Most male–male delayed interactions are detected in July 2020 when young-2 moves back to the southern area of the home range where the adult male is. However, the interaction with young-1 stay minimal (average of 1–2 incidences per month) as he does not return to the southern area.

These results may indicate that although the male tigers avoid encounters, they might have an awareness of one another, as they tend to check the visited locations of the other tiger with a delay of about 1 day up to 3 weeks. Delayed interactions after 3 weeks might be more incidental, as the field observations suggest that the scent marks can last about up to 3 weeks [24].

Female–female interaction between the mother and the neighbor female tiger

The interaction analysis results suggest a relatively low frequency and duration of interaction between the two adult female tigers. During the 5 months tracking period, only two concurrent interactions are detected in October 2018, two incidents in Nov 2018, and one incident in December 2018 (Fig. 12), with the total duration of concurrent interaction of 12 h.

Fig. 12
figure 12

A heat map representing the monthly frequency of concurrent and delayed interactions between the mother tiger and the neighbor female tiger in each month at a time lag from 1 day to 3 weeks. Darker colors represent higher interaction frequencies

Figure 13 and Table 2 demonstrate a small shift in the home ranges of the two tigers at the shared boundary over time. In September 2018, no overlap exists between the home ranges (95% tracking points) of the two female tigers, leading to no concurrent interaction. One delayed interaction with a time lag of 1 week can be detected within the remaining 5% tracking points. During October 2018 and January 2019, the monthly concurrent interaction between the two animals stays low (less than two incidences). Their home range overlaps varies from 0.6 km2 in October to around 3.8 km2 in November and December, and 2.3 km2 in January. The detected monthly delayed interaction is relatively low, at a rate of two to five visits to the same location at a time lag of 1 day to 1 week. These results may indicate that the two tigers effectively established adjacent territories; they avoid encountering one another and scent mark their common boundary less often.

Fig. 13
figure 13

Shifts in home ranges of the mother tiger (in red) and the neighbor female tiger (in brown) in 5 months

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