track_intersection() calculates the number of unique intersections between trajectories.
The function also supports testing with simulations and different permutation procedures for the coordinates
of the simulated trajectories' origins to compute p-values. This allows for a robust assessment of the intersection metrics,
enabling users to evaluate the significance of the observed intersections in relation to simulated trajectories.
Usage
track_intersection(
data,
test = NULL,
H1 = NULL,
sim = NULL,
origin.permutation = NULL,
custom.coord = NULL
)Arguments
- data
A
trackR object, which is a list consisting of two elements:Trajectories: A list of interpolated trajectories, where each trajectory is a series of midpoints between consecutive footprints.Footprints: A list of data frames containing footprint coordinates, metadata (e.g., image reference, ID), and a marker indicating whether the footprint is actual or inferred.
- test
Logical; if
TRUE, the function compares the observed intersection metrics against. Default isFALSE.- H1
A character string specifying the alternative hypothesis to be tested. Options are
"Lower"for testing whether the observed intersections are significantly lower than the simulated ones (e.g., coordinated or gregarious movement), or"Higher"for testing whether the observed intersections are significantly higher than the simulated ones (e.g., predatory or chasing events).- sim
A
track simulationR object consisting of a list of simulated trajectories to use for comparison whentest = TRUE.- origin.permutation
A character string specifying the method for permutation of the coordinates of the simulated trajectories' origins. Options include
"None","Min.Box","Conv.Hull", or"Custom". Default is"None".- custom.coord
A matrix of custom coordinates that define the vertices of an area for permutation of the coordinates of the simulated trajectories' origins.
Value
A track intersection R object consisting of a list containing the following elements:
- Intersection_metric
A numeric matrix of unique intersection counts between trajectories. Each entry represents the number of unique intersection points between the corresponding pair of trajectories.
- Intersection_metric_p_values
(If
test = TRUE) A numeric matrix of raw pairwise p-values, computed by Monte Carlo tail tests according toH1, with the (+1) correction (Phipson & Smyth, 2010): $$p = (1 + \#\{\text{extreme}\}) / (nsim + 1)$$. Each entry reflects the probability of observing an intersection count as extreme as the observed one, given the null hypothesis of no difference.- Intersection_metric_p_values_BH
(If
test = TRUE) A numeric matrix of Benjamini–Hochberg (BH) adjusted p-values controlling the false discovery rate (FDR), applied across the set of unique pairwise tests (Benjamini & Hochberg, 1995).- Intersection_metric_p_values_combined
(If
test = TRUE) A single numeric value representing the combined p-value across all intersections (based on the global statistic: the sum of pairwise intersections). This indicates the overall significance of the observed intersections relative to simulations.- Intersection_metric_simulations
(If
test = TRUE) A list containing matrices of intersection counts for each simulation iteration, allowing for inspection of the distribution of intersections across randomized scenarios.
Details
The track_intersection() function is designed to calculate the number of unique
intersections between trajectories and to evaluate their statistical significance
through hypothesis testing based on simulated tracks.
Pairwise p-values are computed with a Monte Carlo tail test according to the
selected alternative hypothesis (H1), using the (+1) correction to avoid
zero-values (see Phipson & Smyth, 2010):
$$p = (1 + \#\{\text{extreme}\}) / (nsim + 1)$$
These raw p-values are then adjusted for multiple comparisons across the set of unique pairwise tests using the Benjamini–Hochberg (BH) procedure for false discovery rate (FDR) control (Benjamini & Hochberg, 1995). Both the raw and the BH-adjusted p-value matrices are returned in the output object, allowing users to inspect either uncorrected or corrected results. In addition, a global combined p-value is provided, summarizing the overall deviation from the null across all pairs.
This framework provides a robust means of comparing observed intersections against those expected under random conditions, and is intended for testing specific behavioral hypotheses related to trackmaker interactions.
Hypothesis testing is controlled by the H1 argument, which defines the
alternative hypothesis:
"Lower": tests whether the observed intersections are significantly fewer than those generated by simulations. This scenario corresponds to hypotheses of coordinated or gregarious movement, where parallel or group movement would result in fewer intersections than expected at random."Higher": tests whether the observed intersections are significantly greater than those generated by simulations. This scenario corresponds to hypotheses of predatory or chasing interactions, where one trackmaker follows or crosses another, producing more intersections than expected at random.
The choice of H1 must match the biological hypothesis under investigation.
If it is not explicitly specified when test = TRUE, an error will be raised.
The interpretation of the combined global p-value returned by the function
is directly influenced by the choice of H1, as it determines whether the test
detects a reduction or an increase in intersection counts relative to the
simulated dataset.
In addition to hypothesis testing, the track_intersection() function offers several options for altering the initial positions
of simulated tracks through the origin.permutation argument. The available options include:
"None": Simulated trajectories are not shifted and are compared based on their original starting positions."Min.Box": Trajectories are randomly placed within the minimum bounding box surrounding the original starting points."Conv.Hull": Trajectories are placed within the convex hull that encompasses all original starting points, providing a more precise representation of the area occupied by the tracks."Custom": Allows users to define a specific region of interest by providing a matrix of coordinates (custom.coord) that specifies the vertices of the desired area. This option is particularly useful when certain spatial features or environmental conditions are known to constrain movement.
The choice of origin.permutation should reflect the nature of the behavioral hypothesis being tested. For example, using
"None" is most appropriate when testing how intersections compare under scenarios where trackmakers originate from specific
locations. In contrast, options like "Min.Box", "Conv.Hull", or "Custom" are suitable when evaluating how intersections
would differ if the tracks originated from a broader or predefined area.
The track_intersection() function also allows for integration with similarity metrics computed using simil_DTW_metric() and
simil_Frechet_metric(). This combination of intersection counts and similarity metrics can provide a more comprehensive analysis
of how trackmakers interacted, whether their movements were coordinated or independent, and whether their interactions were consistent
with the hypothesized behavioral patterns.
Overall, the selection of H1 and origin.permutation should be carefully considered in light of the specific hypotheses
being tested. By combining intersection metrics with similarity measures, users can obtain a deeper understanding of the
behavioral dynamics underlying the observed trackways.
References
Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal statistical society: series B (Methodological), 57(1), 289-300.
Phipson, B., & Smyth, G. K. (2010). Permutation P-values should never be zero: calculating exact P-values when permutations are randomly drawn. Statistical applications in genetics and molecular biology, 9(1).
Examples
# Example 1: Intersection metrics in the PaluxyRiver dataset.
s1 <- simulate_track(PaluxyRiver, nsim = 5, model = "Directed")
int1 <- track_intersection(PaluxyRiver, test = TRUE, H1 = "Lower", sim = s1,
origin.permutation = "None")
#> 2026-04-04 16:17:27.112005 Iteration 1
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:27.126457 Iteration 2
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:27.139903 Iteration 3
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:27.152671 Iteration 4
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:27.165332 Iteration 5
#>
#> Intersect metric
#> ------------------------------------
#> ANALYSIS COMPLETED
#> ------------------------------------
#>
print(int1)
#> $Intersection_metric
#> Track_1 Track_2
#> Track_1 NA 1
#> Track_2 1 NA
#>
#> $Intersection_metric_p_values
#> Track_1 Track_2
#> Track_1 NA 0.8333333
#> Track_2 0.8333333 NA
#>
#> $Intersection_metric_p_values_BH
#> Track_1 Track_2
#> Track_1 NA 0.8333333
#> Track_2 0.8333333 NA
#>
#> $Intersection_metric_p_values_combined
#> [1] 0.8333333
#>
#> $Intersection_metric_simulations
#> $Intersection_metric_simulations[[1]]
#> Track_1 Track_2
#> Track_1 NA 0
#> Track_2 0 NA
#>
#> $Intersection_metric_simulations[[2]]
#> Track_1 Track_2
#> Track_1 NA 3
#> Track_2 3 NA
#>
#> $Intersection_metric_simulations[[3]]
#> Track_1 Track_2
#> Track_1 NA 0
#> Track_2 0 NA
#>
#> $Intersection_metric_simulations[[4]]
#> Track_1 Track_2
#> Track_1 NA 0
#> Track_2 0 NA
#>
#> $Intersection_metric_simulations[[5]]
#> Track_1 Track_2
#> Track_1 NA 0
#> Track_2 0 NA
#>
#>
# Example 2: Using "Min.Box" origin permutation in PaluxyRiver dataset.
s2 <- simulate_track(PaluxyRiver, nsim = 5, model = "Constrained")
int2 <- track_intersection(PaluxyRiver, test = TRUE, H1 = "Lower", sim = s2,
origin.permutation = "Min.Box")
#> 2026-04-04 16:17:27.803339 Permutation 1
#>
#> Permutation of coordinates at origin using Min.Box
#> ------------------------------------
#> 2026-04-04 16:17:27.997687 Permutation 2
#>
#> Permutation of coordinates at origin using Min.Box
#> ------------------------------------
#> 2026-04-04 16:17:28.087232 Permutation 3
#>
#> Permutation of coordinates at origin using Min.Box
#> ------------------------------------
#> 2026-04-04 16:17:28.378561 Permutation 4
#>
#> Permutation of coordinates at origin using Min.Box
#> ------------------------------------
#> 2026-04-04 16:17:28.827121 Permutation 5
#>
#> Permutation of coordinates at origin using Min.Box
#> ------------------------------------
#> PERMUTATION COMPLETED
#> ------------------------------------
#>
#> 2026-04-04 16:17:28.841498 Iteration 1
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:28.860167 Iteration 2
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:28.872542 Iteration 3
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:28.885314 Iteration 4
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:28.898058 Iteration 5
#>
#> Intersect metric
#> ------------------------------------
#> ANALYSIS COMPLETED
#> ------------------------------------
#>
print(int2)
#> $Intersection_metric
#> Track_1 Track_2
#> Track_1 NA 1
#> Track_2 1 NA
#>
#> $Intersection_metric_p_values
#> Track_1 Track_2
#> Track_1 NA 1
#> Track_2 1 NA
#>
#> $Intersection_metric_p_values_BH
#> Track_1 Track_2
#> Track_1 NA 1
#> Track_2 1 NA
#>
#> $Intersection_metric_p_values_combined
#> [1] 1
#>
#> $Intersection_metric_simulations
#> $Intersection_metric_simulations[[1]]
#> Track_1 Track_2
#> Track_1 NA 1
#> Track_2 1 NA
#>
#> $Intersection_metric_simulations[[2]]
#> Track_1 Track_2
#> Track_1 NA 1
#> Track_2 1 NA
#>
#> $Intersection_metric_simulations[[3]]
#> Track_1 Track_2
#> Track_1 NA 0
#> Track_2 0 NA
#>
#> $Intersection_metric_simulations[[4]]
#> Track_1 Track_2
#> Track_1 NA 1
#> Track_2 1 NA
#>
#> $Intersection_metric_simulations[[5]]
#> Track_1 Track_2
#> Track_1 NA 0
#> Track_2 0 NA
#>
#>
# Example 3: Using "Conv.Hull" origin permutation in PaluxyRiver dataset.
s3 <- simulate_track(PaluxyRiver, nsim = 5, model = "Unconstrained")
int3 <- track_intersection(PaluxyRiver, test = TRUE, H1 = "Lower", sim = s3,
origin.permutation = "Conv.Hull")
#> 2026-04-04 16:17:29.522354 Permutation 1
#>
#> Permutation of coordinates at origin using Conv.Hull
#> ------------------------------------
#> 2026-04-04 16:17:29.625287 Permutation 2
#>
#> Permutation of coordinates at origin using Conv.Hull
#> ------------------------------------
#> 2026-04-04 16:17:29.724065 Permutation 3
#>
#> Permutation of coordinates at origin using Conv.Hull
#> ------------------------------------
#> 2026-04-04 16:17:29.816516 Permutation 4
#>
#> Permutation of coordinates at origin using Conv.Hull
#> ------------------------------------
#> 2026-04-04 16:17:29.91155 Permutation 5
#>
#> Permutation of coordinates at origin using Conv.Hull
#> ------------------------------------
#> PERMUTATION COMPLETED
#> ------------------------------------
#>
#> 2026-04-04 16:17:29.925255 Iteration 1
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:29.936921 Iteration 2
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:29.949081 Iteration 3
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:29.961649 Iteration 4
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:29.974112 Iteration 5
#>
#> Intersect metric
#> ------------------------------------
#> ANALYSIS COMPLETED
#> ------------------------------------
#>
print(int3)
#> $Intersection_metric
#> Track_1 Track_2
#> Track_1 NA 1
#> Track_2 1 NA
#>
#> $Intersection_metric_p_values
#> Track_1 Track_2
#> Track_1 NA 1
#> Track_2 1 NA
#>
#> $Intersection_metric_p_values_BH
#> Track_1 Track_2
#> Track_1 NA 1
#> Track_2 1 NA
#>
#> $Intersection_metric_p_values_combined
#> [1] 1
#>
#> $Intersection_metric_simulations
#> $Intersection_metric_simulations[[1]]
#> Track_1 Track_2
#> Track_1 NA 1
#> Track_2 1 NA
#>
#> $Intersection_metric_simulations[[2]]
#> Track_1 Track_2
#> Track_1 NA 0
#> Track_2 0 NA
#>
#> $Intersection_metric_simulations[[3]]
#> Track_1 Track_2
#> Track_1 NA 0
#> Track_2 0 NA
#>
#> $Intersection_metric_simulations[[4]]
#> Track_1 Track_2
#> Track_1 NA 0
#> Track_2 0 NA
#>
#> $Intersection_metric_simulations[[5]]
#> Track_1 Track_2
#> Track_1 NA 0
#> Track_2 0 NA
#>
#>
# Example 4: Using "Min.Box" origin permutation in MountTom subset.
sbMountTom <- subset_track(MountTom, tracks = c(1, 2, 3, 4, 7, 8, 9, 13, 15, 16, 18))
s4 <- simulate_track(sbMountTom, nsim = 5)
#> Warning: `model` is NULL. Defaulting to 'Unconstrained'.
int4 <- track_intersection(sbMountTom, test = TRUE, H1 = "Higher", sim = s4,
origin.permutation = "Min.Box")
#> 2026-04-04 16:17:30.099538 Permutation 1
#>
#> Permutation of coordinates at origin using Min.Box
#> ------------------------------------
#> 2026-04-04 16:17:30.104786 Permutation 2
#>
#> Permutation of coordinates at origin using Min.Box
#> ------------------------------------
#> 2026-04-04 16:17:30.109207 Permutation 3
#>
#> Permutation of coordinates at origin using Min.Box
#> ------------------------------------
#> 2026-04-04 16:17:30.11322 Permutation 4
#>
#> Permutation of coordinates at origin using Min.Box
#> ------------------------------------
#> 2026-04-04 16:17:30.117802 Permutation 5
#>
#> Permutation of coordinates at origin using Min.Box
#> ------------------------------------
#> PERMUTATION COMPLETED
#> ------------------------------------
#>
#> 2026-04-04 16:17:30.151393 Iteration 1
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:30.184957 Iteration 2
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:30.226891 Iteration 3
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:30.261055 Iteration 4
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:30.293225 Iteration 5
#>
#> Intersect metric
#> ------------------------------------
#> ANALYSIS COMPLETED
#> ------------------------------------
#>
print(int4)
#> $Intersection_metric
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 0 0 0 0 0 0
#> Track_02 0 NA 0 0 0 0 0
#> Track_03 0 0 NA 0 0 0 0
#> Track_04 0 0 0 NA 0 0 0
#> Track_07 0 0 0 0 NA 0 1
#> Track_08 0 0 0 0 0 NA 0
#> Track_09 0 0 0 0 1 0 NA
#> Track_13 0 0 0 0 0 0 0
#> Track_15 0 0 0 0 0 0 0
#> Track_16 0 0 0 0 0 0 0
#> Track_18 0 0 0 0 0 0 0
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 0 0 0 0
#> Track_02 0 0 0 0
#> Track_03 0 0 0 0
#> Track_04 0 0 0 0
#> Track_07 0 0 0 0
#> Track_08 0 0 0 0
#> Track_09 0 0 0 0
#> Track_13 NA 0 0 0
#> Track_15 0 NA 0 0
#> Track_16 0 0 NA 0
#> Track_18 0 0 0 NA
#>
#> $Intersection_metric_p_values
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 1 1 1 1.0000000 1 1.0000000
#> Track_02 1 NA 1 1 1.0000000 1 1.0000000
#> Track_03 1 1 NA 1 1.0000000 1 1.0000000
#> Track_04 1 1 1 NA 1.0000000 1 1.0000000
#> Track_07 1 1 1 1 NA 1 0.1666667
#> Track_08 1 1 1 1 1.0000000 NA 1.0000000
#> Track_09 1 1 1 1 0.1666667 1 NA
#> Track_13 1 1 1 1 1.0000000 1 1.0000000
#> Track_15 1 1 1 1 1.0000000 1 1.0000000
#> Track_16 1 1 1 1 1.0000000 1 1.0000000
#> Track_18 1 1 1 1 1.0000000 1 1.0000000
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 1 1 1 1
#> Track_02 1 1 1 1
#> Track_03 1 1 1 1
#> Track_04 1 1 1 1
#> Track_07 1 1 1 1
#> Track_08 1 1 1 1
#> Track_09 1 1 1 1
#> Track_13 NA 1 1 1
#> Track_15 1 NA 1 1
#> Track_16 1 1 NA 1
#> Track_18 1 1 1 NA
#>
#> $Intersection_metric_p_values_BH
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 1 1 1 1 1 1
#> Track_02 1 NA 1 1 1 1 1
#> Track_03 1 1 NA 1 1 1 1
#> Track_04 1 1 1 NA 1 1 1
#> Track_07 1 1 1 1 NA 1 1
#> Track_08 1 1 1 1 1 NA 1
#> Track_09 1 1 1 1 1 1 NA
#> Track_13 1 1 1 1 1 1 1
#> Track_15 1 1 1 1 1 1 1
#> Track_16 1 1 1 1 1 1 1
#> Track_18 1 1 1 1 1 1 1
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 1 1 1 1
#> Track_02 1 1 1 1
#> Track_03 1 1 1 1
#> Track_04 1 1 1 1
#> Track_07 1 1 1 1
#> Track_08 1 1 1 1
#> Track_09 1 1 1 1
#> Track_13 NA 1 1 1
#> Track_15 1 NA 1 1
#> Track_16 1 1 NA 1
#> Track_18 1 1 1 NA
#>
#> $Intersection_metric_p_values_combined
#> [1] 0.8333333
#>
#> $Intersection_metric_simulations
#> $Intersection_metric_simulations[[1]]
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 0 0 0 0 0 0
#> Track_02 0 NA 1 0 0 0 0
#> Track_03 0 1 NA 0 1 0 0
#> Track_04 0 0 0 NA 0 0 0
#> Track_07 0 0 1 0 NA 0 0
#> Track_08 0 0 0 0 0 NA 0
#> Track_09 0 0 0 0 0 0 NA
#> Track_13 0 0 0 0 0 0 0
#> Track_15 0 0 0 0 0 0 0
#> Track_16 0 0 0 0 0 0 0
#> Track_18 0 0 0 0 0 0 0
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 0 0 0 0
#> Track_02 0 0 0 0
#> Track_03 0 0 0 0
#> Track_04 0 0 0 0
#> Track_07 0 0 0 0
#> Track_08 0 0 0 0
#> Track_09 0 0 0 0
#> Track_13 NA 0 0 0
#> Track_15 0 NA 0 0
#> Track_16 0 0 NA 0
#> Track_18 0 0 0 NA
#>
#> $Intersection_metric_simulations[[2]]
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 0 1 0 0 0 0
#> Track_02 0 NA 0 0 0 0 0
#> Track_03 1 0 NA 0 0 0 0
#> Track_04 0 0 0 NA 0 1 1
#> Track_07 0 0 0 0 NA 0 0
#> Track_08 0 0 0 1 0 NA 0
#> Track_09 0 0 0 1 0 0 NA
#> Track_13 0 0 0 0 0 0 0
#> Track_15 0 0 0 0 0 0 0
#> Track_16 0 0 0 0 0 0 0
#> Track_18 0 0 0 0 1 0 0
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 0 0 0 0
#> Track_02 0 0 0 0
#> Track_03 0 0 0 0
#> Track_04 0 0 0 0
#> Track_07 0 0 0 1
#> Track_08 0 0 0 0
#> Track_09 0 0 0 0
#> Track_13 NA 0 0 0
#> Track_15 0 NA 0 0
#> Track_16 0 0 NA 0
#> Track_18 0 0 0 NA
#>
#> $Intersection_metric_simulations[[3]]
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 0 0 0 0 1 0
#> Track_02 0 NA 0 0 0 0 0
#> Track_03 0 0 NA 0 0 0 0
#> Track_04 0 0 0 NA 0 0 0
#> Track_07 0 0 0 0 NA 0 0
#> Track_08 1 0 0 0 0 NA 0
#> Track_09 0 0 0 0 0 0 NA
#> Track_13 0 0 0 0 0 0 0
#> Track_15 0 0 0 0 0 0 0
#> Track_16 0 0 0 0 0 0 0
#> Track_18 0 0 0 0 0 0 0
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 0 0 0 0
#> Track_02 0 0 0 0
#> Track_03 0 0 0 0
#> Track_04 0 0 0 0
#> Track_07 0 0 0 0
#> Track_08 0 0 0 0
#> Track_09 0 0 0 0
#> Track_13 NA 0 0 0
#> Track_15 0 NA 0 0
#> Track_16 0 0 NA 0
#> Track_18 0 0 0 NA
#>
#> $Intersection_metric_simulations[[4]]
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 0 0 0 0 0 0
#> Track_02 0 NA 0 0 0 0 0
#> Track_03 0 0 NA 0 0 0 0
#> Track_04 0 0 0 NA 0 0 0
#> Track_07 0 0 0 0 NA 0 0
#> Track_08 0 0 0 0 0 NA 0
#> Track_09 0 0 0 0 0 0 NA
#> Track_13 0 0 0 0 0 0 0
#> Track_15 0 0 0 0 0 0 0
#> Track_16 0 0 0 0 0 0 0
#> Track_18 0 0 0 0 0 0 0
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 0 0 0 0
#> Track_02 0 0 0 0
#> Track_03 0 0 0 0
#> Track_04 0 0 0 0
#> Track_07 0 0 0 0
#> Track_08 0 0 0 0
#> Track_09 0 0 0 0
#> Track_13 NA 0 0 0
#> Track_15 0 NA 0 0
#> Track_16 0 0 NA 0
#> Track_18 0 0 0 NA
#>
#> $Intersection_metric_simulations[[5]]
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 0 0 0 0 0 0
#> Track_02 0 NA 0 0 0 0 0
#> Track_03 0 0 NA 0 0 0 0
#> Track_04 0 0 0 NA 0 0 0
#> Track_07 0 0 0 0 NA 0 0
#> Track_08 0 0 0 0 0 NA 1
#> Track_09 0 0 0 0 0 1 NA
#> Track_13 0 0 0 0 0 0 0
#> Track_15 0 0 0 0 0 0 0
#> Track_16 0 0 0 0 0 0 0
#> Track_18 0 0 0 0 0 0 0
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 0 0 0 0
#> Track_02 0 0 0 0
#> Track_03 0 0 0 0
#> Track_04 0 0 0 0
#> Track_07 0 0 0 0
#> Track_08 0 0 0 0
#> Track_09 0 0 0 0
#> Track_13 NA 0 0 0
#> Track_15 0 NA 0 0
#> Track_16 0 0 NA 0
#> Track_18 0 0 0 NA
#>
#>
# Example 5: Customized origin permutation in MountTom subset.
sbMountTom <- subset_track(MountTom, tracks = c(1, 2, 3, 4, 7, 8, 9, 13, 15, 16, 18))
s5 <- simulate_track(sbMountTom, nsim = 5)
#> Warning: `model` is NULL. Defaulting to 'Unconstrained'.
area_origin <- matrix(c(50, 5, 10, 5, 10, 20, 50, 20), ncol = 2, byrow = TRUE)
int5 <- track_intersection(sbMountTom, test = TRUE, H1 = "Higher", sim = s5,
origin.permutation = "Custom", custom.coord = area_origin)
#> 2026-04-04 16:17:30.486337 Permutation 1
#>
#> Permutation of coordinates at origin using Custom
#> ------------------------------------
#> 2026-04-04 16:17:30.490172 Permutation 2
#>
#> Permutation of coordinates at origin using Custom
#> ------------------------------------
#> 2026-04-04 16:17:30.493625 Permutation 3
#>
#> Permutation of coordinates at origin using Custom
#> ------------------------------------
#> 2026-04-04 16:17:30.498714 Permutation 4
#>
#> Permutation of coordinates at origin using Custom
#> ------------------------------------
#> 2026-04-04 16:17:30.50375 Permutation 5
#>
#> Permutation of coordinates at origin using Custom
#> ------------------------------------
#> PERMUTATION COMPLETED
#> ------------------------------------
#>
#> 2026-04-04 16:17:30.543075 Iteration 1
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:30.575437 Iteration 2
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:30.617414 Iteration 3
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:30.655977 Iteration 4
#>
#> Intersect metric
#> ------------------------------------
#> 2026-04-04 16:17:30.697019 Iteration 5
#>
#> Intersect metric
#> ------------------------------------
#> ANALYSIS COMPLETED
#> ------------------------------------
#>
print(int5)
#> $Intersection_metric
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 0 0 0 0 0 0
#> Track_02 0 NA 0 0 0 0 0
#> Track_03 0 0 NA 0 0 0 0
#> Track_04 0 0 0 NA 0 0 0
#> Track_07 0 0 0 0 NA 0 1
#> Track_08 0 0 0 0 0 NA 0
#> Track_09 0 0 0 0 1 0 NA
#> Track_13 0 0 0 0 0 0 0
#> Track_15 0 0 0 0 0 0 0
#> Track_16 0 0 0 0 0 0 0
#> Track_18 0 0 0 0 0 0 0
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 0 0 0 0
#> Track_02 0 0 0 0
#> Track_03 0 0 0 0
#> Track_04 0 0 0 0
#> Track_07 0 0 0 0
#> Track_08 0 0 0 0
#> Track_09 0 0 0 0
#> Track_13 NA 0 0 0
#> Track_15 0 NA 0 0
#> Track_16 0 0 NA 0
#> Track_18 0 0 0 NA
#>
#> $Intersection_metric_p_values
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 1 1 1 1.0000000 1 1.0000000
#> Track_02 1 NA 1 1 1.0000000 1 1.0000000
#> Track_03 1 1 NA 1 1.0000000 1 1.0000000
#> Track_04 1 1 1 NA 1.0000000 1 1.0000000
#> Track_07 1 1 1 1 NA 1 0.1666667
#> Track_08 1 1 1 1 1.0000000 NA 1.0000000
#> Track_09 1 1 1 1 0.1666667 1 NA
#> Track_13 1 1 1 1 1.0000000 1 1.0000000
#> Track_15 1 1 1 1 1.0000000 1 1.0000000
#> Track_16 1 1 1 1 1.0000000 1 1.0000000
#> Track_18 1 1 1 1 1.0000000 1 1.0000000
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 1 1 1 1
#> Track_02 1 1 1 1
#> Track_03 1 1 1 1
#> Track_04 1 1 1 1
#> Track_07 1 1 1 1
#> Track_08 1 1 1 1
#> Track_09 1 1 1 1
#> Track_13 NA 1 1 1
#> Track_15 1 NA 1 1
#> Track_16 1 1 NA 1
#> Track_18 1 1 1 NA
#>
#> $Intersection_metric_p_values_BH
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 1 1 1 1 1 1
#> Track_02 1 NA 1 1 1 1 1
#> Track_03 1 1 NA 1 1 1 1
#> Track_04 1 1 1 NA 1 1 1
#> Track_07 1 1 1 1 NA 1 1
#> Track_08 1 1 1 1 1 NA 1
#> Track_09 1 1 1 1 1 1 NA
#> Track_13 1 1 1 1 1 1 1
#> Track_15 1 1 1 1 1 1 1
#> Track_16 1 1 1 1 1 1 1
#> Track_18 1 1 1 1 1 1 1
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 1 1 1 1
#> Track_02 1 1 1 1
#> Track_03 1 1 1 1
#> Track_04 1 1 1 1
#> Track_07 1 1 1 1
#> Track_08 1 1 1 1
#> Track_09 1 1 1 1
#> Track_13 NA 1 1 1
#> Track_15 1 NA 1 1
#> Track_16 1 1 NA 1
#> Track_18 1 1 1 NA
#>
#> $Intersection_metric_p_values_combined
#> [1] 0.5
#>
#> $Intersection_metric_simulations
#> $Intersection_metric_simulations[[1]]
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 0 0 0 0 0 0
#> Track_02 0 NA 0 0 0 0 0
#> Track_03 0 0 NA 0 0 0 0
#> Track_04 0 0 0 NA 0 0 0
#> Track_07 0 0 0 0 NA 0 0
#> Track_08 0 0 0 0 0 NA 0
#> Track_09 0 0 0 0 0 0 NA
#> Track_13 0 0 0 0 0 0 0
#> Track_15 0 0 0 0 0 0 0
#> Track_16 0 0 0 0 0 0 0
#> Track_18 0 0 0 0 0 0 0
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 0 0 0 0
#> Track_02 0 0 0 0
#> Track_03 0 0 0 0
#> Track_04 0 0 0 0
#> Track_07 0 0 0 0
#> Track_08 0 0 0 0
#> Track_09 0 0 0 0
#> Track_13 NA 0 0 0
#> Track_15 0 NA 0 0
#> Track_16 0 0 NA 0
#> Track_18 0 0 0 NA
#>
#> $Intersection_metric_simulations[[2]]
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 0 0 0 0 0 0
#> Track_02 0 NA 0 0 0 0 0
#> Track_03 0 0 NA 0 0 0 0
#> Track_04 0 0 0 NA 0 0 0
#> Track_07 0 0 0 0 NA 0 0
#> Track_08 0 0 0 0 0 NA 0
#> Track_09 0 0 0 0 0 0 NA
#> Track_13 0 0 0 0 0 0 0
#> Track_15 0 0 0 0 0 0 0
#> Track_16 0 0 0 0 0 0 0
#> Track_18 0 0 0 0 0 0 0
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 0 0 0 0
#> Track_02 0 0 0 0
#> Track_03 0 0 0 0
#> Track_04 0 0 0 0
#> Track_07 0 0 0 0
#> Track_08 0 0 0 0
#> Track_09 0 0 0 0
#> Track_13 NA 0 0 0
#> Track_15 0 NA 0 0
#> Track_16 0 0 NA 0
#> Track_18 0 0 0 NA
#>
#> $Intersection_metric_simulations[[3]]
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 0 0 0 0 0 0
#> Track_02 0 NA 0 0 0 0 0
#> Track_03 0 0 NA 0 0 0 0
#> Track_04 0 0 0 NA 0 0 0
#> Track_07 0 0 0 0 NA 0 0
#> Track_08 0 0 0 0 0 NA 0
#> Track_09 0 0 0 0 0 0 NA
#> Track_13 0 0 0 0 0 0 0
#> Track_15 0 0 0 0 0 0 0
#> Track_16 0 0 0 0 0 0 0
#> Track_18 0 0 0 0 0 0 0
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 0 0 0 0
#> Track_02 0 0 0 0
#> Track_03 0 0 0 0
#> Track_04 0 0 0 0
#> Track_07 0 0 0 0
#> Track_08 0 0 0 0
#> Track_09 0 0 0 0
#> Track_13 NA 0 0 0
#> Track_15 0 NA 0 0
#> Track_16 0 0 NA 0
#> Track_18 0 0 0 NA
#>
#> $Intersection_metric_simulations[[4]]
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 0 0 0 0 0 0
#> Track_02 0 NA 0 0 0 0 0
#> Track_03 0 0 NA 0 0 0 0
#> Track_04 0 0 0 NA 0 0 0
#> Track_07 0 0 0 0 NA 0 0
#> Track_08 0 0 0 0 0 NA 0
#> Track_09 0 0 0 0 0 0 NA
#> Track_13 0 0 0 0 0 0 0
#> Track_15 0 0 0 0 0 0 0
#> Track_16 0 1 0 0 0 0 0
#> Track_18 0 0 0 0 0 0 0
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 0 0 0 0
#> Track_02 0 0 1 0
#> Track_03 0 0 0 0
#> Track_04 0 0 0 0
#> Track_07 0 0 0 0
#> Track_08 0 0 0 0
#> Track_09 0 0 0 0
#> Track_13 NA 0 0 0
#> Track_15 0 NA 0 0
#> Track_16 0 0 NA 0
#> Track_18 0 0 0 NA
#>
#> $Intersection_metric_simulations[[5]]
#> Track_01 Track_02 Track_03 Track_04 Track_07 Track_08 Track_09
#> Track_01 NA 0 0 0 0 0 0
#> Track_02 0 NA 1 0 0 0 0
#> Track_03 0 1 NA 0 0 0 0
#> Track_04 0 0 0 NA 0 0 0
#> Track_07 0 0 0 0 NA 0 0
#> Track_08 0 0 0 0 0 NA 0
#> Track_09 0 0 0 0 0 0 NA
#> Track_13 0 0 0 0 0 0 0
#> Track_15 0 0 0 0 0 0 0
#> Track_16 0 0 0 0 0 0 0
#> Track_18 0 0 0 0 0 0 0
#> Track_13 Track_15 Track_16 Track_18
#> Track_01 0 0 0 0
#> Track_02 0 0 0 0
#> Track_03 0 0 0 0
#> Track_04 0 0 0 0
#> Track_07 0 0 0 0
#> Track_08 0 0 0 0
#> Track_09 0 0 0 0
#> Track_13 NA 0 0 0
#> Track_15 0 NA 0 0
#> Track_16 0 0 NA 0
#> Track_18 0 0 0 NA
#>
#>