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Internal state effects on behavioral shifts in freely behaving praying mantises (Tenodera sinensis)

['Shanel C. Pickard', 'Department Of Mechanical', 'Aerospace Engineering', 'Case Western Reserve University', 'Cleveland', 'Ohio', 'United States Of America', 'David J. Bertsch', 'Department Of Biology', 'Zoe Le Garrec']

Date: 2022-01 

Sequential data is a class of data in which the order of the outputs becomes a very relevant aspect in modeling the given system [57–59]. For example, language relies on the ordering of symbols in specific sequence structures such that embedded meaning can be conveyed [60]. When comparing entire sequences for similarity, specialized approaches are needed such that the sequential ordering of data is not obscured. This section of the analysis approaches the behavior sequences of the praying mantis from the assumption that patterns may in fact exist, not only in the time spent in each behavior as discussed above, but also in the order in which these behaviors present. The following subsections explore different aspects of sequential behavior analysis to draw insight into whether exhibited behavior of the praying mantis takes on different characteristics as the feeding state changes.

3.3.1 Transition probabilities.

By assembling the behavior in each time step, a transition probability matrix can be assembled for each subsequence (i.e. sequence A will produce a 12 x 12 transition matrix, T A while sequence B will produce its own corresponding 12 x 12 transition matrix, T B ). This is a square matrix that holds the observed probabilities of each behavior transitioning into every other behavior during a subsequence (Fig 4A). To provide a qualitative assessment of all the transition matrices as a correlate of satiety, the square matrix shown in Fig 4A is strung out vertically into a “feature vector,” where each row is reorganized and stacked vertically into a single column vector in accordance to Fig 4B). With the probability matrix for each subsequence reconfigured to a column vector, the vectors were grouped in order of increasing satiety (e.g. all 0-fed column vectors grouped side-by-side; Fig 4C).

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TIFF original image Download: Fig 4. Transition Probability Matrix. (A) Example organization of the square transition probability matrix. The probability, P, of transitioning out of behavior i to behavior j is held in the matrix element, i,j. For example, P 3,1 represents the observed probability of the animal transitioning from behavior 3 (specific translation, ST) to behavior 1 (successful strike, SS). The color coding seen in (A) denotes the regime in which each behavior belongs (red = hunting regime behaviors; blue = nonhunting behaviors). The red shaded region of the square matrix corresponds to the probabilities of hunting behaviors further transitioning into hunting behavior. The purple regions show the transition probabilities corresponding to a regime change; this either occurs when there is a transition from a hunting behavior to a nonhunting behavior, or conversely, when transitioning from a nonhunting behavior to a hunting behavior. The blue shaded region signifies transitions that remain in the nonhunting regime. To best show many transition matrices across all feed states in a single figure, the 12 x 12 matrix for each subsequence was reorganized as a column vector. (B) The column vector holds all the probabilities from the square matrix, and is structured according the color coding seen in the figure. (C) After each transition matrix corresponding to each subsequence is converted to a column vector, all the column vectors can be concatenated into a single, 2D matrix, with the maintained shaded regions. SS = successful strike; MS = missed strike; ST = specific transition; SR = specific rotation; SM = specific monitoring; GM = general monitoring; GR = general rotation; GT = general translation; Groom = grooming; Deim = deimatic; Esc = escape. https://doi.org/10.1371/journal.pcbi.1009618.g004

The processing steps of Fig 4 allow the transition matrices to be quickly compared across all feeding states. Applying color-coding to the values found in the probability vertical matrices from Fig 4C generates the heat map in Fig 5A. Looking at the hunting → hunting region (Fig 5Ai), 0-fed and 1-fed states show a dense scattering of colored cells of non-zero transition probabilities, indicating that for low feeding states, hunting behavior tended to lead into further hunting behaviors and that starved animals will predominately remain in the hunting regime. Conversely, as satiety increases across Fig 5Ai, 2-, 3-, and 4-fed animals show progressively sparser scatterings of colored cells, meaning these feeding states did not promote consecutive hunting behaviors as often. This is further supported by the density plot of hunting → hunting transition probabilities in Fig 5Bi. In this density plot, the lower feed states show a low density of smaller probabilities and a higher density of large probabilities, meaning that starved mantises are more likely repeatedly transition within the hunting regime, and by extension, not exit hunting behavior. Fig 5Bi also shows the reverse is true for sated states, where the larger densities of small probabilities means the sated animal is less likely to remain in hunting.

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TIFF original image Download: Fig 5. Transition probability trends across feed states. (A) Probability heat map of transition probabilities across all feed states and organized to show trends among the different transition types: Hunting→ Hunting (i), Hunting→ Nonhunting (ii), Nonhunting→ Hunting (iii), and Nonhunting→ Nonhunting (iv). Dark blue areas correspond to very low probabilities of seeing the transition, while non-blue colors correspond to higher probabilities of state transitions occurring. (B) Quantifies the trends seen in the heat map of part (A). The probability density plots show distribution of transition probabilities that were exhibited across all feed states for each transition type: Hunting→ Hunting transition (i), Hunting→ Nonhunting transition (ii), Nonhunting→ Hunting transition (iii), and Nonhunting→ Nonhunting transition (iv). The area under each curve in the density plots is equal to one, however, how the area is distributed across the probabilities signifies the density. Probability values with higher density means higher frequency of those values in the transition probability matrices. https://doi.org/10.1371/journal.pcbi.1009618.g005

Similar correlations to feed state appear across both hunting → nonhunting (Fig 5Aii) and nonhunting → nonhunting transitions (Fig 5Aiv), where both show increasing colored cells as satiety increases. Progressively wider density distribution are seen on the density plot for hunting → nonhunting transitions (Fig 5Bii), suggesting an increasing tendency of sated animals to transition out of hunting and into nonhunting behaviors. Fig 5Biv shows the same trend in density distribution, indicating that sated animals currently in nonhunting behavior remained in nonhunting behavior more often.

Fig 5Aiii and 5Biii show the transition probabilities for nonhunting → hunting, which do not show a clear trend. The density plot of Fig 5Biii shows an overwhelming density concentration around zero for all feed states; zooming in on this region, all feed states had below a 1% chance of exhibiting nonhunting → hunting transitions, except the 2-fed state for which this transition type slightly more likely.

To further quantify these apparent differences in transition probability matrices, the Euclidean distance [61] was calculated between each probability matrix from every feed state and the resulting distance distributions plotted in Fig 6A. With this approach, the probability vectors occupy a data space, where the vectors belonging to a single feeding state would constitute a cluster of high dimensional “points.” The distances measured within this cluster would represent the spread of these points belonging to the particular feeding state. When the vectors from remaining feeding states are projected into the same data space, distance distributions can also be generated between projections and give a relative metric of probability matrix similarity—with greater similarity indicated by smaller distances. Comparing across all feeding states, the distance means between transition probability vectors consistently show statically significant increases (i.e. progressively greater dissimilarity) as satiety increases.

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TIFF original image Download: Fig 6. (A) Euclidean distances between transition probability matrices for each feed state. Box plot colors (black, red, blue, orange, grey) are used to help focus trends in specific comparisons groupings, while the line is connecting each box plot mean. For example, the black boxes are showing that each feed state exhibits an increasing Euclidean distance away from 0-fed, indicating a greater difference in transition probability profiles. The upward trend seen for the black grouping means that as satiety increases, behavior transitions progressively increased in dissimilarity when compared to the 0-fed state. All the colored groupings show similar trends, with ANOVA analysis showing a pValue < 0.05 for all groups. Tukey pairwise comparisons are shown: *p<0.05 and **p<0.01. (B) Penalty cost as a metric of sequence structure similarity. (Bi) Demonstration of PC calculation showing the cost incurred to edit a mismatch and insert/deletion. (Bii) Penalty cost from each feed state was compared to all other feed states. As was the case with (B), the connecting line in (Bii) is connecting each box plot mean. Black, red, and blue groupings show upward trends in the PC, indicating that sequence structure progressively changes as satiety increases (ANOVA analysis showing a pValue < 0.05 for these groups). Tukey pairwise comparisons are shown: *p<0.05 and **p<0.01. No statistical difference was seen in structure when comparing the 0- to 1-fed sequences, nor when comparing the 3- to 4-fed sequences. https://doi.org/10.1371/journal.pcbi.1009618.g006

When making comparisons across feed states in Fig 6A, colored box plot groups were used to help focus key trends. For the black box grouping, the 0-fed state serves as a reference to be compared to all other feed states. The x-axis shows what feed states are being compared, with the notation 0:0 meaning the distance was calculated between all 0-fed transition probability vectors to every other 0-fed vector. Likewise, 0:4 corresponds to the distances calculated between all 0-fed vectors and 4-fed vectors, and so on. The line connecting the black boxes goes through each box mean, and exhibits an upward trend. This positive slope indicates that higher feed states produce probability vectors that are are increasingly different from the 0-fed transition probability vectors. For the two low feed state comparisons (0:0 and 0:1), however, transition profiles did not statistically differ (Tukey pairwise mean comparison: p > 0.05). In other words, the intrastate distance distribution (mean and standard deviation) seen when 0-fed vectors are compared to all other 0-fed vectors (0:0) was comparable to the distance distribution calculated between 0-fed and 1-fed vectors (0:1). This indicates that both of these nutritional states produced similar behavioral transitions, while increasing satiety (2-, 3-, and 4-fed) correlates with progressively differing transition probability profiles from the food deprived states (0- and 1-fed).

The subsequent color groupings continue this trend, with the red grouping showing higher feed states against 1-fed as the reference, the blue grouping against 2-fed as the reference, and the orange grouping with 3-fed as a reference. These three groupings, red, blue, and orange all show increasingly different transition profiles of higher feed states when compared to the group reference.

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