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. 2020 Sep 28;9:e56619. doi: 10.7554/eLife.56619

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© 2020, Oldfield et al

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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Figure 4. — (A) Granger-causality equations (right) to model fluorescence time-series 2 (TS2) using information from TS1 (left). TS1 and TS2: fluorescence from region 4 and 3 respectively for one representative fish. F(t) is fluorescence for time point t; w₁ and w₂ are the weights calculated for each time point; e denotes prediction error. Figure 4 - equation 1 $F_{2} (t) = \sum_{k} w_{2} (k) F_{2} (t - k) + e_{1} (t)$ and Figure 4 - equation 2 $F_{2} (t) = \sum_{k} w_{2} (k) F_{2} (t - k) + \sum_{k} w_{1} (k) F_{1} (t - k) + e_{2} (t)$ are the autoregressive models for univariate and bivariate signals, respectively. Figure 4 - equation 3 is estimation of Granger-causality level. (B) Average causality level within visual areas in spontaneous (no prey, top row) and evoked (prey present, bottom row) conditions, in prey-experienced (left column) and prey-naïve (right column) fish. Each box represents the F-statistic which quantifies the statistical significance of the directed interaction from the region identified by the row to the region identified by the column. F-statistic values ranged from 0 to 23.7. Fstat values above 15 are yellow. Brain areas shown are: 1, left pretectum; 2, right pretectum; 3, left tectal neuropil; 4, right tectal neuropil; 5, left tectal PVN; 6, right tectal PVN. Significant causal interaction causality link for Fstat > 3.88. No significant difference between prey-experienced and prey-naïve fish in either spontaneous or evoked Granger-causality matrices (pairwise ts, corrected using the Benjamini-Hochberg False Discovery Rate (FDR), see Materials and methods, Behavioral data analysis and statistics; see Supplementary file 2 for p-values). (C) Schematics of functional links in visual areas in spontaneous (left) and evoked (right) conditions. Line width proportional to Granger-causality level (evoked and spontaneous maps indicate links with Fstat > 3.88). (D) Anatomy and known connections of the optic tectum. Dark green: input from pretectum to OT. Bright green: PVNs with dendritic arborization in tectal neuropil. Yellow: axonal projections from PVNs to different layers of OT. SO, stratum opticum; SFGS, stratum fibrosum et griseum superficiale; SGC, stratum griseum centrale; SAC, stratum album centrale. See also Figure 4—figure supplement 1. Data table for panel B in Figure 4—source data 1.

Figure 4—source data 1.

elife-56619-fig4-data1.csv^{(68.1KB, csv)}

Figure 4—figure supplement 1. — (A) Granger-causality equations (right) to model fluorescence time-series 2 (TS2) using information from TS1 (left). TS1 and TS2: fluorescence from region 4 and 3 respectively for one representative fish. F(t) is fluorescence for time point t; w₁ and w₂ are the weights calculated for each time point; e denotes prediction error. Figure 4 - equation 1 $F_{2} (t) = \sum_{k} w_{2} (k) F_{2} (t - k) + e_{1} (t)$ and Figure 4 - equation 2 $F_{2} (t) = \sum_{k} w_{2} (k) F_{2} (t - k) + \sum_{k} w_{1} (k) F_{1} (t - k) + e_{2} (t)$ are the autoregressive models for univariate and bivariate signals, respectively. Figure 4 - equation 3 is estimation of Granger-causality level. (B) Average causality level within visual areas in spontaneous (no prey, top row) and evoked (prey present, bottom row) conditions, in prey-experienced (left column) and prey-naïve (right column) fish. Each box represents the F-statistic which quantifies the statistical significance of the directed interaction from the region identified by the row to the region identified by the column. F-statistic values ranged from 0 to 23.7. Fstat values above 15 are yellow. Brain areas shown are: 1, left pretectum; 2, right pretectum; 3, left tectal neuropil; 4, right tectal neuropil; 5, left tectal PVN; 6, right tectal PVN. Significant causal interaction causality link for Fstat > 3.88. No significant difference between prey-experienced and prey-naïve fish in either spontaneous or evoked Granger-causality matrices (pairwise ts, corrected using the Benjamini-Hochberg False Discovery Rate (FDR), see Materials and methods, Behavioral data analysis and statistics; see Supplementary file 2 for p-values). (C) Schematics of functional links in visual areas in spontaneous (left) and evoked (right) conditions. Line width proportional to Granger-causality level (evoked and spontaneous maps indicate links with Fstat > 3.88). (D) Anatomy and known connections of the optic tectum. Dark green: input from pretectum to OT. Bright green: PVNs with dendritic arborization in tectal neuropil. Yellow: axonal projections from PVNs to different layers of OT. SO, stratum opticum; SFGS, stratum fibrosum et griseum superficiale; SGC, stratum griseum centrale; SAC, stratum album centrale. See also Figure 4—figure supplement 1. Data table for panel B in Figure 4—source data 1.

Figure 4—source data 1.

elife-56619-fig4-data1.csv^{(68.1KB, csv)}