A 137

Estimation of LAIS was performed using the open source Java information dynamics toolkit (JIDT) (Lizier, 2012 ), with a history parameter k_max of ten time points, spaced 2 samples, or (2/150 Hz)= 13.3 ms, apart. The total history length thus covered 133 ms, or roughly one cycle of a neural theta oscillation, which seems to be a reasonable time horizon for a downstream neural population that ultimately must assess these states. To enable LAIS estimation from a sufficient amount of samples, we considered the data pixels as homogeneous variables executing comparable state transitions, such that the pixels form a physical ensemble in terms of information storage dynamics. Pooling data over pixels thus enables an ensemble estimate of the PDFs in question. This approach seems justified as all pixels reported activity from a single brain area (area 18 of cat visual cortex, see below). Mutual information was estimated using a box kernel-estimator (Kantz and Schreiber, 2003 (link)) with a kernel width of 0.5 standard deviations of the data.
Here we assume that the neural system is at least capable of exploiting the statistics arising from the stimulation given throughout the experiment and thus construct PDFs from all data (time points and pixels) for a given condition. Therefore, we pool data over the full time course from −1 to 1 s of the experiment. Thus, each image of the VSD data had a spatial configuration of 67 × 137 spatial data pixels after removal of the two rows/columns on each side of an image because of the median filter that was applied. Each trial (of a total of eight trials per condition) resulted in 288 LAIS values, based on an original data length of 298 samples and a history length (state dimension) of 10 pixels. The product of final image size and LAIS samples resulted in 2.64 · 10⁶ data points per trial for the estimation of the PDF for each of the eight motion direction conditions. Due to computational limitations, LAIS estimates were performed on two blocks of four trials separately, resulting in 1.06 · 10⁷ data points entering the estimation in JIDT.

A field survey to assess whether patterns of bleaching of Pocillopora differed between colonies within a farmerfish garden (territory) and those on adjacent, unprotected substrate was conducted during June and July 2019 before bleached tissues of coral died or recovered. Divers assessed all Pocillopora colonies found on 178 haphazardly encountered bommies that were scattered throughout the 2 x 0.5 km study polygon. The bommies varied in the amount of their surface covered by Stegastes gardens, from lacking gardens altogether to those that were partially to completely covered. Gardens were readily identified by their lush growth of turf red algae (commonly Polysiphonia spp.) and the presence of Stegastes; the substrate surface not defended by farmerfish typically had closely cropped turf and/or crustose coralline algae. All surveyed bommies were measured (L x W x H) and the location of Pocillopora colonies noted (outside or inside of a garden if present). Colonies were then placed into 1 of 5 diameter categories (< 3 cm, 3–10 cm, 11–20 cm, 21–30 cm, > 30 cm dia; see [11 (link)]). Each Pocillopora was photographed, and the proportion of the colony that was (1) alive and unbleached, (2) alive but bleached (i.e., tissues transparent and underlying skeleton visibly white), and (3) dead (no tissue and skeleton overgrown with algae from previous partial mortality) was estimated visually in the field (the 3 categories sum to 1). The live but bleached category was defined as tissue that had substantially lower or no pigmentation (due to lower levels of Symbiodiniaceae) relative to the rest of the colony and followed the Australian Coral Watch Coral Health Chart for scoring coral bleaching (https://coralwatch.org). Quantification of bleaching was made by the same individual (RNH). If present on a bommie, Stegastes garden sizes were measured, and the number of adult farmerfish enumerated. A total of 1,137 Pocillopora colonies was assessed on the 178 bommies surveyed.
Due to the need for a rapid assessment of bleached corals, the total amount of the two ‘substrate types’ (inside vs outside farmerfish territories) in the study area was not estimated during the June to July 2019 survey. Not all the non-garden area of a bommie was suitable for occupancy by Pocillopora since varying portions of the Porites coral bommies were still alive and/or occupied by other benthic space holders such as macroalgae. We used a recent survey of benthic habitats of the study site to estimate the relative areas of garden vs non-garden habitats that were suitable for occupation by Pocillopora as an approximation of the relative sampling effort for the two habitat types. The 2016 benthic survey consisted of 24 band transects each 20 x 5 m where the substrate / space holder was identified at every 0.5 m point on the grid (i.e., 492 point samples per band transect). The benthic categories quantified included, among others, Stegastes gardens, other turf algae, crustose coralline algae (CCA), live coral (by genus or species), live portions of Porites bommies, and macroalgae (by genus or species). The 24 transects were distributed more or less evenly from the mid-lagoon to fringing reef along the 2 km span of the study site. These data were used to estimate the mean proportion of hard substrate at the study site that was covered by farmerfish gardens, and the mean proportion of non-garden hard substrate that was or could have been occupied by branching corals (i.e., cover of branching coral + cover of cropped turf algae / CCA on bommies).
In addition to exploring how Pocillopora responded to the bleaching event as a function of position within or outside a farmerfish territory, responses as a function of colony size also were explored as other studies in Moorea have shown that for a variety of reasons, larger and smaller colonies of Pocillopora can have different susceptibilities to bleaching [4 (link), 30 (link)]. Accordingly, the 1,137 surveyed corals were divided into two size classes, small (≤ 10 cm dia) and large (> 10 cm dia). Several statistical tests were conducted to explore relationships between Pocillopora colony size and location (inside or outside of a garden) with two metrics of bleaching (prevalence and severity, see below). All analyses were performed using the R language for statistical computing version 4.1.1 [38 ].

The sample size was calculated using the statistical program G. Power version 3.1.9.4 (Franz Faul, Universitat Kiel, Germany) with a power of 90% and a significance level of 5%. The study required a sample size of 137 subjects to detect significant interactions with the RRT modality. The effect size was calculated using Cohen’s d-value according to RRT modality (in-center or home-based) and the mean age of each group. Cohen’s d-value was 0.723, and the calculated effect size was 0.345. Data are expressed as mean ± standard deviation and as frequencies or percentages according to the nature of the variable analyzed. To compare the frequency and mean differences, p-values were calculated using Chi-square and Fisher’s exact test for categorical variables and Student’s t-test or the non-parametric Mann–Whitney U-test for continuous variables. Pearson’s Chi-square parametric correlations were examined to assess the strength of the association between the variables. Univariate and multivariate logistic regression analyses were used, and the corresponding odds ratio (OR) and 95% confidence interval (95%CI) were calculated. In-center and home-based dialysis modalities were used as the dependent and dichotomized variables in the univariate and multivariate regression analyses. Only data from the univariate analysis that had a value of p of 0.10 or less were tested a priori to explore possible changes in the response variable during multiple logistic regression analysis. A binary logistic regression model using the forward stepwise conditional method was used. The Statistical Package for Social Science (SPPS for Windows) version 23.0 was used in all statistical analyses. A value of p of <0.05 was considered statistically significant.