**Question, dataset, and approach:**

This research investigated the hydraulic and behavioral impacts of a floating guidance structure in an experimental channel on juvenile Chinook salmon. Three exercises were conducted to determine if any relationships exist between channel hydraulics (which were stationary, measured at discrete locations and interpolated to become spatially-continuous) and the locations of behavior changes (as determined by a behavioral change point analysis tool, “smoove”). Exercise 1 examined differences in the spatial distribution of behavior changes at 20, 30, and 40 degree guide wall angles. Exercise 2 determined which hydraulic variables were most predictive of the location of behavior changes angles using multivariate methods. Exercise 3 used geographically weighted regression (GWR) to examine spatial variation in the relationship between each of the above variables and the location of behavior changes.

**Hypotheses:**

1) Because the hydraulics created by guide wall angles of 20, 30, and 40° differ from one another, we expect the location of behavior changes to vary in space with angle.

2) Because similar flume experiments have found hydraulic thresholds in velocity gradient for fish behavior, we hypothesize that velocity gradient (or another hydraulic variable) will predict the downstream location of behavior changes at all 3 guide wall angles.

**Results:**

Although the spatial distribution of the location of behavior changes appears to vary, no pattern of statistical significance can be concluded from these data (Figure 1). Because potential hydraulic thresholds are created at increasingly downstream positions along the guide wall with increasing angle, it was hypothesized that the average location of behavior changes similarly appear farther downstream with increasing angle. Although such a pattern appears to exist, limited observations withhold the ability to draw statistically significant conclusions from purely the spatial distribution of behavior changes (Figure 2).

##### Figure 1. Two displays of behavior changes and the 95% confidence intervals surrounding their spatial distributions. The data in the graphic on the left, presented in Exercise 2, was displayed backwards.

##### Figure 2. Although average distance downstream of behavior changes varies with guide wall angle, no statistical significance was found in this study.

A comprehensive analysis of channel hydraulics and the location of behavior changes found turbulent kinetic energy (TKE) gradient, water speed, and velocity gradient to be potential predictors of the spatial distribution of behavior changes. A multivariate regression analysis relating the X and Y coordinates of a behavior change with water speed, TKE, TKE gradient, velocity gradient, and acceleration found only TKE to not be significantly correlated with the location of a behavior change (p-value > 0.05). A Principal Component Analysis (PCA) further determined that water speed, as the largest component of the first principal component, may be an important predictor of behavior change (Figure 3). However, PCA’s ability to only model one dependent variable (distance downstream) warranted analysis using Partial Least Squares regression (PLS). PLS found that velocity gradient and TKE gradient best predict the spatial distribution of behavior changes, while water speed contributed the least to each component axis (Figure 4).

##### Figure 3. Principal Component Analysis (PCA) indicated that water speed is an important hydraulic variable in predicting the downstream location of behavior changes.

##### Figure 4. Partial Least Squares (PLS) regression indicated that velocity gradient and TKE gradient are perhaps good predictors of the spatial distribution of behavior changes in both the X and Y directions.

Water speed, TKE gradient, and velocity gradient were found to vary spatially in their relationship with the location of behavior changes in a geographically weighted regression (GWR). GWR differs from other regressions by estimating local relationship coefficients for every point in the dataset, rather than assigning a global coefficient across the entire dataset. In this way, local variation in the relationship between independent and dependent variables can be seen. The relationship of TKE gradient and water speed with the location of behavior changes was both strongly negative and strongly positive at fine local scales (Figures 5 and 6). However, velocity gradient demonstrated a consistent positive relationship with the downstream location of a behavior change (Figure 7). That is, if a behavior change occurred at high (low) velocity gradients, we can expect its location to be relatively far downstream (upstream). Although variability in these data are a result of a fish’s past experience, physiology, and perception of stimuli, velocity gradient may most consistently predict the location of behavior changes in this experiment.

##### Figure 5. Geographically weighted regression depicted local variation in coefficients between water speed and the portion of the boom passed that span positive and negative values.

##### Figure 6. Spatial variability exists in the relationship between TKE gradient and the downstream location of behavior changes.

##### Figure 7. Velocity gradient is the only hydraulic variable that showed a consistent relationship with the distance downstream of a behavior change. This implied that if a behavior change occurred at high velocity gradients, we could expect its location to be relatively far downstream, and visa versa.

**Significance:**

These results may verify previous experiments, which found velocity gradient to be an important predictor of the location of behavior changes in fish. If true, designs for improving fish passage at dams should aim to minimize velocity gradients created by floating guidance structures to promote safe bypass routes. However, substantial variation exists in these results (e.g. the spatial distribution of behavior changes does not vary significantly with guide wall angle, as hypothesized; no one hydraulic variable consistently predicted of the location of behavior changes across all 3 guide wall angles). Perhaps scientists should focus future studies on hydraulic stimuli as experiential (e.g. signal-to-background noise, cumulative to a threshold) rather than absolute (e.g. one magnitude of a hydraulic variable as a single threshold).

**My learning:**

For this course, I was forced to revisit R in order to run complicated statistical analyses. Although I was familiar with multiple linear regression analyses already, more sophisticated approaches (multivariate linear regressions, PCA, PLS, and GWR) were new to me. Furthermore, my ability to troubleshoot in Python in order to visualize the results of my analyses (creating multi-dimensional confidence intervals for Exercise 1, for example) was tested and grew.

jonesju — June 15, 2018 @ 12:00 pm

Excellent work. Points to consider as you write up for publication: This is a good use of GWR, but often GWR is used to reveal contrasting relationships in space, rather than uniform relationships in space, so it’s good for you to be aware of this.. How might the interpolation of the independent variables affect the relationships you tested? Are fish responding independently from one another? How did you control for time of day and lighting? Is lack of signif diff due to small sample size? Can you test the power of your statistical tests?

lundea — June 12, 2018 @ 3:34 pm

Hi Sam, Nice write-up. I wanted to post a question since I missed your presentation in-person. Did you find the GWR analysis easy to execute and interpret? I see that you posted a blog resource that gave good details on this, but it’s not something I’ve spent much time with, so I was curious about how you experienced that. I appreciate your explained example using water speed and location of behavior change. Do you have a sense of whether this relationship implies that the timing of behavior change is consistent, but the speed the fish has moved in the meantime is greater? Would it be interesting to examine “decision time” (time to behavior change) by controlling for speed? Anyway, great work.