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Appendix S1. Example of the impacts of variable detection on scientific inference.
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The following is a stylized example of how variable detection probability can lead to
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incorrect inference when using catch indices such as CPUE to track changes in abundance. We
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constructed this example from simulated data for illustrative purposes, but variation in detection
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probability due to environmental change, similar to what we present here, has been observed in
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the fish literature (e.g. Korman et al., 2009). We present a situation where the mean water depth
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of a study area has increased by about 60% at 5 years into the 10-year time series (Fig. S1, dashed
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line). Changes in depth through time such as this can be quite common in systems with variable
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flows such as the Murray-Darling River of Australia (Lyon et al., 2014) and would be expected
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under changes in environmental flow deliveries. Concurrent with the change in depth, is a decrease
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in detection probability of fish (Fig. S2, solid line). Again, this is a realistic change in detection
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that could be an expected when sampling fish with boat electrofishing or beach seines as many
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sampling gears become less effective in deeper water (e.g. Lyon et al., 2014; Bayley & Austin,
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2002). Furthermore, this variation in detection probability is well within the range observed in the
16
literature, which can exceed an order of magnitude (Hangsleben et al., 2013; Lyon et al., 2014;
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Lauretta et al., 2013). Fig. S2 represents the analysis of 5 samples per year of a fish population
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that experienced small random annual variation in abundance (open circles). The open circles are
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the true abundance of fish in the study area; the dotted line is the mean catch-per-sample estimate
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(CPUE), and the solid line is an estimate of abundance using a multiple-event closed population
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mark-recapture model (model Mt; Otis et al., 1978). Notice how the CPUE in Fig. S2 tracks the
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detection probability in Fig. S1 more closely than it tracks the true abundance. A typical conclusion
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based on these CPUE estimates would be that there was a systematic decrease in abundance
1
24
starting around 2010, when, in fact abundance did not systematically change throughout the 10-
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year time series. Alternatively, the abundance estimates that account for variable detection
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probability (solid line of Fig. S2) continue to track abundance well even when detection probability
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decreases (although there is greater uncertainty in the abundance estimates when detection
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probability is lower). This example illustrates how CPUE indices of abundance can be misleading
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for tracking changes in abundance when detection probability varies during the study period
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31
References
32
Bayley, P.B. & Austen, D.J. (2002) Capture efficiency of a boat electrofisher. Transactions of
33
the American Fisheries Society, 131, 435-451.
34
Hangsleben, M.A., Allen, M.S. & Gwinn, D.C. (2013) Evaluation of electrofishing catch per unit
35
effort for indexing fish abundance in Florida Lakes. Transactions of the American
36
Fisheries Society, 142, 247-256.
37
Korman, J., Yard, M., Walters, C. & Coggins, L.G. (2009) Effects of fish size, habitat, flow, and
38
density on capture probabilities of age-0 rainbow trout estimated from electrofishing at
39
discrete sites in a large river. Transactions of the American Fisheries Society, 138, 58-75.
40
Lauretta, M.V., Camp, E.V., Pine, W.E. & Frazer, T.K. (2013) Catchability model selection for
41
estimating the composition of fishes and invertebrates within dynamic aquatic
42
ecosystems. Canadian Journal of Fisheries and Aquatic Sciences, 70, 381-392.
43
Lyon, J.P., Bird, T., Nicol, S., Kearns, J., O’mahony, J., Todd, C.R., Cowx, I.G. & Bradshaw,
44
C.J.A. (2014) Efficiency of electrofishing in turbid lowland rivers: implications for
45
measuring temporal change in fish populations. Canadian Journal of Fisheries and
46
Aquatic Sciences, 71, 878-886.
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47
48
Otis, D.L., Burnham, K.P., White, G.C. & Anderson, D.R. (1978) Statistical inference from
capture data on closed animal populations. Wildlife Monographs, 3-135.
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Figures
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Fig. S1. Simulated mean depth of study area (dashed line) and resultant detection probability (p)
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of fish (solid line).
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Fig. S2. Simulated true abundance (open circles), abundance estimates (solid line), and CPUE
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estimates (dotted line). Shading represents 95% confidence region of estimates.
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3