library(tidyverse)
library(kableExtra)
library(reshape)
n = 1
# paste('Fig.',(n = n+1))
1 Background
The power of a study is defined as the ability to correctly detect a true effect present in a system (i.e. reject a false null hypothesis). Typically defined as 1-B where ‘B’ is the type II error rate of missing a true effect. Power of a study is often declared sufficient at levels >= 80% - though this limit is somewhat arbitrary. A challenge for ecological studies is the lack of readily available approaches to estimate power within the constraints of realistic, messy ecological data (i.e., integer counts, zero inflation, or overdispersed). Free software like Gpower or built-in power analysis functions in R rely on simple data structures and assumptions of normality (eg those associated with t-tests or ANOVA). This mismatch in assumptions can result in overestimating the true power of a study design. Previous efforts to characterize power of ODFW survey tools used these simplistic approaches( (Watson and Huntington 2021).
Johnson et al 2015 suggest the use of Monte Carlo simulations as an alternative to overcome the limitations of messy ecological data. A Monte Carlo approach generally consists of:
- Simulate data many times with a known set of conditions (~1000)
- Run a statistical test of interest to determine if known effect was detected
- Calculate the percent of tests where the effect was detected - this the power of the test
We performed such a Monte Carlo style ‘power analysis’ to help elucidate the level of sampling needed with multiple ODFW survey tools to achieve reasonable power to detect changes in fish or invertebrate population size. The approach will be similar across survey tools, to allow some relative comparison. The main difference among tools is the nature of the data collected. Across tools, abundance data is collected as count data that is often zero-inflated and overdispersed, but can generally be described by a negative-binomial distribution (Zuur 2009, 2011). For some tools such as video lander and SCUBA fish and invertebrate surveys, effort is standardized and count data can be used directly in analysis. For other tools such as Hook-and-Line, Longline, or ROV surveys, counts are dependent on variable effort, and this effort must be included as an offset in the final model (e.g. Density = individuals/survey-area).
The statistical test used was a negative-binomial GLM model to test the pairwise difference in means between two simulated groups of data. The model was formulated:
MASS::glm.nb(response ~ group, data = simulated_dataset)
Where Y was a simulated response variable taking a defined negative-binomial distribution, and group was a grouping variable (coded as ‘A’ and ‘B’) to represent two populations, different in mean value ‘mu’ by a known amount. Power analysis for size data was conducted using the simple model:
glm(length ~ group, data = simulated_dataset, family = ‘gaussian’)
Two approaches were developed in R to account for either count data (i.e. video lander, SCUBA fish and invertebrate), or density data (i.e. including an ‘offset’ term in the GLM for hook-and-line, longline, and ROV data). Survey data was first subset to Redfish Rocks since the longest time series across tools existed at this Site. For count data, we calculated species-specific values of mean abundance (and relative abundance) as well as an estimate for the negative binomial dispersion parameter “theta”. These values were used to simulate new datasets using a negative binomial distribution. In order to try and generalize disparate results, we lumped some species into ‘groups’ that were quasisimilar across tools. For example, ‘Schooling Rockfish’ often was comprised of Blue/Deacon Rockfish, Canary Rockfish, and Yellowtail Rockfish, but not every tool observed these species and therefore ‘Schooling Rockfish’ was sometimes a subset of the full list. Black Rockfish, while technically a schooling species, were observed across all tools and kept separate as one of the most abundant fish species.This allowed a better 1:1 comparison for this single abundant species across tools. For ROV invertebrates, the list of species was unique, and an attempt was made to choose a range of species groups that represented the spread of densities and theta values observed in the data. See each tool’s results section for greater detail on the species contained in the simplified groups.
The density-based approach used a function that could not average across multiple species, and so representative species were pulled out for analysis. For example, Canary Rockfish were used as a ‘schooling rockfish’ to compare among other tools.
Note that the resulting sample size estimated will the samples needed per comparison group. That is, if we estimate 50 surveys are needed to achieve 80% power, this implies 50 surveys in group ‘A’, 50 surveys in group ‘B’ for a total of 100 surveys collected overall in order to run a pairwise GLM analysis.
There are several caveats with this simulation approach. Zero-inflated data may be influenced in several different ways by temporal shifts in population size.
- The proportion of zeros may decrease through time (e.g. as a species spreads out across previously unoccupied habitat and is more readily encountered)
- The mean value (“mu” in a poisson/negative binomial world) can increase as more extreme count values are observed (e.g. larger clusters/schools of individuals from a species)
- Or some combination of the two
Additionally, there are other ecological constraints (e.g. the upper limit for reasonable population sizes) which we have not accounted for. Below, we’ve assumed that the rate of zeros and overdispersion is constant, and that the only change between the simulated populations is an increase in the mean abundance value (‘mu’). This implies that a negative binomial distribution does not fully describe the empirical data nor the nuances of a true shift in population size in situ. It’s an approximate approach until better methods exist to simulate and sample population growth through time.
This analysis also simulates data on the same scale and sample unit that we used for analysis in the synthesis report. For example for hook-and-line surveys, CPUE is calculated as Counts/Time and reported as fish/angler-hour and the sample unit is the cell-day(a single cell sampled one day). The presented figures for hook-and-line surveys below will therefore show simulations based on the mean CPUE value and the estimated number of Cell-per-day sample units in order to achieve power. SCUBA sample units will be at the level of individual 60m^2 transects. It is unclear what effect (if any) this may have on our ability to appropriately compare power results across tools. However, interpreting sample size for all tools involves a combination of staff capacity, budget, and available weather windows, and previously attained sample sizes provide a starting point to interpret power analysis results.
2 Takeaways
The greater the dispersion of data, the lower the power.
The greater the starting mean value, the greater the power to detect change (as a proportion increase).
Across tools and species, there was greater power to detect change when the data was less dispersed or had a greater starting mean abundance. This suggests (intuitively) that we have a better ability to detect change with our abundant species (i.e. Black Rockfish) or aggregate metrics (e.g. Total Density or CPUE) than we do our rare species (e.g. Yelloweye or China Rockfish). When relative abundance was moderately similar, it was dispersion of the data that had the greatest influence on power. That is, consistently observed species have greater power than those that have patchy distributions.
Some rare species will likely always have low statistical power given the low counts we observe. For example, hook-and-line data for many benthic species like China and Yelloweye Rockfish were estimated to have small values of theta (evidence of overdispersion). As such, it may take a minimum of doubling the observed CPUE to detect change with hook-and-line survey.
We have strong statistical power for aggregate and abundant species.
Black Rockfish, Kelp Greenling, and Lingcod are fish species most consistently observed by ODFW survey tools. As a result, the statistical power to detect change will be greatest for these species. Similarly, Purple Sea Urchin, Burrowing Cucumber, Red Sea Urchin, and Plumose Anemone were the most abundant SCUBA invertebrate species and had the greatest power to detect change for this tool. ROV surveys had high power for abundant sessile invertebrate species including Burrowing Sea Cucumber, and Giant Plumose Anemone as well as mobile invertebrates such as Red Urchin. For many species, a change of 3-fold or greater in abundance would be needed to reasonably detect differences. By using aggregate statistics such as ‘Total Density’ we may be able to increase our power to detect early signs of reserve effects inside and out of the marine reserves, or better describe interannual variability. Simulation with aggregate fish data confirmed that there is greater power with this aggregated metric.
Trends in other species may be missed.
Formal analysis of trends by species (i.e. 2022 Synthesis Report) indicate that we did in fact detect site-specific and temporal trends for other species than Black Rockfish. This highlights that a power analysis indicates how likely you are on average to detect a trend, but that it is possible to detect ecological trends with small sample sizes. However, across tools, the magnitude of change detected was often greater than a 3-fold difference between the less abundant and more abundant comparison group. Future discussions should try to establish what differences in abundance are meaningful biologically or for fisheries management. Because power is relatively low for benthic and schooling rockfish species, our inability to detect change may be a function of low sample size that current staff and budget capacity cannot overcome. Alternatively, abundance may be so low for some species that meaningful results are not possible with any amount of sampling.
ROV has greater power to detect changes in invertebrate densities, but surveys deeper habitat.
Invertebrate surveys appear more powerful using the ROV compared with SCUBA as measured by raw number of surveys needed. The ROV surveys are also the most expensive tool operated by ODFW marine reserves and has limited weather windows for operation. The ROV collects data on a much wider breadth of species than SCUBA; however, ODFW SCUBA surveys are limited to shallower water than ROV and therefore still provide unique and valuable invertebrate data from subtidal areas sampled. Some species including Purple Sea Urchin and Ochre Sea Star are primarily found in shallow waters inaccessible by ROV.
Hook-and-Line and ROV appear to be the most powerful survey tools.
Direct 1:1 comparisons across the tools are not possible due to unique combinations of species observed by each survey method; however, approximate comparisons may still be useful. Across tools, ROV fish surveys were consistently estimated to need the fewest sampling effort for a desired level of statistical power - estimated as individual transects needed. For example, Black Rockfish were consistently the most abundant species observed across survey methods and an estimated 60 ROV transects would be needed in each group to detect a doubling in mean abundance for this species. This compares to an estimated 40 hook-and-line sample units, 70 longline sets, 70 Lander drops, and 60 SCUBA transects to detect this difference.
Hook-and-line is one of the best tools for Black Rockfish, schooling rockfish and Greenling species whereas longline surveys had better power for several benthic rockfish species including Copper and Quillback Rockfish. The longline survey was specifically designed to target commercially important benthic species, and this simulation further provides evidence that longline gear most appropriately targeted these species. Across four fish categories simulated for ROV surveys, power to detect change was lowest for benthic rockfish, yet the estimated 110 ROV transects to detect a doubling of mean abundance is still numerically less than the 130 hook and line surveys, the 80 longline sets, or 250 SCUBA transects needed in each group to detect a similar difference in relative abundance of benthic rockfish species.
For abundant species like Black Rockfish and Greenling, lander and SCUBA appeared to perform similarly. SCUBA fish surveys appeared to be one of the least powerful when compared across survey methods; however, the video lander observed almost no benthic rockfish species, and an estimate of power was not possible. Approximately 45% of lander drops are also excluded immediately due to view, water clarity or other QAQC issues, and this nearly 50% data loss means that the lander survey is actually much less efficient than this power analysis alone might suggest. Together, lander and SCUBA were the least powerful methods for assessing fish relative abundance.
Missing from this analysis is any true-cost analysis that considers the monetary budget and time needed to successfully complete each of these target sample sizes by tool. ROV may need less transects to achieve a set level of power, but the ROV is an expensive tool to maintain and operate compared to other survey techniques. ROV is also more limited by weather windows compared with hook-and-line surveys.
Multiple years of data need to be combined to achieve power.
Evident from these results is the need to pool multiple years worth of data for analysis. Any given year of surveys is unlikely to generate sufficient sample sizes for a powerful analysis. This is especially true across all tools collecting abundance metrics- which are inherently highly variable. An exception may be size analysis for abundant species - such as Black Rockfish or Lingcod where samples generated by hook-and-line surveys at a site-year level may be great enough to detect significant changes.
The use of a negative-binomial simulation power analysis indicates that we have lower power than previously described.
As described above, previous power analysis attempts used simplifying assumptions and may have overestimated the power of our surveys to detect small ecological changes in population size and structure. While this current approach is not perfect, it does attempt to better account for the nature of ecological data and may help prioritize future monitoring based on tool-specific sampling efficiency.
We have greater power to detect changes in size than abundance.
Analysis of hook an line size data (as a proxy for all size data collected by ODFW Marine Reserves Program) indicates that much fewer samples are needed (number of individual fish) to detect change in mean length compared with relative abundance metrics. This is likely due in part to the simplified statistics used that assume normal distribution as well as the advantage of using individual fishes as a sample unit as opposed to more aggregate sample units at a cell or transect level. Species like Black Rockfish and Lingcod may have enough samples to allow for inter annual analysis of size trends. There are still many species-site combinations with low catch rates, and statistical analysis may never be feasible. For example, Yelloweye Rockfish are currently encountered at low rates across reserves, and it will be difficult to accumulate the surveys needed for analysis at an annual basis.
3 Results
3.1 Across Tool Comparison
Results from fish data are combined across tools in the figures below. Results have been standardized to show only a simulated 2X increase in population size or a 50% reduction. Tables below also report the minimum sample sizes needed to attain 80% power.
3.1.1 Tools-Combined 2X Population Increase
Fig XX: Simulated power to detect the doubling of relative abundance across tool types
3.1.2 Tools-Combined 50% Population Decrease
Fig XX: Simulated power to detect the halving of relative abundance across tool types
3.2 Tool Tables 1
These are the estimated minimum sample sizes needed to achieve 80% power by species group. ‘Factor increase’ refers to the multiplicative factor of increase.
3.2.1 Black Rockfish
knitr::include_graphics('figures/sample_size_tables/black_inc_table.png')
3.2.2 Benthic Rockfish
knitr::include_graphics('figures/sample_size_tables/benthic_inc_table.png')
3.2.3 Schooling Rockfish
knitr::include_graphics('figures/sample_size_tables/schooling_inc_table.png')
3.2.4 Greenling
knitr::include_graphics('figures/sample_size_tables/greenling_inc_table.png')
3.3 Tool Tabels 2
These are the estimated minimum sample sizes needed to achieve 80% power by species group. ‘Percent Reduction’ refers to the simulated population decrease (mean abundance).
3.3.1 Black Rockfish
knitr::include_graphics('figures/sample_size_tables/black_dec_table.png')
3.3.2 Benthic Rockfish
knitr::include_graphics('figures/sample_size_tables/benthic_dec_table.png')
3.3.3 Schooling Rockfish
knitr::include_graphics('figures/sample_size_tables/schooling_dec_table.png')
3.3.4 Greenling
knitr::include_graphics('figures/sample_size_tables/greenling_dec_table.png')
3.4 Aggregate Results
Fish abundance data was aggregated across species for the figure below. Estimated power is greater across tools compared with the species group estimates reported in each tool section below.
knitr::include_graphics('figures/agg_catch/aggregate_fish_increase.png')
Aggregate Fish Data
knitr::include_graphics('figures/sample_size_tables/agg_fish_results.png')
Aggregate Fish Data
3.5 Hook-and-Line
For rate-based data, simulations required individual species be tested as representative of the following species groups. Black Rockfish are pulled out separately because they were a common species across survey tools. ‘Schooling Rockfish’ and ‘Greenling’ species were moderately abundant with moderate dispersion. ‘Benthic Rockfish’ species were all lower abundance and generally had higher dispersion of data.
Hook-and-Line
- Black Rockfish pulled out separately due to high abundance
- Schooling Rockfish: Canary Rockfish, Blue/Deacon Rockfish
- Benthic Rockfish: Yelloweye Rockfish, Copper Rockfish, Quillback Rockfish
- Greenling: Lingcod, Kelp Greenling
Power analysis simulations were run to determine approximate power of detecting both population increases as well as population decreases. While the results look similar, increases and decreases in population size are not symmetrical. For example, a population can decrease between 0-100%, but can increase a limitless amount (eg 1000% or a 10 fold increase). As such, increases of 50%, 100%, 200%, and 500% and decreases of 10%, 25%, 50% and 75% were simulated. While arbitrary, these step increases were chosen to bracket what might be considered ecologically meaningful changes.
Hook-And-Line Results
The results below suggest that the hook-and-line survey has the greatest power to detect change for Black Rockfish and the Greenling species group (Kelp Greening and Lingcod). Not surprisingly, Black Rockfish is the most abundant species, and Greenling are reliably sampled (low dispersion). Approximately 100 HL surveys would be need to to achieve 80% power to detect a 50% increase of Black Rockfish mean CPUE, but less than 50 HL surveys would be needed to detect a doubling in mean CPUE. Conversely, Less than 50 HL surveys are expected to detect a 50% reduction in Black Rockfish CPUE, but closer to 250 surveys needed to detect a 25% population reduction.
The results also suggest that our current rates of sampling provide moderate power for Schooling Rockfish but lower power for Benthic Rockfish species. A doubling of mean CPUE might be detected with fewer than 100 surveys in Schooling Rockfish species while a tripling of CPUE in benthic species may be needed to reasonably detect the change with the same effort (i.e. less than 100 surveys). Conversely, decreases greater than 50% mean CPUE would be needed to detect change for these species groups.
These results highlight the fact that catch composition is dominated by relatively few species (Black Rockfish and Greenling). Other abundant species like Blue/Deacon Rockfish are patchy with high variability in catch rate - ultimately limiting the power of the hook-and-line study for these species.
Figure 1 below suggests that the hook-and-line survey has power to detect 2-3x fold differences in CPUE with ~50 or more surveys for Black Rockfish and Greenling species. If our program can achieve similar levels of sampling in the next 8-10 years, then we will likely have the necessary statistical power to detect meaningful change.
3.5.1 Survey sample sizes by site and Year
hl_counts<- read.csv('data/hnl/hl_counts_combined_long.csv') %>%
mutate(Area = str_replace(Area, 'CA', 'Comparison Area')) %>%
mutate(Area = str_replace(Area, 'MR', 'Marine Reserve')) %>%
mutate(Area = fct_relevel(Area, 'Redfish Rocks Marine Reserve','Cape Perpetua Marine Reserve','Cascade Head Marine Reserve','Cape Falcon Marine Reserve'))
hl_survey_counts= select(hl_counts, c(PKCellEffortID, Site, Area, Year)) %>%
unique() %>%
group_by(Site, Area,Year) %>%
tally()
t1 = hl_survey_counts %>%
filter(Site == 'Redfish Rocks') %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2011`:`2019`),na.rm = TRUE)) %>%
kbl(caption = 'Redfish Rocks') %>%
kable_classic(full_width = FALSE)
t2 = hl_survey_counts %>%
filter(Site == 'Cape Perpetua') %>%
filter(Area != 'Comparison Area Outside Cape Perpetua Marine Reserve') %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2013`:`2018`),na.rm = TRUE)) %>%
kbl(caption = 'Cape Perpetua') %>%
kable_classic(full_width = FALSE)
t3 = hl_survey_counts %>%
filter(Site == 'Cascade Head') %>%
mutate(Area = fct_relevel(Area,
'Cascade Head Marine Reserve','Schooner Creek Comparison Area','Cavalier Comparison Area')) %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2013`:`2018`),na.rm = TRUE)) %>%
kbl(caption = 'Cascade Head') %>%
kable_classic(full_width = FALSE)
t4 = hl_survey_counts %>%
filter(Site == 'Cape Falcon') %>%
mutate(Area = fct_recode(Area,
'Moderate Fishing Pressure Comparison Area' = 'Comparison Area Adjacent to Cape Falcon Marine Reserve',
'Low Fishing Pressure Comparison Area' = 'Cape Meares Comparison Area',
'High Fishing Pressure Comparison Area' = 'Three Arch Rocks Comparison Area')) %>%
mutate(Area = fct_relevel(Area,
'Cape Falcon Marine Reserve','Low Fishing Pressure Comparison Area','Moderate Fishing Pressure Comparison Area')) %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2014`:`2019`),na.rm = TRUE)) %>%
kbl(caption = 'Cape Falcon') %>%
kable_classic(full_width = FALSE)3.5.1.1 Redfish Rocks
t1| Area | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2019 | Total |
|---|---|---|---|---|---|---|---|---|---|
| Redfish Rocks Marine Reserve | 20 | 17 | 10 | 20 | 28 | 15 | 20 | 24 | 154 |
| Humbug Comparison Area | 4 | 6 | 11 | 12 | 20 | 10 | 19 | 20 | 102 |
| Orford Reef Comparison Area | NA | NA | NA | 14 | 9 | NA | 17 | 22 | 62 |
3.5.1.2 Cape Perpetua
t2| Area | 2013 | 2014 | 2016 | 2018 | Total |
|---|---|---|---|---|---|
| Cape Perpetua Marine Reserve | 11 | 16 | 15 | 15 | 57 |
| Postage Stamp Comparison Area | 19 | 18 | 25 | 24 | 86 |
3.5.1.3 Cascade Head
t3| Area | 2013 | 2014 | 2015 | 2016 | 2018 | Total |
|---|---|---|---|---|---|---|
| Cascade Head Marine Reserve | 9 | 22 | 27 | 18 | 21 | 97 |
| Schooner Creek Comparison Area | 9 | 10 | 17 | 23 | 17 | 76 |
| Cavalier Comparison Area | 2 | NA | 7 | 17 | 21 | 47 |
| Cape Foulweather Comparison Area | NA | NA | 8 | 5 | 16 | 29 |
3.5.1.4 Cape Falcon
t4| Area | 2014 | 2015 | 2017 | 2019 | Total |
|---|---|---|---|---|---|
| Cape Falcon Marine Reserve | 7 | 20 | 18 | 14 | 59 |
| Low Fishing Pressure Comparison Area | 2 | 5 | 13 | 10 | 30 |
| Moderate Fishing Pressure Comparison Area | 1 | 24 | 11 | 13 | 49 |
| High Fishing Pressure Comparison Area | NA | 2 | 5 | 5 | 12 |
3.5.2 Hook-and-Line Figures
3.5.2.1 Power Analysis: Similated CPUE Increase
Fig. 1: Power Analysis results from species groups simulating CPUE increase. Note that Fold Increase is a multiplicative factor (i.e. 1.1 = a 10% increase in CPUE from the mean value presently observed in the data). A dashed line at 80% power represents a typical rule-of-thumb goal - though this limit is arbitrary
3.5.2.2 Power Analysis: Simulated CPUE Decrease
Fig. 1: Power Analysis results from species groups simulating CPUE decrease. Note that Population Decrease is a multiplicative factor (i.e. 25 = a 25% reduction in mean CPUE from the value presently observed in the data). A dashed line at 80% power represents a typical rule-of-thumb goal - though this limit is arbitrary
3.6 Longline
For rate-based data, simulations required individual species be tested as representative of the following species groups. Black Rockfish are pulled out separately because they were a common species across survey tools. ‘Schooling Rockfish’ and ‘Greenling’ species were moderately abundant with moderate dispersion. ‘Benthic Rockfish’ species were all lower abundance and generally had higher dispersion of data.
- Black Rockfish pulled out separately due to high abundance
- Schooling Rockfish: Canary Rockfish, Blue/Deacon Rockfish
- Benthic Rockfish: Yelloweye Rockfish, Copper Rockfish, Quillback Rockfish
- Greenling: Lingcod, Kelp Greenling
The results below suggest that the Longline survey has comparable power to detect change between Black and Canary Rockfish, two schooling species. The greatest power was found with Lingcod, though Kelp Greenling would likely show similar results due to abundance and low dispersion of data. The top five species (by total count) caught with longline gear were Canary Rockfish, Cabezon, Black Rockfish, Lingcod, and Blue/Deacon Rockfish. The longline survey was designed to better target benthic species at Redfish Rocks, yet a number of schooling rockfishes are still caught in high abundance.
Less than 75 longline surveys would be need to to achieve 80% power to detect a doubling of Black Rockfish CPUE, but roughly 200 longline surveys would be needed to detect a 50% increase in mean CPUE. Conversely, About less than 75 longline surveys are expected to detect a 50% reduction in Black Rockfish CPUE, but closer to 400 surveys needed to detect a 25% population reduction. These results are very similar for the other schooling species: Canary Rockfish - which were caught at similar rates to Black Rockfish with longline gear.
The results also suggest that our current rates of sampling will provide strong power for Greenling species like Lingcod and moderate power for benthic rockfish species. Yelloweye Rockfish CPUE may need to triple in the future to reliably detect changes with 100 surveys or less; however, Copper and Quillback Rockfish simulations indicate 50 surveys to detect a doubling of CPUE- roughly the same level of sampling needed for Black Rockfish. Population reductions less than 50% are unlikely to be detected. If current sampling rates hold true, our program will be positioned to detect differences in CPUE on the magnitude of 2-3 fold.
3.6.1 Survey sample sizes by site and Year
ll_counts_raw<- read.csv('data/longline/counts_longline_matrix_active_cells_long.csv')%>%
mutate(Area = str_replace(Area, 'CA', 'Comparison Area')) %>%
mutate(Area = str_replace(Area, 'MR', 'Marine Reserve'))
longline_survey_counts= dplyr::select(ll_counts_raw, c(PKCellEffortID, Site, Area, Year)) %>%
unique() %>%
group_by(Site, Area,Year) %>%
tally()
x1 = longline_survey_counts %>%
filter(Site == 'Redfish Rocks') %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2015`:`2019`),na.rm = TRUE)) %>%
kbl(caption = 'Redfish Rocks') %>%
kable_classic(full_width = FALSE)
x1| Area | 2015 | 2016 | 2017 | 2019 | Total |
|---|---|---|---|---|---|
| Humbug Comparison Area | 7 | 9 | 23 | 21 | 60 |
| Orford Reef Comparison Area | NA | NA | 23 | 24 | 47 |
| Redfish Rocks Marine Reserve | 14 | 13 | 22 | 24 | 73 |
3.6.2 Longline Figures
3.6.2.1 Power Analysis: Similated CPUE Increase
Fig. 2: Power Analysis results from species groups simulating CPUE increase. Note that Fold Increase is a multiplicative factor (i.e. 1.1 = a 10% increase in CPUE from the mean value presently observed in the data). A dashed line at 80% power represents a typical rule-of-thumb goal - though this limit is arbitrary
3.6.2.2 Power Analysis: Simulated CPUE Decrease
Fig. 2: Power Analysis results from species groups simulating CPUE decrease. Note that Population Decrease is a multiplicative factor (i.e. 25 = a 25% reduction in mean CPUE from the value presently observed in the data). A dashed line at 80% power represents a typical rule-of-thumb goal - though this limit is arbitrary
3.7 Video Lander
- Black Rockfish pulled out separately due to high abundance
- Schooling Rockfish: Canary, Blue/Deacon and Yellowtail Rockfish
- Benthic Rockfish: China and Yelloweye Rockfish
- Greenling: Kelp Greenling and Lingcod
The results below suggest that the Video Lander survey has the greatest power to detect change for Black Rockfish and the Greenling species group (Kelp Greening and Lingcod). Not surprisingly, Black Rockfish was the most abundant species, while Greenling were also reliably sampled (low dispersion of data) by video lander. Approximately 75 lander surveys would be need to to achieve 80% power to detect a doubling of Black Rockfish CPUE, and roughly 250 lander surveys would be needed to detect a 50% increase in CPUE. Conversely, about 100 lander surveys are expected to detect a 50% reduction in Black Rockfish CPUE, but greater than 500 lander surveys are needed to detect a 25% population reduction.
The results also suggest that our current rates of sampling provide relatively low power for other Schooling Rockfish species of rockfishes. Even with a tripling of current MaxN values, there would still need to be roughly 150 lander surveys to reasonably detect schooling rockfish population changes. Conversely, decreases of 75%% or greater in mean MaxN would be needed to detect change for schooling rockfish species.Benthic species (China Rockfish and Yelloweye Rockfish) were observed so infrequently that a simulation was not possible for these species. This suggests that video lander will not be an appropriate tool to monitor changes in rarer benthic species.
These results highlight the fact that lander catch composition is dominated by relatively few species (Black Rockfish and Greenling). The video lander is not well designed to survey schooling species, and due to limited fields of view, water clarity, and other sampling constraints, benthic rockfish species are not well surveyed either.
This analysis suggests that Lander may only have power to detect changes greater than 2-fold for Greenling and Black Rockfish species, and even then, only at a subset of sites with large sample sizes (e.g. Otter Rock, or Schooner Creek Comparison Area).To detect a doubling of Black Rockfish or Greenling species abundance, close to 100 surveys are needed in each group - meaning that 2 years of additional intensive sampling are needed, or another 10 years at the current rate paired with SCUBA. We don’t currently have samples sizes of 200 lander drops at any site across all survey years. It should also be noted that since 2015, approximately 46% of video lander drops are discarded due to quality-control protocols. This implies that nearly double the sample effort is needed to achieve a particular sample size goal with video lander.
3.7.1 Survey sample sizes by site and Year
lander_maxn_long <- read.csv('data/lander/lander_fish_matrix_long.csv') %>%
filter(!Common_Name %in% c("UNID Greenling", "UNID Perch", "UNID Rockfish", "UNID Rockfish YOY", "UNID Roundfish", "UNID Sculpin", "Widow Rockfish")) %>%
filter(Visib !=1) %>%
filter(Drop_Duration_DecMin >=4) %>%
mutate(presabs = ifelse(MaxN == 0,0,1)) %>%
mutate(Treatment = fct_relevel(Treatment, "MR")) %>%
mutate(Area = str_replace(Area, 'CA', 'Comparison Area')) %>%
mutate(Area = str_replace(Area, 'MR', 'Marine Reserve')) %>%
mutate(Area = fct_relevel(Area, 'Redfish Rocks Marine Reserve','Otter Rock Marine Reserve','Cascade Head Marine Reserve','Cape Falcon Marine Reserve')) %>%
droplevels()
#########################
lander_survey_counts= dplyr::select(lander_maxn_long, c(Lander_ID, Site, Area, Year)) %>%
unique() %>%
group_by(Site, Area,Year) %>%
tally()
t5 = lander_survey_counts %>%
filter(Site == 'Redfish Rocks') %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2010`:`2019`),na.rm = TRUE)) %>%
kbl(caption = 'Redfish Rocks') %>%
kable_classic(full_width = FALSE)
t6 = lander_survey_counts %>%
filter(Site == 'Otter Rock') %>%
mutate(Area = fct_relevel(Area, 'Otter Rock Marine Reserve')) %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2010`:`2019`),na.rm = TRUE)) %>%
kbl(caption = 'Otter Rock') %>%
kable_classic(full_width = FALSE)
t7 = lander_survey_counts %>%
filter(Site == 'Cascade Head') %>%
mutate(Area = fct_relevel(Area, 'Cascade Head Marine Reserve', 'Schooner Creek Comparison Area','Cavalier Comparison Area')) %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2012`:`2018`),na.rm = TRUE)) %>%
kbl(caption = 'Cascade Head') %>%
kable_classic(full_width = FALSE)
t8 = lander_survey_counts %>%
filter(Site == 'Cape Falcon') %>%
mutate(Area = fct_recode(Area,
'Moderate Fishing Pressure Comparison Area' = 'Comparison Area adjacent to Cape Falcon Marine Reserve',
'Low Fishing Pressure Comparison Area' = 'Cape Meares Comparison Area',
'High Fishing Pressure Comparison Area' = 'Three Arch Rocks Comparison Area')) %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2016`:`2017`),na.rm = TRUE)) %>%
kbl(caption = 'Cape Falcon') %>%
kable_classic(full_width = FALSE)3.7.1.1 Redfish Rocks
t5| Area | 2010 | 2011 | 2012 | 2014 | 2015 | 2019 | Total |
|---|---|---|---|---|---|---|---|
| Redfish Rocks Marine Reserve | 8 | 13 | 12 | 20 | 18 | NA | 71 |
| Humbug Comparison Area | 5 | 7 | 1 | 11 | 32 | 6 | 62 |
| Orford Reef Comparison Area | NA | NA | 12 | 15 | NA | NA | 27 |
3.7.1.2 Otter Rock
t6| Area | 2010 | 2011 | 2012 | 2015 | 2016 | 2017 | 2019 | Total |
|---|---|---|---|---|---|---|---|---|
| Otter Rock Marine Reserve | 2 | 1 | NA | 65 | NA | 4 | 3 | 75 |
| Cape Foulweather Comparison Area | NA | 13 | 2 | 33 | 17 | 9 | 9 | 83 |
3.7.1.3 Cascade Head
t7| Area | 2012 | 2013 | 2014 | 2016 | 2017 | 2018 | Total |
|---|---|---|---|---|---|---|---|
| Cascade Head Marine Reserve | 29 | NA | 2 | NA | 8 | 15 | 54 |
| Schooner Creek Comparison Area | 29 | 45 | NA | 20 | 7 | 18 | 119 |
| Cavalier Comparison Area | 14 | 2 | NA | 18 | NA | 3 | 37 |
3.7.1.4 Cape Falcon
t8| Area | 2016 | 2017 | Total |
|---|---|---|---|
| Cape Falcon Marine Reserve | 9 | 3 | 12 |
| Low Fishing Pressure Comparison Area | NA | 1 | 1 |
| Moderate Fishing Pressure Comparison Area | 2 | 4 | 6 |
3.7.2 Video Lander Figures
3.7.2.1 Power Analysis: Similated MaxN Increase
Fig. 3: Power Analysis results from species groups simulating MaxN increase. Note that Fold Increase is a multiplicative factor (i.e. 1.1 = a 10% increase in MaxN from the mean value presently observed in the data). A dashed line at 80% power represents a typical rule-of-thumb goal - though this limit is arbitrary
3.7.2.2 Power Analysis: Simulated MaxN Decrease
Fig. 3: Power Analysis results from species groups simulating MaxN decrease. Note that Population Decrease is a multiplicative factor (i.e. 25 = a 25% reduction in mean MaxN from the value presently observed in the data). A dashed line at 80% power represents a typical rule-of-thumb goal - though this limit is arbitrary
3.8 SCUBA Fish
- Black Rockfish pulled out separately due to high abundance
- Schooling Rockfish: Canary, Blue/Deacon and Yellowtail Rockfish
- Benthic Rockfish: China
- Greenling: Kelp Greenling and Lingcod
Black Rockfish were one of the most abundant species observed by the SCUBA fish surveys. An estimated 50 transects would be needed to detect a doubling of the density. Approximately 50 transects are needed to detect a 50% reduction in density of Black Rockfish. For other pooled schooling rockfish, there would need to be a 3X increase of the observed density to detect changes with 100 transects. This contrasts with the estimated 100 transects needed to detect a 50% increase in Greenling, or less than 50 transects to detect a doubling of mean density. This is likely because greenling species are consistently observed across SCUBA surveys and the data is not very dispersed despite having low densities overall.
Benthic species had the lowest power to detect change. At least 75 surveys are estimated to detect a 3X increase in mean density, and 300 surveys needed to detect a doubling of density. Close to 200 surveys are needed to detect a 75% decrease in benthic species, suggesting that only dramatic decreases in already rare fish species would be detected by SCUBA.
During the synthesis report writing, only 5 relationships were found to be significant. 4 of those were for Black Rockfish. The magnitude of difference was 2-4x for significant Area relationships. Temporal trends were only significant twice for changes in density on the order of 5-9.5X change.
SCUBA fish surveys had moderate power to detect change for Black Rockfish and Greenling species. An estimated 50 surveys are needed (per comparison group) to detect a doubling of density for the most abundant species. This implies that the current rates of survey effort may be sufficient at Redfish Rocks Marine Reserve (n = 126) to observe a doubling or greater of mean density - if data is pooled across the 10 survey years. Total sample sizes may need to be doubled or even tripled at other survey sites. Given current rates of sampling, this implies an additional 5 years of surveys are needed to detect change for abundant species. Trends in Schooling and benthic species are unlikely to detected with SCUBA fish surveys.
3.8.1 SCUBA Fish Sample Sizes
scuba_fish<- read.csv('data/scuba_fish/Fish_Counts_matrix_long.csv') %>%
dplyr::rename(
Area.Code = Area,
Area = Area_Description,
Treatment = Type,
Site = SITE,
Counts = Total_Count) %>%
mutate(
Site = fct_recode(Site,
"Redfish Rocks" = "RR",
"Cascade Head" = "CH",
"Otter Rock" = "OR",
"Cape Falcon" = "CF")) %>%
filter(!Common_Name %in% c(
"UNID Hexagrammos", "UNID YOY Rockfish")) %>%
mutate(Common_Name = ifelse(Common_Name == 'Black and Yellow Rockfish', 'B&Y Rockfish',Common_Name)) %>%
mutate(Common_Name = ifelse(Common_Name == 'Blue/Deacon Rockfish', 'Blue_Deacon Rockfish',Common_Name)) %>%
mutate(ttl.area = 60,
ttl.density = Counts/ttl.area) %>%
mutate(Area = str_replace(Area, 'CA', 'Comparison Area')) %>%
mutate(Area = str_replace(Area, 'MR', 'Marine Reserve')) %>%
mutate(Area = fct_relevel(Area, 'Redfish Rocks Marine Reserve','Otter Rock Marine Reserve','Cascade Head Marine Reserve','Cape Falcon Marine Reserve')) %>%
droplevels()
scuba_fish_counts = scuba_fish %>%
select(PK_Trans_ID,Site,Area,Year) %>%
unique() %>%
group_by(Site,Area,Year) %>%
tally()
z1 = scuba_fish_counts %>%
filter(Site == 'Redfish Rocks') %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2010`:`2019`),na.rm = TRUE)) %>%
kbl(caption = 'Redfish Rocks') %>%
kable_classic(full_width = FALSE)
z2 = scuba_fish_counts %>%
filter(Site == 'Otter Rock') %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2011`:`2019`),na.rm = TRUE)) %>%
kbl(caption = 'Otter Rock') %>%
kable_classic(full_width = FALSE)
z3 = scuba_fish_counts %>%
filter(Site == 'Cascade Head') %>%
mutate(Area = fct_relevel(Area, 'Cascade Head Marine Reserve', 'Schooner Creek Comparison Area')) %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2014`:`2018`),na.rm = TRUE)) %>%
kbl(caption = 'Cascade Head') %>%
kable_classic(full_width = FALSE)
z4 = scuba_fish_counts %>%
filter(Site == 'Cape Falcon') %>%
mutate(Area = fct_recode(Area,
'Moderate Fishing Pressure Comparison Area' = 'Comparison Area adjacent to Cape Falcon Marine Reserve')) %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2016`:`2017`),na.rm = TRUE)) %>%
kbl(caption = 'Cape Falcon') %>%
kable_classic(full_width = FALSE)3.8.1.1 Redfish Rocks
z1| Area | 2010 | 2011 | 2014 | 2015 | 2019 | Total |
|---|---|---|---|---|---|---|
| Redfish Rocks Marine Reserve | 44 | 36 | 28 | NA | 18 | 126 |
| Humbug Comparison Area | 14 | 6 | 21 | 9 | 15 | 65 |
| Orford Reef Comparison Area | NA | NA | 19 | NA | NA | 19 |
3.8.1.2 Otter Rock
z2| Area | 2011 | 2015 | 2017 | 2019 | Total |
|---|---|---|---|---|---|
| Otter Rock Marine Reserve | 28 | 11 | 3 | 15 | 57 |
| Cape Foulweather Comparison Area | 9 | NA | 6 | 19 | 34 |
3.8.1.3 Cascade Head
z3| Area | 2014 | 2017 | 2018 | Total |
|---|---|---|---|---|
| Cascade Head Marine Reserve | 7 | 17 | 43 | 67 |
| Schooner Creek Comparison Area | 11 | 9 | 29 | 49 |
| Cavalier Comparison Area | NA | 6 | 1 | 7 |
3.8.1.4 Cape Falcon
z4| Area | 2016 | 2017 | Total |
|---|---|---|---|
| Cape Falcon Marine Reserve | 10 | NA | 10 |
| Moderate Fishing Pressure Comparison Area | 4 | 3 | 7 |
3.8.2 SCUBA Fish Figures
3.8.2.1 Power Analysis: Similated Density Increase
Fig. 4: Power Analysis results from species groups simulating density increase. Note that Fold Increase is a multiplicative factor (i.e. 1.1 = a 10% increase in density from the mean value presently observed in the data). A dashed line at 80% power represents a typical rule-of-thumb goal - though this limit is arbitrary
3.8.2.2 Power Analysis: Simulated Density Decrease
Fig. 4: Power Analysis results from species groups simulating density decrease. Note that Population Decrease is a multiplicative factor (i.e. 25 = a 25% reduction in mean density from the value presently observed in the data). A dashed line at 80% power represents a typical rule-of-thumb goal - though this limit is arbitrary
3.9 SCUBA Invertebrate
- Sea Stars: Henricia spp., Pycnopodia helianthoides, Pisaster ochraceus
- Sea Urchin: Strongylocentrotus purperatus, Mesocentrotus franciscanus
We also simulated potential survey power across a range of plausible density values found within our data.
- High Density : approximately the upper range detected for species like Mesocentrotus franciscanus,Strongylocentrotus purperatus
- Medium-High Density:approximately the mean density for species like Cucumaria miniata,Mesocentrotus franciscanus,Strongylocentrotus purperatus
- Medium-Low Density:approximately the mean density for species like Styela montereyensis, barnacle species, or low density ranges of Mesocentrotus franciscanus or Metridium farcimen
- Low Density :approximately the mean density for species like Pycnopodia helianthoides, Apostichopus californicus, Crassadoma gigantea
Power Analysis for Scuba invertebrate focused on two main species groups: sea urchins and sea stars. These are species of interest due to the sea star wasting syndrome that occurred along the pacific west coast in 2014-15. Results suggest that fewer that approximately 50 transects are needed to detect sea urchin population increases in mean density of 3 fold. Sea stars (Henricia spp., Pycnopodia helianthoides, Pisaster ochraceus) were less abundant but the data was less dispersed and so fewer surveys are estimated to achieve similar power. Less than 50 transects to detect a doubling of mean density are required.
Our Synthesis Report analysis at Redfish Rocks did in fact detect yearly declines in sea star populations through time. For both Pycnopodia helianthoides and Pisaster ochraceus, populations declined severely to nearly zero after the initial survey years. It was in this context that we detected a change (significant smoothed GAM term). Conversely, urchin populations - both Red and Purple Sea Urchins - were observed to increase during the last two years of survey from counts near zero previously.
When we simulate potential survey power across a range of plausible density values (derived from the data), it is apparent that roughly 125 SCUBA transects may be needed to detect shifts in density 2x or greater for ‘High Density’ species. Interestingly, ‘Medium-High Density’ species may need less than 100 surveys to detect a 2x shift in mean density - fewer than ‘High Density’ species. This is likely because these species are more consistently observed, that is less patchy or over-dispersed data. ‘Medium-Low’ density species may need either 150 or more transects, or greater than 3x fold shifts in density to detect change and ‘Low Density’ species would need roughly 200 surveys to detect a 2x increase in density. Collectively, these results suggest moderately similar levels of sampling required for all but the lowest abundance species and highlight that low-dispersion in the data can boost statistical power more than mean abudance.
This analysis indicates that current SCUBA swath survey efforts are powerful enough to detect wide population swings at Redfish Rocks, and will be a valuable tool to track possible sea star recoveries along the Oregon Coast. Subtle changes through time will take longer time scales to detect.The analysis estimated close to 50 SCUBA transects to detect a 2-fold increase in density for sea stars or a 3-fold increase in sea urchins, which is at least double most survey efforts with SCUBA invertebrate. Since 2010, there have been several shifts in density on the order of 10-fold increases/decreases through time and these changes were detectable with current sampling levels. At Cape Falcon, where we have only been able to survey comparison areas ~6 transects in the one year of sampling - It will take another 15 years of surveys to achieve power.
3.9.1 SCUBA invertebrate Sample Sizes
scuba_inverts<- read.csv("data/scuba_invert/SWATH_Invert_Counts_matrix_long.csv") %>%
dplyr::rename(
Area.Code = AREA,
Area = Area_Description,
Treatment = Type,
Site = SITE,
Counts = Total_Count) %>%
mutate(
Site = fct_recode(Site,
"Redfish Rocks" = "RR",
"Cascade Head" = "CH",
"Otter Rock" = "OR",
"Cape Falcon" = "CF")) %>%
mutate(Common_Name = ifelse(Species == 'Strongylocentrotus franciscanus','Mesocentrotus franciscanus',Species) %>% as.factor()) %>% mutate(Area = str_replace(Area, 'CA', 'Comparison Area')) %>%
mutate(Area = str_replace(Area, 'MR', 'Marine Reserve')) %>%
mutate(Area = fct_relevel(Area, 'Redfish Rocks Marine Reserve','Otter Rock Marine Reserve','Cascade Head Marine Reserve','Cape Falcon Marine Reserve')) %>%
mutate(ttl.area = 60,
ttl.density = Counts/ttl.area) %>%
droplevels()
scuba_inverts_counts = scuba_inverts %>%
select(PK_Transect_ID,Site,Area,Year) %>%
unique() %>%
group_by(Site,Area,Year) %>%
tally()
z5 = scuba_inverts_counts %>%
filter(Site == 'Redfish Rocks') %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2010`:`2019`),na.rm = TRUE)) %>%
kbl(caption = 'Redfish Rocks') %>%
kable_classic(full_width = FALSE)
z6 = scuba_inverts_counts %>%
filter(Site == 'Otter Rock') %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2010`:`2019`),na.rm = TRUE)) %>%
kbl(caption = 'Otter Rock') %>%
kable_classic(full_width = FALSE)
z7 = scuba_inverts_counts %>%
filter(Site == 'Cascade Head') %>%
mutate(Area = fct_relevel(Area, 'Cascade Head Marine Reserve', 'Schooner Creek Comparison Area')) %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2013`:`2018`),na.rm = TRUE)) %>%
kbl(caption = 'Cascade Head') %>%
kable_classic(full_width = FALSE)
z8 = scuba_inverts_counts %>%
filter(Site == 'Cape Falcon') %>%
mutate(Area = fct_recode(Area,
'Moderate Fishing Pressure Comparison Area' = 'Comparison Area adjacent to Cape Falcon Marine Reserve',
'Low Fishing Pressure Comparison Area' = 'Cape Meares Comparison Area',
'High Fishing Pressure Comparison Area' = 'Three Arch Rocks Comparison Area')) %>%
cast(Area ~Year) %>%
mutate(Total = rowSums(across(`2016`:`2017`),na.rm = TRUE)) %>%
kbl(caption = 'Cape Falcon') %>%
kable_classic(full_width = FALSE)3.9.1.1 Redfish Rocks
z5| Area | 2010 | 2011 | 2014 | 2015 | 2019 | Total |
|---|---|---|---|---|---|---|
| Redfish Rocks Marine Reserve | 15 | 16 | 1 | 22 | 12 | 66 |
| Humbug Comparison Area | 5 | 10 | 6 | 9 | 6 | 36 |
3.9.1.2 Otter Rock
z6| Area | 2010 | 2011 | 2015 | 2017 | 2019 | Total |
|---|---|---|---|---|---|---|
| Otter Rock Marine Reserve | 4 | 13 | 9 | 15 | 8 | 49 |
| Cape Foulweather Comparison Area | NA | 6 | NA | 8 | 8 | 22 |
3.9.1.3 Cascade Head
z7| Area | 2013 | 2014 | 2017 | 2018 | Total |
|---|---|---|---|---|---|
| Cascade Head Marine Reserve | 16 | 12 | 13 | 27 | 68 |
| Schooner Creek Comparison Area | NA | 11 | 6 | 18 | 35 |
| Cavalier Comparison Area | 10 | NA | 4 | 15 | 29 |
3.9.1.4 Cape Falcon
z8| Area | 2016 | 2017 | Total |
|---|---|---|---|
| Cape Falcon Marine Reserve | 6 | 12 | 18 |
| Low Fishing Pressure Comparison Area | NA | 4 | 4 |
| Moderate Fishing Pressure Comparison Area | NA | 7 | 7 |
| High Fishing Pressure Comparison Area | NA | 6 | 6 |
3.9.2 SCUBA invertebrate Species Figures
Below simulated results are displayed for aggregate sea stars and sea urchin species.
3.9.2.1 Power Analysis: Similated Density Increase
Fig. 5: Power Analysis results from species groups simulating density increase. Note that Fold Increase is a multiplicative factor (i.e. 1.1 = a 10% increase in density from the mean value presently observed in the data). A dashed line at 80% power represents a typical rule-of-thumb goal - though this limit is arbitrary
3.9.2.2 Power Analysis: Simulated Density Decrease
Fig. 5: Power Analysis results from species groups simulating density decrease. Note that Population Decrease is a multiplicative factor (i.e. 25 = a 25% reduction in mean density from the value presently observed in the data). A dashed line at 80% power represents a typical rule-of-thumb goal - though this limit is arbitrary
3.9.3 SCUBA invertebrate Group Figures
Below simulated results are displayed for a range of densities observed in the scuba database. ‘High Density’ might reflect the upper limits of sea urchin densities observed, while ‘Low Density’ could represent any number of rare invertebrate species observed. The dispersion parameter theta was estimated to be similar (.2-.5) across all density groups.
3.9.3.1 Power Analysis: Similated Density Increase
3.10 ROV Fish
Simulations suggest that ROV surveys have the greatest power for Greenling species observed, due in part to their consistency throughout surveys (i.e. low variability in density). Black Rockfish were pulled out separately for this analysis, but likely have comparable power to Blue/Deacon Rockfish in ROV surveys - they are observed at similar densities. Canary Rockfish was lumped with Blue/Deacon Rockfish for this analysis and the results indicate that this grouped ‘schooling species’ category has lower relative power - due to lower abundances. Benthic species have the lowest power to detect change due to low abundances and zero inflation of the data.
Roughly 200 transect-segments are needed to observe a 2x increase in Black Rockfish, and closer to 300 transect-segments are needed to observe a 2x increase in the pooled schooling species. Benthic rockfish needed 400 transect segments to detect a 2x increase, but only 150 segments to detect a 3x increase in density. On average, there were seven 200m-segments per transect. This means a target sample size of 200 segments is roughly 30 full ROV transects.
This suggests that a single high-intensity survey year (e.g. 2010 at Redfish Rocks) could result in greater than 30 transects. For other years, it takes 2 years of surveys to attain this level of sampling.
3.10.1 ROV Fish Sample Sizes
3.10.1.1 Sample Size: Number of ROV Transects
Number of individual ROV transects by survey Site and Year
3.10.1.2 Sample Size: Number of 200m-Segments
Number of 200m^2 transect-segments collected by survey Site and Year. Note that these are subdivided from full transects to create even-sized segments.
3.10.2 ROV Fish Figures
3.10.2.1 Power Analysis: Similated Density Increase
Fig. 7: Power Analysis results from species groups simulating density increase. Note that Fold Increase is a multiplicative factor (i.e. 1.1 = a 10% increase in density from the mean value presently observed in the data). A dashed line at 80% power represents a typical rule-of-thumb goal - though this limit is arbitrary
3.10.2.2 Power Analysis: Simulated Density Decrease
Fig. 7: Power Analysis results from species groups simulating density decrease. Note that Population Decrease is a multiplicative factor (i.e. 25 = a 25% reduction in mean density from the value presently observed in the data). A dashed line at 80% power represents a typical rule-of-thumb goal - though this limit is arbitrary
3.11 ROV invertebrate
- Abundant Sessile: ‘Giant Plumose Anemone’
- Less Common Sessile: ‘Stalked Tunicate’,‘Fish Eating Anemone’
- Rare Sessile: A species of ‘rare’ anemones to test the lower ranges of density observed by ROV: ‘Stubby Rose Anemone’
- Abundant Mobile: ‘Giant Sea Cucumber’ and ‘Red Sea Urchin’
- Other Mobile: A collection of moderately abundant Sea Stars. Note that ‘Blood Star’ was significantly more abundant than any other sea star species: ‘Blood Star’, “Basket Star”,“Leather Star”,“Sunflower Star”,“Pink Star”,“Vermilion Star”
ROV invertebrate simulations were completed for the species groupings listed above. ROV densities ranged from <0.01 to >30.0 individuals per 100m^2 across species. The groups used in this analysis were an attempt to lump species with similar mean densities to create approximate start points for the simulation. For example, species group ‘Abundant Sessile’ contained two species with mean density of 22.2 individuals/100m^2 while ‘Rare Sessile’ has a mean density of 0.05 individuals/100m^2.
Results from the simulation suggest that ROV surveys have the greatest power to detect change for abundant mobile inverts. This group included both Giant Sea Cucumber and Red Sea Urchin and was some of the least dispersed data. To the extent that any species matches this description (abundant and commonly observed), we will have better power to detect change. Much fewer than 100 surveys appear needed to detect differences of 2-fold for these species. Abundant sessile was the most group with greatest densities, yet increases of 2x would needed to detect change with 100 surveys. This decrease in power relative to ‘abundant mobile’ species reflects the interplay between abundance, and variable densities (i.e. patchy distribution) in affecting power. For more rare species, like those lumped in ‘Rare Sessile’, or ‘Other Mobile’, a change of 3x or greater is likely needed to statistically detect change. The ROV tool is limited to depths greater than 15m and is not an appropriate survey tool for several shallow water species such as the Ochre Sea Star or Purple Sea Urchin.
In four years of data collection, roughly 100 ROV transects were collected from each survey site at Redfish Rocks. This suggests that for many species, survey effort will need to be doubled (another 4 years) to reliably detect changes of 2-3x increases in density. Some of the abundant mobile species results suggest that there is much greater power to detect change, and that analysis of interannual variability may be possible.
3.11.1 ROV invertebrate Figures
3.11.1.1 Power Analysis: Similated Density Increase
Fig. 8: Power Analysis results from species groups simulating density increase. Note that Fold Increase is a multiplicative factor (i.e. 1.1 = a 10% increase in density from the mean value presently observed in the data). A dashed line at 80% power represents a typical rule-of-thumb goal - though this limit is arbitrary
3.11.1.2 Power Analysis: Simulated Density Decrease
Fig. 8: Power Analysis results from species groups simulating density decrease. Note that Population Decrease is a multiplicative factor (i.e. 25 = a 25% reduction in mean density from the value presently observed in the data). A dashed line at 80% power represents a typical rule-of-thumb goal - though this limit is arbitrary
3.12 Size data
We used data from hook-and-line surveys to study our ability to detect changes in mean sizes. Because size data more closely conforms to a normal distribution, we were able to use a simplified simulation approach that assumed normal distribution and used simple t-tests to test for significant differences among groups. The simulation investigated a 10%, 25% or 50% increase in mean size from a defined starting point. Starting points were calculated by summarizing the observed mean size and standard deviation of length for species at each survey site. Exploratory analysis revealed that there was little relationship between mean size and standard deviation of length for most species. The exception was lingcod - where standard deviation increased with mean size - possibly an artifact of a few large individuals being caught. As a result, simulations were run with the assumption that standard deviation does not change as the mean size of fishes increases.
Overall the results suggest that we have much greater power to detect simple changes in mean size than we do abundance. This is likely due in part to simplified statistics and high sample size when using individual fish as a sample unit.
hl.size.data <- read.csv("data/hnl/hl_sizes_combined_long.csv") %>%
mutate(Area = str_replace(Area, 'CA', 'Comparison Area')) %>%
mutate(Area = str_replace(Area, 'MR', 'Marine Reserve')) %>%
mutate(Area = as.factor(Area)) %>%
filter(!Common_Name %in% c('UNID Rockfish','UNID Sculpin'))
w1 = hl.size.data %>%
filter(Site == 'Redfish Rocks') %>%
group_by(Common_Name, Area) %>%
tally() %>%
cast(Common_Name ~Area, fill = '--') %>%
kbl(caption = 'Redfish Rocks') %>%
kable_classic(full_width = FALSE)
w2 = hl.size.data %>%
filter(Site == 'Cape Perpetua') %>%
filter(Area != 'Comparison Area Outside Cape Perpetua Marine Reserve') %>%
group_by(Common_Name, Area) %>%
tally() %>%
cast(Common_Name ~Area, fill = '--') %>%
kbl(caption = 'Cape Perpetua') %>%
kable_classic(full_width = FALSE)
w3 = hl.size.data %>%
filter(Site == 'Cascade Head') %>%
mutate(Area = fct_relevel(Area,
'Cascade Head Marine Reserve','Schooner Creek Comparison Area','Cavalier Comparison Area', 'Cape Foulweather Comparison Area')) %>%
group_by(Common_Name, Area) %>%
tally() %>%
cast(Common_Name ~Area, fill = '--') %>%
kbl(caption = 'Cascade Head') %>%
kable_classic(full_width = FALSE)
w4 = hl.size.data %>%
filter(Site == 'Cape Falcon') %>%
mutate(Area = fct_recode(Area,
'Moderate Fishing Pressure Comparison Area' = 'Comparison Area Adjacent to Cape Falcon Marine Reserve',
'Low Fishing Pressure Comparison Area' = 'Cape Meares Comparison Area',
'High Fishing Pressure Comparison Area' = 'Three Arch Rocks Comparison Area')) %>%
mutate(Area = fct_relevel(Area,
'Cape Falcon Marine Reserve','Low Fishing Pressure Comparison Area','Moderate Fishing Pressure Comparison Area')) %>%
group_by(Common_Name, Area) %>%
tally() %>%
cast(Common_Name ~Area, fill = '--') %>%
kbl(caption = 'Cape Falcon') %>%
kable_classic(full_width = FALSE)3.12.1 Size Data Sample Sizes
3.12.1.1 Redfish Rocks
| Common_Name | Humbug Comparison Area | Orford Reef Comparison Area | Redfish Rocks Marine Reserve |
|---|---|---|---|
| Black Rockfish | 856 | 194 | 1666 |
| Blue_Deacon Rockfish | 83 | 68 | 342 |
| Brown Irish Lord | – | – | 1 |
| Buffalo Sculpin | 5 | – | 3 |
| Cabezon | 47 | 43 | 46 |
| Canary Rockfish | 84 | 65 | 172 |
| China Rockfish | 32 | 53 | 87 |
| Copper Rockfish | 7 | 8 | 25 |
| Gopher Rockfish | – | – | 1 |
| Kelp Greenling | 162 | 60 | 230 |
| Lingcod | 260 | 171 | 407 |
| Pacific Staghorn | – | – | 1 |
| Quillback Rockfish | 48 | 16 | 66 |
| Red Irish Lord | 2 | – | 2 |
| Rosy Rockfish | 2 | – | 1 |
| Tiger Rockfish | 1 | 2 | 2 |
| Vermilion Rockfish | 4 | 5 | 20 |
| Widow Rockfish | – | 1 | – |
| Wolf Eel | – | 1 | – |
| Yelloweye Rockfish | 21 | 25 | 31 |
| Yellowtail Rockfish | 41 | 38 | 183 |
3.12.1.2 Cape Perpetua
| Common_Name | Cape Perpetua Marine Reserve | Postage Stamp Comparison Area |
|---|---|---|
| Black Rockfish | 1538 | 1961 |
| Blue_Deacon Rockfish | 17 | 26 |
| Bocaccio | 1 | – |
| Brown Irish Lord | – | 1 |
| Brown Rockfish | 7 | – |
| Buffalo Sculpin | 5 | 45 |
| Cabezon | – | 44 |
| Canary Rockfish | 377 | 14 |
| Copper Rockfish | 45 | 4 |
| Kelp Greenling | 21 | 48 |
| Lingcod | 288 | 143 |
| Pacific Staghorn | – | 2 |
| Quillback Rockfish | 97 | 10 |
| Spotted Ratfish | – | 1 |
| Tiger Rockfish | 1 | – |
| Yelloweye Rockfish | 38 | – |
| Yellowtail Rockfish | 118 | 49 |
3.12.1.3 Cascade Head
| Common_Name | Cascade Head Marine Reserve | Schooner Creek Comparison Area | Cavalier Comparison Area | Cape Foulweather Comparison Area |
|---|---|---|---|---|
| Black Rockfish | 3527 | 406 | 231 | 132 |
| Blue_Deacon Rockfish | 182 | 200 | 8 | – |
| Brown Rockfish | – | – | 1 | – |
| Buffalo Sculpin | – | – | 1 | 2 |
| Cabezon | 126 | 49 | 53 | 36 |
| Canary Rockfish | 123 | 149 | 25 | – |
| China Rockfish | 3 | 8 | 3 | 9 |
| Copper Rockfish | 18 | 10 | 14 | – |
| Kelp Greenling | 149 | 55 | 10 | 42 |
| Lingcod | 485 | 320 | 98 | 59 |
| Pacific Staghorn | 9 | – | – | – |
| Quillback Rockfish | 18 | 25 | 8 | 1 |
| Red Irish Lord | 5 | – | 1 | 2 |
| Tiger Rockfish | 1 | 6 | 2 | – |
| UNID Juvenile Rockfish | – | 1 | – | – |
| Vermilion Rockfish | 1 | 2 | – | – |
| Widow Rockfish | – | 1 | 1 | – |
| Yelloweye Rockfish | 5 | 39 | 5 | – |
| Yellowtail Rockfish | 75 | 66 | 20 | – |
3.12.1.4 Cape Falcon
| Common_Name | Cape Falcon Marine Reserve | Low Fishing Pressure Comparison Area | Moderate Fishing Pressure Comparison Area | High Fishing Pressure Comparison Area |
|---|---|---|---|---|
| Black Rockfish | 586 | 240 | 902 | 297 |
| Blue_Deacon Rockfish | – | 3 | 11 | 3 |
| Brown Irish Lord | – | – | 1 | – |
| Buffalo Sculpin | 66 | 28 | 5 | 5 |
| Cabezon | 10 | 31 | 23 | 55 |
| Canary Rockfish | – | – | 29 | – |
| China Rockfish | – | – | 1 | 3 |
| Copper Rockfish | 1 | – | 1 | 3 |
| Kelp Greenling | 79 | 42 | 55 | 17 |
| Lingcod | 31 | 35 | 145 | 27 |
| Pacific Staghorn | 1 | 1 | 5 | – |
| Quillback Rockfish | – | – | 11 | – |
| Red Irish Lord | 6 | 6 | – | 2 |
| Shiner Perch | 2 | – | – | – |
| Tiger Rockfish | – | – | 5 | – |
| Yelloweye Rockfish | – | – | 24 | – |
| Yellowtail Rockfish | 1 | – | 18 | – |
3.12.2 Size Data Figures
Figures 11 show species-specific estimates of Power for a given level of sampling and used global mean length and standard deviation estimates (i.e. all sites combined). Approximately 10 individual Black Rockfish are needed per test group on average to detect a 10% difference in mean length. Yelloweye Rockfish may need closer to 100 individual fishes per test group in order to detect a similar 10% change in mean length whereas species like Canary Rockfish or Lingcod may only need 50 individuals to detect this change.
3.12.2.1 Spp-Curves 1
Fig. 10: Power Analysis results of HL size data indicating the range of samples needed to detect a 10, 25, and 50% percent increase in size for selected species
4 Discussion
The results of a power analysis indicate, on average, what power might be expected across a range of hypothetical sample sizes. In reality, we have been able to detect changes for species with sample sizes smaller than indicated by the power accumulation curves. This highlights the fact that it is possible to detect change at small sample sizes, but that this is unlikely to occur on average. These results instead could guide future monitoring plans by assessing the relative strengths of each tool across the range of observed species.
If we consider significant results detected in hook-and-line data (as part of the 2022 Synthesis Report), we observe that significant pairwise differences were detected in CPUE rates that differed by factors ranging from 1.5 (larger CPUE 1.5 times greater than smaller CPUE) to 21 (larger CPUE 21 times greater than smaller CPUE).Digging deeper, differences in CPUE for benthic species like China, Copper, Quillback and Yelloweye were only statistically significant when the CPUE differed by factors greater than 4. Similarly, Black and Blue/Deacon Rockfish as well as Greenling species had significant differences detected when CPUE differed by factors ranging 1.5 - 6 (avg = 2.8).
SCUBA invertebrate surveys were also able to detect a range of significant difference among comparison groups. Sea stars and sea urchin species were the most common species with significant trends across reserves. Differences detected were generally on the magnitude of 3X or greater (measured as the ratio of largest density to smallest density). For example red sea urchin at Humbug CA were 4.5x greater densities than at Redfish Rocks while Metridium farcimen had densities 3.5x at Redfish Rocks compared with density at Humbug CA. Many of the differences among sites were even greater magnitude. Both Ochre Star (Pisaster ochraceus) and Red Sea Urchin (Mesocentrotus franciscanus) densities between Otter Rock and Cape Foulweather differed on the order of 6x. Differences in purple sea urchin density detected among Cascade Head Marine Reserve and its comparison areas ranged from 4x-14x. The smallest effect detected was at Cavalier CA where C. gigantea densities were 2x those at Cascade Head Marine Reserve. Temporal trends were more difficult to quantify; however, interannual differences between 4-10x appeared to have driven significant smoothed GAMM model results. For example, P. ochraceus increased through time by 6x at Otter Rock Marine Reserve, and Purple Sea Urchins increased by roughly 10x at Redfish Rock Marine Reserve. In a more extreme case, Pisaster ochraceus decreased by ~99% and Pycnopodia helianthoides decreased by 100% at Redfish Rocks Marine Reserve after the sea star wasting disease in 2013-2015.
While not included in this simulation study, the results of SCUBA Habitat and Cover surveys were similar to the SCUBA invertebrate results with magnitudes of difference ranging between 1.45 - 6x. Coralline algae at Cape Foulweather were 1.45x greater than Otter Rock Marine Reserve - the smallest difference detected and the only significant area-pairwise test. Year effects detected appear to be a greater magnitude. For example, encrusting red algae increased by 2-4x at Redfish Rocks depending on survey site, crustose coraline algae increased by 4x at Cascade Head and by 5-6x at Otter Rock. This suggests that subtle interannual variation may not be detected in a temporal analysis with this data set. Future power analysis may explore the best ways to simulate point-count data that is collected during SCUBA UPC surveys- possibly exploring quasi-poisson GLM models.
Analyses of ROV fish data indicate that several differences of magnitude 1.2-3.8x were detected by formal statistical analysis. The power analysis results here suggest that relative to other tools, the ROV may be more effective at detecting change in density per unit of sampling. This may be due to the large survey area covered by ROV and the resulting decrease in variability of density estimates. ROV power analysis were conducted using two different sample units. For fish, ROV transects were subdivided and standardized by 200m^2 segments while invertebrate surveys were analyzed using full transect data. A caveat to this approach is that the subdivided segments may have had the same properties (mean, distribution) of the transects, thereby increasing the sample size by several fold. As a result, the estimated full transects needed to detect change for fish surveys was considerably less than invertebrate surveys. Further discussion is warranted on the use of standardized transect segments and to what extent these segments may violate assumptions of independence among sample units.
The analysis of hook-and-line size data suggests that we have much greater power to detect spatial and temporal changes in mean size than in abundance. This is likely due to a combination of simpler statistics (t-tests that assume normal distributions) and the relatively high sample sizes obtained by using individual fishes as sample unit. When looking at species-specific power plots, it is apparent that power for a given level of sampling is relatively comparable across species. However, some species are more variable in measured size and will require additional sampling to accurately detect differences among groups. For example, Canary and Yelloweye Rockfish require greater sampling to detect smaller (10%) shifts in mean size compared with either Black or China Rockfish. This is due to the inherent increased variability in sizes observed in our data (i.e. both adult and juvenile Yelloweye Rockfishes caught by hook-and-line). Similarly, Lingcod may need greater levels of sampling to detect shifts in mean size - also a result of wide size ranges captured. This may mean that other statistical approaches, such as top-quartile size analysis - may be more powerful in detecting early changes in mean sizes. Importantly, while species may have similar levels of sampling needed to detect change, our actual collection rates suggest that some species will always be ‘undersampled’ for a robust statistical analysis. Both China and Black Rockfish need approximately 25 fish per sample group to detect 10% shifts in mean length. This is a sample size easily attained in each survey site each sample year for Black Rockfish. However, Redfish Rocks is the only location where China Rockfish have been caught in great enough numbers to do statistical analysis - and even then, data across multiple years likely needs to be pooled.
There have been several attempts to model realistic MPA outcomes and timelines using the California MPA network. Perkins et al (2021) estimated a 44% increase in Brown Rockfish populations over 25 years. Nickols et al (2019) and Kaplin et al (2019) both estimated minimums of 10 years to detect changes and for some species, up to 40+ years to rebuild size and age structures in protected areas. Unpublished CCFRP Data suggests that benthic and schooling rockfish species have been observed to increase 4-10x in relative abundance depending on the marine reserve. These results suggest that the results of this power analysis need to be put into context of natural interanual variability in abundance, and realistic projections of expected population size changes through time.The link between relative abundance or density of a species inside one survey area and the entire Oregon coast has not been formally established. Future work may try to better define what changes in our metrics of relative abundance are biologically relevant or important to fisheries management.
Perkins et al. (2021) also suggested that there is greater power to detect changes in species that were abundant to begin with - a result consistent with our simulation results. The results of this power analysis broadly suggest that surveys - across all tools - will only be useful in detecting temporal changes in abundance for a subset of the more abundant species observed or aggregate abundance. However, analysis such as species diversity and community composition will be better equipped to take advantage of the full range of species observed. These results also imply that multiple years of sampling will need to be combined to attain appropriate sample sizes for strong staticical power. This parallels the finding by Perkins et al. that greater power was achieve by combining data across multiple survey sites. Exploring the true cost of each survey unit (e.g. dollar cost of 1 ROV transect vs 1 hook-and-line survey) will help the ODFW Marine Reserves Program hone its survey efforts with the most efficient and cost-effective tools.
Finally, these analyses relied on the assumption of using a particular pairwise test to detect differences between two populations: the negative-binomial GLM. Future data explorations may deviate from this statistical framework and thereby change the underlying assumptions and results of a power analysis. This approach should be considered the most-sophisticated to date, but there will always be room for improvement and additional simulated complexities.
5 References
Hurlbert, Stuart H. “Pseudoreplication and the Design of Ecological Field Experiments.” Ecological Monographs, vol. 54, no. 2, Ecological Society of America, 1984, pp. 187-211, https://doi.org/10.2307/1942661.
Johnson PCD, Barry SJE, Ferguson HM, Muller P (2015) Power analysis for generalized linear mixed models in ecology and evolution. Methods Ecol Evol 6:133-142.
Kaplan KA, Yamane L, Botsford LW, Baskett ML, Hastings A, Worden S, White JW (2019) Setting expected timelines of fished population recovery for the adaptive management of a marine protected area network. Ecol Appl 29:1202-1220.
Nickols KJ, White JW, Malone D, Carr MH, Starr RM, Baskett ML, Hastings A, Botsford LW (2019) Setting ecological expectations for adaptive management of marine protected areas. J Appl Ecol 56:2376-2385.
Perkins, N. R., Prall, M., Chakraborty, A., White, J. W., Baskett, M. L., and Morgan, S. G.. 2021. Quantifying the statistical power of monitoring programs for marine protected areas. Ecological Applications 31( 1):e02215. 10.1002/eap.2215
Watson, J.L, and B.E. Huntington. 2021. Comparing angling, underwater visual census, and video methods to refine [fishery independent] long-term monitoring of a reef fish assemblage in a temperate marine reserve. Science Bulletin 2021-15. Oregon Department of Fish and Wildlife, Newport.