18 
Fishery Bulletin 1 13(1) 
pute MeanCount for every value of F=[l, 2, 200] 
frames. Therefore, we computed 1000 values for every 
MeanCount v p, a choice that expanded our previous 
nomenclature to MeanCountbyp, where b represents 
a single bootstrap replicate, v represents a particular 
video sampling event, and F represents the number of 
frames read. 
For each species, we quantified error in estimation 
using mean relative error (MRE). On the basis of 1000 
bootstrap replicates, we computed the MRE for each 
video in which a species was observed and for each 
number of frames read with the following equation: 
E 1000 
B= 1 
MRE vF — 
MeanCount b v F - MeanCount vtrue 
MeanCount true 
1000 
( 2 ) 
In addition to their use in determining MRE, we used 
the bootstrap replicates to compute the coefficient of 
variation (CV) for each video and for each number of 
frames read, CV v p. For graphical presentation, these 
CVs were scaled to their minima (which occurred at 
the largest sample size, F=200) to demonstrate the pro- 
portional decline in variability in estimates as sample 
size increased. To quantify the expected response, mean 
CVs across videos ( CVf) were related to the number of 
frames through the use of a power function, CV?=aF b , 
where a and b are parameters. These parameters were 
estimated in log-log space through linear regression, 
with the following equation: 
log(CVp) = a' + b log(F), (3) 
where a 1 = log(a). 
Then, the power function could be inverted to provide 
the number of frames necessary to achieve a desired 
mean CV: 
F = ^CV F /a. 
(4) 
Species richness 
The procedure for estimating species richness for pri- 
ority species was similar to the one for estimating 
MeanCount. However, when estimating species rich- 
ness, we used all 1543 videos. We first computed the 
true species richness observed in each video (i? v ,true) 
as the total number of priority species observed across 
all 1201 frames. Note that J? v ,true is not necessarily the 
true species richness at a particular site but rather 
is the species richness observed in an entire 20-min 
video. That true value was then estimated by tabulat- 
ing the species richness observed during each incre- 
ment of the number of frames read, F=[l, 2, ..., 200]. 
As before, uncertainty in the estimation was quantified 
with a bootstrap procedure with 1000 replicates, where 
each replicate (b) contained a set of 200 frames drawn 
at random and without replacement from the original 
1201 frames. Therefore, for each video, we generated 
1000 estimates of species richness for each number of 
frames read, Rb.v.F- 
Once computed, the estimates of species richness 
were used to evaluate how increasing the number of 
frames read (F) affected the detection of species known 
to be present in a video. For this evaluation, we used 
the average number of species detected across boot- 
strap replicates, scaled to the true value, with the fol- 
lowing equation: 
(saxA/ioop (5) 
T> 
Vftrue 
Therefore, P v p is a proportion equal to zero if no spe- 
cies known to be present were detected on average or 
equal to one if all possible species were detected on 
average. 
To better understand the estimates of species rich- 
ness, we related the probability of being observed to 
behavioral characteristics of those species in videos. 
Specifically, we considered 2 characteristics of each 
priority species (s): 1) the mean number of individuals 
(N s ) seen in a video and 2) the mean duration (D s ; in 
seconds) each individual was observed in the videos. 
These mean values for each species were taken across 
videos in which a particular species was present. To re- 
move rare species for which mean characteristics may 
be poorly estimated, species were included in this anal- 
ysis only if observed in at least 10 videos. We then used 
a generalized additive model (GAM) to relate N s and 
D s , and their interaction, to the proportion of bootstrap 
replicates (Y s ) in which species s was observed, from all 
videos where the species was present and where the 
number of frames read was F= 25. We used 25 frames 
in this study to provide a meaningful contrast across 
families in the probability of being observed; making 
such distinctions is important for detecting the ef- 
fects of predictor variables. All priority species were 
included in this analysis. Before fitting the GAM, the 
response variable Y s was transformed from probability 
space by using the arcsin squareroot transformation to 
achieve approximate normality, and predictor variables 
were taken in log space: 
arcsin = 
^(logOVg)) + g 2 (loglD s ))+ g 3 (log(N s ), (log(Z),)), 
( 6 ) 
where gi, g 2 , and gq represent spline functions. 
The GAM approach strikes a balance between more 
simple and more complicated models, and it was chosen 
for its flexibility and for providing a straightforward 
interpretation of results. The GAM was implemented 
in the R programming language, vers. 2.15.1 (R Core 
Team, 2012) with the mgcv library (Wood, 2006). For 
presentation, the fitted response was transformed 
back into probability space by squaring the sine of the 
response. 
Lastly, we summarized the mean duration in a 20-m 
video segment, mean number of individuals in each vid- 
