Sampling Design Optimization and 

Establishment of Baselines for 

Herpetofauna Arrays at the 

Point Loma Ecological Reserve 

 

 

Prepared for: 

 

National Park Service 

Cabrillo National Monument 

U.S. DEPARTMENT OF THE INTERIOR 

U.S. GEOLOGICAL SURVEY 

WESTERN ECOLOGICAL RESEARCH CENTER 

Photos by Chris Brown, U. S. Geological Survey 
ii 

Sampling Design Optimization and 

Establishment of Baselines for 

Herpetofauna Arrays at the 

Point Loma Ecological Reserve 

By Andrea J. Atkinson, Robert N. Fisher, Carlton J. Rochester, and Christopher W. Brown 

U.S. GEOLOGICAL SURVEY 

WESTERN ECOLOGICAL RESEARCH CENTER 

Prepared for: 

National Park Service 

Cabrillo National Monument 

San Diego Field Station 

USGS Western Ecological Research Center 

5745 Kearny Villa Road, Suite M 

San Diego, CA 92123 

Sacramento, California 

2003 
iii 

U.S. DEPARTMENT OF THE INTERIOR 

GALE A. NORTON, SECRETARY

U.S. GEOLOGICAL SURVEY 

Charles G. Groat, Director 

The use of firm, trade, or brand names in this report is for identification purposes only and does not constitute 

endorsement by the U.S. Geological Survey. 

For additional information, contact: 

Center Director 

Western Ecological Research Center 

U.S. Geological Survey 

7801 Folsom Blvd., Suite 101 

Sacramento, CA 95826 
Sampling Design Optimization iv U.S. Geological Survey 

and Establishment of Baselines

TABLE OF CONTENTS 

INTRODUCTION...................................................................................... 1 

OBJECTIVES ......................................................................................... 1 

 Primary Objectives ............................................................................. 1 

 Secondary Objective .......................................................................... 1 

METHODS ......................................................................................... 2 

 Pitfall trap array protocol and sampling locations ............................................ 2 

 Data used in analysis .......................................................................... 3 

 Historical species list ........................................................................... 3 

 Trend analysis and determination of number of arrays, number of sampling days per 

year, and timing of sampling periods ......................................................... 4 

Step 1) Select the variables to be analyzed ............................................. 4 

Step 2) Sorting variables into three analysis groups depending on the type of 

data involved ................................................................................ 5 

Step 3) Conduct regression analyses to test for existing trends ...................... 5 

Step 4) Conduct sample size calculations for the number of arrays needed to 

detect a change assuming different numbers of sampling days per year (i.e., 20, 

30, 40, and 50 sampling days per year) ................................................... 7 

Step 5) Develop preliminary 90%, 95% and 99% control limits where possible to 

determine when the capture rate during a new year is outside the range of 

variation experienced in the baseline years ............................................. 8 

Step 6) Determine optimum number of arrays, number of sampling days per year, 

and timing of sampling periods by examining the results ........................... 10 

 Analysis of associations between species and habitat variables ........................ 10 

RESULTS .............................................................................................. 11 

 Comparison of current species captured versus historical list ........................... 11 

 Trend analysis ................................................................................. 11 

 Optimization of sampling design ............................................................ 11 

Number of species detect per array (used as surrogate for species richness) ....... 11 

Orange-throated whiptails ................................................................ 11 

Striped racer, ring-necked snakes, and southern Pacific rattlesnake ................. 12 

Patterns of species captures at different arrays ......................................... 12 

Analysis of sample periods per year ...................................................... 12 

 Analysis of associations between species and habitat variables ......................... 13 

DISCUSSION ....................................................................................... 13 

 Declines in species and missing species ................................................... 13 

 Recommended sample design optimization ................................................ 14 

 Changes from five sampling periods to ten ................................................. 15 

 Biases in array locations ...................................................................... 15 

 Improvements to the protocol ................................................................ 16 

 Recommended future analyses ............................................................. 16 

 Using control limits to assist management ................................................. 17 

SUMMARY ......................................................................................... 19 

LITERATURE CITED .............................................................................. 20 
Sampling Design Optimization v U.S. Geological Survey 

and Establishment of Baselines

LIST OF TABLES 

 

Table 1. Start dates for 10-day sampling periods within each year. ....................... 3 

Table 2. Variables grouped by analysis Groups 1, 2, and 3. ................................ 6 

Table 3. Total herpetofauna captures per year for years 1996-2000. ....................... 22 

Table 4. Trend analysis and optimization analysis for average number of species 

detected, species evenness, total herpetofauna captures, and lizard captures per 

array per year. ................................................................... 23 

Table 5. Trend analysis and optimization analysis for orange-throated whiptail captures 

and juvenile orange-throated whiptail captures per array per year .......... 24 

Table 6. Calculation of 95% and 99% confidence levels for total number of snake 

captures per year, striped racer captures per year, and number of arrays 

occupied by snakes, striped racers only, orange-throated whiptails and 

juvenile orange-throated whiptails. ................................................. 25 

Table 7. Calculation of control limits for juvenile striped racers, ring-necked snakes 

and southern Pacific rattlesnake........................................................... 26 

Table 8. Captures during each day in sample period summed across all sampling 

periods from 1996-2000. ............................................................. 27 

Table 9. Total herpetofauna captures per array for years 1996-2000. ...................... 28 

Table 10. Striped racer captures by year and array for adults plus juveniles and juveniles 

 only. ....................................................................................... 29 

Table 11. Number of captures by sampling period from years 1996-2000. .................. 30 

Table 12. Dependent and independent variables in stepwise regression analysis. ......... 31 

Table 13. Environmental variables stepwise regression results. ........................... 32 

Table 14. List of species detected since 1995 versus historical records. .................. 33 

Table 15. Summary table of preliminary control limits for detecting changes from the 

 baseline years 1996-2000. ............................................................. 34 

 

 

LIST OF FIGURES 

 

Figure 1. Map of Point Loma Ecological Reserve herpetofauna arrays .................. 35 

Figure 2. Coefficient of variation (CV) for orange-throated whiptail for arrays with >2 

captures ................................................................................. 36 

Figure 3. Cumulative number of species detected across all 17 arrays at increasing 

number of sampling days per year .................................................. 37 

Figure 4. Number of new captures per day by sampling day within the sampling period... 38 

Figure 5. Juvenile orange-throated whiptails: Number of captures by year and array ...... 39 

 
Sampling Design Optimization 1 U.S. Geological Survey 

and Establishment of Baselines 

INTRODUCTION 

Cabrillo National Monument is the terminal point of the Point Loma Peninsula and part of the 

Point Loma Ecological Reserve, which protects the natural lands remaining on the peninsula in 

urban San Diego, California. This reserve is isolated from other natural lands by the ocean and 

urbanization, and is an effective island of rare habitats. These habitats include maritime 

succulent scrub, coastal sage scrub, and chaparral, and are the home to many sensitive species of 

plants and animals. Historically (through the 1930s), 19 species of reptiles and amphibians 

occurred on the peninsula, of which 6 are now considered sensitive at the state or federal level. 

Herpetofauna inventories were initiated by Robert Fisher of the U.S. Geological Survey (USGS) 

and Ted Case of the University of California at San Diego in August 1995, utilizing 17 arrays of 

pitfall traps and drift fences (Stokes et al., 2004). Data collection occurred from 1995 through 

2001 to collect baseline data for the development of a long-term monitoring plan (Fisher and 

Case, 2000). 

OBJECTIVES 

The National Park Service will be taking over the monitoring arrays for herpetofauna at the Point 

Loma Ecological Reserve from USGS. The purpose of this analysis is to examine the baseline 

data set and determine how many arrays, sampling periods, and days per sampling period are 

needed to assess whether herpetofauna diversity is being maintained on the reserve and suggest 

points for when management actions should be considered. The specific objectives listed below 

were identified by the reserve science manager as the ones most important to target. Although 

financial costs are a consideration in reducing the amount of sampling that is occurring, 

environmental impact is of greater concern. Erosion due to foot traffic is occurring at some 

sampling arrays placed on steeper slopes. Thus the benefits of maintaining the current number of 

sampling days and sampling arrays must be weighed against possible environmental costs. An 

additional constraint is that although reductions in sampling effort would be considered, 

increases in the number of arrays are not likely to be funded. 

Primary objectives 

1) What species are currently found at Point Loma Ecological Reserve versus species that 

have been historically found in this area? 

2) Are any of the targeted species showing significant declines at present? 

3) How many arrays, sampling periods, and sampling days per sampling period would be 

needed to detect a 

• 30% drop in species richness compared with the baseline years 1996-2000, 

• 30% drop in the relative abundance of orange-throated whiptail (Cnemidophorus 

hyperythrus) and striped racer (Masticophis lateralis), compared with the baseline 

years. 

• some measure of drop in abundance or occupancy of western ring-necked snake 

(Diadophis punctatus) and southern Pacific rattlesnake (Crotalus viridis) compared 

with the baseline years. 

Secondary objective 

4) What relationships are found between targeted species and environmental variables? 
Sampling Design Optimization 2 U.S. Geological Survey 

and Establishment of Baselines 

METHODS 

Pitfall trap array protocol and sampling locations 

The draft herpetofauna pitfall trap array protocol, techniques, and design are described in 

Stokes et al. (2004). To better understand the status and distribution of reptiles and amphibians 

throughout the Point Loma Ecological Reserve, pitfall trap array sites were chosen to represent 

the range of habitats found in the peninsula. Point Loma was stratified by vegetation, and the 

numbers of arrays were placed in each habitat type in approximate proportion to the proportion 

of that habitat type present, with the additional inclusion of unique landscape features if present 

(e.g., open sandy washes). The primary components of native vegetation at Point Loma include 

baccharis, black sage, buckwheat, cacti, chamise, cliffspurge, and manzanita and vary depending 

on aspect, exposure and slope, substrate, and disturbance. 

Several additional considerations affected array site locations including feasibility, access, 

visibility, habitat sensitivity. Arrays could not be placed on steep slopes or in areas where it was 

not possible to bury 5-gallon buckets and drift fencing in the ground. Soil type, however, did not 

limit array location, because the substrates on the peninsula include mostly soils, sand and 

sandstone deposits. Arrays were placed near roads and trails so that they could be reasonably 

accessed by surveyors on a daily basis without trampling large amounts of native vegetation. 

Sensitivity to habitat was considered. Arrays were built with caution to impact native vegetation 

as little as possible, with arms bent around plants rather than running through them. Visibility of 

the array to park visitors was another important factor. To minimize visitation to the arrays by 

park visitors, arrays within the park were placed on slopes facing away from trails and in areas 

that had sufficient vegetation to hide the array. 

Although the locations of arrays within vegetation types were not chosen with strict random 

procedures, the area of Point Loma is so small and so much of the terrain has steep slopes that 

arrays were placed in nearly all locations where it was physically feasible to do so and access 

was allowed. The sampling design contains some admitted biases, since areas with steep slopes 

are not sampled and areas that are far from roads and trails may be underrepresented. However, 

given the small size of the park, the effects of these biases are expected to be minimal. Locations 

of the 17 pitfall trap arrays are shown in Figure 1. 

Steps were taken to minimize direct impacts by park visitors on the survey efforts, including 

careful array placement as previously mentioned. Trails to arrays were often covered with brush 

to discourage off-trail travel, and information labels were placed on the array equipment. 

However, the large numbers of visitors and relatively small size of the park resulted in trails and 

roads being heavily traveled. Arrays #13-17 are located near a popular trail. Arrays #13 and #14 

are directly below the Old Lighthouse, which attracts many visitors. Arrays #1-4 are near the 

tide pools, another area with high traffic. Although not documented, it is likely that visitation 

rates to these arrays are much greater than to arrays #5-12, which require security clearance to be 

accessed. 

The sampling protocol may have some inherent biases towards capturing fauna that are very 

active and mobile and travel on the surface of the ground, rather than those that move 

infrequently or travel beneath the soil surface. The traps are passive, not baited. For animals to 

be captured by the traps, the animals must be active enough to encounter and enter the traps. In 

general, animals that move around more actively through an area may be more likely to 
Sampling Design Optimization 3 U.S. Geological Survey 

and Establishment of Baselines 

encounter the traps. For example, the striped racer, an active forager, may move around in an 

area more than a southern Pacific rattlesnake, generally a sit-and-wait predator. Live traps 

similar to the funnel traps used in this survey are documented to work better with medium-sized 

snakes. Larger-bodied snakes including gopher snakes and rattlesnakes are more commonly 

detected by visual observation than captured (Fitch, 1992). Furthermore, the trap openings are 

above ground or on the immediate surface. Animals that spend larger amounts of time 

underground, such as the silvery legless lizard (Anniella pulchra), may encounter the trap 

openings less frequently than other species. 

Data used in analysis 

Analyses were conducted on data collected from the 17 existing herpetofauna arrays at the 

reserve during the years 1996–2000. Each year consisted of 5 sampling periods (see Table 1). 

Although data are available for years 1995 and 2001, these data did not consist of a complete set 

of sampling periods at the time of analysis and thus are not included in this analysis. 

Table 1. Start dates for 10-day sampling periods within each year. 

Year 

Period within year 1996 1997 1998 1999 2000 

1 2/20 2/18 2/3 1/27 2/9 

2 4/23 4/22 3/31 4/6 4/5 

3 6/25 6/24 6/2 6/8 6/6 

4 8/27 9/3 8/4 8/18 8/29 

5 10/29 10/28 10/6 11/10 11/10 

Data from all 5 sampling periods within each year were combined into a total capture rate per 

array per year for analysis. Although sampling dates were not exactly the same in all years, they 

were roughly comparable. Animals recaptured at the same array within the same 10-day 

sampling period were only counted once. 

It should be noted that 1998 was considered an El Niño year, with associated increases in 

rainfall. The years 1996, 1999, and 2000 were considered drought years with very low rainfall. 

Historical species list 

A historical list of species present or presumed present at Point Loma was compiled by 

examining species records at the San Diego Natural History Museum, California Academy of 

Sciences, Los Angeles County Museum, University of California at Berkeley Museum of 

Vertebrate Zoology, and the field notes and species maps of Laurence M. Klauber (unpublished 

notes from San Diego Natural History Museum). 
Sampling Design Optimization 4 U.S. Geological Survey 

and Establishment of Baselines 

Trend analysis and determination of number of arrays, number of sampling days per year, 

and timing of sampling periods 

The overall process to optimize the sampling design was in fact multi-dimensional. The level of 

sampling effort could be affected in three ways: 

• number of arrays 

• number of sampling days per year 

• timing of sampling throughout the year (i.e., number and timing of sampling periods 

and days per sample period) 

Additional factors that affected the final result were the species and variables of interest plus the 

acceptable level of Type I error (α) and Type II error (β =1-Power) (described further below). 

The process used to optimize the sampling design and identify potential management thresholds 

was broken into six steps. These included: 

1) Select the variables to be analyzed. 

2) Sort variables into three analysis groups, depending on the type of data involved. 

3) Conduct regression analyses to test for existing trends. 

4) Conduct sample size calculations for the number of arrays needed to detect a change, 

assuming different numbers of sampling days per year (i.e., 20, 30, 40, and 50 sampling 

days per year). 

5) Develop preliminary 90%, 95% and 99% control limits, where possible, to determine 

when the capture rate during a new year is outside the range of variation experienced in 

the baseline years. 

6) Determine optimum number of arrays, number of sampling days per year, and timing of 

sampling periods by examining the results. 

Step 1) Select the variables to be analyzed.

The variables analyzed include 

• Number of species detected per array (used as surrogate for species richness) 

• Simpson’s measure of species evenness 1

• Total herpetofauna captures (lizards, snakes, and salamanders) 

• Lizard captures 

• Snake 

- captures or sightings 

- # arrays with 1 or more snake captures 

• Orange-throated whiptail (Cnemidophorus hyperythrus) 

- Total captures 

- Juveniles captures 

- # arrays with 1 or more captures 

- # arrays with 1 or more juvenile captures 

 

1

 Simpson’s evenness is a measure that evaluates the degree to which all species present are equally common (i.e., is the 

community dominated by a few species and all other species put in rare occurrences, or are all species present equally common).

Simpson’s evenness is calculated as E = (1 /Σ1

s

 (pi )

2

) / s 

where s = # species in the sample and 

pi

= proportion of total sample belonging to the ith species (Krebs, 1999, p.449)
Sampling Design Optimization 5 U.S. Geological Survey 

and Establishment of Baselines 

• Striped racer (Masticophis lateralis) 

- captures or sightings 

- juvenile captures or sightings 

- # arrays with 1 or more striped racer captures 

• Ring-necked snake (Diadophis punctatus) captures or sightings 

• Southern Pacific rattlesnake (Crotalus viridis) captures or sightings 

Step 2) Sorting variables into three analysis groups depending on the type of data involved.

Variables were separated into three different “analysis groups” depending on the number of 

captures that occurred and the distributions of the variables (see Table 2). 

Group 1 – Variables in this group had large numbers of captures at all or nearly all arrays. It 

was possible to analyze these data using averages per array per year, and these were the 

variables used to conduct sample size calculations. Analyses for this group included a) a 

regression analysis in which arrays were treated as class variables and years were treated as a 

regression variable, b) sample size calculations, and c) calculation of control limits. 

Group 2 – This group involved species such as striped racer which had much smaller 

numbers of captures than Group 1 species, even when captures were summed across all 

arrays (15 or less captures per year). This group of variables consists of either i) total 

number of captures summed across all arrays or ii) the number of arrays at which an 

organism was present. Analyses for this group included: a) a regression analysis and b) 

calculation of control limits. 

Group 3 – This group involves species with very low capture rates summed across all arrays 

per year (i.e., 3 or less captures per year). Analysis included calculation of the control limits 

for the observed number of years with zero captures. 

Since variance strongly increased with number of captures, a square root transformation was 

used on most variables in Group 1 with the exception of species evenness. 

Sample size analyses on orange-throated whiptail were performed on all arrays and then a subset 

of arrays #1-4, 9-10, and 13-17. Arrays #5-8 and 11-12 were dropped from the analysis, since 

they had fewer than 2 captures across all 5 years and this artificially inflated the variance and 

coefficient of variation (CV) during sample size calculations. 

Although separate analyses were not conducted on all species, the number of captures per year 

for all species are included in Table 3. 

Step 3) Conduct regression analyses to test for existing trends. 

A regression analysis was performed on variables in Groups 1 and 2 to test for trends occurring 

in the existing data sets. This was both of interest biologically and as a necessary prerequisite for 

calculating control limits in the next section. Results are given in Tables 4 and 5. 
Sampling Design Optimization 6 U.S. Geological Survey 

and Establishment of Baselines Table 2. Variables grouped by analysis Groups 1, 2, and 3. Group 1 was analyzed by year and array. Direct sample size calculations were performed on this group. Group 2 variables were summed across arrays and were analyzed as total captures per year or number of arrays with organism present. Group 3 consisted of small numbers of captures (i.e., 3 or fewer captures per year) and were analyzed using Poisson probability calculations. Analysis Group Variable name Specific variables Data transformation Number of species detected # species detected / array / year Square root 

Simpson’s evenness Evenness / array / year Herpetofauna capture rates Captures / array / year Square root Lizard capture rates Captures / array / year Square root 

Captures / array / year (all arrays included) Square root Captures / array / year (arrays 1-4,9-10,13-17) Square root 

1 

Analysis performed by array and year; - Sample size calculations; - Regression analysis; 

- Control limits Orange-throated whiptails capture rates 

Juvenile captures/array/year (arrays 1-4,9-10,13-17) Square root 

# arrays with whiptails present Orange-throated whiptails # arrays with juveniles present Captures / year Snake capture rates # arrays with snakes present Captures / year 

2 

Analysis performed on totals or percentages across all arrays by year; - Regression analysis; - Control limits Striped racer capture rates # arrays with racers present 

Striped racers – juvenile capture rates Captures / year Ring-necked snakes Captures / year 

3 

Analysis performed on totals across all arrays by year; - Estimated probabilities of 

consecutive years with zero captures 

Southern pacific rattlesnake Captures / year 
Sampling Design Optimization 7 U.S. Geological Survey 

and Establishment of Baselines 

Step 4) Conduct sample size calculations for the number of arrays needed to detect a change 

assuming different numbers of sampling days per year (i.e., 20, 30, 40, and 50 sampling days per 

year).

Sample size calculations (i.e., number of arrays) were done directly for variables in Group 1 and 

indirectly for Groups 2 and 3. For Group 2, confidence intervals were calculated to determine if 

there was any power to detect change. If the lower confidence limit is a 1 or 0, then the number 

of arrays was considered too small to detect any change whatsoever. Group 3 calculations were 

also very indirect. In Group 3, the probabilities for increasing numbers of years with zero 

captures were calculated. If this number of years with zero captures seemed exceedingly high, 

then a higher level of effort would be needed to realistically track the species. Thus, although an 

assessment of the power to detect differences could be made for Group 1, no assessment of 

power could be made for Groups 2 and 3 variables. 

To detect a change in the future, the recommended method of analysis for Group 1 variables is to 

a) conduct an analysis of variance and perform a contrast analysis that compares any future 

year’s data with the baseline set of 5 years, and b) conduct a regression analysis. The analysis of 

variance offers greater power for detecting future trends, if no trend is occurring in the baseline 

data set. The regression analysis offers greater power for detecting a trend, if a trend is occurring 

in the baseline data set. 

To calculate the recommended sample size, an analysis of variance was performed in which both 

years and arrays were included as class variables (i.e., each year was treated as a separate class 

rather than as a single regression variable). The error variance (i.e., the mean square error or 

MSE), from this analysis is used to estimate sample sizes. The following equation: 

( ) 2

/ 2

2 2 / * ( ) d Zα Zβ n ≥ s + (Steel and Torrie, 1980, p.232) Eqn 1.1

was converted into a more easily used format by dividing both s and d by the mean x for ease of 

calculation. Z values were replaced by t-values as recommended by Geng and Hills (1989) when 

dealing with potentially small sample sizes. 

( ) 2

/ 2, ,

2 2 / *( ) df df n CV D t t ≥ α + β (Geng and Hills, 1989, p.86-87) Eqn 1.2

where n = number of arrays 

CV= s / x = Coefficient of Variation

D= d / x = proportional difference from mean (i.e., a 30% drop in the mean) 

x = sample mean of all 5 years

s

2

 = mean square error (MSE) from the analysis of variance

d = difference from the mean

df = error degrees of freedom = (number of years – 1) * (number of arrays – 1) 

α = probability of a Type I error

β = probability of a Type II error, (Note: Power = 1- β)

Note: A Type I error is the conclusion that a capture rate in a new year is different from the 

baseline when in fact it is not. A Type II error is the conclusion that a capture rate in a new year 

is not different from the baseline years when in fact it is different. 
Sampling Design Optimization 8 U.S. Geological Survey 

and Establishment of Baselines 

Sample size calculations were conducted for α =0.05 and β =0.10, 0.20, and 0.30 (i.e., power 

levels of 1- β = 90%, 80%, and 70%, respectively). All sample size calculations for Group 1 

variables were based on two-tailed tests, since it was assumed that managers would be interested 

and likely to report increases as well as declines of species of interest. 

To evaluate the effect of reducing the number of sampling days, four versions of the data were 

created for each species including all 10 days, and the first 8 days, 6 days, and 4 days of each 

sampling period, resulting in data sets of 50, 40, 30, or 20 sampling days per year. Separate 

sample size calculations were conducted on each data set on each Group 1 variable. These results 

are shown in Tables 4 and 5. 

Based upon the results, orange-throated whiptail capture rates appeared to be a driving factor in 

determining sample size. Figure 2 shows how the Coefficient of Variation for orange-throated 

whiptail captures varies in response to number of sampling days per year. 

Step 5) Develop preliminary 90%, 95% and 99% control limits where possible to determine when 

the capture rate during a new year is outside the range of variation experienced in the baseline 

years.

Control limits is a technique used in industrial quality control to monitor whether a process such 

as the frequency of defective units (e.g., toys with defective packaging) is under “control” (i.e., 

within acceptable limits) without having to continually re-run statistical analyses. We are 

adapting these methods to allow easier analysis by reserve managers for Group 2 variables 

(McBean and Rovers, 1998; Manly, 2001; Montgomery, 2001). Analysis of Group 1 variables 

should preferably use an analysis of variance coupled with a contrast analysis to achieve greater 

sensitivity. However, if a year falls outside the control limits for Group 1 variables, it will also be 

found to be significantly different in an analysis of variance. Thus, the control limits can be used 

as a coarse guide for Group 1 variables, in addition to Groups 2 and 3. All control limits were 

calculated as two-tailed control limits, with the exception of Group 3 variables which were 

calculated as one-tailed only, i.e. only able to detect declines. 

Frequently, these control limits are calculated from 90%, 95% and 99% confidence limits. 

Calculation of these confidence limits varies, depending on whether the data are normally 

distributed or are Poisson distributed. 

 Normal distribution 

Confidence Limits = x ± Zα/2 S (based on Montgomery, 1998, p. 207-208) Eqn 1.3 

 Poisson distribution 

Lower limit = χ2

(1- α/2, ν ) / 2 where ν = 2* x 

Upper limit = χ2

(α/2, ν ) / 2 where ν = 2*( x +1) (Zar, 1999, p.574-574) Eqn 1.4

Since only five years of data were used to create these control limits, they should be considered 

“preliminary” control limits. 

It’s important to note that the calculation of these control limits and number of years of zero 

captures are dependent on the assumption that variation observed during the baseline 5 years was 
Sampling Design Optimization 9 U.S. Geological Survey 

and Establishment of Baselines 

due to normal fluctuations and not due to longer-term directional trends in the target resource. If 

a long-term trend occurred during this period, then these limits are not valid. Any data 

transformations performed prior to calculation of these limits must also be applied to data 

collected in the future before comparing with these limits. 

Group 1 control limits 

All the control limits for Group 1 variables were calculated using equation 1.3 and are based 

upon the average capture rate per array per year for each of the five years. 

If the average per array in some future year falls outside the control limits, then those data are 

considered significantly different from the baseline. Please note that such averages must be 

calculated from appropriately transformed data as mentioned in the tables. Control limits are 

given in Tables 4 and 5. 

Group 2 control limits 

For Group 2 variables, the control limits given in this report, coupled with regression analyses 

will be the primary ways of determining whether a new year of data collection is considered 

significantly different from the baseline 5 years. Since these data consist primarily of small 

numbers in which the variance is approximately equal to the mean, the Poisson control limits 

were most appropriate (i.e., Equation 1.4). The exception was number of arrays with orangethroated whiptail present which had such a small variance that the normal distribution calculation 

was more appropriate, (i.e., Equation 1.3). Control limits are given in Table 6. 

Group 3 control limits: Number of years with zero captures 

Analyses for this group consisted of calculating the probability of observing two or more 

consecutive years with zero captures based upon a Poisson distribution. Group 3 consisted of 

species with 8 or fewer captures summed across all 5 years, or 3 or fewer captures in any single 

year (i.e., southern Pacific rattlesnake, ring-necked snake, and juvenile striped racers; see Table 

7). Snakes observed while walking to and from the arrays were included under the assumption 

that the amount of effort was roughly equivalent across years. If the number of years with zero 

captures at the 5% probability level was unrealistically high, then a larger sample size would be 

recommended. 

Probability of zero captures per array = P(0) = e-μ (Steel and Torrie, 1980,p.528) Eqn 1.5

Probability of multiple zero captures = (e-μ ) n · y

μ = true population average number of captures per array per year assuming an infinite number 

of years (this analysis substituted x , the average across all arrays and 5 years, for μ ) 

n = number of arrays 

y = number of years 

Control limits were calculated based on when the probability for a given number of consecutive 

years of zero captures fell below 5%. One capture was added and subtracted from the 

calculations to determine how robust the limit was, and if the number of years calculated 

changed, the control limits were expanded accordingly. The control limit range given represents 

the number of years with zero captures when the expected probability is below 5% (see Table 7). 

These control limits should be used with extreme caution and wisdom, since they were calculated 

based on an exceedingly small samples. 
Sampling Design Optimization 10 U.S. Geological Survey 

and Establishment of Baselines 

Step 6) Determine optimum number of arrays, number of sampling days per year, and timing of 

sampling periods by examining the results.

The following factors were taken into consideration in optimizing the sampling design: 

• Optimal design needed to assess trends in number of species detected per array, orangethroated whiptails, striped racers, ring-necked snakes, and southern Pacific rattlesnakes.

To start determining the optimum number of arrays and number of sampling days per 

year required looking at the results of all the response variables and determining which 

would require the highest number of arrays to detect a desired level of change (see Tables 

4, 5, 6, and 7). In addition, species that appeared to be experiencing declines during 

baseline years were flagged, because the sampling design would need to continue 

tracking these species effectively (e.g., striped racer). Other factors, such as the time 

required to detect rarer species under differing numbers of sampling days per year (see 

Figure 3) and the decline in the capture rate late in the sampling period compared with 

early in the sampling period, were also taken into account (see Figure 4 and Table 8). 

• Species captured at each array. Not all species were captured consistently at all arrays. 

The number of captures of each species at each array is shown in Table 9, and in greater 

detail for striped racer in Table 10. Since the number of arrays was so small, rather than 

randomly selecting arrays to eliminate, arrays were identified that were consistently 

yielding low captures of targeted species and expected to continue doing so in the future. 

• Capture rates during different sampling periods. The number and timing of sampling 

periods per year were examined qualitatively after the other sample size calculations were 

conducted (see Table 11) to determine if some sampling periods could be eliminated 

without affecting results, e.g. sampling periods that consistently yielded low captures for 

all species. 

All of these factors were taken into consideration for making final recommendations to optimize 

the sampling design. 

Analysis of associations between species and habitat variables 

A stepwise forward/backward regression analysis was conducted to determine the variables most 

strongly correlated with the distribution of various species and categories of fauna. The variables 

used are shown in Table 12 and are defined more completely in Fisher et al. (2002) and Case and 

Fisher (2001). The data set was expanded to include all data collected for 1995-2001. 

For “number of lizards and salamanders” and “number of orange-throated whiptails,” the 

analysis was run first with environmental variables only, and then a second time with the 

Argentine ant density category included. 

For the “number of snake captures” and “number of striped racer captures only,” the analysis 

was run including environmental variables plus the number of small mammals captured, the 

number lizards and salamanders captured, and Argentine ant density category as possible 

independent variables. 

In our analysis of Argentine ant density category, only environmental variables were considered 

as potential explanatory variables. Results are shown in Table 13. 

 
Sampling Design Optimization 11 U.S. Geological Survey 

and Establishment of Baselines 

RESULTS 

Comparison of current species captured versus historical list 

Table 14 contains a list of species currently found during sampling at Point Loma versus those 

found historically (see page 3). Only 12 of the 19 historic species were detected between 1995 

and 2001 after 294 sampling days and 1696 herpetofauna observations. Night Snake (Hypsiglena 

torquata) was not known from museum records but was added to the historical species list when 

a single individual was found in 1997 by a park ranger (i.e. not at the pitfall traps). This is a very 

cryptic species which is difficult to detect and could easily have been missed during earlier 

surveys, and thus is considered to have historically occurred in this area. Further targeted surveys 

found only one more individual in 2001 (Yang and Fisher, 2003). Neither detection occurred as 

part of the systematic sampling addressed in this report. Two occurrences of coastal rosy boa 

(Charina trivirgata) were recorded. Both were along a roadside and are thought to have been 

released pets (and probably the same released pet), based on its historic absence and high 

detectability (Brown and Fisher, 2002). A radio-tracking study included this individual and 

found it had the largest home range of any of the rosy boas tracked (Rochester et al, 2001), 

another indication that this was probably an introduced animal. Neither the night snake or the 

coastal rosy boa were included in this analysis. 

Trend analysis 

Significant negative trends were detected during the baseline period (1996-2000) for the 

following variables: numbers of species detected per array per year (p= 0.0370), annual captures 

of striped racer (p= 0.0079) and number of arrays with striped racer present (p= 0.0418) (see 

Tables 3, 4 and 6). In the case of striped racer, however, this decline was very marked with 12 

individuals being found in 1996 and only 4 being found in 2000 (see Tables 6 and 9). The 

declining number of species detected per year may be explained by demographic responses to 

climatic variation during the past decade. Both 1995 and 1998 were El Niño years, while 1999 

and 2000 were both below average rainfall years (see Table 3). 

Optimization of Sampling Design 

Number of species detected per array (used as surrogate for species richness) 

Only 5 arrays sampled 50 days per year or 8 arrays sampled 20 days per year would be needed to 

detect a decline of 30% with a power of 80% (see Table 4). 

However, decreases in the number of sampling days per year can increase the number of years 

needed to detect rare species (see Figure 3). 

Orange-throated whiptails 

Given the high level of variance in orange-throated whiptail capture rates compared with the 

mean (CV=44% with all arrays or 32% with only arrays with >2 captures), detection of a decline 

of 30%, as originally requested by the reserve science manager, would require increasing the 

number of arrays (see Table 5). However, a decline of 40% could be detected with 80% power 

with the 11 arrays that currently capture high numbers of whiptails (i.e., arrays #1-4, 9-10, 13-

17). If the number of sampling days per year were reduced from 50 to 40 sampling days, these 11 

arrays could detect a decline of approximately 45% with 80% power. Any further decrease in 

sampling effort will result in increases in the CV and will require increasing the number of arrays 

(see Figure 2). 
Sampling Design Optimization 12 U.S. Geological Survey 

and Establishment of Baselines 

Juvenile orange-throated whiptails have a very high level of variance from array to array and 

from year to year (see Figure 5). The 11 arrays with high orange-throated whiptail captures will 

only detect a 65% decline with 80% power even when sampled 50 days per year. At 40 sampling 

days per year, those 11 arrays will detect a 75% decline with 80% power. 

Thus, to detect changes in orange-throated whiptail capture rates, the 11 arrays which have high 

capture rates should be maintained (i.e., arrays #1-4, 9-10, 13-17). The number of sampling 

days per year should be kept to 40-50 days per year. 

Striped racer, ring-necked snakes, and southern Pacific rattlesnake 

Given the small number of captures of striped racer, ring-necked snake, and southern Pacific 

rattlesnake, only a small reduction in sampling effort, if any, would be advised to maintain any 

ability to detect changes in these species, especially since there is concern that striped racer 

abundance may be declining (see Tables 6, 7, and 10). Any arrays that are eliminated should not 

include arrays with large numbers of captures of any of these snake species (see Table 9). 

Patterns of species captures at different arrays

Maintaining the ability to detect changes in capture rates for orange-throated whiptail, striped 

racer, ring-necked snake, and southern Pacific rattlesnake appears to be driving the sampling 

design optimization. 

The only array that showed no captures of any snakes or orange-throated whiptails is array #6 

(see Table 9). Arrays #2 and 16 had no striped racer captures but did have high capture rates of 

orange-throated whiptails. Array #12 had only one capture of orange-throated whiptail and only 

one capture of striped racer in 1996. Arrays #5, 7, 8, and 11 all had 3-4 captures of striped racer 

and ring-necked snakes and thus should be maintained, if the ability to detect changes in these 

snake species is desired. 

Analysis of sample periods per year

In order to maintain captures of striped racers and also the potential to detect all species, 

sampling should continue during all 5 sample periods. The number of species captured in each 

sampling period is included in Table 11. Based upon the sampling design optimization analysis, 

capture rates for orange-throated whiptail, striped racer snake, ring-necked snake, and southern 

Pacific rattlesnake drove the determination of the number of arrays necessary. Thus, any 

reduction or alterations to the number of sample periods per year must not increase variability in 

captures of these four species. None of these species was captured in large numbers in the 

Jan/Feb sampling period (period 1). Eliminating period 1 would have little impact on analysis of 

orange-throated whiptail but would possibly affect capture rates of striped racer. In addition, 

Jan/Feb is the primary period when the garden slender salamander is collected. If tracking at 

least the continued presence of the garden slender salamander is important, then some sampling 

needs to be maintained in this period. 

Note: Although the only detection of the silvery legless lizard occurred during the Jan/Feb 

sampling period in this data set, it was also captured once each in 1995 and 2001 during summer, 

so its detection is not limited to winter months.
Sampling Design Optimization 13 U.S. Geological Survey 

and Establishment of Baselines 

Analysis of associations between species and habitat variables

The results of the stepwise regression are given in Table 13. Only a few highlights are 

mentioned here, as a more comprehensive analysis is planned for 2004 using data from multiple 

sites. The overall number of snakes captured was positively associated with percent cover but 

negatively associated with canopy height. However, striped racer capture rates were most tightly 

correlated with the number of small mammals, lizards, and salamanders captured at the same 

array. Argentine ants were positively associated with percent grass cover and negatively 

associated with percent coastal sage scrub cover. When the density category of introduced 

Argentine ants (1, 2 or 3) was added to the analysis, this variable replaced one or more 

environmental variables in the regression equations for number of lizards and salamanders, and 

for number of orange-throated whiptails. Thus, higher densities of Argentine ants were 

negatively associated with lizard and orange-throated whiptail capture rates. 

DISCUSSION 

Declines in species and missing species 

Only 12 of the 19 historically reported species were detected during the pitfall trap array 

sampling during 1995-2001. Only 11 of these species were represented in the 1996-2000 data 

used to determine necessary sample sizes (Table 14). A single night snake (Hypsiglena 

torquata) was found in a bucket in array #10 in 2001. Species that were not detected include 

Coronado skink (Eumeces skiltonianus), coast horned lizard (Phrynosoma coronatum), 

California glossy snake (Arizona elegans), yellow-bellied racer (Coluber constrictor), red 

diamond rattlesnake (Crotalus exsul ruber), coachwhip/red racer (Masticophis flagellum), and 

long-nose snake (Rhinocheilus lecontei). All of these species have been detected using pitfall 

trap arrays or walking to and from these arrays at other sites in southern California, although the 

number of red diamond rattlesnakes, long-nose snakes, California glossy snakes, and night 

snakes generally tended to be detected in low numbers (Fisher and Case, 2000b). Thus the failure 

to detect these species at the Point Loma Ecological Reserve is a concern and suggests that 36% 

of the herpetofauna species that were historically detectable are either missing or present in very 

low numbers below thresholds detectable by this large sampling effort (i.e., 294 sampling days 

across 17 arrays). 

The sharp downward trend (p= 0.0079) in striped racer (Masticophis lateralis) captures from 

1996-2000 is a concern. Three different hypotheses have been put forward: 1) the species is in 

decline at Point Loma Ecological Reserve, 2) the snakes are learning to avoid the traps, 3) the 

decline is an artifact of 1998, an El Niño year, preceding 2000, a drought year, thereby creating a 

downward trend in captures that is a response to annual rainfall variation rather than a larger 

trend, or some combination thereof. 

Table 10 shows the pattern of striped racer captures by array and the pattern of juvenile captures. 

The pattern does not immediately suggest that learning by snakes is occurring. However, a larger 

scale analysis of Robert Fisher’s data of herpetofauna captured from pitfall trap arrays 

throughout San Diego County will occur in 2004 and the data can be examined to see if other 

sites show similar immediate declines in striped racers after initiation of sampling. Another way 

of separating these hypotheses is to pay particular attention to juvenile striped racers and see if 

they are experiencing a decline, since juveniles would not have experience with the traps. 
Sampling Design Optimization 14 U.S. Geological Survey 

and Establishment of Baselines 

Regardless, the capture rates of striped racers should be closely watched in the near future to see 

if this apparent decline continues. 

The slight negative trend in the number of species detected per array (p= 0.0370) and marginal 

trend in number of arrays with orange-throated whiptail present (p= 0.0805) should be watched 

but may be an artifact of the 1998 El Niño year preceding the 2000 drought year (see Tables 4 

and 6). 

The stepwise regression analysis showed that Argentine ant density category was negatively 

associated with capture rates of lizards and salamanders in total (p=0.0004) and for orangethroated whiptail in particular (p=0.0008) (see Table 13). This result is similar to the findings 

that Argentine ants have negative impacts on shrews (Laakkonen et al., 2001) and coastal horned 

lizard (Fisher et al., 2002) and are frequently associated with urban edges. Management of 

Argentine ants to prevent establishment and expansion throughout the reserve is thus assumed to 

be important for maintaining native herpetofauna species diversity. 

Brown and Fisher (2002) recommended management strategies to try and prevent further 

declines in herpetofauna species at the Point Loma Ecological Reserve, including suggestions for 

curbing road mortality, protecting continuous habitat, reducing pet collection and disturbance of 

fauna, public education regarding rattlesnakes, controlling invasive vegetation such as ice plants 

and eucalyptus, controlling irrigation runoff into reserve which may promote spread of argentine 

ants, and encouraging pet owners to keep cats indoors. 

Recommended sample design optimization 

The ability to detect changes in orange-throated whiptails and in snake species such as striped 

racer, ring-necked snake, and southern Pacific rattlesnake were what most strongly influenced 

recommendations regarding sampling design. In short, the recommendations are: 

• Reduce the number of sampling days per year from 50 to 40. 

• Eliminate arrays #6 and 12 

Maintaining all 11 arrays at which orange-throated whiptails are currently captured in large 

numbers is recommended, as this will allow detection of trends in orange-throated whiptail 

captures of 40% - 50% with a power of 80% (1-β). Specifically these are arrays #1-4, 9, 10, 13-

17 (see Table 9). The variables of number of species detected per array and total herpetofauna 

capture rates required even fewer numbers of arrays to detect trends (see Tables 4 and 5). 

However, so few snake captures were occurring (63 across all 5 years), that only small changes 

in the sampling design would be advisable to maintain an ability to detect trends in snakes, 

especially since there is concern that striped racer may be showing a decline. Only arrays with 

little to no snake captures should be considered for elimination. And the number of sampling 

days per year should not be reduced below 40 unless the ability to detect snakes can somehow be 

improved. 

Looking at the pattern of species captured across arrays, only arrays # 6 and 12 should be 

considered for elimination at this time. Neither of these arrays captured orange-throated 

whiptails or snakes in large numbers and both are spatially redundant with nearby arrays. 

Captures at array #6 had the lowest species detected of all the arrays, and array #12 had the 

lowest overall capture rate of all the arrays. Array #6 is placed closely in between arrays #5 and 
Sampling Design Optimization 15 U.S. Geological Survey 

and Establishment of Baselines 

#7 but features fewer habitat elements than the other two arrays. While all three arrays are 

located in the same sandy wash habitat, arrays #5 and 7 have arms located in chaparral elements 

that are not immediately proximate to array #6. While array #6 may be useful in determining 

movements across an open wash from arrays #5 or 7 if recapture rates are high enough, the wash 

is a sensitive area, containing a population of the protected Orcutt's Spineflower (Chorizanthe 

orcuttiana). Removing array #6 will have little effect on detecting trends in the targeted 

herpetofauna species and will prevent any unintended impacts to the rare plant by researchers 

walking through the area. Array #12 has the lowest number of herpetofauna captures of any of 

the arrays and is located near arrays #10 and #11 and so is somewhat redundant in spatial 

coverage. Only 1 striped racer capture occurred at array #12 and none at array #6 and elimination 

of these arrays shouldn’t affect the control limits for this species. No other snake species were 

captured at these arrays. Arrays #5, 7, 8, and 11 all had one or fewer captures of orange-throated 

whiptails. However they all had at least 3 snake captures and should therefore be maintained at 

present. 

The pattern of species captures changes depending on the season. The garden slender salamander 

(Batrachoseps major) was primarily captured during January-February with no captures in JuneSeptember. However less than 2% of the orange-throated whiptail captures occurred in JanuaryFebruary and only 5% of the snake captures occurred in this time period. It might be possible to 

reduce the sampling in this time period from 10 days to 4 days rather than from 10 days to 8 days 

as in the other sample periods, unless the ability to detect trends in the salamander is a concern. 

To optimize detection of salamanders, sampling during this time period should occur after rain 

events. 

If these recommendations are implemented this should result in a 30-35% reduction in effort. If 

a further reduction in effort is necessary due to budget limitations, it would be better to sample 

the 15 arrays every other year than to further reduce the number of arrays to enable sampling 

every year. 

Changes from five sampling periods to ten 

Once the decision was made to reduce the number of sampling days per year from 50 to 40 days, 

divided as five 8-day sample periods that would occur at approximately the same time of year as 

the original five 10-day sample periods used in 1996-2000, the question was raised as to whether 

this could be divided into ten 4-day sample periods instead. From a management point of view, 

4-day sample periods are easier to schedule since they can be completed in a single week and 

don’t require surveyors to work weekends or overtime. 

While technically it is preferable to follow the protocol used during the baseline years as closely 

as possible, using ten 4-day sample periods instead of five 8-day sample periods will probably 

have little effect on the results. The five sample periods during the baseline years varied in their 

start date by about a month anyway. So shifting to ten 4-day sample periods sampled 

approximately a month apart is still roughly comparable to five 8-day sample periods sampled 

about two months apart. 

Biases in array locations

Array location selection was limited because arrays could only be placed in areas that did not 

have steep slopes and were accessible to surveyors while being out of sight from park visitors. 

Thus areas that had steep slopes or were otherwise inaccessible to surveyors are under-sampled. 
Sampling Design Optimization 16 U.S. Geological Survey 

and Establishment of Baselines 

Given the small size of the reserve, this is expected to have minimal impact on the results. 

However, it is possible that some species that were not detected may remain in these undersampled areas, albeit in small numbers. Results from the arrays will have the strongest inference 

in areas near the arrays. Extrapolation of results from the arrays to robust population size 

estimates across the entire peninsula is not possible. However, trends at the arrays can be used to 

identify when problems are developing, at least in the areas nearest the arrays, and used to 

hypothesize (infer) the status of species on the peninsula. 

Improvements to the protocol 

Capture rates for all snake species were much lower than for lizards and salamanders. The ability 

to assess trends in ring-necked snake and southern Pacific rattlesnake were especially poor with 

very low power to detect changes— these snake species will need to be virtually wiped out in the 

reserve before a decline is detectable with statistical certainty. Thus the control limits for these 

species, in effect, provide a warning of when such species are falling below detectable thresholds 

and managers may need to consider reintroductions from other larger reserves. To improve the 

protocol, it may be worthwhile to investigate supplementing the current monitoring methods 

(buckets and wire snake traps, random encounters at array sites) with additional techniques to 

increase detectability of snakes. Although Fitch (1992) suggests supplementing with artificial 

shelters such as boards about 0.75 m2

, which could be checked by turning them over while at 

array sites. We have experimented with boards 0.09 m2

 in size without improvement in capture 

rates. Such boards can also become shelters for Argentine ants (Robert Fisher, personal 

observation). However, ideas to improve detectability of snakes should continue to be explored. 

Recommended future analyses 

Group 1: Number of species detected, species evenness, herpetofauna captures, lizard captures, 

and orange-throated whiptail captures per array per year. 

Two alternatives are presented for analyzing these variables. Although control limits were 

calculated for these variables, using an analysis of variance coupled with a contrast analysis is 

preferred because it will be more sensitive to detecting changes. 

• Alternative 1) Conduct an analysis of variance and covariance on appropriately 

transformed data 

- Trend detection: Conduct an analysis of covariance with arrays set as a “class” 

variable and years set as a “regression” or “quantitative” variable. It may be more 

appropriate to only perform this analysis on the most recent 5-7 years. 

- Comparison with baseline years: Conduct an analysis of variance with arrays and 

years as “class” variables. Arrays can be treated as “random” effects or as “fixed” 

effects. Years 1996-2000 should be considered the “base” years. A contrast 

analysis should be performed to test whether the results of the latest monitoring 

year is different from these first 5 years. (Steel and Torrie, 1980, p. 177). 

Differences between individual years are less important than whether a given year 

is different from the 5 base years. 

• Alternative 2) Transform data from each new year, calculate the average per array for 

that year, and compare with control limits (see Table 15). If the average is outside the 

control limits, then the analysis of variance (Alternative 1) should also result in a 

significant difference detected, since the control limits are less sensitive than the analysis 

of variance. 
Sampling Design Optimization 17 U.S. Geological Survey 

and Establishment of Baselines 

After 5 additional years of monitoring, if no trends have been discerned, the “Baseline data” 

years (i.e., 1996-2000) could be extended to include all 10 years, and control limits recalculated 

so they can be based upon a larger sample of data. It may even be possible to include rainfall as 

a covariate in the analysis. 

Group 2: Snake captures per year, striped racer captures per year, number of sites with snakes 

present, number of sites with striped racer present, number of sites with orange-throated whiptail 

present, number of sites with juvenile orange-throated whiptail present. 

• Trend detection: Conduct a regression analysis on the total counts per year or number of 

arrays that an organism is present per year with year set as a “regression” or 

“quantitative” variable. It may be more appropriate to perform this analysis on only the 

most recent 5-7 years. 

• Comparison with baseline years: Compare total count per year or number of arrays with 

organism present per year with control limits (see Table 15). 

After 5 years of data collection, if no trends have been discerned, recalculate the control limits. 

Group 3: Striped racer juvenile counts per year, southern Pacific rattlesnake counts per year, 

ring-necked snake counts per year (counts include both captures and sightings of the species). 

• Comparison with baseline years: If no individuals are collected that year, compare with 

control limits for number of zero years in a row (see Table 15). 

After 5 years of data collection, if no trends have been discerned, recalculate the control limits. 

Using control limits and analyses to assist management 

A summary of all the control limits calculated for analysis Groups 1, 2, and 3 is given in Table 

15. When a variable drops below a control limit or is found to be significant at the 5% 

significance level, what this means is that given the variation seen in the baseline 5 years, we 

would only expect such results to occur by random chance about 5% of the time. Thus usually 

we conclude in natural resource management that the result did not occur by random chance and 

we instead accept our alternative hypothesis (i.e., that a trend is occurring). Basically in a big 

picture sense we are checking to see if a new year falls within a range we would expect given the 

amount of variation seen in the baseline 5 years. 

However, it is important to realize that there is nothing “magical” about this number. These 

control limits and significance levels are guides to assist management but do not replace 

common sense. If resource managers see a problem occurring that will likely result in a decline 

in herpetofauna over the next several years (i.e., non-native plant invasion, new predator, 

increased pet collection), they should not wait until a control limit is exceeded before acting. The 

earlier intervention occurs, the easier and less costly it is to correct a problem. This is especially 

important in the case of Group 2 and Group 3 variables whose control limits have very low 

power to detect change. Group 2 variables will need to decline by 60-70% before a trend is 

detectable, and Group 3 species, i.e. ring-necked snakes and southern Pacific rattlesnakes, will 

need to be virtually wiped out in the reserve before their decline is detected with statistical 

certainty, i.e. with statistical power of greater than 80%. However, such management 

interventions should also be evaluated for their effectiveness and possibly set up as experiments, 

depending on the degree of uncertainty involved. 
Sampling Design Optimization 18 U.S. Geological Survey 

and Establishment of Baselines 

As another example, a severe drought could result in a significant decline compared with the 

baseline years. Managers will have to decide if intervention is required to prevent species loss, or 

whether it is simply best to wait for higher rainfall years to return. 

The five years from 1996-2000 used in this analysis include a range of weather conditions 

including an El Niño year in 1998 and drought years in 1996, 1999, and 2000. This variation 

appeared to be reflected in the large variation in captures of the 11 species and, hopefully, has 

improved the robustness of the sample size calculations and control limits. However, the results 

and conclusions should be tempered with the understanding that only 5 years of data were used 

and this may not encompass the full range of “naturally occurring” variation. In industry, it is 

preferred that 20-25 points be gathered before calculating control limits (Montgomery 2001). In 

addition, it is suspected that annual rainfall may be an important cofactor, but there were not 

enough data to provide a good test for this. After monitoring continues for another 5 years and if 

no trends are detected, this sampling design optimization analysis can be repeated, control limits 

re-evaluated, and the number of arrays and sampling days needed reassessed. The relationship 

between capture rates of different species and annual rainfall could also be assessed. 

It is important for the sake of future analyses that the same number of sampling days per year be 

used in all years and that sampling be conducted at roughly the same times during each year. 

Comparison of data in subsequent years with the 5 baseline years (1996-2000) assumes that data 

is collected in the same way with the same number of overall sampling days and with 

comparable error rates and sources of variation. If sampling is not conducted consistently, it 

becomes difficult to separate changes within the species from changes in the methods of 

collecting. Also, although snakes seen on trails while samplers go to and from the arrays should 

be included, herpetofauna seen during other activities such as weed control efforts, along roads, 

or routine maintenance should not be used in the analysis (e.g., not counted in the number of 

captures compared with the control limits). However, such observations are useful in other ways 

such as documenting where species are occurring in the preserve and the continued presence of 

the species in the preserve. 

This analysis and resulting recommendations have assumed that it is preferable to control a Type 

II error than a Type I error. A Type I error occurs when it is concluded that a change (e.g. a 

decline) has occurred when in fact the results are nothing more than randomly occurring 

variation and no change has in fact occurred. A Type II error occurs when one concludes that no 

change has occurred when in fact a decline is actually happening. However, in management of 

sensitive species, it is better to err on the side of giving a false alert of a problem to management 

than to fail to detect a change. Several factors may increase the probability of a Type I error in 

this analysis. 

• If data are highly autocorrelated (i.e., capture rates in one year are related to the capture 

rates in a previous year), then there can be an increased probability of a Type I error 

(Montgomery, 2001). This may be a small problem with this data. 

• Use of Poisson regression and a Poisson distribution in the analysis of variance is 

preferred when dealing with such small whole numbers. If the analysis of variance 

assumes a normal distribution, there can be an increased likelihood of a Type I error. 

However, calculations using a Poisson distribution require sophisticated computer 

packages and may not change the final conclusion (i.e., that a decline is or is not 

occurring). 
Sampling Design Optimization 19 U.S. Geological Survey 

and Establishment of Baselines 

• The control limits are calculated using a Z-distribution rather than a t-distribution. While 

this is typical in quality control literature, this does increase the probability of a type I 

error. 

These problems are assumed to be slight and manageable. However if “false alarms” are 

occurring too frequently, then analysis of variance incorporating the Poisson distribution can be 

used (SAS statistical software provides this option), or alternatively the 99% control limit can be 

used instead of the 95% control limit (i.e., an α=0.01 rather than α=0.05). 

Why conduct both a regression analysis and an analysis of variance (or comparison with control 

limits)? If a downward trend (decline) is already occurring within the baseline data set, a 

regression analysis will detect this trend, whereas the control limits will be set too low, are not 

really valid, and will tend to cause Type II errors. However, if a trend is not occurring in the 

baseline data set and only starts, for example, 5 -10 years from now, the control limits will detect 

it more quickly. Since several variables may be showing a decline (i.e., striped racer capture 

rates, number of species detected per array per year, and number of sites occupied by orangethroated whiptail), conducting a regression analysis as well as using the control limits is advised. 

SUMMARY 

Only 12 of the original 19 species thought to be present at Point Loma Ecological Reserve were 

detected during pitfall trap sampling from 1995-2001 (see Table14) and only 11 during the actual 

time period used in this analysis (1996-2000). Monitoring for declines in species still present at 

Point Loma is necessary to provide information for timely management intervention. Striped 

racer captures and number of species detected per array declined from 1996 to 2000. While 

striped racer declines could be caused by the snakes learning to avoid the traps, the decline is a 

concern and should be monitored. Declines in the number of juvenile striped racers would be 

especially important to track, since they will not yet have learned to avoid the traps. 

The following recommendations are made for refining monitoring for herpetofauna using pitfall 

trap arrays at Point Loma Ecological Reserve at Point Loma, California. Refinements should 

provide some reduction in sampling effort while maintaining an ability to detect approximately a 

20% drop in the number of species detected per array, a 40-50% drop in orange-throated whiptail 

(Cnemidophorus hyperythrus) capture rates, and an ability to continue monitoring trends in 

striped racer (Masticophis lateralis), ring-necked snake (Diadophis punctatus), and southern 

Pacific rattlesnake (Crotalus viridis), which were variables requested by the reserve manager. 

- The number of sampling days per year could be reduced from 50 to 40. 

- Only arrays #6 and #12 should be discontinued. 

- Control limits were calculated for the various response variables (see Table 15 for a 

summary of all control limits). 

- The 40 sampling days per year could be distributed across five 8-day sampling periods 

(similar to the original design of five 10-day sample periods) or alternatively across ten 

4-day sampling periods with little effect on the results, provided they occur at 

approximately the same time during the year as the baseline data. This should allow work 

to be scheduled within a single work-week. 

- If further reductions in sampling are required due to budget considerations, sampling the 

15 arrays every other year is preferred to reducing the number of arrays sampled. In 

addition, it may be possible to reduce sampling in the January-February sampling period 

to only 4 days if tracking declines in salamanders is not a concern. Sampling in JanuaryFebruary should be timed after rain events to maximize detection of salamanders. 
Sampling Design Optimization 20 U.S. Geological Survey 

and Establishment of Baselines 

LITERATURE CITED 

Brown, C. W. and R. N. Fisher. 2002. Inventory and Management Needs Study of Point Loma 

Herpetofauna (Reptiles and Amphibians) with Comments on Mammals and Invertebrates, 

2001. U.S. Geological Survey Technical Report. Prepared for National Park Service 

Cabrillo National Monument. 33 p. 

Case, T. J. and R. N. Fisher. 2001. Measuring and Predicting Species Presence: Coastal Sage 

Scrub Case Study, pp. 47-71. In: Spatial Uncertainty in Ecology. Hunsaker, C., M. 

Goodchild, M. Friedl and T. Case (Eds.). Springer-Verlag, New York. 

Fisher, R. N. and T. J. Case. 2000a. Distribution of the Herpetofauna of Coastal Southern 

California with Reference to Elevation Effects, pp. 137-143. IN: 2nd Interface Between 

Ecology and Land Development in California. J.E. Keeley, M. Baer-Keeley, and C.J. 

Fotheringham (eds). U.S. Geological Survey Open File Report 00-62. 

Fisher, R. N. and T. J. Case. 2000b. Southern California Herpetofauna Research and Monitoring: 

1995-1999 Data Summation Report. U. S. Geological Survey Technical Report submitted 

to U.S. Fish and Wildlife Service and California Department of Fish and Game. 200 p. 

Fisher, R. N., A. V. Suarez, and T. J. Case. 2002. Spatial Patterns in the Abundance of the 

Coastal Horned Lizard. Conservation Biology. 16(1): 205-215. 

Fitch, H.S. 1992. Methods of Sampling Snake Populations and Their Relative Success. 

Herpetological Review. Volume 23(1): 17-19. 

Geng, S. and F. J. Hills. 1989. Biometrics in Agricultural Science. Kendall/ Hunt Publishing Co. 

Dubuque, Iowa. 251 p. 

Krebs, C. J. 1999. Ecological Methodology, 2nd edition. Addison Wesley Longman, Inc., Menlo 

Park, California. 620 p. 

Laakkonen, J., R. N. Fisher and T. J. Case. 2001. Effect of land cover, habitat fragmentation and 

ant colonies on the distribution and abundance of shrews in southern California. Journal 

of Animal Ecology. 70: 776-788. 

Manly, B. F. J. 2001. Statistics for Environmental Science and Management. Chapman and 

Hall/CRC: Boca Raton, Florida. 326 p. 

McBean, E. A. and F. A. Rovers. 1998. Statistical Procedures for Analysis of Environmental 

Monitoring Data and Risk Assessment. Prentice Hall PTR Environmental Management 

and Engineering Series, Vol. 3. Prentice Hall PTR, Upper Saddle River, N.J. 313 p. 

Montgomery, D. C. 2001. Introduction to Statistical Quality Control, 4th Edition. John Wiley and 

Sons, Inc. New York, N.Y. 796 p. 
Sampling Design Optimization 21 U.S. Geological Survey 

and Establishment of Baselines 

Rochester, C. J., J.Diffendorfer, and R. N. Fisher. 2001. Natural History of the Rosy Boa 

(Charina trivirgata). Technical Report. Prepared for U.S. Geological Survey-Species at 

Risk. 71 p. 

Steel, R. G. D., and J. H. Torrie. 1980. Principles and Procedures of Statistics, A Biometrical 

Approach, 2nd Edition. McGraw-Hill Book Company. New York, NY. 633 p. 

Stokes, D. C., C. J. Rochester, R. N. Fisher, and T. J. Case. 2004. Herpetological Monitoring 

Using a Pitfall Trapping Design in Southern California. DRAFT. U. S. Geological Survey 

Open File report. 53 p. 

Thompson, W. L., G. C. White, and C. Gowan. 1998. Monitoring Vertebrate Populations. 

Academic Press, Inc. San Diego, California. 365 p. 

Yang, B. S. and R. N. Fisher. 2003. Surveys for rare reptiles at Cabrillo National Monument on 

the Point Loma Peninsula in San Diego, California. U. S. Geological Survey Technical 

Report. Prepared for Cabrillo National Monument. 15 p. 

Zar, J. H. 1999. Biostatistical Analysis, 4th Edition. Prentice Hall, Upper Saddle River, N.J. 

663 p. 
Sampling Design Optimization 22 U.S. Geological Survey 

and Establishment of Baselines 

Species 1996 1997 1998 1999 2000 Totals

Amphibians

Batrachoseps major

 Garden slender salamander 19 4 39 22 2 86

Anniella pulchra

 Silvery legless lizard

1 1

Cnemidophorus hyperythrus

 Orange-throated whiptail 55 91 114 63 60 383

Elgaria multicarinatus

 Southern alligator lizard 25 36 49 14 22 146

Sceloporus occidentalis

 Western fence lizard 100 66 104 81 73 424

Uta stansburiana

 Side-blotched lizard 47 53 61 78 56 295

Crotalus viridis

 Southern Pacific rattlesnake 11 3 5

Diadophis punctatus

 Ring-necked snake 2212 7

Hypsiglena torquata

 Night snake (detected in 2001)

Lampropeltis getula

 California king snake 23 5

Masticophis lateralis

 Striped racer 12 9 7 7 4 39

Pituophis melanoleucas

 San Diego gopher snake 1321 7

Total herpetofauna captures / year 258 263 383 271 223 1398

Total lizard captures / year 246 250 368 258 213 1335

Total snake captures / year 12 13 15 13 10 63

# species detected across all arrays 6 9 11 9 9 11

Average # species detected / array 4.06 4.12 4.59 3.65 3.41

Simpson's species eveness 0.72 0.72 0.68 0.70 0.75

Shannon-Weiner diversity index 1.14 1.15 1.22 0.95 1.00

Year

Table 3. Total herpetofauna captures per year for years 1996-2000. Data for 1995 and 2001 were excluded (see text). 

Recaptures within same sampling period not included. Snakes observed by surveyers while walking to and from arrays 

are included. The species Hypsiglena torquata (night snake) was detected in 2001. Note: 1998 was an El Niño year with 

elevated rainfall. The years 1996, 1999, and 2000 were considered drought years with very low rainfall. Lizards Snakes Summary statistics Diversity indices
Sampling Design Optimization 23 U.S. Geological Survey 

and Establishment of Baselines 

20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50

1.65 1.81 1.92 1.99 0.85 0.81 0.75 0.72 2.57 2.97 3.41 3.78 2.40 2.80 3.18 3.521.71 1.88 1.96 2.00 0.82 0.78 0.75 0.72 2.49 3.07 3.43 3.75 2.34 2.92 3.26 3.571.88 1.98 2.03 2.12 0.76 0.72 0.71 0.68 3.08 3.90 4.25 4.61 2.84 3.59 3.88 4.221.59 1.73 1.85 1.87 0.83 0.77 0.73 0.70 2.74 3.15 3.47 3.79 2.53 2.90 3.18 3.481.49 1.67 1.74 1.82 0.89 0.83 0.78 0.75 2.12 2.72 3.12 3.42 2.04 2.63 3.01 3.321.66 1.81 1.90 1.96 0.829 0.781 0.746 0.715 2.60 3.16 3.53 3.87 2.43 2.97 3.30 3.620.12 0.11 0.09 0.08 0.016 0.022 0.024 0.021 0.46 0.43 0.39 0.40 0.45 0.41 0.38 0.360.21 0.18 0.16 0.14 0.150 0.188 0.210 0.201 0.26 0.21 0.18 0.16 0.28 0.22 0.19 0.172.03 2.13 2.19 2.27 0.95 0.89 0.81 0.78 3.51 4.31 4.62 5.00 3.19 3.91 4.16 4.521.94 2.05 2.12 2.20 0.92 0.87 0.80 0.77 3.29 4.03 4.36 4.73 3.01 3.68 3.96 4.301.38 1.57 1.69 1.73 0.74 0.70 0.70 0.66 1.91 2.29 2.70 3.01 1.86 2.25 2.65 2.941.29 1.50 1.62 1.65 0.71 0.67 0.68 0.65 1.69 2.02 2.44 2.74 1.68 2.03 2.44 2.73

Power

Difference 

to detect

30% 11 8 7 6 6 9 11 10 17 11 8 7 19 12 9 740% 7 5 4 4 4 6 7 6 10 7 5 4 11 7 6 550% 5 4 3 3 3 4 5 4 7 5 4 3 7 5 4 360% 4 3 3 2 3 3 4 3 5 4 3 3 5 4 3 370% 3 3 2 2 2 3 3 3 4 3 3 2 4 4 3 230% 8 7 5 5 5 7 9 8 13 8 6 6 14 9 7 640% 5 4 4 3 3 4 5 5 8 5 4 4 8 5 4 450% 4 3 3 3 3 3 4 4 5 4 3 3 6 4 3 360% 3 3 2 2 2 3 3 3 4 3 3 2 4 3 3 270% 3 2 2 2 2 2 3 2 3 3 2 2 4 3 2 230% 7 5 5 4 4 6 7 6 10 7 5 5 11 7 6 540% 4 4 3 3 3 4 4 4 6 4 3 3 7 5 4 350% 3 3 2 2 2 3 3 3 4 3 3 3 5 3 3 360% 3 2 2 2 2 2 3 3 3 3 2 2 4 3 2 270% 2 2 2 2 2 2 2 2 3 2 2 2 3 2 2 2

upper 99% CLupper 95% CLlower 95% CLlower 99% CL

not significant yes

-0.048

p=0.0370

Summary

Averages 

(Transformed 

Data)

Regres

sionIs trend present? slope

Number species detected

# species/array/yr

Simpson's Evenness

evenness index/array/yr

Herpetofauna captures

captures/array/yr

Lizard captures

captures/array/yr

sampling days per year sampling days per year

square root square root --- square root

not significant not significant

Transformation 

sampling days per year

19961997199819992000

sampling days per year

Table 4. Trend analysis and optimization analysis for average number of species detected, species evenness, total herpetofauna captures, and lizard captures per array per year. Results are presented assuming 20, 30, 40, and 50 sampling days per year (i.e., 4-day, 6-day, 8-day, or 10-day sample period). Mean Square Error (MSE) is taken from an analysis of variance which included year and array as class variables. Regression analyses were performed on all variables using the 10-day sample period data to determine if a trend existed from 1996 - 2000. All data presented have been transformed with a square root transformation, with the exception of Simpson's Eveness. Confidence Limits are given as a rough guide to determine when variables are different from baseline years, but using a contrast analysis is expected to detect a change earlier. 

prob. > |t|

70%

Sample size estimates 

for contrast analysis

90% 80%

Confidence 

Limits

averageMSE CV

# arrays recommended at given power and 0.05 alpha level 

(Cells in gray would require an increase in number of arrays)
Sampling Design Optimization 24 U.S. Geological Survey 

and Establishment of Baselines 

20 30 40 50 20 30 40 50 20 30 40 50

0.76 0.95 1.25 1.41 1.18 1.37 1.85 2.00 0.47 0.60 0.75 0.891.05 1.40 1.60 1.70 1.63 2.07 2.38 2.54 0.94 1.27 1.41 1.521.37 1.76 1.84 2.00 2.02 2.64 2.75 3.00 1.11 1.49 1.53 1.641.10 1.23 1.33 1.40 1.69 1.90 2.05 2.16 0.66 0.71 0.80 0.820.55 0.87 1.07 1.22 0.55 1.26 1.57 1.79 0.18 0.27 0.53 0.640.96 1.24 1.42 1.55 1.47 1.85 2.12 2.30 0.69 0.87 1.00 1.100.32 0.46 0.43 0.46 0.42 0.55 0.54 0.56 0.26 0.26 0.35 0.340.58 0.55 0.46 0.44 0.44 0.40 0.35 0.32 0.74 0.59 0.59 0.531.78 2.17 2.19 2.34 2.94 3.29 3.30 3.53 1.65 2.15 2.13 2.251.59 1.95 2.01 2.15 2.59 2.94 3.02 3.24 1.42 1.84 1.86 1.970.34 0.54 0.83 0.95 0.36 0.75 1.22 1.36 -0.04 -0.11 0.14 0.230.15 0.31 0.64 0.76 0.01 0.41 0.93 1.07 -0.27 -0.42 -0.13 -0.05

Power

Difference 

to detect

30% 80 71 51 46 46 38 29 25 130 83 82 6740% 45 40 29 26 26 22 17 15 74 47 47 3850% 29 26 19 17 17 14 11 10 47 30 30 2560% 21 18 13 12 12 10 8 7 33 21 21 1770% 15 14 10 9 9 8 6 5 25 16 16 1330% 60 53 38 34 35 29 22 19 97 62 62 5040% 34 30 22 20 20 17 13 11 55 35 35 2950% 22 20 14 13 13 11 8 8 36 23 23 1960% 16 14 10 9 9 8 6 6 25 16 16 1370% 12 10 8 7 7 6 5 4 19 12 12 1030% 48 42 30 27 28 23 17 15 77 49 49 4040% 27 24 17 16 16 13 10 9 44 28 28 2350% 18 16 12 11 11 9 7 6 28 18 18 1560% 13 11 8 8 8 6 5 5 20 13 13 1170% 9 9 6 6 6 5 4 4 15 10 10 8

All Arrays Arrays 1-4, 9-10,13-17 Arrays 1-4, 9-10,13-17

Orange throated whiptail Orange throated whiptail Juv. Orange throated whiptail 

2000

sampling days per year sampling days per year sampling days per year

1996199719981999

square root square root square root

Table 5. Trend analysis and optimization analysis for orange-throated whiptail captures and juvenile orange-throated whiptail captures per array per year. Results 

are presented assuming 20, 30, 40, and 50 sampling days per year (i.e., 4-day, 6-day, 8-day, or 10-day sample period). Mean Square Error (MSE) is taken from an analysis of variance which included year and array as class variables. Regression analyses were performed on all variables using the 10-day sample period data to determine if a trend already existed from 1996 - 2000. All data presented have been transformed with a square root transformation. Confidence Limits are given as a 

rough guide to determine when variables are different from baseline years, but using a contrast analysis is expected to detect a change earlier. Results for orangethroated whiptails are presented with data from all arrays included and again with only arrays that had >2 captures of whiptails.

Summaryaverage MSE CVTransformation 

Averages 

(Transformed 

) Data

Sample size estimates 

for contrast analysis

90%

slope -0.12

Regres

sionIs trend present? not significant not significant maybe

Confidenc

e Limits

80% 70%

# arrays recommended at given power and 0.05 alpha level 

(Cells in gray would require an increase in number of arrays)

prob. > |t| p=0.0792

upper 99% CLupper 95% CLlower 95% CLlower 99% CL
Sampling Design Optimization 25 U.S. Geological Survey 

and Establishment of Baselines Response variable= Sampling days per year= 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 20 30 40 50 1996 4 5 9 12 3 4 6 8 4 5 9 12 3 4 6 8 8 10 12 13 4 5 6 7

1997 8 9 11 13 8 9 9 9 7 8 9 9 7 8 9 9 8 10 11 11 8 8 8 91998 6 9 11 15 6 9 10 12 3 3 5 7 3 3 5 6 11 11 11 12 7 9 9 91999 7 8 11 12 4 5 6 7 3 4 6 7 3 4 5 6 10 11 11 11 5 5 6 62000 3 5 8 8 3 4 5 5 0 2 4 4 0 2 4 4 6 8 9 10 2 2 4 4average 5.6 7.2 10.0 12.0 4.8 6.2 7.2 8.2 3.4 4.4 6.6 7.8 3.2 4.2 5.8 6.6 8.6 10.0 10.8 11.4 5.2 5.8 6.6 7.0Std. Dev. 2.1 2.0 1.4 2.5 2.2 2.6 2.2 2.6 2.5 2.3 2.3 2.9 2.5 2.3 1.9 1.9 1.9 1.2 1.1 1.1 2.4 2.8 1.9 2.1Variance 4.3 4.2 2.0 6.5 4.7 6.7 4.7 6.7 6.3 5.3 5.3 8.7 6.2 5.2 3.7 3.8 3.8 1.5 1.2 1.3 5.7 7.7 3.8 4.5CV 0.37 0.28 0.14 0.21 0.45 0.42 0.30 0.32 0.74 0.52 0.35 0.38 0.78 0.54 0.33 0.30 0.23 0.12 0.10 0.10 0.46 0.48 0.30 0.30Type of distributionTrend present?prob. > |t|upper 99% CL 14.9 17.1 21.4 24.1 13.4 15.7 17.1 18.6 11.0 12.6 16.4 17.9 11.0 12.6 14.9 16.4 13.6 13.2 13.6 14.3 14.1 14.9 16.4 17.1upper 95% CL 12.4 14.4 18.4 21.0 11.0 13.1 14.4 15.8 8.8 10.2 13.7 15.1 8.8 10.2 12.4 13.7 12.4 12.4 12.9 13.6 11.7 12.4 13.7 14.4upper 90% CL 11.2 13.1 17.0 19.4 9.8 11.8 13.1 14.4 7.8 9.2 12.5 13.8 7.8 9.2 11.2 12.5 11.8 12.0 12.6 13.3 10.5 11.2 12.5 13.1lower 90% CL 2.3 3.3 5.4 6.9 1.7 2.6 3.3 4.0 0.8 1.4 2.9 3.6 0.8 1.4 2.3 2.9 5.4 8.0 9.0 9.5 2.0 2.3 2.9 3.3lower 95% CL 1.9 2.8 4.8 6.2 1.4 2.2 2.8 3.5 0.6 1.1 2.5 3.1 0.6 1.1 1.9 2.5 4.8 7.6 8.7 9.2 1.6 1.9 2.5 2.8lower 99% CL 1.3 2.0 3.7 4.9 0.9 1.5 2.0 2.6 0.3 0.7 1.8 2.3 0.3 0.7 1.3 1.8 3.6 6.8 8.0 8.5 1.1 1.3 1.8 2.0Warning -90% CL **(# captures or # arrays) 2356123401230122 5 8 9 9 2 2 2 3Warning -95% CL **(# captures or # arrays) 1246122301230112 4 7 8 9 1 1 2 2Warning -99% CL**# captures or # arrays) 1234012200120011 3 6 8 8 1 1 1 2

not significant yes

Poisson Poisson Poisson

Striped Racer

# arrays present/year # arrays present/year captures/year captures/year

All snakes

not significant

Poisson Normal

Data Reg. 0.0418 yes 0.0079Summary

not significant

Table 6. Calculation of 95% and 99% confidence levels for total number of snake captures per year, striped racer captures per year, and number of arrays occupied by snakes, striped racers 

only, orange-throated whiptails and juvenile orange-throated whiptails. Results are presented assuming 20, 30, 40, and 50 sample days per year (i.e. a 4-day, 6-day, 8-day, or 10-day sample 

period). The type of distribution determined the method of calculation for confidence limits (Poisson, normal). Warning limits are the 90% and 95% confidence limits converted to whole numbers 

of individuals captured or numbers of arrays with individuals present. Regression analyses were conducted on all variables using the 10-day sample period data to determine if a trend already existed from 1996 - 2000.

** Calculation of "Thresholds" is based on the assumption that variation occuring during 1996-2000 is randomly occuring variation. If a trend is in fact occuring during that time period, then the thresholds are not valid.

Confidence Limits

Poisson

# arrays present/year

Orange Throated Whiptail 

(Juveniles+Adults)

Orange Throated Whiptail - 

Juveniles

# arrays present/year

maybe

0.0805
Sampling Design Optimization 26 U.S. Geological Survey 

and Establishment of Baselines 

Year 20 days/yr 30 days/yr 40 days/yr 50 days/yr 20 days/yr 30 days/yr 40 days/yr 50 days/yr 20 days/yr 30 days/yr 40 days/yr 50 days/yr

1996 1 1 1 2 0 0 0 0 0 0 0 01997 2 2 2 2 0 0 1 2 0 0 0 11998 0 0 1 1 1 2 2 2 1 1 1 11999 1 2 2 2 0 0 1 1 0 0 0 02000 0 1 1 1 1 1 2 2 3 3 3 3

Total 4 6 7 8 2 3 6 7 4 4 4 5

Average 0.8 1.2 1.4 1.6 0.4 0.6 1.2 1.4 0.8 0.8 0.8 1.0

Probability of zero captures P(0) 0.4493 0.3012 0.2466 0.2019 0.6703 0.5488 0.3012 0.2466 0.4493 0.4493 0.4493 0.3679

1 year 0.4493 0.3012 0.2466 0.2019 0.6703 0.5488 0.3012 0.2466 0.4493 0.4493 0.4493 0.3679

2 years 0.2019 0.0907 0.0608 0.0408 0.4493 0.3012 0.0907 0.0608 0.2019 0.2019 0.2019 0.13533 years 0.0907 0.0273 0.0150 0.0082 0.3012 0.1653 0.0273 0.0150 0.0907 0.0907 0.0907 0.04984 years 0.0408 0.0082 0.0037 0.0017 0.2019 0.0907 0.0082 0.0037 0.0408 0.0408 0.0408 0.01835 years 0.0183 0.0025 0.0009 0.0003 0.1353 0.0498 0.0025 0.0009 0.0183 0.0183 0.0183 0.00676 years 0.0082 0.0007 0.0002 0.0001 0.0907 0.0273 0.0007 0.0002 0.0082 0.0082 0.0082 0.00257 years 0.0037 0.0002 0.0001 0.0000 0.0608 0.0150 0.0002 0.0001 0.0037 0.0037 0.0037 0.0009

3-5 years 3 years 2-3 years 2-3 years 5-? years 4-8 years 3 years 2-3 years 3-5 years 3-5 years 3-5 years 3-4 years

Table 7. Calculation of control limits for juvenile striped racers, ring-necked snakes and southern Pacific rattlesnake. Control limits were determined as the point when the 

probability for multiple years in a row with zero captures or sightings of these snakes at the pitfall trap arrays drops below 5%. One capture was added and subtracted to each calculation to determine how robust the calculation was, and the control limits were expanded accordingly. (Numbers remain the same if array # 6 and #12 are dropped from the analysis since none of these snakes were found in array #6 or #12.) Probability of multiple years with zero captures in a rowControl Limit : # of years with zero captures or sightings at arrays =

Juvenile Striped Racer

Masticophis lateralis

Ring-necked Snake

Diadophis punctatus

Number captures and sightings at arrays / year

Southern Pacific Rattlesnake

Crotalus viridis
Sampling Design Optimization 27 U.S. Geological Survey 

and Establishment of Baselines Species 1 2 3 4 5 6 7 8 9 10 Total

AmphibiansBatrachoseps major Garden slender salamander 6 10 17 3 7 12 14 3 4 10 86

Anniella pulchra

Silvery legless lizard 1 1

Cnemidophorus hyperythrus

Orange-throated whiptail 65 40 40 43 55 35 36 23 22 23 383

Elgaria multicarinatus

 Southern alligator lizard 13 7 15 18 25 15 10 13 19 11 146

Sceloporus occidentalis

Western fence lizard 66 42 57 41 36 45 35 29 36 37 424

Uta stansburiana

Side-blotched lizard 54 42 24 20 36 24 16 27 28 24 295

Crotalus viridis

Southern Pacific rattlesnake 1 3 15

Diadophis punctatus

Ring-necked snake 1 1 1 3 17

Hypsiglena torquata

 Night snake (detected in 2001)Lampropeltis getula California king snake 1 22 5Masticophis lateralis

 Striped racer 5 4 3 5 4 1 9 2 3 3 39

Pituophis melanoleucas

San Diego gopher snake 11 2 1 117

Total herpetofauna captures 211 148 157 138 166 132 124 97 113 111 1398

# species detected 8 9 7 10 8 6 8 6 7 9 11

Summary

Day in sampling period (1-10)

Table 8. Captures during each day in sample period summed across all sampling periods from 1996-2000. The rate of new captures declines as the day in the sampling period progresses. 

Lizards Snakes
Sampling Design Optimization 28 U.S. Geological Survey 

and Establishment of Baselines Species 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Not Recorded Total Batrachoseps major Garden slender salamander 3 2 8 5 35 2 19 4 1 3 1 3 86 Anniella pulchra

Silvery legless lizard 1 1

Cnemidophorus hyperythrus

Orange-throated whiptail 59 22 112 41 1 1 14 6 2 1 27 43 21 23 10 383

Elgaria multicarinatus

 Southern alligator lizard 9 15 22 14 2 5 2 5 7 8 9 22 8 10 5 3 146

Sceloporus occidentalis

Western fence lizard 17 8 40 34 20 12 27 20 25 9 16 15 41 53 27 30 30 424

Uta stansburiana

Side-blotched lizard 3 27 22 14 39 54 8 3 1 3 1 1 13 34 32 21 19 295

Crotalus viridis

Southern Pacific rattlesnake 1 11 2 5

Diadophis punctatus

Ring-necked snake 12 2 1 1 7

Lampropeltis getula

 California king snake 121 1 5Masticophis lateralis

 Striped racer 3 3 1 4 3 3 7 3 1 1 3 3 3 1 39

Pituophis melanoleucas

San Diego gopher snake 1111 11 1 7

Grand total # captures 92 77 203 106 66 69 51 35 90 31 49 31 109 144 94 81 67 3 1398Number species detected 6 7 8 7 5 4 5 7 8 7 7 6 8 6 6 6 7 2 11Table 9. Total herpetofauna captures per array for years 1996-2000. Recaptures within same sampling period are not included. Array #6 and array #12 

could be discontinued. Three snake observations were not recorded with an array number and were seen while walking on trails to arrays.

Array
Sampling Design Optimization 29 U.S. Geological Survey 

and Establishment of Baselines Array # 1996 1997 1998 1999 2000 Total Array # 1996 1997 1998 1999 2000 Total 1 21 3 1 11 2 2 0 2 0 3 11 1 3 3 1 1 4 1 1 4 0 5 112 4 5 1 1

6 0 6 0

7 21 3 7 0

8 111 3 8 0

9 3121 7 9 1 1

10 11 13 10 0

11 1 1 11 1 112 1 1 12 0

13 11 13 13 1 1

14 1 1 13 14 0

15 11 1 3 15 1 116 0 16 0

17 1 1 17 0

Total captures 12 9 7 7 4 39 Total captures 221218# arrays present 8 9 6 6 4 14 # arrays present 221217

Striped Racer (Adults + Juveniles) Striped Racer (Juveniles Only) 

Table 10. Striped racer (Masticophis lateralis) captures by year and by array for adults plus juveniles and for juveniles only.
Sampling Design Optimization 30 U.S. Geological Survey 

and Establishment of Baselines 

Species Jan/Feb Apr/May June/Jul Aug/Sep Oct/Nov Grand Total

Batrachoseps major

 Garden slender salamander 72 12 0 0 2 86

Anniella pulchra

 Silvery legless lizard 10000 1

Cnemidophorus hyperythrus

 Orange-throated whiptail 5 54 180 55 89 383

Elgaria multicarinatus

 Southern alligator lizard 34 70 20 6 16 146

Sceloporus occidentalis

 Western fence lizard 63 133 98 61 69 424

Uta stansburiana

 Side-blotched lizard 48 56 58 66 67 295

Crotalus viridis

 Southern Pacific rattlesnake 01121 5

Diadophis punctatus

 Ring-necked snake 10312 7

Lampropeltis getula

 California king snake 01400 5

Masticophis lateralis

 Striped racer 2 11 8 11 7 39

Pituophis melanoleucas

 San Diego gopher snake 01312 7

Grand total # captures 226 339 375 203 255 1398

# species detected 8 9 9 8 9 11

Sampling Period Time in Year

Table 11. Number of captures by sampling period from years 1996-2000. Based upon 50 sample days 

per year (i.e., 10-day sample periods).

 
Sampling Design Optimization 31 U.S. Geological Survey 

and Establishment of Baselines 

Table 12. Dependent and independent variables in stepwise regression analysis. 

Dependent variables Independent variables 

Fauna** Vegetation Physical 

# Snakes 

# Striped racers 

# Lizards and salamanders 

# Orange-throated 

whiptails 

Argentine ants category 

# Lizards 

# Small mammals 

Argentine ants category 

Canopy height 

% Cover 

# Shrub hits 

# Herb Hits 

% Coastal Sage Scrub 

% Chaparral 

% Grass 

Elevation (meters) 

Slope (degrees) 

Cosine aspect 

Leaf litter 

Sandy soil 

Cryptogamic rock 

Bare Rock 

Cryptogamic soil 

Organic soil 

Moss 

** Note: # lizards and # small mammals variables were only used in analysis for number of snakes captures and 

number striped racer captures. Dependent variables were first analyzed without including the argentine ant category 

so the habitat associations could be examined. The dependent variables were then reanalyzed with argentine ant 

categories included as a potential independent variable. 
Sampling Design Optimization 32 U.S. Geological Survey 

and Establishment of Baselines 

Table 13. Environmental variables stepwise regression results. The results from the stepwise regression analyses to 

determine what environmental variables were most strongly associated with each dependent variable are 

summarized below. For a variable to enter or exit the regression model required a probability >F of at least 0.15. 

Dependent variables are shown in bold in the table below. The data transformation and the associated R2

 of the 

model are also given. Although Argentine ant density category was not included initially in the analysis for number of 

lizards and salamanders and number orange-throated whiptails, when this variable was added, it became significant 

in the stepwise regression for these variables and replaced some environmental variables in the resulting equations. 

Argentine ant density category did not alter the regression equations for number of snakes or number of striped 

racers. 

 Parameter Name Parameter Probability >F 

Results when Argentine ant density category is not allowed as regression variable 

# snakes (transformation = Ln(n+1); R2 = .53 ) 

 Intercept -0.7768 0.2208 

 Canopy Height -0.9385 0.0782 

 % Cover 0.0326 0.0020 

# striped racers (transformation =Ln(n+1); R2=.48) 

 Intercept -6.4391 0.0335 

 Ln (# mammals) 1.2939 0.0041 

 Ln (# lizards and salamanders) 0.6876 0.0860 

# lizards & salamanders (transformation=square root (n); R2=.60) 

 Intercept 4.0046 0.0001 

 # herbaceous plant hits 0.0249 0.0028 

 % grasses -0.0316 0.0007 

# orange-throated whiptails (transformation =square root (n); R2=.46) 

 Intercept 3.5261 0.0559 

 # Shrub hits -0.0709 0.0485 

 % coastal sage scrub 0.0807 0.0057 

Argentine ants density category (no transformation; R2=.82) 

 Intercept 1.9316 0.0001 

 % Coastal sage scrub -0.0104 0.0030 

 % Grass 0.0174 0.0027 

Results when Argentine ant density category is allowed as regression variable 

# lizards and salamanders (transformation=square root(n); R2=.63) 

 Intercept 6.4112 0.0001 

 # Shrub hits -0.0140 0.0082 

 Argentine ant density category -0.7836 0.0004 

# orange-throated whiptails (transformation =square root (n); R2=.63) 

 Intercept 6.9950 0.0001 

 # Herb hits 0.0939 0.0044 

 Argentine ant density category -3.7502 0.0008 
Sampling Design Optimization 33 U.S. Geological Survey 

and Establishment of Baselines 

Table 14. List of species detected since 1995 versus historical records. The coastal rosy boa (Charina 

trivirgata) was a single individual found by the roadside and is thought to have been a released pet, since 

this species is not known historically from the peninsula. The night snake (Hypsiglena torquata) was not 

known historically in museum records, but a single specimen was documented in 1997 as well as in 

current surveys. This is a very cryptic, difficult to detect species and could easily have been missed 

during earlier surveys, and thus is considered to have historically occurred in this area. 

SPECIES Current surveys Historical records 

Amphibians 

Batrachoseps major 

 Garden slender salamander 

X X 

Lizards 

Anniella pulchra 

 Silvery legless lizard 

X X 

Cnemidophorus hyperythrus 

 Orange-throated whiptail 

X X 

Eumeces skiltonianus 

 Coronado skink 

 X 

Elgaria multicarinatus 

 Southern alligator lizard 

X X 

Phrynosoma coronatum 

 Coast horned lizard 

 X 

Sceloporus occidentalis 

 Western fence lizard 

X X 

Uta stansburiana 

 Side-blotched lizard 

X X 

Snakes 

Arizona elegans 

 California glossy snake 

 X 

Charina trivirgata 

 Coastal rosy boa 

X (introduced) 

Coluber constrictor 

 Yellow-bellied racer 

 X 

Crotalus exsul 

 Red diamond rattlesnake 

 X 

Crotalus viridis 

 Southern Pacific rattlesnake 

X X 

Diadophis punctatus 

 Ring-necked snake 

X X 

Hypsiglena torquata 

 Night snake 

X X 

Lampropeltis getula 

 California king snake 

X X 

Masticophis lateralis 

 Striped racer 

X X 

Masticophis flagellum 

 Coachwhip / red racer 

 X 

Pituophis melanoleucas 

 San Diego gopher snake 

X X 

Rhinocheilus lecontei 

 Long-nose snake 

 X 
Sampling Design Optimization 34 U.S. Geological Survey 

and Establishment of Baselines Table 15. Summary table of preliminary control limits for detecting changes from the baseline years 1996-2000. These control limits and data in this table assume that specified data transformations have been conducted, that arrays #6 and #12 are discontinued, and that the number of sampling days per year has been reduced from 50 to 40 days, either divided as 5 8-day sampling periods per year or as 10 4-day sampling periods per year. Lower Control Limit Variable name Variable Transfor mation Is Trend Significant 1996 1997 1998 1999 2000 90% 95% 99% # Species detected Average # species / array / year Square root Yes P=.0370 1.99 1.99 2.08 1.91 1.75 < 1.74* < 1.70* < 1.62* 

Relative Species Evenness Average Evenness / array / year No .75 .73 .70 .73 .80 < 0.68** < 0.67** < 0.65** Herpetofauna Average # herpetofauna Captures / array / year Square root No 3.54 3.54 4.44 3.57 3.10 < 2.84** < 2.68** < 2.38** Lizards Average # lizard captures / array / year Square root No 3.29 3.39 4.03 3.27 2.99 < 2.76** < 2.64** < 2.41** 

Total snake captures / year across all arrays 

No 9 10 11 11 8 5 4 3 Snakes 

# arrays with snakes present / year No 6 8 10 6 5 3 2 2 Average # captures / array / year Square root No 1.42 1.81 2.02 1.50 1.22 < 1.07** < 0. 97** < 0.77** # arrays with adults or juveniles present / year 

 Maybe 

P=0.0805 12 11 10 11 9 8 8 7 Orange-throated whiptail 

# arrays with juveniles only present / year No 6 8 9 6 4 2 2 1 Total captures / year Yes P=0.0079 9 8 5 6 4 2* 2* 1* Striped racer 

(adults & juveniles) # arrays with adults or juveniles 

present / year 

 Yes 

P=0.0418 6 8 5 5 4 2* 1* 1* 

Striped racer (juveniles only) # consecutive years with zero captures 1 2 1 2 1 2-3 years*** Ring-necked snake # consecutive years with zero captures 0 1 2 1 2 3 years*** Southern Pacific rattlesnake # consecutive years with zero captures 0 0 1 0 3 3-5 years*** * If a trend is present then limits are not valid. A test for a trend should be conducted in subsequent (new) years before using control limits. ** A contrast analysis will have greater power to detect a change. However if a variable drops below the given control limit, there will also be a significant difference if a contrast analysis is conducted. Data must be transformed before comparing with control limits (see variable description) *** These control limits represent the # of consecutive years with no captures that would be expected to occur with a probability of 5% or less if no trend were occurring. A range is given because the limits were re-calculated after adding and subtracting 1 snake from the actual number of captures and the limits were adjusted to include any changes.
Sampling Design Optimization 35 U.S. Geological Survey 

and Establishment of Baselines 

Figure 1. Map of Point Loma Ecological Reserve herpetofauna arrays 
Sampling Design Optimization 36 U.S. Geological Survey 

and Establishment of Baselines 

0

0.70.60.50.40.30.20.1

10 20 30 40 50

Number of sampling days per year

Coefficient of Variation (CV)

Figure 2. Coefficient of Variation (CV) for orange-throated whiptail capture rates for arrays with > 2 captures. 
Sampling Design Optimization 37 U.S. Geological Survey 

and Establishment of Baselines 

86420

1210

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Years

# Herpetofauna Species 5 days/yr

10 days/yr15 days/yr20 days/yr25-30 days/yr35-45 days/yr50 days/yr

Figure 3. Cumulative number of herpetofauna species detected across all 17 arrays at increasing number of sampling days per year. Please note that night snake (Hypsiglena torquata ), the twelfth species, was not captured until 2001.
Sampling Design Optimization 38 U.S. Geological Survey 

and Establishment of Baselines 

0

0.5

1

1.5

2

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Average # new captures / day

Figure 4. Number of new captures per day by sampling day within the sampling period. Recaptures within same 10-day sampling period were not included.
Sampling Design Optimization 39 U.S. Geological Survey 

and Establishment of Baselines 

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Year and Array Number

# captures / year

Figure 5. Juvenile orange-throated whiptails: Number of captures by year and array.