Upper Mississippi River Restoration Program Long Term Resource Monitoring

Estimating means and temporal trends using LTRM data: details with examples

Estimating population means - Estimating a stratum-specific mean for a single year

LTRM samples are selected at random from within strata and years. Hence, estimating strata means for a single year represents the simplest estimation procedure for use with LTRM data.

For SAS, the basic form of computer code for any of the LTRM components will look like this, with exceptions provided below:

proc surveymeans data = <enter the name of your dataset here>;
var <list variables for which you want to calculate statistics here>;
by <list design components, such as field station, year and stratum, for which you want statistics (this statement is optional)>;
where <list restrictions, such as field station or stratum, for your analysis>;
run;

Fish data

CPUE. LTRM sampling is designed to estimate relative abundance as estimated by catch-per-unit-effort (CPUE).  For some gears and for some field stations, effort may vary among samples. In such cases, adjustment of the variable of interest (e.g., a fish count) for effort is accomplished using ratio analysis. Doing so acknowledges that effort itself is also a random variable. For example, bluegill CPUE from day electrofishing, expressed in units of 15 minutes of effort (effmin15; sampled minutes divided by 15), may be analyzed as:

proc surveymeans data= BLGLP8;
var catch;
ratio catch / effmin15;
by fstation year stratum;
run;

Frequency of detection. The LTRM assumes that catchability is constant over time and so treats percent frequency of detection as an index of percent frequency of occurrence.  For convenience, we hereafter term this index “percent frequency of occurrence.”

Calculating percent frequency of occurrence requires the creation of an occurrence indicator. For example, the following estimates occurrence of bluegill detection by field station, year and stratum:

data BLGLP8b; set BLGLP8; detect = count; if count then detect=1;

proc surveymeans data= BLGLP8b;
var detect;
by fstation year stratum;
run;

While percent frequency of occurrence is a function of effort, that statistic cannot easily be adjusted for effort (unlike the case when calculating CPUE).

Estimating statistics from LTRM fish length data is addressed under Estimating means from portions of one or more strata.

For comments on treating periods as temporal strata, see Calculating sampling weights for fisheries data.

Macroinvertebrate data

Methods for estimating strata-specific means from macroinvertebrate count data largely follow those supplied above for fish data. Hence, mean number of invertebrates per unit area may be calculated using the surveymeans code supplied for fish CPUE after replacing “effmin” by 0.053 (the surface area, in m2, of the ponar grab used in LTRM macroinvertebrate sampling). Alternatively, because surface area was constant for macroinvertebrate samples (caveat: volume may not have always been constant), each count may be divided by 0.053 to create a new variable for analysis—thereby eliminating the need for the ratio statement. The following code uses this alternate method to estimate mean mayfly density (where mayflym2 = mayflies / 0.053):

proc surveymeans data= invert;
var mayflym2;
by fieldsta year stratum;
run;

The estimation of percent frequency of occurrence follows that described above for fish.

Vegetation data

The LTRM reports statistics derived from visual and rake data (Yin et al. 2000, Yin et al. 2001). Detection of a species at a site constitutes evidence of species occurrence at that site while, if a species is not recorded at the site, it is treated as absent.  As noted above for fish, this definition of absence may lead to underestimation of percent frequency of occurrence. For submersed aquatic vegetation, we also generate an approximation to abundance by averaging the six rake scores within sites. While rake scores are ordinal, averages of the scores have been associated with log-transformed mean biomass; associations may vary among species (Kenow et al. 2006). At each site, percent cover of vegetation is estimated to be in one of six cover classes (Table 2, Yin et al. 2001). Means of percent cover data are commonly analyzed by substituting the midpoints of each percent cover range for the recorded cover class. However, doing so may yield precision estimates that are biased low.

The code used above for fish and invertebrates may be used to generate annual estimates of percent frequency of occurrence, mean rake score and cover class within strata. Each of these variables may be estimated using the following code (here using wild celery data):
 
proc surveymeans data= VAAM3FS3;
var sitedetect meanrake cov_nrf cov_rf cov_e;
by pool year mstratum;
run;

Adding a class statement with any of the cover variables will yield estimated probabilities for each cover class:
 
proc surveymeans data= VAAM3FS3;
class cov_nrf cov_rf cov_e;
var cov_nrf cov_rf cov_e;
by pool year mstratum;
run;

Water data

The following may be used to estimate strata means for all water quality constituents, and for all field stations, seasonal sampling episodes, years, and strata.

proc surveymeans data=WQall;
var chlf ss vss;  * variable statement can supply one to many variables;
by fs year episode strat;
run;

Output tip

The use of "by" statements can save considerable coding but can create voluminous output to the computer screen. An easy way to address this issue is to route output to electronic files. The resulting, much-condensed output can then be printed (possibly after further manipulation) to the screen or hard copy. For example, the code for water data may be modified by adding "ods" [output delivery system] statements:

In the above example, all requested statistics are saved in a single file called "stats. "  The contents of "stats" can then be printed to screen.

References

Kenow, KP, JE Lyon, RK Hines and A Elfessi. 2007. Estimating biomass of submersed vegetation using a simple rake sampling technique. Hydrobiologia 575:447-454.

Yin Y, JS Winkelman and HA Langrehr. 2000. Long Term Resource Monitoring Program procedures: Aquatic vegetation monitoring. U.S. Geological Survey, Upper Midwest Environmental Sciences Center, La Crosse, Wisconsin. LTRMP 95-P002-7. Available on the world wide web at http://www.umesc.usgs.gov/documents/reports/ltrm_components/vegetation/95p00207.pdf.

Yin, Y, H Langrehr, T Blackburn, M Moore, J Winkelman, R Cosgriff and T. Cook. 2001. 1998 annual status report: Submersed and rooted floating–leaf vegetation in Pools 4, 8, 13, and 26 and La Grange Pool of the Upper Mississippi River System. U.S. Geological Survey, Upper Midwest Environmental Sciences Center, La Crosse, Wisconsin. LTRMP 2001-P001. Available on the world wide web at http://www.umesc.usgs.gov/documents/reports/ltrm_components/vegetation/01p001.pdf.

Contact: Questions or comments may be directed to Brian Gray, LTRM statistician, Upper Midwest Environmental Sciences Center, La Crosse, Wisconsin, at brgray@usgs.gov.