Abundance Indices

ChesMMAP - Estimating Abundance:

Time‐series of abundance information are standard products developed from the basic catch data of a fishery independent monitoring survey. For each species sampled by the ChesMMAP Survey, a variety of relative abundance trends can be generated according to year, season, and location within Chesapeake Bay.


While minimum total or absolute abundance estimates are important for certain bioenergetics and ecosystem level analyses, fishery assessments typically depend upon relative abundance indices from surveys as important indicators of abundance. Previous ChesMMAP project progress reports have presented an evolving series of relative and absolute abundance estimates.  Indices are presented here based on the previous ‘geometric mean’ calculation method.


Using the restricted data, annual geometric mean catch per area swept indices for each species for all ages combined, were calculated according to the formula:

 

       equation 3

 

          Where:

          I = Index
          C = number or biomass caught at a station
          a = area swept at a station
          i = ith stratum
          n = number of strata
          w = stratum weight

 

NEAMAP - Estimating Abundance:

Abundance Indices: The methodology employed to calculate relative abundance indices for the NEAMAP survey has evolved with nearly every annual report and is still being developed.

• Initially, as it was considered impractical to report point estimates with only one or two data points, abundance was reported as ‘minimum trawlable abundance’ by state. These were area‐expanded area‐swept calculations and helped show the general pattern of distribution of species of interest.

• Catch data from fishery‐independent trawl surveys tend not to be normally distributed. Preliminary analyses of NEAMAP data showed that, at least for some species, these data followed a log‐normal distribution. As a result, following reports utilized the stratified geometric mean of catch per standard area swept, including catch data from all stations for every species so analyzed, as an appropriate form for the abundance indices generated by this survey.

• The next iteration involved making two simultaneous changes to the methodology used for calculating abundance indices. First, due to the small number of years sampled through 2009, as stated above, prior abundances had been calculated using data from all survey strata, for all species. Given the broad geographic range of the survey, for many species this resulted in a larger than necessary number of zero values entering the calculation, as some species were rarely captured in many survey strata. These zero values both unnecessarily biased point estimates and inflated variance estimates. In 2010‐2011 it was considered that enough data had been gathered over relatively warm and relatively cold years so that reasonable restrictions could be defined as to which strata were to be used for each species. Therefore strata were selected for inclusion and exclusion on a species by species basis (these defined strata can still be refined as more data are gathered in future years).

• The other change made in 2011 involved the ‘transformation’ and ‘back‐transformation’ involved in calculating the geometric mean. As stated above, this and many other fishery surveys have used the geometric mean for reporting indices of abundance because survey data catch rates often approximate a log‐normal distribution. However, the process of calculating the geometric mean introduces statistical anomalies in and of itself. For example, back‐transformed confidence limits are non‐symmetrical, and because the variance estimate itself cannot be back‐transformed, coefficients of variation have to be calculated on transformed data and then reported on the backtransformed means. To address these issues, in the immediately preceding NEAMAP annual report we reported indices without retransforming data from the log scale. This was done on an exploratory basis and subsequently NEAMAP survey investigators recognized that the disadvantage of compression of the ranges of abundance indices due to the logarithmic scale outweighed any perceived advantages.

• Abundance estimates are presented here as the (back‐transformed) geometric mean, using only the strata of importance for each species.

 

For a given species, its abundance index for a particular survey cruise is given by:

neamap abundance indices equation

 

• In addition to the overall abundance estimates, for several species in this report, either separate young-of-year (YOY) or several age-specific indices are also reported.

• For species for which either a reliable literature source or examination of NEAMAP length-frequency plots (or both) revealed a dependable single YOY length cutoff value (separately for spring and fall surveys to allow for growth) this value was used to segregate the youngest survey age class (typically age-0 in the fall and age-1 in the spring as the species passed its assigned assessment birthdate during the succeeding winter) to calculate indices for that youngest age class. These species are alewife, Atlantic menhaden, black sea bass, blueback herring, silver hake, and smooth dogfish.

• For species for which a sufficient numbers of otoliths have been examined to allow estimation of age-length keys, these keys were developed and the proportional age-at-size assignments were made to NEAMAP length data and age-specific abundance indices then calculated. For certain species aged specimens from other VIMS surveys were pooled with NEAMAP samples to achieve adequate sample sizes.  Wherever sufficient data was available, these age-specific indices were calculated for the same age classes as were used in the most recent assessments. These species are Atlantic croaker (ages 0 – 4+), bluefish (age 0 – spring and summer cohorts separately), summer flounder (ages 0 – 7+), weakfish (ages 0 – 3+), and winter flounder (ages 1 – 7+).

• NEAMAP investigators are still evaluating alternatives for abundance index calculation. Preliminary examination of NEAMAP catches indicates that for at least some species a delta lognormal based index may best fit the underlying statistical distribution of catches.  While these investigators realize that these several changes can result in a certain amount of confusion by users of these data, it is still (hopefully!) early in the NEAMAP time series and it is considered preferable to eventually make these calculations as statistically robust as they can be rather than to too-early settle on an inferior methodology simply for the sake of consistency.