Fisheries metrics

CensusIO computes several fisheries metrics from your measured fish. Two of them, relative weight and size structure, use published standards, so they only run for species CensusIO has the reference data for. Age and growth, recruitment, and CPUE are computed from your own data, so they work for any species, given the fields each needs.

Relative weight (Wr)

Relative weight compares a fish’s weight to the standard weight of a fish of the same length and species, on a scale where 100 is average: below 100 is thin (poor condition or forage), above 100 is heavy (well fed). It is reported as the mean across the measured fish of a species, with a 95% confidence interval.

The standard weights come from the American Fisheries Society (the Ws75 equations). CensusIO ships the equations for:

Largemouth bass, smallmouth bass, bluegill, black crappie, white crappie, walleye, yellow perch, northern pike, channel catfish, rainbow trout, and brown trout.

Condition by size class

Because condition changes with size, CensusIO also reports it by size class, not just as one number per species:

For a species with a standard, it is mean Wr by Gabelhouse category (stock-quality, quality-preferred, and so on), which shows where in the size range condition is good or poor.
For a species without a standard, it is Le Cren’s relative condition (Kn) by size class. Kn is the weight divided by the weight the species’ own fitted length-weight curve predicts, so a class above 1 is heavier than the population norm and below 1 is thinner. (A pooled mean Kn would be about 1 by construction, which is why it is only shown split by size.)

Size classes are the Gabelhouse categories where they are published, otherwise simple length terciles (small, medium, large). A class needs at least three fish to be shown.

Size structure (PSD)

Proportional size distribution (PSD) is the percent of stock-length fish that also reach quality length, a quick read on whether a population has good numbers of larger fish. CensusIO also reports the finer steps (the share reaching preferred, memorable, and trophy length).

The length thresholds are the standard Gabelhouse categories (stock, quality, preferred, memorable, trophy). CensusIO ships them for the common warmwater species:

Largemouth bass, smallmouth bass, bluegill, black crappie, white crappie, walleye, yellow perch, northern pike, and channel catfish.

A balanced population usually sits around 40 to 70. PSD is reported as a value without a confidence interval.

Age, growth, and mortality

When a survey records a fish’s age (read from otoliths, scales, or spines) alongside its length, CensusIO builds an age-and-growth view for each species you have aged:

Mean length at age: the average length of fish at each age, the simplest growth summary.
Von Bertalanffy growth: the standard growth curve fitted to your age-length data. It reports the asymptotic length Linf (the length fish grow toward), the growth coefficient K (how fast they approach it), and t0 (the modeled age at length zero), with an R-squared for how well the curve fits.
Catch-curve mortality: total annual mortality and survival, from the decline in numbers across the older ages (the Chapman-Robson estimator).

Growth and mortality need a good spread of ages, including older fish, to be reliable. CensusIO holds back a growth curve when the sample is too small or too near-linear to pin down the asymptote.

Recruitment

From the same aged fish, CensusIO reads how strong each year class was and how steady recruitment has been (Maceina 1997). On the catch curve, the line through the older ages is what you would expect if every year class had been average; a year class that sits above the line was strong (more fish survived than the trend predicts), one below it was weak.

Year-class strength: for each age, the residual from the catch-curve line (in natural-log units) and a label of strong, average, or weak. With a survey date, each age is tagged with its year class (the sample year minus the age).
Recruitment variability: the catch-curve R-squared and the spread of the residuals. A high R-squared (a tight fit) means recruitment was consistent year to year; a low one, with a wider residual spread, means it varied, the signature of boom-and-bust year classes.
Young-of-year (YOY) index: the share of aged fish that were age 0, by year, a read on the most recent year class. Age-0 fish sit below the peak of the catch curve, so they inform this index rather than the residuals.

Recruitment needs at least three age classes on the descending limb, and reads the residuals as distinct cohorts, so it is most meaningful for a single sampling period rather than pooled across many years.

When the aged survey also records the sampling effort and a haul key (a site field or a GPS point) on each fish, recruitment adds a young-of-year (YOY) CPUE: the age-0 catch divided by effort, averaged over hauls, by year. Because it divides by effort, it holds up when effort changes from year to year, where the plain age-0 share does not.

Catch per unit effort (CPUE)

CPUE is the standard relative-abundance index: the catch divided by the sampling effort that produced it, so a net set overnight and a longer trawl tow land on the same scale. It needs a survey type that records, per sampling event, a species, a catch (the number caught), and the effort (net-nights, electrofisher on-time, trawl hours, and the like). For each species it reports:

CPUE (overall): total catch divided by total effort across events, effort-weighted.
Mean CPUE: the average of each event’s own catch rate, with a 95% confidence interval.

Compare CPUE only within the same gear and effort unit: a gillnet CPUE and an electrofishing CPUE are not on the same scale, since gears differ in what they catch.

Stock and recruitment

A stock-recruitment curve relates the recruits a population produces to the spawners that produced them, the relationship behind sustainable harvest. From a survey that records, per year, a stock’s spawners (escapement) and its resulting recruits (age-0 or a recruit index), CensusIO fits the two classic curves:

Ricker: recruitment rises, peaks, then declines as spawners crowd (overcompensation). The report gives the peak recruitment and the spawner level it occurs at.
Beverton-Holt: recruitment rises to a ceiling set by a fixed carrying capacity. The report gives that asymptotic ceiling.

Both are fitted to each stock; compare their R-squared to see which describes your data better. The parameter a is recruits per spawner at low density (productivity), and b is density dependence. The fit needs at least three years of paired data and assumes each row is one year of one stock with roughly lognormal recruitment variation.

Fish biotic integrity (IBI)

The fish index of biotic integrity (Karr 1981) scores a stream’s whole fish community on its biological health, not one species at a time. From a fish survey that records the species seen at each reach (and a count, when a row stands for more than one fish), CensusIO scores the transferable, fixed-threshold metrics:

Trophic make-up: the percent of individuals that are omnivores (lower is better), invertivores or insectivores (higher is better), and top carnivores (higher is better).
Tolerance: the percent of tolerant individuals and the percent of introduced individuals (both lower is better).
Condition: the percent of fish with a DELT anomaly (deformity, eroded fin, lesion, or tumor), scored only when the survey records anomalies.

Each metric scores 5, 3, or 1, and the total is reported as a percent of the maximum, which maps to an integrity class: excellent (90% and up), good (80 to 89), fair (67 to 79), poor (47 to 66), or very poor (below 47). When the survey has a site, station, or reach field, each reach is scored on its own community, since the IBI describes one stream reach; a pooled view gives the per-metric breakdown.