Biological research

Researchers measure, weigh and sex fish at the landing site and stage their maturity. eResearch gathers those specimens from FAIMS research forms into one table and runs size structure, length-weight and maturity analyses on them, with every method and its source written next to the result.

fish measured: 147,721
species: 113
sampling sites: 134
with a maturity stage: 47,565

One table of specimens

Research teams design their own forms in FAIMS: a biometrics sheet for Lake Tanganyika sardines, an octopus sheet for the coast, a tuna sheet, a ring-net study. Each form names its fields differently. eResearch keeps a map from each form’s fields to a common set of columns and copies every fish into one specimen table, so an analysis can run across forms, years and countries.

A specimen row holds the species, gear, landing site and date, a length of the type that suits the animal, the weight, gonad weight, sex and maturity stage. Seven length types are kept apart and never mixed in one analysis: total length, fork length, standard length, disc width for rays, carapace length and width for crabs and lobsters, and mantle length for octopus and squid. A biometric record can also be linked to the catch record of the boat it came from.

Measuring from photos

Lake Tanganyika’s sardines and small lates are landed by the tonne and are a few centimetres long, so measuring hundreds by hand at dawn is slow. On the biometrics form an enumerator can photograph fish on a measuring board instead. A detection model finds each fish, converts its length in pixels to millimetres with a fixed scale for the species, and returns the lengths for the enumerator to check before anything is saved.

The scales are set for three species, Limnothrissa miodon, Stolothrissa tanganicae and Lates stappersii, photographed in a fixed setup. The feature is not meant for other species, and no accuracy figure has been published for it yet.

Size structure and reference points

The starting point is a length-frequency table in classes one unit wide, one centimetre or one millimetre depending on how the species is measured, which can be split by district, month or gear. From the same lengths eResearch derives the reference points used in length-based screening. It needs at least ten fish.

log₁₀ L∞ = 0.044 + 0.9841 × log₁₀ Lmax log₁₀ Lm = 0.8979 × log₁₀ L∞ − 0.0782 Lopt = 3 L∞ / (3 + M/K) Lc = first length class with at least half the modal count

Lmax: largest fish in the sample
L∞: asymptotic length, from a stored growth study when one exists, otherwise from Lmax (Froese and Binohlan, 2000)
Lm: length at first maturity, used only when the stock's own maturity ogive is missing
Lopt: length at which a cohort reaches its largest biomass (Beverton, 1992), with M/K = 1.0 unless a value is stored
Lc: length at first capture

The regressions were fitted on total length in centimetres, so they are applied only there. Samples measured in millimetres are converted; samples measured as mantle or fork length get the observed figures but no predicted reference points until a conversion to total length is stored.

The share of mega-spawners, fish longer than 1.1 × Lopt, is reported without a verdict, because whether it is high or low depends on how the fishery is harvested (Froese, 2004). The comparison of Lc, L50 and mean length with Lopt is labelled screening only. eResearch says in plain words that size comparisons do not establish the state of a stock, and it never shows a stock status badge.

Length and weight

The weight of a fish grows roughly with the cube of its length. The exponent b says how far a stock departs from that: below 3 the fish get relatively thinner as they grow, above 3 relatively stouter.

W = a × L^b ln W = ln a′ + b × ln L, a = a′ × exp(s² / 2)

s²: residual variance of the log fit, used to correct the bias of back-transforming (Sprugel, 1983)

eResearch fits the curve three ways: least squares on the logs with that correction, a direct power fit by Levenberg-Marquardt, and a penalised spline that lets the shape bend. It shows all three side by side and does not pick a winner. A fit needs at least thirty fish whose lengths cover a third of the species’ known range, because a fit through a narrow size band says little about the rest.

Maturity

Stages I and II count as immature; III, IV, V and spent count as mature, since a spent fish has already spawned. A logistic curve is fitted to the share of mature fish by length, for each sex and for both together, and its uncertainty comes from resampling the fish 500 times by default, fewer for very large samples.

P(mature | L) = 1 / (1 + exp(−(β₀ + β₁ L))) L50 = −β₀ / β₁ L95 = L50 + ln(19) / β₁ GSI = 100 × gonad weight / body weight

Alongside the ogive come the sex ratio tested against 1 to 1 with a chi-square test, the gonadosomatic index by month, which shows when a stock spawns, and the share of the sample caught below L50, before it had a chance to breed.

Checking specimens

Sixteen rules run over the specimen table and send what they find to a review register. Most catch a slip that is easy to make in the field and hard to see in a spreadsheet:

millimetres typed into a centimetre field, or the reverse;
a length outside the known range of the species;
a weight a thousand times too big or too small for the length;
a gonad heavier than the fish;
a collection date in the future;
the same fish entered twice.

Analyses use only lengths inside the species’ range for that length type, and report how many fish were left out.

Results

Fish measured per year By water body

Most measured species Specimens, all years

Length frequency Specimens by length class

Maturity ogive Share mature by length class, with the fitted curve

Length and weight Median weight by length class, with the fitted curve

Where fish were measured Landing sites, sized by the number of specimens

Figures are refreshed from FAIMS every night. They are provisional and not for citation. The curves on this page were fitted for the website with the same definitions: logistic ogives without the resampling, and length-weight by least squares on the logs. A curve is shown only when it passes a basic plausibility check, which ruled out the length-weight fits of four of the five species, where weights look recorded per batch or in another unit. The octopus samples, the largest set, are left out of the length charts until their units are confirmed.

References

Beverton, R. J. H. (1992). Patterns of reproductive strategy parameters in some marine teleost fishes. Journal of Fish Biology 41 (Suppl. B), 137 to 160.
Efron, B. and Tibshirani, R. J. (1993). An introduction to the bootstrap. Chapman and Hall, New York.
Froese, R. (2004). Keep it simple: three indicators to deal with overfishing. Fish and Fisheries 5, 86 to 91.
Froese, R. (2006). Cube law, condition factor and weight-length relationships: history, meta-analysis and recommendations. Journal of Applied Ichthyology 22, 241 to 253.
Froese, R. and Binohlan, C. (2000). Empirical relationships to estimate asymptotic length, length at first maturity and length at maximum yield per recruit in fishes. Journal of Fish Biology 56, 758 to 773.
Gayanilo, F. C., Sparre, P. and Pauly, D. (2005). FAO-ICLARM stock assessment tools II (FiSAT II), user's guide. FAO, Rome.
King, M. (2007). Fisheries biology, assessment and management. Second edition. Blackwell, Oxford.
Le Cren, E. D. (1951). The length-weight relationship and seasonal cycle in gonad weight and condition in the perch. Journal of Animal Ecology 20, 201 to 219.
Sparre, P. and Venema, S. C. (1998). Introduction to tropical fish stock assessment. Part 1: manual. FAO Fisheries Technical Paper 306/1, revision 2. Rome, FAO.
Sprugel, D. G. (1983). Correcting for bias in log-transformed allometric equations. Ecology 64, 209 to 210.
Wood, S. N. (2017). Generalized additive models: an introduction with R. Second edition. CRC Press.
Zar, J. H. (2010). Biostatistical analysis. Fifth edition. Pearson.