^{1}

^{1}

^{*}

The worldwide increase of the publications concerning the assessment of marine renewable living resources is highlighting long-standing problems with symbols and annotations. Starting from the symbols presented within the classic fisheries masterpieces produced, mainly in the fifty of the last century, a first “Milestone” list was organised. Thereafter, the pertinent literature was (not exhaustively) browsed in order to integrate this Milestone list on the base of a set of decisional criteria. The present contribution consists in using the Latin letters as well established symbols for the corresponding parameters, leaving free to specific use (with few historical exceptions) the Greek letters in view to open a discussion among all the fisheries scientists and bodies in order to move towards a common language and better communication standards.

The intuition to separate out the effects of births, deaths and growth on fish populations in order to estimate the surplus production of an exploitable stock has been developed since the first decades of the twentieth century [1-4]. The origin of fisheries science, as an integrated and structured discipline, however, might be generally placed at the second half of fifties and first half of sixty, when the milestones of Beverton and Holt [5-7], Gulland [8-11], and Ricker [12,13] were published. At that time, the main goals of such discipline were assessing and managing the living renewable aquatic resources under a theoretical based exploitation pattern. Just little after the Beverton and Holt and Ricker works, it was evident the opportunity to be clear about the definition of physical quantities and naming conventions came [14- 16]. Almost half a century later, notwithstanding the growing importance of assessments to promote credible and effective rebuilding or managing plans for the highly depleted fishable resources in the world, on our knowledge no general agreement exists about a proper and unambiguous annotations and symbols. That notwithstanding a big effort has been realised regarding the definitions [17-23]. In the present contribution, which recalls the Holt’s heading of a section in one of his reports presented at the Biarritz symposium in 1956, the most common pitfall, ambiguities and lack of consistency arising from the literature in the field were analysed and a scheme of symbols usage was proposed in order to encourage fisheries scientists and bodies to move towards the establishment of a common language and better communication standards in assessments terminology.

The pertinent fisheries literature was browsed to highlight the different symbols uses and attributions within a “classic” definition of assessment. In fact, it is worth noting that different assessment interpretations can be found in both grey [

On the contrary, the goals of the classic and narrower assessment definitions can be identified in a) for any given fish populations 1) what are the present quantities that will be available for capture in one or more years and what factors are determining the quantity of the fish and how are they changing [

Considering the classic definitions, the first step consisted in establishing a “Milestone” list with the historical symbols on the base of the fisheries science masterpieces produced in the fifties and sixties, and integrated with the successive contributes of the same Authors. In particular, the following contributes were consulted: Beverton [

Hence, the literature (both official and grey), books, manuals and programmes dealing with fisheries assessments were (not exhaustively) consulted in order to compare and integrate the basic scheme previously established. The final step was proposing a standard set of symbols, preferably (or whenever possible) according to the following Decalogue of criteria and conventions [14-16]. In particular, the symbols:

1) should be referred to the most relevant and studies items in “classic” fishery assessment;

2) should have a unique correspondence for each quantity, at least in base of their position (prefix, suffix, subscripts, superscript);

3) should be found within a standard commonly and easily available (in the specific case, the symbols lists in word Microsoft) avoiding other difficult, already existing, to find symbols [

4) should avoid special characters, such as the circumflex accent or the “ ” symbol, which was employed for example by Gulland [11,30] with the meaning of “therefore” or “consequently” [60; page 415];

5) should be different from those symbols traditionally well established in other related discipline (such as statistics);

6) in the masterpieces proposals or traditionally established should be maintained;

7) should consist of one to three “components” (never more than four letters), considering that in many instances many subscripts could be necessary [

8) should represent the initial words of the considered variable;

9) should help in expressing the relevant formula in a simple and compact form, which is easy to write, type and print;

10) similar should indicate similar measures.

In both Milestone and proposed list, the symbol § and §§ denote some remarks relative to the proposed symbol definition and alternative meanings of the same symbols, respectively. At the beginning of the proposed list, the X symbol was employed to represent some generalisations. Finally, the following abbreviations were adopted: coef. for coefficient, cons. for constant, n˚ for number, par. for parameter, prop. for proportion, and VBGF for von Bertalanffy Growth Function.

a—BH_ Coef. of linear equations relating growth to density; unit haul swept area; intersect in regression line; const.; time interval (for example, in length increment— average length regression); average (strictly speaking) median length in Tauti’s expression. G_ Probability (in age estimation); slope in the linear density dependence regression between asymptotic length and abundance; coef.; hook catch probability; area or volume under the influence of a gear; prop. of full fishing mortality rate; age at recruitment; proportionality coef. (usually 0.5) among yield, natural mortality and stock biomass (Y = aMB) in potential yield computation. I_ Mesh size. R_ Annual (or seasonal) total mortality rate; annual expectation; actual mortality; the first (multiplier) coef. in the (individual) length-weight functional relationship; coef. in Ricker’s recruitment curve (when stock size and recruitment are in the same units); competition coef.; intercept in regression; sex ratio as males over females; Brody’s coef.; intercept in yield per effort against effort; initial size; cons.

α (alfa)—BH_ Derived coef. of pre recruited mortality in the eggs-recruitment relationship; angle definition; cons. G_ Vulnerability; proportionality coef. R_ Par. in the Ricker (dimensionless) and Beverton and Holt R/S curves.

A—BH_ The area occupied by the fish population; Russell’s recruitment. G_ Sum of squares; coef. in ageing error; area of fished region; Russell’s recruitment; (Heincke’s) annual death rate; cons. in stock recruitment curves. I_ Fish breadth/fish depth ratio. R_ Average population in successive years; annual (also Heincke) or seasonal mortality rate; A' annual or seasonal rate of disappearance of fish; maturity categories n˚ in Murphy’s method; par. in other growth model than VBGF; par. in the Beverton and Holt R/S curve when S and R are in the same units; A_{0.95} upper age limit according to Taylor’s approximation [

b—BH_ Selection factor; ratio of length at 50% point of selection ogive (or mean selection length) to mesh size; coef. of linear equations relating growth to density; Huxley’s coef. in fish length-weight relationship (w = bl^{k}); coef. (scale factor) in the Richards curve; coef. in length increment—average length regression; oldest age in Tauti’s expression. G_ Probability (in age estimation); generic coef.; selection factor; density dependence in recruitment; generic slope in linear regression; b_{n} expanding term in the analytical computation. R_ The exponent in the allometric (b ≠ 3) and isometric (b = 3) length-weight (individual) relationship; the slope of any line; proportionality coef. in recruits parental relationships; Brody’s coef.; annual catch in Baranov’s food biomass relationship; intercept in yield-effort (Y/f) against f; cons.

β (beta)—BH_ Derived coef. of pre recruited mortality in the eggs-recruitment relationship; cons. R_ N˚ of marked fish; incomplete beta function; par. in the Ricker and Beverton and Holt R/S curves.

B—G_ Stock biomass (size in weight); sum of squares; coef. in ageing error; biomass, B' in exploited phase; B_{∞} at maximum population (carrying capacity); B_{P} predators; cons. in stock recruitment curves. I_ Mesh length/mesh width ratio. R_ N˚ of natural death; biomass of a group of fish or an entire stock; maturity categories n˚ in Murphy’s method; par. in other growth model than VBGF; prop. of new recruits in the catch (Allen’s method); B_{∞} and B_{S} maximum stock size (the environment will support) and “optimum” stock size corresponding to maximum Y at equilibrium in Graham surplus production curve.

c—BH_ Cons. given by the ratio of fishing mortality and “effective overall fishing intensity” (effort); catch per net. G_ Cons.; c' proportionality coef. relating catch per unit of effort to density of fish (provided that the availability is cons.); reciprocal of vulnerability—aggregation product; coef.; ratio of length at capture and maximum length (in potential yield computations); mean selection or entry to the catch or first capture; Y/Y_{max} ratio in marginal yield analysis; raising factor (from haul catch to stock size). I_ Capture related general par.; X_{c} at first capture; first liable to capture by the fishing gear in use; t_{c} age at entry to the exploited phase or first liability to capture; selection factor. R_ The catch up to any time; Widrig’s catchability; the fraction of the whole stock captured in a single unit of effort; Brody’s coef.; X_{c} compensatory component in natural mortality; par. in growth models different from (or previous than) VBGF.

C—BH_ Catch in n˚; local density (concentration) of fish; C’ catch per effort. G_ Catch in n˚; sum of squares; total catch. C_{1}…_{c} species competing with target species; cons. in stock recruitment curves. I_ N˚ of fish in the catch (catch in n˚); head girth/head breadth ratio. R_ Cons. of integration; catch in n˚ (usually in 1 year); n˚ of fish examined for tags or marks; maturity categories n˚ in Murphy’s method; average minimum age limit of usable stock.

χ (chi)—BH_ Fecundity (/g) coef. G_ χ^{2 }chi square statistic.

d—BH_ Average distance of fish in random movement. G_ Catch per unit of effort; sample catch; density of fish as derived in a given haul catch; mean depth. R_ Annual increase in length in Baranov’s Yield method; absolute increase in length.

D—BH_ Dispersion coef.; unconditional natural mortality rate; expectation of death by natural causes; average density of fish. G_ Density of fish on fishing grounds; n˚ dying of disease; cons. in stock recruitment curves. I_ Expectation of death by capture (unconditional natural mortality rate); expectation of death by natural causes. R_ Total deaths; maturity categories n˚ in Murphy’s method.

Δ (delta)—BH_ R_ Interval; variation; change. G_ One or unit operation.

e—G_ Sample effort. R_ Base of the natural (or Napierian) logarithms.

ε (epsilon)—BH_ Coef. of food utilisation for growth and maintenance; efficiency of utilization of food for growth. G_ Coef. in mortality estimation; random variable in fishing effort analysis.

η (eta)—BH_ Suffix denoting reference to spawning or (first) maturity; marked change in growth; cons. in the differential Richards.

E—BH_ G_ I_ R_ Exploitation rate [F/Z(1 − exp^{−}^{Z})]. BH_ Egg production; X_{E} equilibrium; coef. of anabolism; unconditional fishing mortality rate; expectation of death by capture; par. in the differential length based VBGF; Taylor’s KL_{∞} product. G_ X_{E} expected value; probability of ultimate capture (often exploitation ratio in steady state condition). I_ Unconditional fishing mortality rate; expectation of death by capture. R_ Escapement; (absolute) n˚ of eggs; X_{E} equilibrium (steady state); cumulative fishing effort.

E.F.—I_ Escape factor as length/mesh size.

f—BH_ Fishing activity; effort; intensity; power; overall; weighed mean fishing effort per unit area. G_ Fishing intensity; fishing effort (in some suitable units); f' adjusted; f(X) function. I_ “Japanese” mortality rate; effective overall fishing intensity. R_ Fishing effort (n˚ of units of gear in use); Widrig’s effective fishing effort adjusted, when necessary; f_{S} corresponding to MSY (optimum f).

♀—R_ Females (reproducing the Petersen 1892 table). I_ ♀♀.

φ (phi)—BH_ Dummy (time) variable or general funcion.

ф (phi)—BH_ Dummy (time) variable or general function; ф' and ф'' function relating cost and revenues to F; ratio (generic).

Ф (phi)—BH_ Total n° of age groups into which recruitment occurs.

F—BH_ G_ I_ R_ Instantaneous fishing mortality coef. BH_ 'F/K. G_ F_{1}… F_{f} species on which the target species feed. R_ Size of a progeny in the recruits parental relationships.

g—BH_ Grazing mortality coef. (individual); total fishing effort; fishing effort as recorded; standardized fishing effort. G_ Fishing effort; F/K ratio; rate of growth in short time interval. I_ Fishing effort as collected (uncorrected) or “crude”. R_ Instantaneous rate of growth in models different from VBGF.

γ (gamma)—BH_ Annual egg-production per recruit.

G—B_ Grazing mortality coef.; Russell’s population growth; standardized total fishing effort. G_ exponential growth rate; net (and long term) gain from a change in gear selectivity or area closure. I_ Girth factor; weight of a fish. R_ Instantaneous growth rate (general); Russell’s population growth.

G.F.—I_ Girth factor as fish length/max. girth; girth/length ratio.

Γ (gamma)—BH_ Index of competition (force of concurrence).

h—BH_ N˚ of hour fished; par. in the egg-production per recruit computation, h_{1} and h_{2} cons. in dependence growth on food. G_ Cons. in growth equation. I_ Degree of precision. R_ Annual (or seasonal) relative individual growth rate; weight increment/initial weight ratio; annual growth rate.

H—BH_ Coef. of synthesis in the differential VBGF; par. in M at age variation; par. in the egg-production per recruit computation.

i—G_ X_{i} generic group identification. I_ X_{i }year class. R_ Widrig’s instantaneous rate of (total) mortality of a stock; X_{th} period; X_{i }density-independent component of natural mortality.

I—BH_ Index of fishing intensity; par. in M at age variation.

j—BH_ Exponent related to maintenance requirements (usually 2/3). I_ Fishing intensity; X_{j }age group. R_ X_{th} period of recovering.

k—BH_ Coef. of catabolism in the differential VBGF; growth equation coef.; Huxley’s coef. in w = bl^{k}; k_{2 }and k_{0 }Baranov’s fishing and natural mortality coef.; k_{1} coef. in linear approximation to a selection ogive; coef. G_ Total n˚ of fish in unit weight; n˚ of strata; sub-areas proportionality coef.; coef. in the Ricker exponential and VBGF; slope in the linear density dependence regression between mortality and abundance; cons. in growth equations; average fecundity. R_ Factor of proportionality; growth coef. in model different than VBGF; Ford’s growth coef.; a rate used in various connections; instanttaneous rate of increase in Graham surplus production curve (V of Graham); instantaneous growth rate of a stock.

κ (cappa)—BH_ Cons. relating F to “destruction” mortality.

K—BH_ I_ One of the two main par. of the VBGF, proportional only to the catabolism coef. (hence, more sensible to temperature variation); par. expressing the relative rate of approach to asymptotic size; coef. Defining the sampling efficiency of a gear (in fish dispersion); X_{K} an alternative gear to be compared. G_ Coef. Proportional to the rate at which the fish completes its growth; the rate at which the limiting length is reached in the VBGF; selection factor in gill-nets; a new gear. I_ Coef. in the allometric relationship W = KL^{n}; head depth/head breadth ratio. R_ A rate used in various connections; rate of change in length increment in VBGF; Brody coef.; any rate; generic cumulative catch; integration cons.; n˚ of degree days; Ivlev’s growth efficiency coef.

l—BH_, I_, R_ Length. BH_ l' some arbitrary length above which all fish are considered recruited to the gear. G_ Length; mean n˚ per unit weight for a length group; l_{c} at first capture; l_{d} gill net deselection; l_{m} gill net maximum efficiency; l_{p} partial recruitment (discards); l_{r} recruitment; l_{s} minimum size.

λ (lambda)—BH_ Fishable life span; maximum age a fish can attain; end of (fishable) life span; the age above which older fish contribute to fisheries can be considered practically negligible (in most cases considered λ = ∞). G_ True mean n˚; true survival rate. R_ The last period (the greatest age) considered in which an appreciable catch is made; the end of life span or maximum age attained; Halliday’s (1972) “maximum age of significant contribute to fisheries”; λ_{1} the probability of capture between competing species; difference between maximum and recruitment ages.

L—BH_ Length of individual fish (particular); loss rate of marks; L_{∞} upper asymptote of length; X_{L} age at which the fish do not appear in the catch (for different reasons). G_ Mean n˚ per unit weight for a length group; total life span in the fishery; L_{∞} maximum length, especially in the VBGF; immediate losses after gear selectivity change or area closure. I_ Fishable life span; length. R_ (Mean) length at recruitment (in Baranov’s yield method); fork length.

Λ (lambda)—G_ Average n˚ of landed fish.

m—BH_ Apparent mortality coef.; m_{0} and m_{1} in linear regression; coef. in M at density; instantaneous mortality (in fish dispersion); slope coef. in regression line; exponent in the differential Richards; X_{m} size at maturity. G_ Mesh size; average n˚ of fish; exponent in general production model; cons. in Richard’s growth curve; M/K ratio; haul catch. I_ Mesh size. R_ The fraction of the initial population which has been caught up to time t for which the term “fishing mortality” will be reserved; m_{1} the fishing mortality up to the season end (also rate of exploitation); annual or seasonal/(fishing) mortality rate (if no other causes operate; Widrig’s m); conditional fishing mortality; sample size; variable exponent in Pella and Tomlinson surplus production curve; c_{m} maximum recruitment; slope of the Richards curve at the inflexion.

♂—R_ Males (reproducing Petersen 1892 table). I_ ♂♂.

μ (mi)—BH_ Density independent and interaction components of mortality; μ_{1} and μ_{2} linear coef. in M at density. G_ Apparent survival rate. I_ Coef. defining the relationship between mesh size and fish girth. R_ (Annual) expectation of death by capture; rate of exploitation.

M—BH_ G_ I_ R_ Instantaneous natural mortality coef. BH_ M'; M/K; M_{1} and M_{2} density independent and dependent. G_ M' limiting value approached by biggest fish; apparent n˚ in a year class; X_{M} maximum. I_ Mesh; mesh size. R_ M' n˚ of fish marked; mean abundance of predators; average age of first recruitment.

M.I.—I_ Mesh index.

n—BH_ N˚ of marked fish recaptured; generic n˚ of items. G_ Generic n˚ (ships, years, sampling days, hooks in a long-line); generic exponent in the VBGF in weight. I_ X_{n }age group; exponent in the allometric relationship W = KL^{n}. R_ Annual or seasonal (natural) mortality rate (if no other causes operate), Widrig’s n; conditional fishing mortality; sample size; exponent in growth related models (Richards, Ursin and growth—temperature models); any generic n˚.

υ (ni)—BH_ Nutritional factor. R_ (Annual) expectaion of natural death.

N—BH_ G_ R_ N˚ of fish in a homogeneous group (N_{X} year class). BH_ Total n˚ in stock. G_ N˚ of fish measured; real n˚ in a year class; abundance; n˚ in the stock; sampling days; N_{R} and N_{k} released and retained after a change in gear selectivity. I_ Total n˚ of fish in the exploitable phase of the stock. R_ N˚ of fish in a year class or populations; N_{0} at the beginning.

o—G_ Subscript denoting observed values.

ω (omega)—BH_ Average weight of individual food organisms during their “grazeable” life span.

O—G_ N˚ of fish dying of other causes than fishing.

Ω (omega)—BH_ Expanding term (summation cons.) in year class weight computation.

p—BH_ Standing crop; prop. of fish caught in unit haul swept area; probability of capture; fish of a given length present in the swept area; shape related coef. G_ Fraction; n˚ (or prop.) of fish (also retained) or items (hooks) of a given type; p_{i} relative fishing power; X_{p} production of plant; positive cons. in the incomplete Beta function. R_ Population at the start of the fishing season; Widrig’s instantaneous rate of fishing mortality; total mortality multiplied by the ratio of fishing deaths to all deaths; complement of catchability; par. in Allen’s recruitment method; generic coef. in regressions.

π (pi)—G_ Prop. in the whole sample.

P—BH_ Generic (mean) abundance or population size in weight (P_{W}) or n˚ (P_{N}); (annual) production; total weight in stock; P_{m} fishing power; P_{l} n˚ of fish of length l which is liable to capture by the gear. G_ Probability level; year period; population size; n˚ of fish dying from predation; P_{H} production of herbivorous; P_{1} … P_{p} predators eating the target species; selective gill-net; fishing power; generic par. I_ Total weight (biomass) of fish in the exploitable phase of the stock; probability. R_ Size (n˚, weight, egg production etc) of parental stock; level of statistical probability; par. in Jones yield computation.

Π (pi)—BH_ Population size.

ψ (psi)—BH_ Dummy time variable.

Ψ (psi)—BH_ Dummy time variable; par. in M at age variation. I_ Girth related probability of escaping.

q—G_ I_ R_ Catchability coef. relating F to f. BH_ Weight-length coef. in W = ql^{3}; prop. completion (q = 1 − p); fish of a given length retained in the cod-end; generic n˚ of years. G_ Availability. I_ The ratio between the best index of effective overall fishing intensity and the resulting instantaneous fishing mortality coef. R_ Widrig’s instantaneous rate of natural mortality; total mortality multiplied by the ratio of fishing deaths to all deaths; Baranov’s integration factor; generic coef. in regressions.

Q—BH_ Physiological-temperature coef.; expansion term; maintenance energy coef. (also per unit physiological surface); Q_{10} physiological-temperature coef. (Arrhenius) rule. G_ Gross long term increase in catch following change in selectivity or area closure; prop.; coef. in non linear catch per unit effort—effort relationship. I_ Initial slope of the eumetric catch curve (Holt’s responsiveness of the stock); fishing intensity/fishing mortality ratio. R_ The yearly n˚ of fish which reaches the minimum reference age (X_{Q}) used in yield computations; the cons. which appears in the integration of Baranov’s yield computation; par. in Jones yield computation; par. in Allen’s recruitment method.

r—BH_ Annual recruitment to a food population; r_{th} period; amount of food consumed per unit time (unit ration); generic cons.; fish escaping from parts of the net other than the cod-end. G_ Replacement; radius (or influence) of a fishing gear; maximum rate of population growth; time intervals; prop. recruited to the gear; age at first capture. I_ X_{r} at recruitment to fishable stock; t_{r} age at entry to the exploitable phase. R_ The fraction of the population remaining at time t; Widrig’s availability fraction; the fraction of the stock susceptible to fishing; rate of accession (analogous to survival rates); greatest age involved; difference between recruitment and initial ages; food ration; correlation coef..

ρ (ro)—BH_ Pre exploitation phase; recruitment at the area where the fishing is in progress; ρ’ entry to exploited phase (first retained). R_ Rate of fishing.

R—BH_ G_ I_ R_ Recruitment related par. B_ N˚ of fish recruited annually to the exploited area; n˚ entering the exploitable phase in a given period; R’ n˚ entering exploited phase each year at age t_{ρ’}; maximal ration; n˚ of recaptured marks. G_ R' n˚ at the age of first capture; R_{1} … R_{R} species affecting the recruitment of target species; raising factor. I_ N˚ of recruits entering the exploitable phase. R_ (Absolute) n˚ of recruits to the vulnerable (catchable) stock whatever by movements in to the region fished or by change in size or behaviour; n˚ of recaptured marks; multiple correlation coef.; feeding ration.

s—BH_ Sex ratio as % of mature females in total mature population; physiological surface area; mean survival rate; fish which would have been caught in a large cover applied to the body of the gear; ratio of the catch obtained in a haul to the saturation catch. G_ Surface area of a fish; raising factor. I_ Observed annual fraction surviving; selection factor. R_ Rate of survival; standard deviation; X_{s} condition of maximum sustainable yield.

σ (sigma)—BH_ Standard deviation; σ^{2} variance; generic cons. G_ σ^{2} population variance (var for the sampling variance).

S—BH_ Grazing efficiency; Russell’s stock size in weight; variance (in recruitment). G_ (Annual) rate of survival; Russell’s stock size; abundance of spawning stock; prop. of retained fish; X_{S} minimum limit; standard deviation. I_ Annual fraction surviving (survival rate); selection factor; the girth at which the fish is meshed. R_ Rate of survival; S' apparent.

S.F.—I_ Selection factor as fifty percent (retention or escaping) point/mesh size.

Σ (sigma)—BH_ R_ Summation sign.

t—BH_ Age of fish; t' and t'' coef. in linear approximation to a selection ogive; t_{0} scale cons. in the VBGF (or theoretical age at which the size is zero); t_{r} age at recruitment; t_{c} age at which fish are liable to be retained by the gear; t_{L} mean age of the oldest fish. G_ Time period; t_{0} some previous time and cons. in VBGF; t_{c} at first capture; t_{L} maximum age in the fishery; t_{p} partial length recruitment; t_{r} at recruitment. I_ Time or age. R_ Time or age; time required for growth in growth—temperature models.

τ (tau)—BH_ Recapture period in marking; calendar date.

θ (theta)—BH_ Age group n˚; X_{θ} prop. of females of age-group θ that are mature; angle definition; the youngest age group free from the influence of recruitment of gear selectivity.

T—BH_ Transport coef. (rate of interchange of fish between adjacent areas); mean age in catch or exploited phase; T_{max} maximum age in the sample; gross tonnage; fraction surviving; total. G_ Upper bound of a given time interval; time; non selective gear; gross tonnage. I_ Transport coef. R_ Interval of time; successive intervals in the life of the fish (not necessarily of equal length); weighed summation of age groups n˚ (also in Chapman and Robson); totals; temperature (in Celsius); metabolism.

u—BH_ Yield per recruit contributed by fish; ratio of grazing mortality coef.; weighting coef.; co-ordinate defining sub-areas. R_ The fraction by n˚ of fish caught by men; rate of exploitation (annual expectation); ratio of recovery to marked fish released; generic ratio; u_{E} equilibrium rate of exploitation (as captures divided by recruits).

υ (upsilon)—BH_ Age group.

U—G_ R_ Catch per unit of effort in n˚ (U_{C}) or weight (U_{Y}). BH_ Sum of square residuals; cons. Summation in yield analytical computation. G_ U_{0} U_{3} cons. in the expression for yield in weight. R_ Instantaneous rate of “other loss” (also emigration and shedding of tags).

v—B_ Co-ordinate defining sub-areas; fraction of a year. R_ Expectations of natural death; v' apparent.

V—G_ R_ Virtual population and cohort analysis par. BH_ Effective velocity of (random) movements; whole n˚ of years; vulnerability. G_ Value of individual fish; fish surviving the n_{th} year of life (in cohort analysis). R_ Utilized stock; variance.

w—BH_ R_ Weight of individual fish. BH_ w_{c} weight corresponding to the (theoretical) greatest steady catch obtainable by catching all fish at once (F = ∞). G_ Mean weight in a group; weight sampled. R_ N˚ of spawners divided by the replacement n˚ of spawners.

W—BH_ Weight of individual fish (particular) and at stock level; W_{∞} one of the two main par. of the VBGF proportional to the cube of the ratio of the coef. of anabolism and catabolism (hence, less sensible to temperature variation); W_{∞} upper asymptote of weight. G_ Weight of landings; mean weight of a age group; individual fish; weight; W_{∞} maximum (limiting) especially in VBGF; W_{c} at mean selection length; average larger than mean selection length; W_{k} of retained catch. I_ W^{∞} par. of the VBGF in weight; fish weight. R_ Reproductive stock; weight of a group of fish (year-class, stock); W_{0} initial weight of a stock; W_{∞} theoretical maximum stock weight in unfished condition; prop. of recruits in Allen’s recruitment method; n˚ of spawners divided by the replacement n˚ of spawners.

x—BH_ Mid point of the length interval. G_ Independent variable in regression generic coef.; X_{x} value in a particular year. I_ X_{x} year class. R_ The ratio of two initial populations; any (mainly dependent) variable (in regression); fractional representation of each age in the catch.

ξ (xsi)—BH_ Annual food consumption (individual).

X—BH_ Denotes a particular year, usually as suffix; “other loss than fishing” coef. in marking theory; fishing effort (in case of no ambiguity). G_ Effort in surplus production; fishing power; other loss rate (in tagging). I_ Mean girth; effective overall fishing intensity (“Japanese” fishing intensity); to be used only in case of no ambiguity (otherwise f should be employed). R_ Different kind of fishing effort; classification of stock composition; par. in Jones yield computation.

Ξ (xsi)—BH_ Annual food consumption of a fish population.

y—BH_ Growth increment (and increment per unit time) in length increment—average length analysis. G_ Dependent variable in regression; generic coef.; instanttaneous rate of capture of hooks. R_ Instantaneous rate of emigration; ratio in Baranov’s food biomass relationship.

Y—BH_ G_ I_ R_ Yield (catch in weight). BH_ Yield in weight (Y_{W}) or n˚ (Y_{N}); total weight in fish catch; Y* expected post-regulation catch; maximum sustained yield or potential yield. G_ Catch in n˚; (yield) in weight; ultimate yield after (Y_{2}) a change in size limit (Y_{K}); performance. I_ Weight of fish in the catch (catch in weight). R_ Catch by weight; Y_{S} maximum sustainable yield; Y' surplus production; different kind of fishing effort; classification of stock composition; dependent variable in regression; individual n˚ of eggs.

z—BH_ Ratio of fished to unfished areas (z = ∞ when the whole area is fished); cons. in year to year recruits variation. R_ Newcomers; instantaneous rate of recruitment or immigration; n˚ of recruits divided by the replacement n˚ of spawners (and recruits).

Ζ (zeta)—BH_ Maintenance food coef..

Z—R_ G_ I_ Instantaneous total mortality coef. BH_ Correction term (in recruitment-egg relations); 'Z/K. R_ Recruitment; recruits to a stock divided by the “replacement” n˚ of recruits; instantaneous rate of disappearance (F + M + U).

The x, X—Individual—(lower case) observation and stock- (capital letter) level par., respectively. § Individual “fish” refers to any generic fish, shellfish or other organism exploited or exploitable [

*X—The asterisk, as left superscript, denotes that the X symbol results already well established (and maintained), but with a different meaning. §§ As right subscript (or superscript) denotes equilibrium quantity [

'X'—A special variant of the X par. As left superscript, a conceptual close par. (for example see 'U). As right superscript, a special case of the same given par. (for example, see A'). Another example is the Y' defined as total yield as a fraction of the RW_{∞} product or X' as an adjusted value[

X^{+}—Cumulated par., integrated beyond an age, size or time limit. _{t}X^{+} plus (terminal) group. _{(x,y)}X^{+} accumulation over the considered range, for example, all previous ages [_{t} terminal catch in VPA; C(L_{1}, _{∞}) [^{+} cumulated catches [_{+} total; overall [^{+} at extinction [

_{c}X—Constrained estimation (to be specified).

X_{(•)}—Estimated via invariants or empirical equations rather than a true estimate. § Estimates uncertain [

_{[}X—The dot at the left subscript denotes a variant (to be specified) from the basic definition. For example, _{•}K_{j} denotes the juveniles K in the biphasic or double VBGF.

_{₪}X—Non equilibrium condition. § Not cons. or random variation without trend par. condition (alternative to steady state).

_{↨}X—Array of values. § X_{array} [

X_{∆}—Par. referring to a finite interval. For example in Chen and Watanabe [

_{∩}X—The Maximum value of a par. § The “maximum” has been often interpreted [_{cri} age at maximum cohort weight t_{cri} in [_{opt }the value which maximizes yield when fishing mortality rate is fixed at the F_{0.1} [_{cri} the length above which all fish are vulnerable [_{y} in [_{opt} ~ M); the maximum value of an equilibrium curve as function of fishing intensity [78; 6, page 389]; the L_{opt} as the length at maximum yield-per-recruit [_{SUP} [_{m} maximum or optimum [

X_{obs}—Observation [

_{}X—Inflexion. For example, W_{a} = 0.29W_{∞} in the isometric (cubic) VBGF.

X_{•}—25, 50, 75 the par. corresponding to 25%, 50% and 75% of a logistic (anti symmetric) curve (or ogive) mostly in selection studies [_{50} are often used to indicate size at (first) maturity or size at gear retention. The 50% has been defined “fifty percent (retention or escaping) point [

_{c}X—Conventional par. For example, the Taylor’s 95% maximum length approximation as index of longevity [62,71].

a—Age [25,61,64,65,67,82-84]. (Absolute) individual age [85,70]. _{r}a relative. § t, T. Population age [^{2} as mean square coefficient of dispersion [^{b} or non exponent coefficient in the length/ weight relationship [

*a—Area fished (interested) by the gear by unit of effort [94;65]. Reference unit area interested by a fishing or experimental unit. a_{s} swept [_{f} over which the fishing effort is distributed. § a [25,71,74,76].

α—Free, to be specified. §§ Season [^{γ} [_{0.1}, F_{ey} and MSY [_{i} Manly-Chesson food preference index [

A—Age [_{r}A relative. § t, T. Total n˚ of age classes [_{0} frequency of age a fish in a random sample A [_{∞}, L_{1}, and L_{2} with M/K [_{j} “total age” of predators [

A_{c}—Age of entry to capture. Age at which 50% of fish enters the exploited phase. A^{c} knife edge (the probability of capture becomes suddenly finite at this point). § t_{ρ’}, t_{c}. Age at which fish are first retained; age at first capture; 50% of selection age for the mesh in question.

A_{ch}—Age of the cohort; all the fish born in a discrete time interval of a given year. For example: A_{1st80}. § Usually coincident with the age class in case of continuous recruitment or one discrete recruitment per year; in case of multiple recruitment pulses, “micro cohort” or “stock let” [

A_{cl}—Age of the year class; age class. All the fish born in the same year. For example, A_{1980}.

A_{g}—Age at generation. Average age of the parents when their offspring are born. § t_{g}.

A_{m} – Age at 50% onset of sexual maturity, based on the present gonadic activity. A^{m} knife edge. _{•}A_{m} other to be specified; for example, mean age of spawners. § t_{m}, T_{m}. Age at first maturity; mean age at maturity; massive maturation [_{m} onwards are usually considered adults [

A_{mean}—Mean age of the stock. Ratio between the integrals of the weighed by age consistency of the different cohorts (numerator) and the consistency of the different cohorts. § T, t, t_{media}.

A_{mx}—Massive age at maturity, the minimum size above which all the fish are able to reproduce independently from the present activity or the production pattern (discrete, continuous, intermittent, batch ecc.). § Almost never implemented; often confused with A_{m}.

A_{M}—Age at end of the reproductive span. Age above which the contribute to spawning of a cohort is negligible. § t_{M.} [

A_{∩}—Age at maximum. Age at which an unexploited or exploited (_{•}A_{∩}) cohort reaches its maximum living biomass corresponding to the balance between growth rate and natural mortality. § Originally referring to the unexploited condition as t_{cri} or t*; critical age [_{∩}/A_{max} ≈ 0.38; 11].

A_{l}—Age of ultimate significant contribute to the fishery. The greatest age for which adequate data usable for fisheries assessment are available. Maximum age above which scanty and not statistical representative samples can be gathered from the stock given the reduction in n˚ as a consequence of fishing mortality (arbitrary threshold: 5% of caught or sampled specimens). § t_{l}, L, A_{L}. Fishing or ecological longevity; maximum exploited age. A par. variable according to the fishing pattern and true longevity of the stock often confused with life span after the classic Jones’ approximation t_{l} ~ ∞.

A'—Age of fully capture. The youngest age that is fully represented in the gross catch sample. A'' the age immediately successive to A' (which should be preferred in computations). § t' [

A_{R}—Age at which the 50% of fish enter the area where the fishing is in progress and becomes liable to encounter with the gear. § t_{ρ}, t_{r}. Recruitment at the fishing grounds; age at which the fish become present in the exploited area and susceptible to the capture with the given gear.

A_{dR}—Age at de-recruitment from the fishery. Age at which the fish are still present in the exploited area, but become no more susceptible to the capture with the given gear (fish will no longer be vulnerable or accessible to the gear for a given fishing pattern). § A_{d}, D50%, R, t_{rif}. Deselection (length) [

A_{L}—Longevity. True life span in unexploited condition. Estimated or observed theoretical (true) longevity (maximum age). Average age of the specimens in the upper tail (95^{th} quantile) [111,112] as estimated from a representative (not biased) sample extracted from an unexploited (or lightly exploited) stock sampled from its natural environment. § T_{max} [_{L} experimental wild longevity. T_{m} [_{max} [

A_{Lx}—Present longevity. The maximum age recorded for the present investigated stock or (A_{Lx}) species by aging just the largest few fish at hand [as proxy of A_{L}; 112]. A_{mx}^{ }estimated according to a method to be specified (mean of n^{th} extremes, extreme values theory etc). § T_{max}, a_{max} [_{max} [

A_{Lxe}—Ever observed longevity. The maximum age ever recorded for the investigated stock or (A_{Lxe}) species in nature (*A_{Lxe} from captivity data). § T_{max}.

_{c}_{x}A_{L}—Conventional longevity. Age at which the cohort has been reduced to _{0.05} (x = 5) or _{0.01} (x = 1) of the initial reference abundance. _{c}_{95}A_{L} age at 95% of the asymptotic length or Taylor’s approximation, originally expressed as = (2.966/K) + t_{0}; often reported as ≈ 3/K).

A_{x}—Age group where x varies from _{I}, _{II}, _{III} _{IV} etc [

A—Age at inflexion. Age at which a discontinuity occurs (to be specified). § t_{η}.

A_{0}—Age at theoretical zero size in the VBGF and allies [_{0} any initial or starting age (such as length at birth in sharks); scale par. to be specified. § a_{0} [_{0} theoretical age at which the weight/length is zero; cons. which simply moves the curves along the abscissa and can be interpreted as the time measured from 0 at which the animal would had zero length if it had followed the same growth curve all its life [

*A—Amount of area occupied by the population or stock [94,76,65]. Reference area of stock distribution. *A_{s} study area. *A_{ f} over which the fishing effort is distributed. § A [67,71].

AA'—The eumetric line joining the (locus) of maxima of yield-mortality curves in the yield-isopleths diagram.

ASP—Annual surplus production [

b—The exponent in the length-length (_{•}b) and lengthweight relationships[25,66,70,74,76,116,117] according to = *kL^{b}. b_{e} and b_{10} after ln and log transformation. b = 1 and b = 3 conventionally denote an isometric (or isogonic) relationship in length-length and weight-length relationship, respectively. ≠1 and ≠3 denote a positive or negative allometry (heterogonic or disharmonic relaionship) [^{k}. Strictly speaking, the isometry and allometry would be used for length-length relationship. n [118,119]. §§ Instantaneous rate of hooking fish [_{0}) such as at settlement [_{∞}.

b'—Slope in the relationship between trophic level and body weight § b [

β—Free. §§ Season indices of adult stock [_{0}), when in fact it is false [

B—Biomass [65,67,76,83,104,107,117]. Average biomass of the fishable stock at equilibrium [_{0} the pristine (unexploited, unfished, prior of any fishing) level [_{∞} theoretical asymptote biomass, the level to which an unexploited (or lightly exploited) stock tend in an undisturbed environment. B_{s} spawning stock. B_{m} at which MSY occurs [_{F} fecund biomass [_{0} virgin or unfished; B_{∞} asymptotic or “pristine”, “virgin”, “unfished” analogous to the logistic K; births [_{inf} or K carrying capacity or unexploited biomass [_{0} natural (no fishing) biomass curve; B** escapement [

BB'—The eumetric line (contours) joining the (locus) of maxima of yield-age at entry (mesh) curves F in the yield-isopleths diagram.

BI—Biomass index. Estimation of local abundance in weight of fish standardized to 1km^{2}. BI_{h}; in case of hour based standardization.

B/R—Biomass per recruit. B'/R, relative [66. § BPR [

c—Capture related general par. with the exception of the (commercial) catchability coefficient (q) relating fishing mortality to fishing effort. X_{c} of entry to fishery; at first liable to capture by the fishing gear in use. Fishable size [65,70]. c_{s} the fraction of fish captured in an experimental set (0 < 1); > 1 in case of herding effect [_{c} at first capture. c, Q, overall gear efficiency, i.e. the prop. of fish which have been in touch of the gear and were at the end captured; exceptionally, fish can be attracted and actively enter inside the codend by the mesh [^{c}; CPUE [_{y} operating cost and cost per unit caught [^{n} [^{m} [Bayley’s method; 70]. Par. in different contexts, for example, as correlation coefficient in the Shepherd’s stock recruitment model; district-specific escapements vector in “run reconstruction” [

*c—Ratio of length at capture and maximum (asymptotic) length in potential yield computations. § c [67,76].

*c_{1}*c_{2}—Hoenig and Lawing’s coefficients; multipliers for estimating Z and its standard error using one of Hoenig’s methods given the sample size from which the longevity estimation was derived. § c_{1}-c_{2} [_{1}-c_{2} interaction coefficients in Lotka-Volterra model [70,71]. Coefficients in Beddington and Cooke potential yield computations [

cov—Covariance [

C—Catch in n˚ [64,67,86,89,95,104,117] related to the fishing activity [25,65,107,70]. C_{g} gross; C_{b} not target; C_{r} retained on board; C_{l} live; C_{r} rejected; C_{u} landed. § Catch in weight [88,129]. N˚ of tagged fish which will be caught [_{W} catch in weight [_{n} food intake [_{im} cumulative catch in n˚ for mesh size m; t terminal catch in VPA. C_{(t)} cumulative catch; n˚ of fish in age a group; capture of marked specimens [_{24} daily ration [

˚C—Sea water temperature in Celsius degrees. ˚C_{b} at bottom; ˚C_{s} at surface.

*C—Factor which expresses the amplitude (or magnitude) of the growth oscillation in the Pauly and Gatschuz’s seasonal length growth VBGF [66,72]. § C [

C^{2}—Par. in Powell Z/K estimation [

CC—Catch curve, the ln of the abundance in n˚ (or index) at successive ages (CC_{a}) or sizes (CC_{l}).

CE—Coefficient of error [

CF—Condition factor [70,116], generally as [w/l^{b}] × 100. _{T}CF Tesch w/L^{b}. _{F}CF Fulton (in case of isometry). _{C}CF Clark. _{rel}CF Le Cren’s relative [_{mean} for Clark [

CH—Cohort (see A_{ch}).

CI—Confidence interval [

CL—Age class (see A_{cl}).

C/R—Catch per recruit in n˚.

CR—Covered region [132,133]; the area included between the trawl doors.

CV—Coefficient of variation [_{•}CV as standard error/mean ratio. As % if not otherwise specified. § C.V. [

χ—Free. §§ Arbitrary reference age in Francis’ VBGF reparameterization [^{th} length frequency interval in MULTIFAN [^{2} [65,66].

d—Average distance of fish in random movement. Distance travelled [_{1} and d_{2} weighting factors in ELEFAN fit; pseudo-random n˚ [_{1} and d_{2} density independent and dependent recruitment effects, respectively; par. in different contexts, for example, correlation coefficient between weight at recruitment and n˚ of eggs; n˚ of deaths [

df—Degree of freedom. § DF [

δ (delta)—Free. §§ Par. in growth model derivation [^{2}) variance [_{t} additive and independent error in each year [^{2} of fish [_{∞} = DK^{−}^{h} relationship [_{D}, it denotes discards; D as diet related par., for example, in Ecopath [

*D—The shape par. in Pauly’s generalised VBGF. § D (gill) surface factor [71,138].

DC—Diet composition [68,82].

DI—Density index. Estimation of local abundance in n˚ of fish standardized to 1km^{2}. DI_{h} in case of hour based standardization.

Δ—Any finite difference [

e—Base of the natural (or Napierian) logarithms; e = 2.71828… [65,66,107]. §§ Unit effort in tagging studies [_{detritus} instantaneous export rate of detritus [

ε—Error term. §§ Mean of the logarithms of n˚ sampled [

є—To not be used in order to avoid confusion with similar symbol. §§ Particle size conversion efficiency [

η—Shape par. in different models (especially in growth curves). §§ Random variable in population equilibrium catch relationship [

E—Exploitation rate [67,74,76] or fraction [_{∞} (t→∞) or E annual (t = 1) expectation of capture. § Fishing effort [_{∞} - t_{c}), hence, as t_{∞} → ∞ E → F/Z. Rate of exploitation (u in [69,123]. E' probability of ultimate capture [118,119]; in case of cons. F/M ratio, it is equal to the exploitation rate. Exploitation pattern in Lleonart [

EE—Ecotrophic efficiency [68,82]. § Fraction of mortality not due to predation or fishing in Ecopath [

ER—Expected revenue [

f—(General) fishing effort [27,74,94,117,127]. f_{c} capacity; f_{n} fishing effort as collected (uncorrected; nominal); f_{e} overall (fleet and time); f_{i} intensity (by unit surface and time); f_{t} time; f_{o} effective overall intensity (weighted sum); f_{MSY} corresponding to MSY [_{MSY} a.k.a. optimum f [_{y} first year of fishery data [_{(x)} net fecundity; average net fecundity; degree of freedom; females; par. in the (fixed allocation) age sample size determination; age [

♀—Females [72,87].

φ—Free. §§ Retention rate; function [

φ—To not be used in order to avoid confusion with similar symbol. §§ Generic par.; function [

Ф—Pauly and Munro growth performance index in weight and Ф' in length; logK + 2/3logW_{∞} and (in case of isometry) logK + 2logL_{∞ }[

F—Instantaneous coefficient of fishing mortality [63, 65,67,70,74,76,86,117,130]. If not specified (see below) it indicate the average (overall weighed) F over the range of age groups which can be considered fully represented in the samples. F_{J} juveniles. F_{p} parental (adults). F_{MAX} at maximum equilibrium yield. F_{max} corresponding to Y/R_{max} for a given entry to fishery. F_{MSY} at maximum sustainable yield [F_{msy} ≡ F_{m }according to 65]. F_{r} ratio of fishing mortality on the oldest age group to the fishing mortality of the preceding age group, used in many tuned VPA assessments [_{λ} terminal (last year for which data are available for assessment; mainly in VPA). F_{↨} array of values according to a model or equation to be specified. F' collateral mortality induced by fishing; for example, mortality due to discard [_{f} [_{ey}, F_{p} where marginal yield per recruit is 10% or p-times the marginal equilibrium yield in a lightly exploited stock [_{max} force of fishing mortality. To remember that F_{MAX} is usually different than F_{MSY}. §§ Biomass flow up the size spectrum; scalar-valued function [

F_{c}—Fecundity (general). N˚ of “mature” (hydrated) “eggs” (strictly speaking oocytes) produced on average by a female of a given size-age. aF_{c} absolute; pF_{c} potential (as the stock of eggs in the ovary before spawning; F_{pot} in [_{c} free eggs released into water (F_{rea} realised fecundity, in [_{c} relative (as function of size or age); mF_{c} life time fecundity (i.e. the progeny derived by a female during its life); dFc daily; Fc_{/R} annual egg-production per recruit. § Often replaced by spawning biomass as a proxy. fec [76,86]. F_{atr} as fecundity and prop. of atresic eggs [

FP—Fishing power. Relative unit efficiency of capture of different vessels versus a standard vessel. § ρ, P, Q. Efficiency. [148,149].

FR—Fished region [

g—Individual general growth rate. g_{a} absolute; g_{r} relative; g_{i} instantaneous; g_{f} finite; g_{s} specific. § Σg sum of growth increments of all individuals surviving at the end of year [_{1} and g_{2} density independent and dependent growth effects, respectively; F/K ratio in the allometric Y/R model; index of gear type [^{γ} [

G—General growth rate at stock level. _{a}G absolute; _{r}G relative; _{i}G instantaneous; _{f}G finite; _{s}G, specific; _{•}G other to be specified. § Stock growth in weight [

*G—General growth rate at stock level as whole population; for example, in surplus production [

Γ—Free. §§ Index of competition. Notation for the gamma distribution; environmental variable affecting recruitment in semelparous population modelling [

GI—Gonosomatic (or gonadosomatic) index; ratio between gonadic (ovaries or testis) and body weight. GI_{o} whole body; GI_{e} eviscerated; _{•}GI to be specified in case gonad weight includes also other reproductive annexes (for example, the ovary glands in cephalopods). § Usually it is considered an index of the state of maturity or of the level of sexual activity (especially in females).

Ger—Gastric evacuation rate. § E [

GML—Growth-maturity-longevity-plot [

GOF—Goodness-of-fit [

h—Hour [25,109]. §§ Time required to capture and consume [_{∞} = DK^{−}^{h} relationship [^{2} measure of genetic heritability; squared of caudal fin. Harvest rate related to fishing mortality [

H—Loss rate of marks. §§ Weight synthesised per unit surface area in the derivation of the VBGF [

HI—Hepatosomatic index; ratio between liver and body weight. HI_{o} whole body; HI_{e} eviscerated.

i—As subscript, generic index to designate stock or site [

ι (iota)—To not be used in order to avoid confusion with similar symbol.

I—Ingestion of food and related par. Food consumption in a given period. Coefficient of food utilisation for growth and maintenance. _{g}I gross food conversion efficiency. I_{S} stock’s feeding requirement (I) in [_{dr} daily ration i.e. the amount of food consumed by a fish of a given weight in one day, and often expressed as % of its own weight [

*I—Separation Index [

∞—Infinite. The upper limit which can (probabilistic) or cannot (asymptote; integral) be touched by the considered par. In the asymptotic case, it might characterise the maximum size towards which a fish (or a stock; [

IALK—Iterate age length key [

j—Juvenile. Fish which has not reached the maturity condition. j_{a}, always, which maintain non developed gonads in spite of a size larger than A_{m} [_{j} as subscript in Walters et al. [

J—Juvenile at stock level. §§ N˚ of recapture period [

k—The coefficient in the allometric length-weight relationship according to w = kl^{b}. k_{e} and k_{10} after ln and log transformation. § C in [118,119]. §§ Catchability in tagging studies [_{a} and k_{t} growth coefficient related to mean length at age and length increment (tagging) analysis [_{1}, k_{2},… k_{n} growth coefficients or rate in different compared models; n˚ of estimable par. in AIC computation [

κ—To not be used in order to avoid confusion with similar symbol. §§ Eigenvector; difference between intrinsic rate and exit rate in migration model [

K—Rate of curvature [_{n} gross production efficiency of food [

*K—Threshold biomass in surplus production model [upper limit or carrying capacity; 65] and different stockrecruitment relationships (above which the relationship departs from linearity ([_{•}l—Individual body length as effective or index of the whole fish extension [total in 11]_{e}l extreme (total with the caudal tips joined). _{n}l natural (total with tail tips in natural position). _{f}l fork. _{s}l standard. _{c}l carapace (crustaceans). _{d}l dorsal mantle (cepahalopods). _{h}l height. l recently killed. l_{•} defrosted. l^{•} other to be specified (see also age for other subscripts). § Length at 50% of release [_{x} probability of living at age x [_{t} landing tax [_{y} last year of fisheries data [

•_{l}—Body component (organ, appendix etc) length.

l—Ultimate significant contribute to the fishery. § Maximum age [

log—10 based logarithm [66,70] § log_{10}, log, lg.

ln—e based logarithm [_{e}.

L—Length (generic) at stock level [67,70]L_{m} at 50% sexual maturity [70,113]. L_{rt} at 50% of retention. L_{ml} minimum landing length. See l (individual length) and A (age) subscripts for other specifications. § N˚ of length class [_{50%}, (l_{50} in 73) length at which 50% of fish are retained [_{L} longevity [_{L}, also denoted fish caught and landed [

L^{∞}—Asymptotic length. Length to which the curve approaches closer and closer as the independent par. Becomes extremely large (→∞) or extremely small (→ −∞) [_{∞a} mean length of “old fish”, where old means of an age beyond which the mean length at age does not increase appreciably [_{∞} in65]. In the VBGF, the size at t = ∞ ]70] or that an average fish would achieve if it continued to grow indefinitely according to the VBGF [^{∞ }> L_{mxe}). § Usually reported as L_{∞}. The same symbol (L^{∞}) was recommended for VBGF by ICNAF [_{∞•t} maximum length achieved in a population where the subscript t refers to tag data analysis [_{inf} in Rosenberg and Beddington [^{∞} ≡ L_{max} approximation [

L∞—Pristine infinite. The mean length the fish of a given stock would reach if they were to grow forever [66, 72]. Mean size according to a probabilistic distribution function [_{mxe}.

L_{∞}—Actual infinite. Mean size of oldest specimens esimated in the exploited condition. Mean size according to a probabilistic distribution function [_{n} successsive (pseudo-) infinite lengths in seasonal VBGF [_{∞}< mxe.

L_{mx}—The present maximum size recorded for the investigated stock. L_{mx}^{ }ever recorded; L_{mx }estimated according to a method to be specified such as mean of n extremes, 95^{th} percentile, extreme values theory etc LC50—Median lethal concentration [

LFA—Length frequency analysis [

Λ (lambda)—To not be used in order to avoid confusion with similar symbol. §§ Test statistic [

_{•}m—Mesh [66,68,76,125,126] Mesh size [_{d}m diamond or _{q}m squared; m_{b} bar, m_{s} stretched size. § Codend mesh remain open [_{(x)}, probability of maturity; males; M/K ratio; n˚ of marked fish recaptured; index of consumption of species I by species j [

♂—Males [72,87]. § M, m.

μ—Free. §§ Mortality rate [

mp_{a}—Mean parental age, the average n˚ of progeny produced by a females during its life weighed by the different age class. § Most suitable for iteroparous species. As the mean fecundity, it is a par. not simple to estimate [163; pag. 128].

M—Instantaneous rate of natural mortality, where “natural” refers to all causes of mortality except fishing [61,63-65,67,74,76,86,117,130]. If not specified (see below), it indicates the average (overall weighed) M over the range of age groups which can be considered fully represented in the samples. M_{∞} infinite mortality (≈ 0), or mean of infinitely old and big fish [_{j} juveniles. M_{pa} parental (adults). M_{bur} bursts, the high M values in early period such as eggs and larvae lifetime [_{asy} the mathematic theoretical (lower) asymptotic natural mortality [M_{a} in163]. M^{asy} the asymptotic upper biological mortality to which tend the oldest specimens of a stock. M↨ array of values according to a model or equation to be specified. M_{Δt} phase mortality, defined as the product MΔt (in the presence of fishing, ZΔt) and represents the cumulative mortality which occurs in the time interval under consideration [_{0} and M_{1}, M_{2} etc., natural mortality excluding predators [_{n} [_{asy} is a mathematical par. without any biological meaning (may also assume negative values). M% in % as recorded in aquaculture experiments [_{M} age at reform; X_{M} at MSY [

MC—Migration coefficient [

MPA—Modal progression analysis.

*MPA—Marine protected areas. § MPA [

MS—Mean square [

MSY—Maximum sustainable yield [65,74,117] § At equilibrium [

MSEY—Maximum sustainable economic yield [

n—Generic n˚ of specimens or items to be specified [68,70] § As superscript, indicates the order of a moment [^{n} [

υ—To not be used in order to avoid confusion with similar symbol. §§ Fraction of the total mortality [

N—N˚ [_{0} total at the beginning of a given year. § Initial population [

o—To not be used in order to avoid confusion with similar symbol. §§ Term in stochastic mortality model [

ω—Gallucci and Quinn’s [_{∞}). §§ Fraction of the total biomass due to newly recruited fish [

O—N˚ of dead fish in a given time interval. O_{Z} dying of total causes. O_{F} dying of fishing (C plus n˚ of fish dying for collateral effects of fishing). O_{M} dying of other causes than fishing (all natural causes). O_{Mp} predators. O_{Md} diseases. § Estimate of total fish taken [

OI—Omnivore index [

Ω—Expanding term or factor [

p—Prop. [_{r} retained in the cod-end [_{m} mature. p_{♂} of males over females. p_{♀ }females over males. p_{♀s} females over sexed specimens. p_{m♀s} mature females over mature sexed specimens (operational sex ratio; [_{R} sex ratio [_{p} age at reruitment in the fishing ground [

π—3.14 [_{a} prop. of each cohort which recruits at age a; fixed prop.; harvest rate [

ψ (psi)—To not be used in order to avoid confusion with similar symbol. §§ Generic par. [

P—Production [67,70,82,83,167], the quantity of overall (dead and still alive) biomass produced during the interval under consideration. P_{n} net production, amount of living matter [_{W} biomass in weight [_{W} average population or standing stock in weight [_{e} n˚ of eggs spawned [_{m} “mature” fish which are almost mature or fully mature. *P_{s} spawners. *P_{a} adults, i.e. fish which have reached the capacity to reproduce independently from their present contribute to reproduction (i.e. including abortive fish).

Π—Free. § To not be confounded with “product”.

Ψ—Free. §§ Dummy time variable. Function [76,96]. Natural survival rate; elasticity (sensitivity) [

P/B—Production biomass ratio [70,167]. § Turnover rate [

PF—Power factor [cfr Fig. 1 in 34]. Fishing power. The relative performance of each vessel computed by applying a specific equation; for example, PF = cons. *(vessel length)^{n}. § P, P.F., P_{i} and Q_{j} for power factor of the ith vessel and jth location [

PDF—Probability density function [

q—Catchability [65,67,70,74,76,86,94,97,107,117,169]. Coefficient of proportionality between F and f (specified for the f used). q_{f} the stock fraction taken by 1 unit of effort (usually < 0.1). See “effort” for other speciications. § The fraction taken by 1 unit of fishing effort [_{01} [_{10} (Arrhenius) rule [70,103]. §§ Fishing effort efficiency [_{∞})^{–h} invariant [

QO_{2}—Weight-specific oxygen uptake [

r—Product-moment (Pearson) and (r^{2}) determination coefficient [^{2} [_{1} and r_{2} density independent and dependent natural mortality effects, respectively; par. in Francis’ growth model; (knife edge) recruitment age; sequential observation of biomass; logarithmic (median and average) growth rate of a population; the first age group; prop. of fish of length l and age a; par. in the age sample size determination; generation length in semelparous (once-breeding) population modelling [

*r—sIntrinsic rate of initial population growth; the rate showed at very low abundance (assuming no depensation). § r intrinsic rate of growth [_{m} intrinsic rate of growth of a stock [_{pop} [

ρ—Ratio [_{N} ratio of surviving (absolute rate of surviving per year). ρ_{Z} ratio of complementary surviving (absolute rate of total mortality per year). ρ_{GR} part of the metabolic energy available for growth and reproduction. ρ_{E} part of the reproductive energy used for zygotes formation [

R—Recruitment related par. [25,61,63-65,67,70,76,86, 95,107,127]. N˚ of recruits [_{af} to the area interested by fishery. R_{gf} to the gear used by fishery. R_{X} effective recruitment (the total n˚ of fish recruited in one year from X year-classes. § Whatever recruitment by movements in to the region fished or by change in size or behaviour [56; page 40]. R as recruits abundance [_{0} net reproductive rate [_{d} daily ration [_{m}) and L_{∞} [

RP—Recruitment pattern.

RV—Reproductive value [

RSS—Residual sum of square [65,67].

s—Sampling standard deviation and (s^{2}) variance [25, 70,107] § s.d. and s.e. [_{0} time when the organism begins to react to the net’s approach [_{s}, earliest age at spawning, and asymptotic length; gear selectivity; district-specific catches vector in “run reconstruction” [

σ—Stock standard deviation and σ^{2} variance [65,86] § SE^{2} [

S—Stock size in n˚. S' unit stock. S_{0} the pristine level. S_{∞} asymptote size in n˚, the level to which an unexploited stock tends. § Catchable stock in weight [_{•}, is used in case of short living species such as most cephalopods [_{R} sex ratio [_{0} early life survival; average size of a school; size of any hard body structure uses for back calculation; escarpment of adults from the fishery [_{50%} maturity estimation [

*S—Generic score, such as the S function in Shepherd’s method [

SF— Selection factor [66,74] The ratio between the 50% of entry to capture and mesh size. § S.F. [

SR—Selection range [

SS—Sum of squares [

ST—Steady state, situations in which all the demographic processes (recruitment, growth and mortality) are cons. along the time (deterministic models) or the same processes are randomly varying in time without no trend (stochastic models). § One of the more common hypotheses in classic fisheries science and the most criticised assumption nowadays [

St_{c}—Stomach contain in weight. § F [

SPR—Spawning stock-biomass per recruit [

SRR—Stock-recruitment relationships [11,70,117]. § Recruitment curve as a graph of recruits (Y ax) against spawners [

SSB—Spawning stock biomass [70,117] § SP [

Σ—Summation sign [65,71]

t—Time [63,76]. Time in month [_{0} cons. that adjust the time scale to an origin at the inflexion point of a curve [_{h} at hatching. t_{s} sets the beginning of sinusoidal growth oscillating with respect to t = 0 (72) in the seasonally version of the VBGF (also summertime; 74). As subscript, tagging related par. [_{z} origin of the VBGF in calendar time expressed as fraction of a year (in Shepherd’s method). § Age [_{D} end of (finite) lifetime [_{s} as the age at the end of the first fishing season [_{s} earliest age at spawning; time dimension in migration model; maximum age of the cohort [_{L} age when the year class leaves the fished area; t_{0} age at maximum biomass peak [

τ—Free. §§ Portion of the ration ultimately recovered as net energy [_{P} age at which 100(P)% of the population remains [

θ—Z over K ratio (72). θ_{B} Beverton and Holt. θ_{S} Ssentongo and Larkin. θ_{P} Powell. θ_{R} regression. θ_{W} Wetherall. θ_{J} Jones and van Zalinge [_{α }period of marking; ratio in Allen’s recruitment method. Total metabolism [98,143]. Different par. in tagging experiments [_{h} time at hatching; T_{0} time of recruitment; test function; mean environmental [_{max} maximum age in absence of exploitation [^{th} moment; T_{0} mean generation length or mean age of reproduction; objective function; vector of tag release in different areas; threshold level [

TL—Trophic level [

Θ (theta)—M over K ratio. Θ_{∞} as M_{∞}/K [

u—Ratio of recovery to marked fish released. §§ Unavailable population (in unfished area) [

υ—To not be used in order to avoid confusion with similar symbol.

U—Catch per unit of effort [25,27,65,70,76,107,129]. U_{C} in n˚ (pieces). U_{Y} in weight. U_{M} per unit mortality (equivalent to CPUM by Quinn and Deriso [_{c}/L_{∞} as U= 1- L_{c}/L_{∞} (74). Random variable; expansion factor in B&H Y/R model; penalty weight function in LFA; utility function [

v—Co-ordinate defining sub-areas. §§ Natural death fraction [

*v—Value of fish in the specified monetary unit. § v as average price [_{$}. p as price or V as value of income [

V—Virtual population [_{0} volume of eggs in the ovaries; penalty function for mortality and variance within length interval in LFA; accumulated variance among ages; variance-covariance matrix [

*V—Swimming speed [

VBGF—Von Bertalanffy Growth Function [70,71,82] or formula [71,113]. § VBGE, equation [

VPA—Virtual population analysis [65,70]. § Age structured, sequential, integrated or synthetic analysis [

w—Individual [74,120] measured fish weight. Body mass [_{r} round (overall-total). w_{g} gutted (eviscerated). w_{dry} dehydrated organism after a standard time in an oven (incorporated in McGurk [_{k} weight at recruitment; normally distributed random variable [

_{•w}—Individual body component weight.

wd—Individual measured fish width; especially in rays and skates it indicates the distance from the tip of the left to the tip of the right “wing” [

W—Theoretical (parametric) fish weight at stock level [25,61,67,70,76,86]. See a for other specifications (such as W_{c} and W_{R}). § Somatic weight [

W_{∞}—Asymptotic weight. See L_{∞} and allies for the analogous specifications.

WP—Winter Point in the seasonal VBGF; the period of the year (expressed as fraction of year) when growth is slowest; related to t_{s} through WP = t_{s} + 0.5 [66,72] § t_{w} [

x—Independent variable generally in linear regression [_{0} expression [128,173]. Label for categories of interest in gear selectivity; sampling units; position dimension in migration model [_{m} age at maturity in Jensen’s invariant [

ξ—Free. §§ Probability of being recaptured [

Ξ (csi)—Free. §§ Annual food consumption of a fish population.

X—Mark (tagging) and recapture related par. N_{X} n˚ of tagged specimens before the samplings [_{r}N_{X} n˚ of tags (tagged fish) recovered [25,151] X_{D }disappearance rate of marks [_{OL} other loss rate (in tagging). X_{P} probability of recapture. § m in Jones [^{∞} [_{MSY} [

y—Dependent variable generally in linear regression [_{0})W_{∞} product [_{l }and y_{2}; 93] in Schnute’s growth model; position dimension in migration model [

*y—Year. § y [74;61;70]

Y—Yield [25,67,76,83,120]. (Total) catch in weight [70,82,105,117,122]. Total yield from a year-class [_{∞} total yield over the lifetime of a cohort. Y_{*} at equilibrium [_{g} gross. Y_{by} not target. Y_{r} retained on board. Y_{l} live. Y_{d} landed. _{R}Y replacement yield [RY in 117]. § Net economic yield [_{W }average weight of fish and other related par. [

Y/R—Yield-per-recruit [76;65]; catch in weight per recruit. Y/R_{max} maximum value (at F_{max}). Y/R_{F∞} maximum possible value in the isopleth diagram. Y'/R relative. § (Y_{W}/R)_{max}. (Y/R)' relative (74). YPR [

YEB—Yield exploitable biomass; the fraction of a stock which is considered economically usable. In case M is low then YEB ≈ MSY (on the opposite YEB > MSY) [170-172].

z—Ratio of fished to unfished areas (→ ∞ when the whole area is fished). §§ Function of the virtual population [_{t} – N_{* }or_{ }B_{t} – B_{*}) in delay difference models [

ζ—Free. §§ Maintenance food coefficient. Efficiency or correction factor [

Z—Instantaneous rate of stock total mortality from all causes [130,76,67,86,107,25,82,74,65,61,70]. Z_{H} Heincke. Z_{R} Robson and Chapman. Zr = 0 maximum level that a population can withstand [_{*a} area specified (as Z_{y,a,Ar,q} in [_{stock} [

A simply insight in both “Milestone” and “proposed” list allows the immediate perception that convenience and opportunity were the general criteria followed by the Authors in defining and using the symbols. Even in the same contribute or textbook, the same symbols were often employed with different meanings [^{th} point in [

Another interesting aspect consists in a sort of reluctance in using symbols in most of the contributes and books produced at the beginning of the fishery science. At the Symposium on Fish Populations, held in Toronto in 1947 [

As previously stated, the opportunity of symbols standardisation was highlighted at the end of fifty [14-16], but thereafter, the feeling is that the Authors were more worried about the agreement on definitions instead of symbols.

The consequences of a lack of standardization have determined long-standing problems mainly due to confusing symbols, definitions and applications. One of the most interesting examples of such as ambiguity might be referred to the “asymptotic” length in the von Bertalanffy growth function. Beside the biological interpretation (where it has any), the main troubles arise from a) confounding the maximum individual length with maximum mean length at age [101,160]; b) assuming that the maximum ever length could be used as the theoretical asymptotic length [_{∞} ≈ L_{max}/0.95; 71); and c) forgiving that present maximum length in a exploited stock might be quite lower than the maximum length in the pristine condition (even at small rate of fishing; [_{∞} (more rarely L_{inf} or L_{asy}) is generally used for different defined asymptotic length estimations, which are on their turn used to compare data or to get invariants [177,178], it is evident of the possible confusing effects and the opportunity for a better correspondence between the symbol and the defined parameter.

Another example of misusing is represented by what Beverton and Holt (see the Milestone list) have defined as the “fishable life span” (denoted with λ), which represented an arbitrary upper bound to the computations, reflecting the progressive rarefaction of the oldest age classes in the samples. Convenience has induced the Authors to set λ ≈ ∞, obtaining a simplification in the computations. Thereafter, the fishable life span was often associated to the longevity, which is evidently an error at least because the two parameters have a different definition.

Finally, present results support the Beverton and Holt’s 1957 sentence about the discrepancy between the number of items employed in fisheries assessment and the number of possible not confusing symbols. The present proposal tends to offer an operative solution by associating all the Latin letters to key quantities/items relevant to fisheries assessment and leaving free (with few consolidated exceptions) the Greek letters to identify different parameters and items (

A special thank to Lady Alexis Pacey, Publications Manager of the North Atlantic Fisheries Organisation (NAFO), Dartmouth, NS, who has provided the original historical ICNAF reports and Dr. Adamo Giovanna for her genuine interest in this paper.