Desirability of a standard notation for fisheries assessment

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.


INTRODUCTION
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][2][3][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][6][7], Gulland [8][9][10][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][15][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][18][19][20][21][22][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.

Organising the Symbols Lists
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 [24] and "official" publications [25,26] according to a more or less broad application of the word.In particular, within the "broader" interpretations can be quoted 1) the part of fisheries science that studies the status of a fish stock as well as the possible outcomes of different management alternatives; it tells us if the abundance of a stock is below or above a given target point and by doing so lets us know whether the stock is overexploited or not; it also tells us if a catch level will maintain or change the abundance of the stock [27]; and 2) the application of statistical and mathematical tools to relevant data in order to obtain a quantitative understanding of the status of the stock as needed to make quantitative predictions of the stocks reactions to alternative future regimes [22].
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 [28]; 2) providing a means of expressing population properties by a relatively few parameters [26] and of codifying the effects of fishing on stocks [29]; 3) using stock demographic parameters to determine the total catch and how the catch and the catch per unit of effort varies with changes in the pattern of fishing [30]; and 4) the study of population structure, dynamics, and past exploitation of a single population [31] and its reaction to the dominant influence of fishing pressure [32].
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][15][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 [60]; 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 [61]; 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.

The "Milestone" List
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 incrementaverage 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 [62].
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 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 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 in-fluence) 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).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).

S-BH_
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_  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).

The "Proposed" List
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 [22], if not otherwise specified.
*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 [63] or condition (also in unfished equilibrium), or "critical" par.[25].As right superscript, it also specifies better an almost equivalent (or homologous) par.; for example, N and N* as n˚ and biomass of recruits at the start of year [64], R and R* as recruitment in n˚ and weight [65] or L* as maximum observed length (or largest specimen) in a sample [66].Other diffuse uses are: "true" value [67]; generic critical or optimum (optimal in [67,68]) the average size of a fish of a given cohort when the instantaneous rate of natural mortality equals the growth.It also characterises symbols not used in Ricker's textbook; a par.estimated with methodology different from the usual.Further as right superscript, it has been used to identify a statistic or estimate of a par.[69] or a value at maximum or at stable condition [70].
'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 [67].§ § As superscript, a statistic or estimate of a par.[69].Pristine level or condition [70].
[ 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 [74].X ∆ -Par.referring to a finite interval.For example in Chen and Watanabe [75] procedure to estimate M. ∩ X-The Maximum value of a par.§ The "maximum" has been often interpreted [72] as "optimum" [6, page 389] or "critical" [56].For example, a cri age at maximum cohort weight t cri in [76]; c* and t* critical size and age as the value where biomass of a cohort is maximum in the absence of fishing and c opt the value which maximizes yield when fishing mortality rate is fixed at the F 0.1 [67]; l cri the length above which all fish are vulnerable [25] or optimum age at exploitation); t y in [77].The most famous example is the Holt's optimum age (valid only in case of no dependence relationships) at which an (unexploited) cohort reaches its maximum abundance or reflecting the catch obtainable allowing a year class to reach its greatest total weight and hence catch it at once [6, page 374].Other cases are: the Gulland's approximation (F 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 [70]; the X SUP [76] and X m maximum or optimum [74].Strictly speaking, "optimum" (i.e.any point which might be considered the "best" within the ultimate objective of fishery regulation) should be restricted to economic criteria [6, page 390] or management, but not to assessment."Optimum" should not be confounded with the optimum sustainable yield, OSY, or Roedl's optimum yield OY [19]."Critical" should not be confounded with the Hjort's critical period in which the numeric consistency of a cohort is determined; it is classically the larval or plankton stage (Hjort's hypothesis) or (more recent) the juvenile stage [79,80].
X • -25, 50, 75 the par.corresponding to 25%, 50% and 75% of a logistic (anti symmetric) curve (or ogive) mostly in selection studies [81].§ X50 or X 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 [49].The 75% -25% difference has been denoted as "selection span" [49]; nowadays, it is often denoted as "range" [66].Reference [49] attributed a different (and apparently more appropriated) meaning to "selection range" as the range in fish length over which a fishing gear exercise selection. X-Conventional par.For example, the Taylor's 95% maximum length approximation as index of longevity [62,71].
*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 [74] or covered unit area.a f over which the fishing effort is distributed.§ a [25,71,74,76].
α-Free, to be specified.§ § Season [95].Cons.per unit of effort [96].Level of significance of a test [97].Cons. in the generalisation of the VBGF [91].Par. in total metabolism (T) and weight (W) according to T = αW γ [98].Coefficients in Jones and Johnston [99] growth, reproduction and mortality analysis.Age [100].Par. in different models, especially SRR i.e. stock recruitment relationship [76].Par. of the "asymptotic (overall) yield model" [71].Par. in the recruitment function [64].Par.(also scaled) of the Ricker stock-recruitment relationship; special values related to F 0.1 , F ey and MSY [67].Par. in age-length growth model [101].Subscript indexing length frequency data in MULTIFAN [102].Instantaneous tagging mortality (dying immediately after tagging); par. in catching power and vessel standardization; intercept in the Ford-Walford plot [25].Biological lower critical value [103].Model par.; density independent coefficient (also slope at the origin) in SRR; coefficient (condition factor) in both isometric and allometric weight-length models; coefficient in Brody model; significance level; prop. of fish of length l; tag loss [65].Generic par., for example, governing stock production especially at small size (such as intrinsic rate of natural increase) or specifying the state variable in Individual Based Models; slope at the origin in the general form of the SRR also defining the compensation capability of a stock; age at maturity; α i Manly-Chesson food preference index [70].Cons. in SRR; limit of R/S when S → 0 [104].
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" [110] should be used and specified.
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 [66].A50 [22].Fish from A m onwards are usually considered adults [22].
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. [75].
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 [65].In case of isometric VBGF, the critical age is empirically related to maximum age [A ∩ /A max ≈ 0.38 ; 11].
A  -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, 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  ~ ∞.
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' [74].To not be confounded with the age at entry to capture.
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) [74].Gill net de-selection; age at de-selection; at reform; right-end de-selection [66].
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 [113].T L experimental wild longevity.T m [74].t max [114].
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 [70].t max [114].
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 .
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.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 [8].
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 [70].The theoretical (hypothetical, artificial, arbi-trary) "age" at which the fish would have been zero length/weight if it had always grown according to the VBGF (hence, it can be either positive or negative).Location par [65].A 0 any initial or starting age (such as length at birth in sharks); scale par. to be specified.§ a 0 [64].t 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 [115].Adjusting par.[22].Almost always it takes non-zero negative values [108], and does not usually express "prenatal growth" [66].Strictly speaking, the par.should be referred to isometric (cubic) weight-length relationship.Often it is omitted in the general treatment or assessment based on the VBGF, but it must be considered in real computations [113].
*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.
b'-Slope in the relationship between trophic level and body weight § b [70].
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.
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 [94].§ Σc sum of the weights of all fish caught during the year [88].c = l/m relative releasing effect or ratio between the length at 50% of release and inner mesh size [125].t 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 [126].Cons. of proportionality between F and f [127].Proportionality coefficient relating to the efficiency of the gear [94].§ § Instantaneous rate of loss of hooked fish [90].Juvenile survival rate to maturity in Schaffer formula [121].Index of ecological similarity [71].Cons. in P/B = bw c ; CPUE [67].Cons.[64].Upper and lower limits for the mean asymptotic length [101].Par. in different models; competition coefficient; shape par. in Deriso's SRR; n˚ of prey; capacity in multistage SRR [25].Exponent in the height of the growth production function [87].Food consumption rate per unit biomass [82].c and c y operating cost and cost per unit caught [68].Coefficient in the allometric W = cl n [77] or W = cl 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" [65].Competition [70].Positive cons. in the von Bertalanffy (isometric) weight function [63].
*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 [66].§ § c 1 -c 2 interaction coefficients in Lotka-Volterra model [70,71].
Coefficients in Beddington and Cooke potential yield computations [128].To not be confounded with unit costs of measuring length and age [65].
cov-Covariance [65].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 [130].C W catch in weight [94].C n food intake [67].Tags caught and returned; change in weight from tagging to recovery; total catch in weight units; catch per unit of time; aggregate productivity in multistage SRR [25].From [66]: CLi∞ cumulative catch in n˚ from length i to L∞ and C 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 [65].
Cons. in integration and matrix; total cost of measuring length and age; consumption rate in multispecies modelling [65].C* prey consumption [68].Consumption [61].Amount of food consumed; cost per unit of effort; energy cost in handling or searching for prey; control; C 24 daily ration [70].Cons. of the SRR generalising the model [104].Cost coefficient [63].˚C-Sea water temperature in Celsius degrees.˚Cb at bottom; ˚Cs 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 [117].It ranges between 0, no oscillation, up 1, growth stops at WP [109].Values higher than 1 can be also obtained indicating a prolonged no growing phase (length shrinkage is a rare phenomenon in wild marine organisms [72]. C 2 -Par. in Powell Z/K estimation [71].CC-Catch curve, the ln of the abundance in n˚ (or index) at successive ages (CC a ) or sizes (CC l ).

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 [65], as standard deviation/mean ratio [21].• CV as standard error/mean ratio.As % if not otherwise specified.§ C.V. [71].CSC-Contact and selection curves; the relationships describing the probability of a fish to avoid, contact and escape after the contact/capture with a given gear.aCSC availability, rCSC contact-selection and sCSC selection [73].§ Selection curves [73].
χ-Free.§ § Arbitrary reference age in Francis' VBGF reparameterization [101].Mid point of the i th length frequency interval in MULTIFAN [102].Sex ratio as fraction of spawning population that are mature females by weight; prop. of fertilised eggs that will result in females [65].To not be confounded with the chi square statistic χ 2 [65,66].
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.
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 [21].F 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 [65].§ M f [95].F ey , F p where marginal yield per recruit is 10% or p-times the marginal equilibrium yield in a lightly exploited stock [67].Fishing loss rate; fleet size [25].(F) 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 [67].Variance within length interval in LFA [65].Stomach content; starting area in fish migration [70].
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 [68]; fF c free eggs released into water (F rea realised fecundity, in [68]; rF 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 [76].DEPM, daily eggs production model in Lleonart [22].
FP-Fishing power.Relative unit efficiency of capture of different vessels versus a standard vessel.§ ρ, P, Q. Efficiency.[148,149].
FR-Fished region [150], the area covered by the wings of the gear.§ Fished area; 50% of the head rope length according to the Baranov's approximation.
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 [88].Mean annual growth increment [101].Net growth of adult population [65].Coefficients of predator negative growth in Lotka-Volterra model [70].Growth per unit time [27].§ § Par.related to food [140].g gonad [99].F/K; global [76].Probability density of fish length; ration requirement coefficient [72].N˚ of groups [64].Par. group or stratum index [86].Par.combining mortality and growth effects; observation error; age specific vulnerability to fishing induced mortality [25].Index identifying a group of fish tagged and released over a short period of time [151].Gross food conversion efficiency [82].Probability of a fish to be retained by a grid [73].Coefficient in Fletcher's quadratic model; g 1 and g 2 density independent and dependent growth effects, respectively; F/K ratio in the allometric Y/R model; index of gear type [65].The greatest true age group [70].Gear type [27].To be not confounded with gram [66].γ-Free.§ § Par. in total metabolism (T) and weight (W) according to T = αW γ [98].Area successfully searched [143].Shape par. in the Shepherd's SRR [76].Par. in the recruitment function [64].Par. in catching power and vessel standardization; tag shedding rate [25].Par. in Fletcher's modification of the Pella-Tomlinson model; exponent in different stock recruitment models; coefficient in Brody model; par. in the Schnute and Schnute-Richards growth models; inflexion in the maturing model; vector of movement and population par.[65].Transformation or shape par.; degree of compensation par. in Shepherd's general SRR relationship [70].Fraction of individuals in a stage moving to the next stage; population growth rate [27].Shape par. in Schnute-Richards' growth model [135].
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 [95].Instantaneous growth rate [67,76].Growth survival factor [25]. g in [70].Specific growth rate.Increase due to growth of individuals [65].Par.relating Z/K or Z/H to length and weight [118,119].§ § Par.related to food [140].Scalarvalued function [67].Cumulative length-distribution function [72].Par. in the recruitment function [64].Total n˚ of group or strata; true age composition [86].Income for the fishing industry; fishing induced mortality [25].Natural mortality factor in Pope's cohort analysis [74].Sea area over which egg production is expressed [68].Anabolic component [70].Probability of moving form one stage to another stage [27].
*G-General growth rate at stock level as whole population; for example, in surplus production [70].
Γ-Free.§ § Index of competition.Notation for the gamma distribution; environmental variable affecting recruitment in semelparous population modelling [65].
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).
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 [72].I 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 [109]; I in Ware [143].§ Growth efficiency, for example, the ratio between production and food consumption [70].§ § Marked specimens [92].Par.related to "optimal grouping"; index of cohort [72].Money invested in a new boat [25].As subscript, inflexion; groups deriving from cohort stratification; survey index in ADAPT approach; integral [65].Index of relative abundance (68,70).Income [70].
*I-Separation Index [74].§ SI [66].∞-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; [70] would grow if it could assimilate energy at the maximum possible rate throughout its life. IALK-Iterate age length key [65].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 [152] § j as subscript in Walters et al. [82].Usually in Mediterranean stocks, they include the recruits or the young(est) of the year (YOY).Immature.§ § Location or area [94].Time interval [86,97].N˚ of par.[67].For counting items [108].Index for predators or consumers [82].A given gear [73].Different periods of life; as subscript, generic index or group identification [65].
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 [139].Cons. in surplus model [96].Terms which do not contain F or M in virtual population analysis [127].Destruction per unit weight in the derivation of the VBGF [91].Rate of deceleration in growth increment [77].N˚ of discrete sampling occasion in Jones [92].New age or length at capture related index [76].Age at (of full) recruitment; discount rate; ratio of the size-specific mortality to the size-specific growth rate [67].Youngest possible age at recruitment [64].As k a and k t growth coefficient related to mean length at age and length increment (tagging) analysis [101].Cohort index [86].Carrying capacity; cost of a new boat [25].Identifies size-at-release class of fish from a given group [151].Coefficient of catabolism or n˚ of par.[108].Time at recruitment to the adult stage [82].Often employed to represent the growth coefficient in the VBGF [70,87].Par. in effort standardisation; intrinsic growth par.analogous to r in surplus models [65].Sampling effort factor; k1 and k2 cons.relating mode/spread with mesh size [73].Catch per unit capital [68].Cohort Index in Extended Survivors Method; coefficient of proportionality between Y and f in case of cons.density of fish; n˚ of prey categories [70].Cons. in the SRR and (as carrying capacity) production model [104].N˚ of par.estimates in a given procedure [66].k 1 , k 2 ,… k n growth coefficients or rate in different compared models; n˚ of estimable par. in AIC computation [135].
κ-To not be used in order to avoid confusion with similar symbol.§ § Eigenvector; difference between intrinsic rate and exit rate in migration model [65].Log of spawning level; curvature par. in different (growth and maturing) model; identifying the Ricker's conventional Brody coefficient in the VBGF; coefficient in Brody model [70].
Par. in predator model to estimate natural mortality [61].Size of the fishing fleet; threshold (biomass) level in the SRR relationship [70].
*K-Threshold biomass in surplus production model [upper limit or carrying capacity; 65] and different stockrecruitment relationships (above which the relationship departs from linearity ( [70].• 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 [125].§ § l x probability of living at age x [121].l t landing tax [25].l y last year of fisheries data [86].Annual survival rate [65,70] after natural mortality [68].Early life survival from the egg stage to recruitment; annual survival from natural sources; index for length interval [65].
-Ultimate significant contribute to the fishery.§ Maximum age [104].§ § Par.relating variance and n˚ of observations [130].Fraction of the catch inspected for tags [97].Par.related to the growth in yield computation [120].Length in the Putter expression of the VBGF [91].
Coefficients which takes account of the difference in summer and winter feeding [99].Fecundity per recruit; cons.relating the resulting recruitment from a given spawning biomass [76].Annual growth rate in Schaffer's formula [121].Importance of residual [67].Convenience notation to relate two growth expressions for tagging data [101].Max par. in fish vision [109].Probability that a tag is lost due to tag shedding or tag-induced mortality [151].Coefficient of variation of length at age [153].
L ∞ -Asymptotic length.Length to which the curve approaches closer and closer as the independent par.Becomes extremely large (→∞) or extremely small (→ −∞) [30] l ∞a mean length of "old fish", where old means of an age beyond which the mean length at age does not increase appreciably [101].Mean length of infinitely old fish [153].Length at maximum age [t ∞ 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 [13], without touching it (L ∞ > L mxe ).§ Usually reported as L ∞ .The same symbol (L ∞ ) was recommended for VBGF by ICNAF [47].Limiting size [11].Maximum expected length [158].Maximum possible length [154,72].l ∞•t maximum length achieved in a population where the subscript t refers to tag data analysis [101].L inf in Rosenberg and Beddington [115].Infinite; the mean length of very old (strictly speaking, infinitely old) fish" [22].Sometimes it is assumed [in Elasmobranchs VBGF modelling;159] or mistaken [21] for the largest observed size for the species (i.e.L ∞ ≡ L max approximation [76].
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 [160].§ Mean length of oldest specimens estimated in the pristine condition.In the VBGF, L∞ < L 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 [109].LFA-Length frequency analysis [65].
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][64][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 [153] to which approach the M (assuming no senescence); it is analogous to Gulland [45] M' limiting value.M j juveniles.M pa parental (adults).M bur bursts, the high M values in early period such as eggs and larvae lifetime [164].M 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 [165] M* the combination between M and the instantaneous rate in tags shedding [65].M 0 and M 1 , M 2 etc., natural mortality excluding predators [82], and other forms of natural mortality, for example, in multispecies VPA [68,70].§ M n [95].M asy is a mathematical par.without any biological meaning (may also assume negative values).M% in % as recorded in aquaculture experiments [109].M* due to predation by marine mammals [68].M = + ∞ catastrophic mortality at the end of lifetime [63].§ § Maximum population which the environment will support under average conditions and with no fishing [129].Metabolism par. in the "surface law" or "two-thirds rule" or "Rubner's rule" [91].t M age at reform; X M at MSY [76].N˚ of fish in a sample [64].N˚ of predators [25].Projection matrix [65].).Mature specimens [61].Metabolism term or catabolic losses [70].
υ-To not be used in order to avoid confusion with similar symbol.§ § Fraction of the total mortality [64].Par. in Schnute-Richards growth model; vector of par.(general and related to mark recovery) [65].Selection par.related to haul [73].Par. in Schnute-Richards' growth model [135].
N-N˚ [67] of fish [25,130] in a homogeneous group [61,68] N˚ of survivors of a cohort [70,76] Population in n˚ [63].N 0 total at the beginning of a given year.§ Initial population [69] in n˚ [89] N˚ of fish of a given cohort alive at age a; n˚ marked and total recaptured [65].§ § Par.related to Hill diversity [68] N˚ of schools; egg production [65].Sample size in n˚ [70].
o-To not be used in order to avoid confusion with similar symbol.§ § Term in stochastic mortality model [65].ω-Gallucci and Quinn's [166] growth performance index (KL ∞ ).§ § Fraction of the total biomass due to newly recruited fish [64].Weight at age ratio [65].
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 [86].§ § Coefficient related to the age at maturity of a cohort [76].
p-Prop.[70] of related, but not dependent variables.p r retained in the cod-end [81] p 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; [70] § S R sex ratio [76].Prop.[67].Prop. of ration (72).Probability [86].Probability in selection curves [73].Generic prop.[65] Prop. of mature at age [70] § § Instantaneous rate of fishing mortality [89,120].Annual mortality rate (1-exp-Z) [127].Index of intensity of exploitation or mortality owing to catches; standard fishing effort [123].Cons. of proportionality in the derivation of the VBGF [91].Term for correcting injested to utilizable energy [98].t p age at reruitment in the fishing ground [77].Assimilation factor [143].Duration of each recapture period in Jones [92].Movement probability in diffusion model [141].Price [67].Weighting factor [72]. Landed price; probability of moving from an area to the other; movement rate; residence prop.; generic par. in GLM; productivity in multistage SRR; probability of encounter-chase-capture [25].Probability that an individual is caught in stochastic mortality model; model par.; n˚ of tests; generic fraction; true prop. of fish by length interval; par. in the (proportional allocation) age sample size determination; probability of finding a marked member at time t; prop.Mature at age [65].Relative fishing effort [73].Coefficient related to food energy; index of predator type; predation [70].Net price per unit weight [63].To be not confounded with the probability level in statistical inference.
ψ (psi)-To not be used in order to avoid confusion with similar symbol.§ § Generic par.[96] N˚ of tidal cycle per day [145in key papers].The mean direction of movement [92].Arbitrary reference age in Francis VBGF reparameterization [101].Moment-generating function; monotically decreasing function of r; instantaneous rate of movement from region i to region j [65].Ratio between C and pristine biomass [70].
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 [22].§ Population of usable size [95].Population size [56].Biomass of adult stock [67].Latent productivity; dynamic resource (or prey) term [65].Productivity of the prey's food resource [70].Cons. of the production model generalising the model [104].§ § Prop. of tagged [139].Survival rate [130].Population size [96].P W biomass in weight [77].P W average population or standing stock in weight [94].Pressure (m off the bottoms) in Harden Jones [146].P e n˚ of eggs spawned [145].Rate of growth; price; probability [67].Prop.[72].Previously exploited fish in Schnute [64] model.Availability [86].Points in a score (or objective) function; prop.; aggregate productivity in multistage SRR [25].Probability of obtaining a catch distribution in stochastic mortality model; fishing power; ratio of catchability; average egg production per day; probability; prop. of individuals in size class [65].Prey biomass and egg production in n˚ [68].PM as prop. of mature [61].Population; fish price; generic par.[70].Probability of capture or of occurrence [66].Probability of remaining in the same stage [27].*P-Parental, the non juvenile component of a stock.*P 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).
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 [168].
*r-sIntrinsic rate of initial population growth; the rate showed at very low abundance (assuming no depensation).§ r intrinsic rate of growth [25].r m intrinsic rate of growth of a stock [108].Pollard's Malthusian par. in Quinn and Deriso [65].r pop [70].
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 [88].Escarpment biomass; adult abundance [67].Spawning stock [65,157], usually as proxy of egg production [70].N as stock size in n˚ [107].Post harvest biomass in delay difference model; spawning biomass; n˚ of sets [25].Stock size in n˚ or biomass [117].(Standing) stock as an (homogeneous) group of fish which occupy a given area in a given period, which are subject to the same opportunities of growth and reproduction and to the same risks of natural and fishing mortality [25].The unit stock represents a stock which can be kept unitary from the point of view of fishing when the assessments carried out on the basis of this assumption does not give contrasting results with the real situation [24,30,42].Both terms are often synonym with assessment/management unit, even if there is migration of the same species to and from adjacent areas."Stock let", S • , is used in case of short living species such as most cephalopods [110].§ § Selection function [122].Speed of the (fishing boat) ship [147].Competition coefficient [131].Partial recruitment factor [85]. Squared deviations [141].Fishing mortality subdivisions; S R sex ratio [76].(Generic individual) length or weight size [71,121].Selectivity; recruitment; survival rate [67].Index of samples or cruises; standard deviation of a distribution [72].Survival rate [86,107].N˚ of sets; natural survival rate [25].Survival fraction over one year; S 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 [65].From Jennings et al. [68].species richness (n˚ of species), survivorship, scale radius, spawner abundance, and escarpment related par.Prop [61].Swimming speed; fishing mortality on age group in the separable VPA; index for predator species in multispecies VPA; species-specific selection pattern; score; strategy vector in Individual Based Models; measure of suitability; coefficient in the logistic; for example, the ML 50% maturity estimation [70].
SR-Selection range [73].The size range in which the probability of capture varies.§ sr [81].§ § To not be confounded with the reversed logistic curve [SR in 74].
SS-Sum of squares [25].§ SQ [104].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 [25].
Σ-Summation sign [65,71] t-Time [63,76].Time in month [61].t 0 cons.that adjust the time scale to an origin at the inflexion point of a curve [66] t h at hatching.t s sets the beginning of sinusoidal growth oscillating with respect to t = 0 in the seasonally version of the VBGF (also summertime; 74).As subscript, tagging related par.[151].Time or phase shift according to Jennings et al. [68] and Quinn and Deriso [65], respectively.t z origin of the VBGF in calendar time expressed as fraction of a year (in Shepherd's method).§ Age [67].t D end of (finite) lifetime [63].§ § Total population [69].N˚ of tags liberated [97].t˚ temperature [98].Freedom period in tagging experiments [92].t s as the age at the end of the first fishing season [72].t s earliest age at spawning; time dimension in migration model; maximum age of the cohort [65].Age.t L age when the year class leaves the fished area; t 0 age at maximum biomass peak [63].
τ-Free.§ § Portion of the ration ultimately recovered as net energy [143].Time [120] interval [72].Fraction of population at some stage or condition [67].Different par.related to survival from fishing and natural mortality [64].Variance related par. in MULTIFAN [102].Age at sex or sex ratio change [87].Time interval; density independent mortality component [70].Fraction of or whole year; time spent in searching and handling; reference ages in growth models; n˚ of years represented in the plus group [65] τ P age at which 100(P)% of the population remains [114].Mean length at first recruitment; as subscript, size at recapture [66].
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 [72].§ Z/K [119].r [115].§ § Angle [147].Fraction of the total mortality [64].Generic par. of interest; a priori estimate of a par.within the Bayesian-type approach; prop. of specimens which change sex; true prop. of fish by age; survival curve in length frequency analysis (LFA); ratio between the true but unknown n˚ of age a fish in a random sample and the overall fish population; annual rate of movement from region i to region j; migration prop.[65].T-Transport coefficient or rate of interchange of fish between adjacent areas [140].Instantaneous rate of transfer [65].§ T'' immigrating [145].Destination area in fish migration [70].§ § T α period of marking; ratio in Allen's recruitment method.Total metabolism [98,143].Different par. in tagging experiments [2].Duration of pregnancy or time to hatching in Elasmobranchs VBGF modelling [159].Time interval [76].Total n˚ of marked and non marked specimen [71].Time delay or horizon; temperature as degree days [67].T h time at hatching; T 0 time of recruitment; test function; mean environmental [72] or annual habitat temperature in ˚C [66].Age [93,101].T max maximum age in absence of exploitation [113].Tonnage of a vessel; balance index; ocean-surface temperature anomaly; fishing time [25].Age at which transition to the next pool occurs [82].Total death; transformation of original data; time periods; age of recruitment; n th moment; T 0 mean generation length or mean age of reproduction; objective function; vector of tag release in different areas; threshold level [65].Marked specimens [68].
υ-To not be used in order to avoid confusion with similar symbol.
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.
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 [68].Z *a area specified (as Z y,a,Ar,q in [70].§ Z* reference mortality in a variant of B&H expression relating mortality to length at maturity [128].S stock [70] See F ad M for other specifications.§ § Catch in term of n˚ of fish on the line [90].Standardised normal variate [97].Mean depth [67].Average weight within the previously exploited population and other related par.[64].Logarithm of relative rate of change in Schnute model [65].

Final Thoughts
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 [68] and rarely according to any point of the decalogue, with some exception (for example, the 8 th point in [25].Overall, only an handful of symbols resulted to be used in a quite consistent and standard manner; in particular, those related to natural (M) and total (Z) instantaneous mortality rates, and the coefficient of proportionality (q as catchability) relating fishing mortality (F) to fishing effort (f).
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 [174], few specific symbols were used only in two of the nine contributes presented [59;95]; few symbols were also used in Ricker [53], a contribution likely prepared before his 1958 handbook).Apparently, the burst of the use of symbols in fisheries occurred with the Beverton and Holt contributes, especially those published in 1956, 1957 and 1959; in the 1957 book, in particular, the Authors were forced to adopt almost the whole Latin and Greek alphabet.
As previously stated, the opportunity of symbols standardisation was highlighted at the end of fifty [14][15][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 [175] or as a proxy of it (L ∞ ≈ 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; [54]), resulting in lower asymptotic length even maintaining the same rate of approaching it [176].Considering that L ∞ (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 repre-sented 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 (Table 1 in Annex).Obviously, the scheme presented here should be intended as a consistent example which should be used as a starting point towards the establishment of an international communication standards in fisheries assessment.
Table 1.Synoptic table of correspondence between item/parameters and symbols proposed (PS) in the present contribute.In the examples column, a selection of other meanings attributed to the given symbol in fishery science are presented (see both the "Milestone" and "Proposed list" sections for abbreviations and other details).

Item/parameter PS Examples
Age a, A Age at recruitment; area occupied by the fish population; hook catch probability; mesh 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.; 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.
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 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/lengthratio.Γ (gamma)-BH_ Index of competition (force of concurrence).h-BH_N˚ of hour fished; par. in the eggk-BH_ Coef. of catabolism in the differential VBGF; growth equation coef.; Huxley's coef. in w = bl k 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˚ Total mortality fraction; instantaneous rate of loss of bait; recruitment in weight Growth coef. in model different than VBGF; total n˚ of fish in unit weight.Catchability in tagging studies; destruction per unit weight in the derivation of the VBGF Mesh length/mesh width ratio; prop. of new recruits in the catch.N˚of fish perished by natural causes; larger mesh size in gill net selection experiment Average minimum age limit of usable stock; head girth/head breadth ratio.Amount of food consumed; cost of the fishing effort; energy cost in handling or searching for prey Coef. of pre recruited mortality in the eggs-recruitment relationship.Age; season; generic parameter; instantaneous tagging mortality Free, to be specified β N˚ of marked fish; incomplete beta function.Season indices of adult stock; exponent in the length weight relationship Free, to be specified χ Fecundity coef.Arbitrary reference age, prop. of fertilised eggs that will result in females; sex ratio Free, to be specified δ Effective discount rate; successive age increment; shape par. in selection curves Free, to be specified φ Dummy (time) variable Retention rate; function Free, to be specified γ Annual egg-production per recruit.Area successfully searched; fraction of individuals in a stage moving to the next stage; shape par. in the Shepherd's SRR Free, to be specified Γ Index of competition.Environmental variable affecting recruitment in semelparous population modelling Free, to be specified μ Coef.defining the relationship between mesh size and fish girth.Mortality rate; n˚ of tagged fish recaptured Girth related probability of escaping.Natural survival rate; elasticity (sensitivity) Free, to be specified τ Recapture period in marking; calendar date.Fraction of population at some stage or condition; portion of the ration ultimately recovered as net energy Free, to be specified ξ Annual food consumption (individual).Probability of being recaptured Average weight of individual food organisms during their "grazeable" life span.Fraction of the total biomass due to newly recruited fish; weight at age ratio Growth performance index in weight (Pauly & Munro) Ф Total n˚ of age groups into which recruitment occurs.Fraction of the year before the start of fishery; gear saturation par.; golden ratio Fishing effort as collected (uncorrected) or "crude"; net (and long term) gain from a change in gear selectivity or area closure.Age specific vulnerability to fishing induced mortality; F/K; par.related to food; income for the fishing industry; fishing induced mortality Annual (or seasonal) relative individual growth rate.Annual harvest rate; haul; instantaneous long-line fishing mortality; time required to capture and consume Continued Mortality; total (instantaneous rate) Z Correction term (in recruitment-egg relations).Average weight within the previously exploited population; catch in term of n˚ of fish on the line Mortality (total)-K ratio θ The youngest age group free from the influence of recruitment of gear selectivity.Fraction of the total mortality; survival curve in length frequency analysis Annual or seasonal (natural) mortality rate (if no other causes operate); generic exponent in the VBGF in weight.Exponent in the allometric W = cl n Number of specimens in a homogeneous group N Total n˚ in stock.Egg production; par.related to Hill diversity; sample size in n˚ Gross long term increase in catch following change in selectivity or area closure.Amount of food consumed; fishing effort efficiency; fraction of fish taken from a cohort Fish escaping from parts of the net other than the cod-end.Distance; multipliers in yield per recruit equations; n˚ of tags recovered Production P Fishing power; n˚ of fish dying from predation.Population size; price; prop. of tagged; rate of growth Population at the start of the fishing season: standing crop.Annual mortality rate; assimilation factor, instantaneous rate of fishing mortality Ratio of dependent variables ρ Recruitment at the area where the fishing is in progress.Probability of individual fish to be available; slope in the Ford-Walford plot Ratio of recovery to marked fish released u Co-ordinate defining sub-areas.Ratio of exploitation; unavailable population (in unfished area) U Instantaneous rate of "other loss" (also emigration and shedding of tags).Energy introduced in the growth process in the "equation of continuity"; exploitation rate Catchability q Widrig's instantaneous rate of natural mortality.Condition factor; instantaneous rate of natural mortality, recruitment ratio; total mortality