A. Symbols used in formulas for fish stock assessment
A |
attrition rate |
11.5 |
a |
swept area (effective path swept by a trawl) |
13.5 |
ASP |
available sum of peaks (ELEFAN) |
3.5 |
b |
constant in length-weight relationship W = q * L^{b} |
2.6 |
B |
biomass |
8.6 |
Bv |
virgin (unexploited) biomass |
8.3, 9.1 |
B/R |
biomass per recruit |
8.2 |
C |
catch in numbers (VPA) |
5.0 |
C(t, ¥) |
cumulated catch (from age t to maximum age) |
4.4 |
C |
amplitude (0-1) (ELEFAN) |
3.5 |
C_{0} |
fixed costs of a sampling programme |
7.2 |
CPUA |
catch per unit of area |
13.6 |
CPUE |
catch per unit of effort |
4.3, 9.0, 9.5 |
D |
number of natural deaths (VPA) |
5.0 |
D50% |
deselection, length at which 50% is not caught |
6.2 |
dL |
interval size of length |
2.1 |
E |
fishing effort |
7.4 |
E |
exploitation rate (F/Z) |
8.4 |
ESP |
explained sum of peaks (ELEFAN) |
3.5 |
f |
fishing effort |
4.3 |
F |
fishing mortality coefficient or instantaneous rate (per time unit) |
4.2 |
Fm |
maximum fishing mortality |
6.6 |
F-array |
array of F-at-age, fishing pattern |
5.1 |
F-factor |
multiplication factor of F (Thompson and Bell), X |
8.6 |
G |
natural mortality factor in Pope's cohort analysis |
5.2 |
H |
natural mortality factor in Jones' length-based cohort analysis |
5.3 |
I |
separation index |
3.5 |
K |
curvature parameter |
3.1 |
KO |
index of metabolic rate |
3.4 |
L |
length |
general |
L1 - L2 |
length class |
general |
L1, L2 |
from length L1 to length L2 |
general |
L_{¥ } or L¥ |
L infinity, asymptotic length (mean length of very old fish) |
3.1 |
L' |
some length for which all fish of that length and larger are under full exploitation (lower limit of corresponding length interval) |
4.5 |
_{} |
average length of the entire catch |
4.5 |
Lc or L50% |
length at which 50% of the fish is retained by the gear and 50% escape |
4.5 |
L75% or L75 |
length at which 75 % of the fish is retained in the gear |
6.1 |
Lm |
optimum length for being caught |
6.2 |
m |
= K/Z |
8.4 |
M |
natural mortality coefficient or instantaneous rate of natural mortality or natural mortality rate (per time unit) |
4.1, 4.7 |
MSE |
Maximum Sustainable Economic Yield |
8.7 |
MSY |
Maximum Sustainable Yield |
1.1, 4.5, 8.2, 9.1-9.7, 13.7 |
N |
number of survivors (VPA) |
4.1, 5.0 |
N(t) |
number of survivors of a cohort attaining age t |
4.1 |
N(Tr) |
number of recruits to the fishery |
4.1 |
_{} |
average numbers of survivors of a cohort |
4.2 |
f ' |
(phi prime), ln K + 2 * ln L_{¥ } |
3.4 |
q |
condition factor, constant in length-weight relationship |
2.6, 3.1 |
q |
catchability coefficient |
4.3, 4.6, 9.2 |
R |
recruitment, number of recruits, N(Tr) |
4.1 |
S |
survival rate |
4.2 |
SF |
selection factor |
6.1 |
S_{L} or S(L) |
logistic curve (length-based gear selectivity) |
6.1 |
S_{t} or S(t) |
logistic curve (age-based gear selectivity) |
6.4 |
S1 and S2 |
constants in the formula for the length-based logistic curve |
6.1 |
SR |
reversed logistic curve |
6.2 |
S/R |
stock recruitment relationship |
12.0 |
t |
time (usually in years) |
general |
t' |
some age for which all fish of that age and older are under full exploitation |
4.5 |
_{} |
mean age of all fish of age t' and older |
4.5 |
T |
ambient temperature in °C |
4.7 |
Tc |
age-at-first-capture (start of exploited phase) |
4.1 |
Tm |
longevity (maximum age) |
4.7 |
Tm50% |
age of massive maturation (50% of population mature) |
4.7 |
t_{0} |
t-zero, initial condition parameter (in years) |
3.1 |
Tr |
age-at-recruitment to the fishery |
4.1 |
ts |
summerpoint (0-1) (ELEFAN) |
3.5 |
tw |
winterpoint (0-1) (ELEFAN) |
3.5 |
t50% |
age at which 50% of the fish is retained in the gear (Thompson and Bell) |
6.4 |
T1 and T2 |
constants in the formula for the age-based logistic curve |
6.4 |
U |
1 - Lc/L_{¥ } |
8.4 |
_{} |
average price (Thompson and Bell) |
8.6 |
V |
value (Thompson and Bell) |
8.6 |
VPA |
Virtual Population Analysis |
5.0 |
w |
weight (usually of one specimen) |
general |
W_{¥ } or W¥ |
weight infinity, asymptotic weight (W infinity, mean weight of very old fish) |
3.1 |
X |
multiplication factor of F (Thompson and Bell) |
8.6 |
y |
year (usually as an index) |
8.6 |
Y |
yield (catch in weight) |
8.2, 8.6 |
Y/R |
yield per recruit (Beverton and Holt) |
8.2 |
(Y/R)' |
relative yield per recruit (Beverton and Holt) |
8.4 |
Z |
total mortality coefficient, instantaneous rate of total mortality or total mortality rate (per time unit) |
4.2 |
B: Mathematical notation (general)
* |
multiplication sign |
/ |
division sign |
ln |
natural logarithm (base e = 2.7182818) |
log |
10 based logarithm |
exp(x) or e^{x} |
exponential function, exp(x) = e^{x} |
_{} |
sum of all values of X(i), for i from 1 to n; the sum X(l) + X(2) +... + X(n) |
Ö or _{} |
square root |
¥ |
infinity |
D x |
delta x, a small increment of the variable x |
MAX {X(j)} |
maximum value among the elements in the set {X(j)} = {X(l), X(2),... X(j),...} |
_{} |
mean value of x |
x(i, j) |
i, j indices of x (usually printed as x_{i, j}) |
p |
pi = 3.14159 |
a < b |
a smaller than b |
a > b |
a greater than b |
a => b |
a greater than or equal to b |
tanh |
hyperbolic tangent |
C. Statistical notation
y = a + b * x |
linear regression |
a |
intercept of ordinary regression |
a' |
intercept of functional regression |
b |
slope of ordinary regression |
b' |
slope of functional regression |
e |
(epsilon) maximum relative error |
f |
degrees of freedom |
F |
observed frequency |
Fc |
calculated or theoretical frequency |
n |
number of observation |
r |
correlation coefficient |
s/Ö n |
standard error |
s |
standard deviation |
s^{2} |
variance |
sa |
standard deviation of the intercept (a) |
sa^{2} |
variance of the intercept (a) |
sb |
Standard deviation of the slope (b) |
sb^{2} |
variance of the slope (b) |
sx |
standard deviation of the independent variable (x) |
sx^{2} |
variance of the independent variable (x) |
sxy |
covariance |
_{} |
relative standard deviation or coefficient of variation |
sy |
standard deviation of the dependent variable (y) |
sy^{2} |
variance deviation of the dependent variable (y) |
t_{f} |
quantil of t distribution (Student's) for f degrees of freedom |
x |
independent variable |
_{} |
mean value of x |
y |
dependent variable |