Description Usage Arguments Details Value References See Also Examples
Generation of Age-Length Keys (ALK) using incomplete data, by methods based on inverse ALKs.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | gascuel(x, fi1, fi2, initial_values, threshold = 1e-04,
maxiter = 2000, age_classes = colnames(x),
length_classes = rownames(x), name = "",
description = "")
hoenig_heisey(x, fi1, fi2, threshold = 1e-04,
maxiter = 2000, age_classes = colnames(x),
length_classes = rownames(x), name = "",
description = "")
inverse_ALK(x, fi1, fi2, age_classes = colnames(x),
length_classes = rownames(x), name = "",
description = "")
kimura_chikuni(x, fi1, fi2, threshold = 1e-04,
maxiter = 2000, age_classes = colnames(x),
length_classes = rownames(x), name = "",
description = "")
|
x |
A i \times j matrix with |
fi1 |
A vector of length |
fi2 |
A vector of length |
age_classes |
A vector with the name of each age class. |
length_classes |
A vector with the name of each age class. |
threshold |
The value at which convergence is considered to be achieved: see ‘details’. |
maxiter |
The maximum number of iterations of the EM algorithm: see ‘details’. |
initial_values |
A vector with the initial values for α, β and γ: see ‘details’. |
name |
A string with the name of the ALK. |
description |
A string describing the ALK. |
inverseALK
calculates an ALK from a sample of
aged-fish, the length distribution of the sampled
population and the length distribution of a population
with unknown age-length data, as described by Clark
(1981), Bartoo and Parker (1983) and Hilborn and Walters
(1992).
kimura_chikuni
, hoenig_heisey
and
gascuel
use the same inputs as inverseALK
to calculate an ALK as described respectively by Kimura
and Chikuni (1987), Hoenig and Heisey (1987) and Gascuel
(1994).
hoenig
employs the generalized method proposed by
Hoenig et al. (1993, 1994), which takes an
undefined number of data sets with known and unknown age
information and combines them to calculate the ALK.
The returned ALKr
object contains information on
the convergence threshold that was used, the number of
iterations ran, and if convergence was reached.
The method proposed by Gascuel (1994) is based on the assumption that the length distribution within each age class follows a Normal distribution, where the standard deviation of length at age σ(j) is given by a linear model as a function of three parameters α, β and γ:
σ(j) = α + β l(j) + γ Δl(j)
where Δl(j) is the difference
between the mean lengths at age-class j
and
age-class j-1
.
The methods proposed by Kimura and Chikuni (1987), Hoenig and Heisey (1987) and Gascuel (1994) are all based on the EM algorithm as defined by Dempster et al. (1997), and build the ALK by a series of iterations which are repeated until convergence is acheived.
The convergence is tested by evaluating the sum of the
absolute differences between the ages distributions
calculated on the previous and current iterations:
sum(abs(pj_prev - pj_curr))
. The algorithm exits
when either this value is smaller than the specified
threshold
or when the number of iterations reaches
maxiter
.
An ALKr
object, containing a i \times j
matrix with the probability of an individual of length
i
having age j
, i.e. P(j|i), a i
\times j matrix with the estimated number of individuals
of length i
and age j
, and information
about the method used to generate the key.
Bartoo, N.W., Parker, K.R. (1983). Stochastic age-frequency estimation using the von Bertalanffy growth equation. Fishery Bulletin, 81/1, 91-96
Clark, W.G. (1981). Restricted Least-Squares Estimates of
Age Composition from Length Composition. Canadian
Journal of Fisheries and Aquatic Sciences,
38/3, 297-307. DOI: 10.1139/f81-041
Dempster, A.P., Laird, N.M., Rubin, D.B. (1977). Maximum
Likelihood from Incomplete Data via the EM Algorithm.
Journal of the Royal Statistical Society. Series B
(Methodological), 39/1, 1-38. DOI:
10.2307/2984875
Gascuel, D. (1994). Une methode simple d'ajustement des
cles taille/age: application aux captures d'albacores
(Thunnus albacares) de l'Atlantique Est. Canadian
Journal of Fisheries and Aquatic Sciences,
51/3, 723-733. DOI: 10.1139/f94-072
Hilborn, R., Walters, C.J. (1992). Quantitative fisheries
stock assessment: Choice, dynamics and uncertainty.
Reviews in Fish Biology and Fisheries,
2/2, 177-178. DOI: 10.1007/BF00042883
Hoenig, J.M., Heisey, D.M. (1987), Use of a Log-Linear
Model with the EM Algorithm to Correct Estimates of Stock
Composition and to Convert Length to Age.
Transactions of the American Fisheries Society,
116/2, 232-243. DOI:
10.1577/1548-8659(1987)116<232:UOALMW>2.0.CO;2
hoenig
1 2 3 4 5 6 7 8 9 10 11 | data(hom)
inverse_ALK(hom$otoliths[[1]], fi1 = hom$F1992, fi2 = hom$F1993)
kimura_chikuni(hom$otoliths[[1]], fi1 = hom$F1992, fi2 = hom$F1993) # converges
kimura_chikuni(hom$otoliths[[1]], fi1 = hom$F1992, fi2 = hom$F1993, maxiter = 10) # won't converge
hoenig_heisey(hom$otoliths[[1]], fi1 = hom$F1992, fi2 = hom$F1993)
gascuel(hom$otoliths[[1]], fi1 = hom$F1992, fi2 = hom$F1993,
initial_values = c(0.1, 0.07, 0.06))
|
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