# Scottish Marine and Freshwater Science Vol 6 No 12: The demography of a phenotypically mixed Atlantic salmon (Salmo salar) population as discerned for an eastern Scottish river

This report investigates the potential for assessment of fish populations at a sub-river

scale. A sophisticated mathematical model was used to separate salmon from a

single river (North Esk, eastern Scotland) into three sub-stocks, based on the

number

### A Sub-stock Structured View of the North Esk Population

** Sub-stock productivity **

Although the sub-stock results for early2 SW' fish closely resembled those for the single stock (Fig. 4.a vs Fig. 2.a), with spawner numbers approaching the pre-estuary numbers as the study period progressed (thus indicating increasing proportional escapement), results for both late2 SW' fish (Fig. 4.d) and grilse (Fig. 4.g) exhibited much weaker overall temporal trends and a lesser degree of convergence between PEA and spawner numbers. Furthermore, annual fluctuations for both sets of MSW fish were higher towards the start and end of the study period, whereas grilse showed bigger annual variations near the middle.

The Bayesian-estimated BH SR curves showed reasonably narrow credibility regions, with a few outlying points (Fig. 4.c,f,i). Note that those SR relationships were less similar than at first appears, due to factors of three and five difference in the maxima of their vertical and horizontal axes (necessary to clearly show details of the SR curves and the distribution of data-points around them). Ideally, a rigorous comparison of the SR curves would be performed using fish *densities* rather than numbers. Unfortunately this was not possible because the sub-catchment areas utilised by the different sub-stocks were unknown. The tabulated SR parameter values and 95% credibility regions (Table 2, Fig.4) showed that the uncertainties around the sub-stocks' SR estimates were quite large compared to the differences between them. Given the inability to re-scale to a common density, a useful comparison was achieved by examining the 95% credibility estimates of β (smolts-per-female at low densities, Table 2).

The stock recruitment relationships obtained for both the early2 SW' and the grilse sub-stocks broadly approximated the single stock results. Rather similar asymptotic numbers of smolts (60,000 vs 100,000) were produced by twice as many grilse of about half the body-mass of the early2 SW's. The estimated noise parameters ( *θ*) for these two relations, which imply CVs of 36% and 35% respectively, were closely comparable with the CV of 35% implied by the value of *θ* obtained using the same procedure on the aggregated (single-stock) data-set.

**Figure 4. Demography of the North Esk salmon population viewed as three distinct sub-stocks (Early MSW, Late MSW and all grilse) derived using grilse-error corrected rod-capture data and the default allometric marine-mortality model ( DAM).** Note the use of different vertical scales between frames of the same type, needed to clearly illustrate the trends and the variation about those trends. Frames a), d) and g) show the yearly time-series of pre-estuary (dashed) and spawner (solid) numbers. Frames b), e) and h) shows a yearly time-series of sub-stock smolt production, estimated via the default allometrice marine-mortality model ( DAM). Frames c), f) and i) show the inferred sub-stock BH stock-recruitment relations (hundreds of adults, thousands of smolts); note the differing horizontal (stock) scales needed to show detail of the SR curves, their credibility regions and the data-point distributions around the relationships. The points are smolt data re-interpreted using equation 6 for annually varying smolt-age compositions truncated to two smolt age-classes, S2 & S3. The solid line shows the median expected stock-recruitment relation, and the dashed and dotted lines respectively show the 95% and 50% credibility limits

.

**Table 2. Posterior parameter distribution for the North Esk 1980-2004 spawner to smolt data regarding the system as comprising three sub-stocks using the default allometrice marine mortality model ( DAM) and Beverton Holt ESRs with control priors.** First two columns show the pair of parameters *O _{max}, H,* defining the BH SR curve-shape. The third column,

*θ*

**represents the negative binomial error distribution factor**

*,***The next two columns are biologically informative values derived from the former three columns. The fourth column shows the (approx) modal coefficient of error variation implied by**

*.**θ*(see Gurney

*et al*. (2010) equation 2). The fifth column shows maximum individual productivity,

*β*, (equation 8). The top line of each pair shows the mode and lower line shows the upper and lower 95% credibility limits. The upper section of the table shows results for the default (grilse-error corrected) data, while the lower section shows results without grilse-error correction.

Sub-stock | O _{max}mode |
H mode |
θ mode |
CV(%) ≈ 1/√ mode |
β mode= O _{max}/H |
|||||
---|---|---|---|---|---|---|---|---|---|---|

2.5% | 97.5% | 2.5% | 97.5% | 2.5% | 97.5% | |||||

Data Corrected for grilse error | ||||||||||

MSW early | 7.52×10 ^{4} |
785 | 7.64 | 36% | 95.8 | |||||

5.95×10 ^{4} |
11.8×10 ^{4} |
330 | 2242 | 3.78 | 16.8 | 51% | 24% | 53 | 180 | |

MSW late | 4.11×10 ^{4} |
261 | 3.26 | 55% | 157 | |||||

3.13×10 ^{4} |
6.87×10 ^{4} |
125 | 874 | 1.65 | 6.78 | 77% | 38% | 78 | 250 | |

Grilse | 13.72×10 ^{4} |
1313 | 7.96 | 35% | 104 | |||||

11.1×10 ^{4} |
19.4×10 ^{4} |
585 | 3961 | 3.92 | 17.1 | 51% | 24% | 49 | 190 |

The SR results for the late2 SW' sub-stock appeared much less similar to the others. First, the maximum expected recruitment ( *O _{max}*) was a much lower proportion of the asymptotic values for early2 SW' and grilse (55% and 30% respectively). Secondly, the half-saturation spawner stock was an even smaller proportion (20%) than that expected by comparison with the (approximately co-located) grilse population. Finally, the noise parameter had an appreciably higher value, with a CV of 55%.

An approximate expectation of the relative productivities of female grilse and late MSW fish (via their average body-weights), suggests that late MSW ova fecundity should be about 2.4 times that of grilse. So if their offspring approximately co-locate with those of the grilse, and developed at the same rate with the same survival, then their individual smolt productivity should be about 154. This value was extremely close to the modal value of *β=O* * _{max}/H* = 157 estimated via our MCMC determination of the model's parameters (Table 2). However, a similar comparison of the β values between early2 SW' and grilse showed a large discrepancy, of a

*factor*of two. Similar fecundity-ratio anomalies occurred between different sub-stocks for the other marine-mortality models (see

*Productivity Implications…*).

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