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Benjamin Gibson
BIO 332
Data Assignment #2
Spawner-recruit relationships
1. Per capita recruitment decreases at high spawner densities because of density-dependent
mortality. This is highly probable due to limited resources. Some likely scenarios include
competition among abundant larvae which could lead to starvation, adults eating their
own eggs and larvae at high densities, predators aggregating at high egg and larvae
densities, increased accumulation of toxic waste and spread of disease at high densities.
2. Density-dependent compensation due to the slope being less than 0. This leads to an
almost inevitable population crash and lack of recovery.
3. One valuable generalization is that there is always low recruitment when there are low
spawners. Another generalization is that density-dependent mortality is evident,
regardless of which model is used.
Parameters Beverton & Holt Model Ricker Model
a
b
0.584
0.124
0.143
0.009
Table 1. Calculated parameters for both the Beverton & Holt and Ricker
models using 40 years of spawner-recruit data of Atlantic Menhaden.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.84399
R2 0.71232
Adjusted R2 0.70474
Std. Error 0.52948
Observations 40
ANOVA
df SS MS F P-value
Regression 1 26.3781 26.3781 94.0895 7.9061E-12
Residual 38 10.6533 0.28035
Total 39 37.0314
Coefficients Standard
Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 0.73073237 0.3482151 2.09851 0.042561 0.0258 1.4357 0.02580782 1.43565692 X Variable1 -0.87801647 0.0905174 -9.69997 7.9061E-12 -1.0613 -0.6948 -1.06125940 -0.69477354
Table 2. Using Excel’s Data Analysis add-in, a full statistical output
is provided. Gray cells indicate importance to the diagnostic test.
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0
Observed
Predicted Ricker
Predicted B&H
Figure 1. Fitting both the predicted Beverton & Holt (B&H) and
the predicted Ricker model to 40 years of observed spawner-recruit
data of Atlantic Menhaden.
y = -0.878x + 0.731R² = 0.712P < 0.0001
-6.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00
Ln(R
/SSB
)
Ln(SSB)
Figure 2. Natural log of per capita recruitment (R/SSB) as a function of the
natural log of spawning stock biomass (SSB) for Atlantic Menhaden.
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