Keewenaw Bay Lake Trout

With 9-13

  1. This is a cross-sectional catch-curve.
  2. Ages 9-13.
  3. Answers are below.
    1. Z=0.4818402 (CI: 0.3877375,0.575943)
    2. A=38.2354266 (CI: 32.1409544,43.7825496)
    3. S=61.7645734 (CI: 56.2174504,67.8590456)
  4. A=1-e-Z=1-e-0.4818402=0.3823543

With 8-13

  1. This is a cross-sectional catch-curve.
  2. Ages 8-13.
  3. Answers are below.
    1. Z=0.4163626 (CI: 0.3026487,0.5300766)
    2. A=34.0558914 (CI: 26.1141358,41.144013)
    3. S=65.9441086 (CI: 58.855987,73.8858642)
  4. A=1-e-Z=1-e-0.4163626=0.3405589

With 9-14

  1. This is a cross-sectional catch-curve.
  2. Ages 9-14.
  3. Answers are below.
    1. Z=0.5649092 (CI: 0.3923675,0.7374509)
    2. A=43.1588249 (CI: 32.4544167,52.1668328)
    3. S=56.8411751 (CI: 47.8331672,67.5455833)
  4. A=1-e-Z=1-e-0.5649092=0.4315882

With 8-14

  1. This is a cross-sectional catch-curve.
  2. Ages 8-14.
  3. Answers are below.
    1. Z=0.4892748 (CI: 0.3334172,0.6451323)
    2. A=38.6929156 (CI: 28.3528805,47.5406879)
    3. S=61.3070844 (CI: 52.4593121,71.6471195)
  4. A=1-e-Z=1-e-0.4892748=0.3869292

R Appendix

library(FSA)
library(tidyverse)
library(ggplot2)

d <- data.frame(age=3:14,ct=c(5,18,21,10,45,109,95,63,42,25,13,4))

ggplot(data=d,mapping=aes(x=age,y=ct)) +
  geom_point() +
  scale_y_continuous(trans="log") +
  theme_bw()

## With 9-13
cc1 <- catchCurve(ct~age,data=d,ages2use=9:13)
sum1 <- cbind(summary(cc1),confint(cc1))
plot(cc1)
cc1w <- catchCurve(ct~age,data=d,ages2use=9:13,weighted=TRUE)
sum1w <- cbind(summary(cc1w),confint(cc1w))

## With 8-13
cc2 <- catchCurve(ct~age,data=d,ages2use=8:13)
sum2 <- cbind(summary(cc2),confint(cc2))
plot(cc2)
cc2w <- catchCurve(ct~age,data=d,ages2use=8:13,weighted=TRUE)
sum2w <- cbind(summary(cc2w),confint(cc2w))

## With 9-14
cc3 <- catchCurve(ct~age,data=d,ages2use=9:14)
sum3 <- cbind(summary(cc3),confint(cc3))
plot(cc3)
cc3w <- catchCurve(ct~age,data=d,ages2use=9:14,weighted=TRUE)
sum3w <- cbind(summary(cc3w),confint(cc3w))

## With 8-14
cc4 <- catchCurve(ct~age,data=d,ages2use=8:14)
sum4 <- cbind(summary(cc4),confint(cc4))
plot(cc4)
cc4w <- catchCurve(ct~age,data=d,ages2use=8:14,weighted=TRUE)
sum4w <- cbind(summary(cc4w),confint(cc4w))

Stannard Rock Lake Trout

  1. 1956 year-class.
  2. Shown below.
  age  yr63 yc63  yc54 yc67
1   6 129.0   45    NA  101
2   7 339.0   NA    NA  733
3   8 331.0   NA    NA 1517
4   9 192.0   NA 192.0 1560
5  10  70.0  491  63.0 1031
6  11  16.0  163  39.0  445
7  12   0.5  117   5.0  300
8  13   0.5   18   0.5   NA
9  14   0.5    7   0.5   NA
  1. Data for the 1963 capture year is cross-sectional, whereas data for the 1963, 1954, and 1967 year-classes are all longitudinal.
  2. Answers for the 1954 year-class:
    1. Z=1.0757708 (CI: 0.2190936,1.9324479)
    2. A=65.8965206 (CI: 19.6753505,85.5206675)
  3. Answers for the 1967 year-class:
    1. Z=0.5789745 (CI: 0.3128332,0.8451158)
    2. A=43.9527174 (CI: 26.8628131,57.0492383)
  4. Difficult to tell as the CI for 1954 captures the estimated value from 1967 but the opposite is not true. Would be best to perform an IVR with both sets of data.