add calculate M function

[sgaichas]

Use calc_Z then take the F applied in scenario out to get M

[sgaichas]

Ran into problems with output F. The Z we back-calculate from survivors over time is lower than the input F in some years, resulting in negative M when we do Z-F=M. See below for a snippet from the updated testing calc_Z vignette.

So what is M? This is an approximate annual M as Z-F from mort.txt (which assumes F is not rescaled!). If we need annual and age specific M then we need a new Z calc function that is cohort specific I think.

annM1 <- merge(annZ1, relF_ss, all.x = T) %>%
  mutate(M = Z-relF)

annZ2_Time <- annZ2 %>%
  mutate(Time = yr*365)

annM2 <- merge(annZ2_Time, relF_ss) %>%
  mutate(M = Z-relF)

plotM <- ggplot() +
  geom_line(data=Zish, aes(x=Time/365, y=relZ, color="mort.txt Z")) +
  geom_line(data=Zish, aes(x=Time/365, y=relM, color="mort.txt M")) +
  geom_point(data=annM1, aes(x=Time/365, y=M, color="M = endyr Z-F")) +
  geom_point(data=annM2, aes(x=yr, y=M, color="M = sum timestep Z-F")) +
  theme_tufte() +
  theme(legend.position = "bottom", legend.box = "horizontal") +
  scale_color_discrete(NULL) +
  guides(color = guide_legend(nrow = 1)) +
  labs(subtitle = paste(scenario.name, species_ss))

plotM + ylim(0, 2.0)

So the problem here is we get negative M if we use our calculated Z from annual numbers at age or timestep numbers at age and subtract the F from mort.txt. (Negative M does not show up as points above because I restrict the y axis scale to 0-2.0.) The F from mort.txt is actually higher than our estimated Z. So Atlantis must rescale F too???

Need to investigate backing out F…