Thinking on on figures in outline

[lizzieinvancouver]

@dbuona In your outline (prief_outline) figures, is T_50actually tau_g50?

When you send updated figures, can you also include a version where you give the actual model terms in the axes? We probably should also label the axes in Fig 4a (with arrows, see Fig 5 in the 2021 paper by Megan and me). For now I am jotting down a reminder of the 4 panels:

• Upper left: Species 2 has superior Rstar and Species 2 is less sensitive (and thus tends to have `early advantage')
• Lower left: Species 1 has superior Rstar while Species 1 is less sensitive (and thus tends to have `early advantage')
• Upper right: Species 2 has superior Rstar while Species 1 is less sensitive (and thus tends to have `early advantage')
• Lower right: Species 1 has superior Rstar and Species 1 is less sensitive (and thus tends to have `early advantage')

[lizzieinvancouver]

Some queries we have now (in order of importance):

1. How did you get the 12 weeks versus 6 weeks exactly (is the code somewhere, if not, try to explain)?
2. What exactly is plotted (what is each axis)?

[lizzieinvancouver]

Also, for understanding these figures later -- would be good to grab the DIFFERENCE in germination timing each year and thus be able to plot average germination diff across runs.

[lizzieinvancouver]

@dbuona reports: Chillling comes from PriEff_Envt.r lines 24-32, which is this:

if (runif(1,0,1)<c_warm) {

xi.mu <- log(12)                       # mean of chilling distribution ## 
xi.sigma <- .2                      # sd of chilling distribution
xi <- rlnorm(nyrs, xi.mu, xi.sigma)
}else {

  xi.mu <- log(6)                       # mean of chilling distribution ## 
  xi.sigma <- .2                   # sd of chilling distribution
  xi <- rlnorm(nyrs, xi.mu, xi.sigma)  
}

[lizzieinvancouver]

@dbuona adds: The plots come from the bottom half of PriorityEffects.r Lines 57-179 so @lizzieinvancouver looked at this and PriEff_Output.R and discussed with @dbuona and came up with:

Plot 4a X axis: xi_tau[1] / xi_tau[2] which is same as 5b x axis

Fig 5 is plots/coexistance_chilldiffs.jpeg which is logsens1sens2, logt501t502 and those are:

• check$logsens1sens2<-log(check$sen1/sen2) which is check$sen1/sen2<-check$sp1_xi_tau/check$sp2_xi_tau which comes from (output file): sp1_xi_tau=xi_tau[1],sp2_xi_tau=xi_tau[2]
• check$logt501t502<-log(check$t501/t502)which is check$t501/t502<-check$sp1_mean_tau_g50/check$sp2_mean_tau_g50 which comes from (from output file): sp1_mean_tau_g50=mean(tau_g50[,1]

[lizzieinvancouver]

@dbuona Can you add this to your next outline (caption to figure or text, or both -- or just a suggestion called 'reminders for Lizzie'):

For Fig 4a (above right): Under 12 weeks the advantage due to sensitivity differences is smaller (because species germinate at similar times), so a smaller Rstar difference (between species) is needed to offset it (shallow slope), whereas under 6 weeks, the sensitivity advantage increases and you need a larger Rstar difference to balance this (steeper slope).

[lizzieinvancouver]

As for this figure:

Note on the math: We are worried that there are possibly a lot of tau_g50 that end up with a mean of 0. In these cases the ratio (e.g., 1/0 for sp1/sp2) and the log of the ratio could be undefined (for example, you end up with -Inf and then try to take log) -- so you need to be careful of what happens when you're plotting that.

But more than that, it seems best to plot here:

1. For all Fig 5 plots -- make it MUCH easier to visualize the co-existing runs (so, color coexisting for 6 weeks, coexisting for 12 weeks -- and ideally two other colors, or separate plots for 6 weeks and 12 weeks that show coexisting versus non-coexisting, or however you come up with to best visualize this).
2. Also plot another version of 5b (a third plot) -- the difference on the Y axis (aka, what you have on X in Fig 5a) vs. what you already have for X (sens sp1/sens sp2), again always with the co-existing vs not coexisting being clear.

Back to 4a (above):

1. Bound x and y axes by -5 to +5
2. Fill color (in ggplot, fill gradient continuous) with t50sp1-t50sp2 (aka difference shown in x axis of Fig 5a)

[dbuona]

is there any reason not to plot the differences in sensitivity, R2 t50 etc as (Xsp1-Xsp2) [intead of log(Xsp1/Xsp2) as it currently is]? This solves the dividing by zero and taking log of 0 problem. When I do this the plots seem to make more sense to me.

[lizzieinvancouver]

@dbuona It's seems fine to do it for now as we figure out what is going on. The reason for a ratio is in part that it gives a unitless value that we can interpret, if you do +/- then you need to explain the units (and perhaps defend the absolute numbers also).

[lizzieinvancouver]

@donahuem Probably has even better reasons for this.

[lizzieinvancouver]

RIGHT shows that Rstar x phenology trade-off is CONSTANT across two scenarios, while LEFT shows that trade-off between Rstar and sensitivity is steeper with low chill.

[lizzieinvancouver]

RIGHT shows 50% germinate at same time under 12 weeks, but only 10% under 6 weeks. LEFT here shows `realized phenology' on vertical by sensitivity to chill on horizontal.

These plots are showing DIFFERENT community composition ... so you end up with different species traits (cues or sensitivities or whatever you want to say) under different environments.

[lizzieinvancouver]

You can trade-off timing with Rstar. When chilling is lower and we end up with phenological difference from sensitivity so need higher Rstar. When chilling is 12 weeks, advantage due to phenology is low so Rstar differences (stabilizing mechanism) can be low ... we think we can say that under low chill you need greater stabilizing via Rstar because phenology produces bigger differences.

Sensitivities have different phenological outcomes under diff environments.

[lizzieinvancouver]

Meeting again!

Current Fig 2a (diff R vs diff realized phenology) shows the R vs time (aka phenology -- days different) is CONSTANT, it does not vary with 6 or 12 weeks chilling. You might then think that nothing changes, but you'd be wrong because time (aka phenology) is a not a species-level trait -- phenological sensitivity is a species level trait. And you see in Fig 2b (diff R* vs diff phenology sensitivity) that the communities would be different under these two environments (this is about coexistence).

The second two panels (2c-d) are about how species respond to the two environments (and so we show all points).

We also discussed how to get people to understand that 6 week chill world and 12 week chill world does not mean these two worlds do not have variability (because people may think 'hey, 6 week chill can happen the year after 12 week chill') ... so would be good to add:

1. Plot of distributions underlying 6 week and 12 week worlds (two density plots)
2. Show examples of species coexisting under 6 but not 12 weeks and vice versa (coexisting under 12 weeks but not 6 weeks).