Data and hypotheses

This recreates the analysis from the following paper:

Dey CJ, O’Connor CM, Wilkinson H, Shultz S, Balshine S & Fitzpatrick JL. 2017. Direct benefits and evolutionary transitions to complex societies. Nature Ecology & Evolution. 0137.

This is, to my knowledge, the first study to employ PPA on binary traits.

The study investigates the evolution of cooperative breeding in cichlids. In short (my summary), there has been intense debate about what factors drive species towards evolving systems of cooperative breeding. Many have argued (and provided evidence in birds and mammals) that cooperative breeding chiefly evolves from monogamous mating systems because helpers can gain indirect fitness benefits through kin selection. However, a non-exclusive alternative hypothesis is that direct benefits due to ecological factors may be important and provide direct benefits. Therefore, both hypotheses should be considered at the same time.

The data is included in this paper as cichlids and cichlids_tree

It contains five variables:

• C: Cooperative breeding, cooperative or non-cooperative.
• M: Mating system, monogamous or non-monogamous.
• P: Parental care, maternal or biparental.
• G: Social grouping, grouping or non-grouping.
• D: Diet, piscivore or non-piscivore.

Under the indirect fitness hypothesis, monogamy is expected to be a major driver of cooperative breeding, while group living, biparental care and diet type may be important contributors towards a direct benefits scenario.

Defining the causal models

Following the paper in question, we define 12 putative causal models.

library(phylopath)

models <- define_model_set(
  A = c(C~M+D),
  B = c(C~D),
  C = c(C~D, P~M),
  D = c(C~D, M~P, G~P),
  E = c(C~D, P~M, G~P),
  F = c(C~D, P~M+G),
  G = c(C~D, M~P, P~G),
  H = c(C~D, M~P),
  I = c(C~D, M~M, G~P),
  J = c(M~P, G~D),
  K = c(P~M, G~D),
  L = c(C~M+D, P~M+G),
  .common = c(C~P+G)
)

plot_model_set(models, algorithm = 'kk')

Comparing the models

Now that we have our models, data and a tree, we can compare the models using phylo_path

(cichlids_results <- phylo_path(models, cichlids, cichlids_tree))

## 15 rows were dropped because they contained NA values.

## Pruned tree to drop species not included in `data`.

## Warning in phylo_path(models, cichlids, cichlids_tree): Some models produced warnings. Use `show_warnings()` to view them.

## A phylogenetic path analysis, on the variables:
##  Continuous:   
##  Binary:      G P D M C 
## 
##  Evaluated for these models: A B C D E F G H I J K L 
## 
##  Containing 67 phylogenetic regressions, of which 22 unique

Note that three messages are printed. This is because there are missing values in our data set that are first being removed. Also, since the tree includes species for which data is missing, the tree had to be pruned. This is done automatically with a message to the user. You should check whether the amount of data removed is correct.

The third messages notes that warnings have been generated, see the Important notes at the start of this vignette. I will continue with these results here, but models with warnings should not be trusted.

phylo_path notes that indeed all variables are binary.

(s <- summary(cichlids_results))

##   model k  q     C       p CICc delta_CICc        l        w
## F     F 5 10  7.95 0.63385 33.1       0.00 1.000000 0.511385
## L     L 4 11  6.66 0.57358 34.9       1.88 0.390236 0.199561
## G     G 5 10 10.94 0.36231 36.1       2.99 0.224235 0.114670
## E     E 5 10 11.63 0.31052 36.7       3.68 0.158648 0.081130
## D     D 5 10 11.73 0.30322 36.9       3.79 0.150632 0.077031
## C     C 6  9 18.91 0.09081 41.0       7.93 0.018945 0.009688
## H     H 6  9 20.40 0.05992 42.5       9.42 0.008987 0.004596
## I     I 6  9 23.79 0.02170 45.9      12.82 0.001646 0.000842
## K     K 6  9 25.37 0.01316 47.5      14.40 0.000748 0.000382
## J     J 6  9 25.86 0.01124 47.9      14.88 0.000586 0.000300
## B     B 7  8 28.84 0.01099 48.0      14.97 0.000560 0.000287
## A     A 6  9 27.55 0.00643 49.6      16.58 0.000251 0.000129

plot(s)

We see that model F is the best supported model. This model notably does not include a link between monogamy and cooperative breeding, giving support to the direct benefits hypothesis.

Evaluating variable importance

Now that we have selected F as our best model, we still have three factors that affect cooperative breeding: diet, social grouping and parental care. Which one is more important? For this we can fit the model and look at magnitude of the coefficients. In this case, since we want to use the best model we use the function best(). One can use choice() to choose any arbitrary model, or average() to average over several models.

best_cichlids <- best(cichlids_results)

To see the individual coefficients and their standard errors, simply print best_cichlids:

best_cichlids

## $coef
##   G M        P D        C
## G 0 0 2.244975 0 4.488997
## M 0 0 2.879175 0 0.000000
## P 0 0 0.000000 0 3.415208
## D 0 0 0.000000 0 3.415140
## C 0 0 0.000000 0 0.000000
## 
## $se
##   G M         P D        C
## G 0 0 0.8132303 0 1.200057
## M 0 0 0.8602750 0 0.000000
## P 0 0 0.0000000 0 1.348669
## D 0 0 0.0000000 0 1.376391
## C 0 0 0.0000000 0 0.000000
## 
## attr(,"class")
## [1] "fitted_DAG"

Or plot those:

coef_plot(best_cichlids, error_bar = "se", reverse_order = TRUE) + ggplot2::coord_flip()

But we can also plot the final model:

plot(best_cichlids)