Models with origin status

[achauffou]

I will post here any update, question or thought worth sharing regarding the models that include origin status...

Retrieving species origin status: I have now retrieved the origin status of all species for which it was available. Altogether, 3,632 / 9,010 species had available distribution data in at least one of the database queried. For these species with available information, I could deduce the origin status at all sites where they are present:

Status	Nb of species/site combinations
Native	4601
Unknown	302
Introduced	172
Neighbouring native area	87
Neighbouring introduced area	4
Conflict betweent the two databases	14

[bernibra]

Hey Alain,

I am not sure I understand all the information in the table. It seems, however, that we have a good amount of data but far from a majority of the data. We can discuss things further on Monday because I need to think about this a bit furter.

[achauffou]

Hey,

The information on the table summarizes the origin status of species in the data. The same species will have as many origin status as sites where it is present, since it can be native somewhere but introduced somewhere else. Altogether, there are 13409 combinations of species/sites and the table gives the numbers for the 5180 combinations for which data is available. Indeed, it is a good amount but far from the majority of data (only 40% species have distribution data in the two databases I queried). Hopefully my next post will clarify the situation a little bit, but it is a good idea that we discuss it on Monday.

[achauffou]

Adding origin status to the Bayesian models: I will now try to add the origin status to the Bayesian models. I suggest that we try two different models:

1. One model in which the origin status of both partners is taken into account as an intercept, that is ... + mu[functional_group[sp1]] * is_native[sp1, site_id] + mu[functional_group[sp2]] * is_native[sp2, site_id]. Just as I did for the sigma_gamma, there would be as many mu parameters as functional groups but they would be independent (no pooling). With this model, I would end up with 3406/4189 seed dispersal interactions and 941/18507 pollination interactions (compared to the current amount of data).
2. It is also possible to include a mu parameter only for the plants. Doing so would enable to keep much more interactions: 16501/18507 pollination interactions, 3670/4189 seed dispersal interactions, and 414/414 plant-herbivore interactions.

In both cases, I would also run the previous models (that do not account for origin status) with the same data, so that it is possible to compare WAIC.

[bernibra]

This sounds really good. Definitely run these two models. As you pointed out, it is very important that we also run the models without the 'is_native' parameter for the filtered data (in both cases 1 and 2), so you can then compare WAIC values as well as compare posterior distributions (potentially with those posteriors estimated with the full dataset, to ensure that the restrictions on the data do not affect the overall results). Very excited to see these results.

[achauffou]

Hi, here is a very long update about the results (feel free to skip parts and read it later if you don't have time). The models we discussed on Monday seem to yield results that make sense, although some are sadly not very conclusive. I have uploaded them on polybox. I have not uploaded models that were made just for the purpose of comparison and some old models we found less interesting. Below is a quick description of each model as well as some thoughts I had when looking at the results.

Models description:

• pol stands for models with pollination interactions only, all stands for all interaction types (sadly only pollination and seed-dispersal at the moment, but I guess it still is worth it to have other interactions in the database if we want to extend the models or use it for something else one day)
• Models that start with 0 (e.g. pol_binom_04a) do not include origin status, while those that start with 1 include origin status of plants, and those that start with 2 include origin status of plant and pollinator/disperser (be careful, there is much less data for models that start with 2)
• Models that end with 3-4 are non-neutral (e.g. all_binom_14a), 5-6 are neutral, and 9 are non-neutral with bioclimatic suitability split into two terms
• Models that end with 3 and 5 have per-site pooled lambdas, while models that end with 4, 6, 9 have a single lambda per interaction type (possibly functional group)
• Note: parameters with several indices are usually ordered in this fashion: when distinguished by interaction type, pollination comes before seed dispersal; when distinguished by functional group, plants come before pollinators/dispersers; when distinguished by both, the order is plants (pollination), plants (dispersal), pollinators, dispersers.

Thoughts and results worth highlighting:

• Comparisons between the models without origin status reveal that the non-neutral models have a lower WAIC than the neutral ones by a landslide, that is not new nor surprising but I think a result that is worth including/discussing in the manuscript.
• The comparisons also reveal that models with two terms for bioclimatic suitability have a slightly lower WAIC, but the difference is extremely small (and not significant when compared to model 03), so I would not say it is necessarily better.
• Similarly, the model with per-site pooled lambdas (03) is better than with a single lambda (04), but the difference is again not significant. I feel that one criticism/question that might come is why I chose to run the model with 2 bioclimatic suitability terms with non-pooled lambdas and did not try with pooled lambdas (which the result suggest could be the one with lowest WAIC).
• The comparison between models with and without origin status is less clear to me. It seems that models with no origin status have slightly lower WAIC than the ones with it for only plants. When including origin status of both functional groups, the model with origin status has lower WAIC (but again there is much less data for these ones). As before, the difference is not large (although it is significant), so I believe it does not necessarily mean that one model is 'better' and the results for influence of origin status are definitely worth taking into account.
• Regarding the posterior of the lambdas, using two distinct terms enable to see differences between functional groups. As with the other model, the effect is positive but quite small, and all confidence intervals cross zero (to the exception of pollinators). I guess comparing the functional groups is still interesting, and it is an interesting result in itself that the role of climatic suitability in driving interactions is suggested to be smaller than we could have thought.
• Regarding the effect of origin status, the effect is negative (meaning that natives have lower probability to interact) but the confidence intervals are large and cross zero. So I guess the data sadly does not enable to draw a clear conclusion on this one, maybe because there are not that many introduced species in the data.
• When comparing the values of a parameter for different interaction types or functional groups (such as sigmas, lambdas, etc), often their confidence intervals cross one another. But when reporting the results, I will take advantage of the Bayesian nature of the model by comparing the two values for each draw from the posterior distribution, and looking at the proportion of draws for which one is lower/higher than the other. I think this enables to test with more confidence whether one is higher/lower, despite being unsure about their exact value.
• I would have been very interested to include information on co-evolution and functional traits, but I think it is time to stop researching and focus on the manuscript (unless you see a mistake that could be fixed). Anyway, I will work on the manuscript plan now and send you a simplified version of it probably next week.

[bernibra]

Sounds good, Alain. Let's focus on the writing of the thesis. Feel free to arrange a meeting if you are unsure about any aspect of the thesis throughout the writing process.