Would there by any way to do a comparison of the three methods using your data to look at possible differences in results, if any?

Support for each system isn't really as important, provided that the methodology is valid and provides accurate and precise predictions.

Thank you for your comment. I compared the methods and find almost the same for the additive or the multiplicative method. If I enter the number of predator and prey species separately I get a bit different results, but it may be due to a problem of collinearity between the number of hosts and the number of parasitoids.

In that case why not provide all three results? That way you're covered on methodology, if that is unfeasible is there any way you can determine which result is more accurate? If so, go with that one.

Or you could average the results of the two different systems that appear to be providing the more accurate results.

I think providing all will not be that feasible. The additive method is appealing because it directly links to information on the number of species occurring in the networks. The multiplicative way would be more representative of the total number of possible interactions. However, in a host-parasitoid webs not all interactions are possible, such that the multiplicative total is not a true representation of network size. I have to think a little bit more about which method makes more sense for my data. But as you say it's not a big issue since my results are similar. The tricky thing is that almost all my indices are entirely explained by network size...this suggests that they are not really comparable between the networks.

Cheers

Seems like the multiplicative method *is* representative of the total number of interations since all parasites could theoretically parasitize all hosts which can be used to calculate connectance. Vermatt et al. (2009 Ecology 90:278) finds connectance to be a primary dimension for structural variability in food webs with species richness being the 2nd most important.

Clarification: as long as there is no hyperparasitism, parasite-host connectance = # of links / (# parasite species * # of host species)

The "problem" is that there are certainly forbidden links between some hosts and parasitoids, which are not considered by connectance. The presence of forbidden links is anyway somehow problematic for most indices, isn't it? I'll have a look at the paper of Vermatt, sounds very interesting.

ah, 'forbidden links'... kevin lafferty is a big fan of including them in measures of connectance. I like a more mathematical perspective. That is, all nodes within any network can be connected or not. That they are connected is a key decriptor of the data at hand. One hypothesis (constant connectance) hypothesizes that dividing the latter by the former puts that information in its more scientifically useful perspective. For example, it allows the biological assertion of "no hyperparasitism" to be expressed in the measure rather than being assumed as a biological assertion (parasites can't parasitize parasites, plants can't eat animals, etc.) in the calculation of the measure. Another and not necessarily competing hypothesis asserts that the number of species/links is more informative. That framework might put your empirical networks to good use. That is, which assertions do your data suggest are most accurate? Perhaps most importantly, the purpose of the analyses needs to guide your choice. would love to hear your purpose and whether you find Vermatt useful.

Hi Neo,

I read and tried to understand the paper of Vermatt. I find very interesting the finding that connectance and species richness were on different orthogonal axis, meaning that they can be independent from each other. I previously generally read that connectance may not be a useful index because of its strong dependence on species richness. However what is less convicing to me (but I am not an experienced statistician!), or less applicable to my data, is that they looked I thing at large webs, such that the effect species richness may be less important. I think that the smaller the webs, the larger the problem with the comparability between them. This is in my view similar to simple diversity measures. It is difficult to compare diversity indices between sites that have large differences in the number of individuals.

To my study: I would like to assess the impact of fragmentation on bipartite host-parasitoid networks. The networks are highly variable in size, some are very small containing only three species. Almost all indices are strongly related to the number of species in the networks. As a result it is difficult to say if my findings are real facts or simple arose as a consequence of difference in network size. I though about simulating random networks to assess the effects of network size, but I don't know exactly how and if it is feasible for such small webs anyway.

What I found good in the species number approach is that I can link fragmentation directly to the number of species in the networks, but of course I can do this even if I take the multiplicative approach to control for network size. Now my concern is if I have to say that the indices cannot be meaningfully interpreted because of their dependence on network size or if they may still provide information on ecological processes / robustness.

Cheers,

Valérie

I just read Dormann et al. (The Open Ecology Journal, 2009, 2, 7-24) and they report that 78 % of the variance in bipartite network indices was due to the number of higher trophic level species, which therefore represent the fundamental factor of influence on network properties. My point of view is that the influence of network size on the comparison between different networks depends on the magnitude of the difference in the dimension of the networks being compared. I would be happy to have your opinion about this.

Best,

Valérie