Understanding linkage rules in plant-pollinator networks by using hierarchical models that incorporate pollinator detectability and plant traits

Abstract

The analysis of mutualistic networks has become a central tool in answering theoretical and applied questions regarding our understanding of ecological processes. Significant gaps in knowledge do however need to be bridged in order to effectively and accurately be able to describe networks. Main concern are the incorporation of species level information, accounting for sampling limitations and understanding linkage rules. Here I propose a simple method to combine plant pollinator effort-limited sampling with information about plant community to gain understanding of what drives linkage rules, while accounting for possible undetected linkages. I use hierarchical models to estimate the probability of detection of each plant-pollinator interaction in 12 Mediterranean plant-pollinator networks. As it is possible to incorporate plant traits as co-variables in the models, this method has the potential to be used for predictive purposes, such as identifying undetected links among existing species, as well as potential interactions with new plant species. Results show that pollinator detectability is very skewed and usually low. Nevertheless, 84% of the models are enhanced by the inclusion of co-variables, with flower abundance and inflorescence type being the most commonly retained co-variables. The predicted networks increase network Connectance by 13%, but not Nestedness, which is known to be robust to sampling effects. However, 46% of the pollinator interactions in the studied networks comprised a single observation and hence could not be modeled. The hierarchical modeling approach suggested here is highly flexible and can be used on binary or frequency networks, accommodate different observers or include collection day weather variables as confounding factors. An R script is provided for a rapid adoption of this method.

Keywords: Connectance; Linkage density; Nestedness; hierarchical models; occupancy models; pollination web; specialization.

Figure 1. Histogram of the Detectability of each pollinator modeled.

Despite some pollinator species show very high detectability, most show values below 10%.

Figure 2. Frequency distribution of the number of models including five different potential co-variables of pollinator detectability (plus no covariate).

In grey the proportion of models retaining only one co-variable. Note that most models retained more than one co-variable (186 models; median of 2 variables retained; 30 models retained no co-variables).

Figure 3. Observed and estimated visualization for one network (network MED2 in Bartomeus et al. 2008).

Pollinators (numbers) are represented in the upper level, and plants (letters) in the lower level. Box size is proportional to the total number of visits recorded, and the link size to the frequency of this particular link. A) Observed data. B) Links estimated with the hierarchical models, which incorporate pollinator detectabilities.

Figure 4. Network parameters of the observed networks, and its paired estimated network.

Different colors are used for visualization purposes. A) Connectance, B) Linkage density, C) Nestedness, D) Robustness to pollinators extinction, E) Robustness to Plant extinctions and F) Specialization H2 index.