Most pollinators are generalist foragers that can, in some contexts, switch between plant species within a single foraging bout . When pollinators are promiscuous within a single foraging bout, they may transfer heterospecific pollen to floral stigmas, which can have negative effects on both male and female elements of plant reproduction . While heterospecific pollen deposition is highly variable in nature , it can represent a substantial percentage of total pollen on a stigma, often more than 50% of grains . Second, there is the extreme example of an antagonistic interaction from pollinators wherein the visitors do not visit the flower “legitimately” but rather pierce holes in a flower’s corolla to access the nectar rewards without ever touching the reproductive parts of the flower and therefore not acting as a pollinator . Some researchers suggest that most all flowering plants with accommodating floral architecture will experience some degree of nectar robbing . Furthermore, if a pollinator possesses mouth parts capable of robbing, they are likely to act as both legitimate pollinators on some plant species and primary or secondary robbers on others . On the other side of the interaction, blueberry plant pot some plants produce chemicals in pollen or nectar that that can be harmful to the development of the bees that visit their flowers, reducing bee fitness .
It has long been recognized that exploitation of mutualisms is commonplace and can have substantial impacts on the evolutionary persistence of mutualisms . While our understanding of the extent to which antagonistic interactions between plants and their pollinators is not complete, the examples listed above are common enough that the inclusion of such demonstrated negative interactions on network dynamics and how they might impact the robustness of interactions to extinctions warrants exploration. Recent network studies have begun to explore interactions in a continuous, rather than binary positive-or-not framework . While such studies do not take the potential for negative interactions into account, these models allow for some pollinators to be “better” than others in the services they provide or, in the case of Vieira and Neto , to vary the amount of dependence that the mutualistic partners have on one another. Here, we build on binary network simulation modeling approaches to asses show negative interactions impact the effects of pollinator species losses on plant species persistence, i.e. network robustness. In previous simulations where all network interactions are considered positive, the removal of a given pollinator species could result only in the loss of one or more plants. By contrast, after incorporating negative interactions, extinction cascades, also become possible , who produce extinction cascades in an all positive framework by relaxing the assumption that extinctions only take place after all partners are lost). In other words, if the removal of a pollinator species causes plant extinctions, those losses can tip the balance of interactions toward the negative for remaining pollinator species, which can then go extinct, in turn potentially leading to further plant species losses, thus an extinction cascade.
Our study examines the overall robustness to extinctions in two ways R, or, the area under each extinction curve and extinction cascade length –i.e. higher order extinctions that occur beyond the induced pollinator knockout and the resulting plant extinction. To our knowledge there is only one network study that incorporates the possibility for negative interactions between plants and pollinators while examining the robustness of the network when faced with extinctions This model classifies interactions as either mutually beneficial or beneficial for one species and detrimental to the other. This is in contrast to our model that examines robustness of networks with all positive interactions to those that incorporate negative interactions . Importantly the Campbell model focuses on hypothetical networks and does not directly evaluate the role of assigned negative interactions in determining the robustness of the network to extinctions and furthermore does not compare networks with and without negative interactions. Our method of incorporating negative interactions in to empirical networks will allow for higher order extinction cascades, giving us a more realistic impression of what might happen to a network after pollinator extinctions. This is not the case in extinction simulations that simply allow for asymmetric positive interactions , as noted above. We examined the effects of two factors on network robustness: the proportion of negative interactions in the network, including an all-interactions positive control; and the order of extinction, random pollinator losses vs. specialist-to-generalist vs. generalist-to-specialist.
Removing specialists first could be the most probable extinction sequence as specialist pollinators also tend to be the rarest species , but see who show that loss of specialists can accelerate the rate of species loss. By contrast, generalists are thought to be the “backbone” of networks and when highly connected nodes are lost, networks are expected to collapse rather quickly . While losing generalist pollinators first from a network may seem unlikely, we have seen rapid declines and range contractions in several highly generalist bumble bee species which had previously been abundant .First, we hypothesized that increasing the proportion of negative interactions would lead to both a decrease in the robustness of the network and greater number of extinction cascades. Second, we hypothesized that inclusion of negative interactions would not change the effects of extinction order relative to all-interactions-positive networks, in which specialist-to generalist pollinator species removals had the least impact on plant extinctions, generalist-to-specialist removals had the most, and random removals intermediate between the two .Following previous binary network assessments of robustness , we used empirical networks to conduct our robustness assessments. We selected three plant-pollinator networks of varying size and connectance that represent a range of natural plant-pollinator interactions; as in previous assessments, this selection is not meant to be exhaustive . 1) The Clemens and Long network was collected on Pikes Peak, Rocky Mountains, Colorado USA. This is by far the largest with 97 plant species forming 918 unique pairwise interactions with 275 pollinator species. Data were collected in various subalpine habitats at 2500 m elevation over 11 years . 2) The Arroyo et al network data were collected at an elevation between 2200m and 2600m between 1980 and 1981 in the alpine zone of Cordon del Cepo in Central Chile. The network is medium in size with 87 plant species forming 372 unique pairwise interactions with 98 pollinator species. 3) The Dupont network is the smallest as data were collected on the sub-alpine desert above 2000 m on the island of Tenerife, Canary Islands. Data were collect between May 7 and June 7, 2001. The network consists of 11 plant species forming 109 unique pairwise interactions with 38 pollinator species. These networks were retrieved from the NCEAS Interaction Web Database .We simulated extinctions by sequentially removing pollinator species one at a time and recording the number of plant species that were left with a positive sum of pollinator interactions. Plant species left with an interaction sum less than or equal to zero were then considered extinct and removed from the network due to assumed failure to sexually reproduce. Next, we evaluated if the secondary removal of those plant species left a pollinator species with an interaction sum less than or equal to zero. If yes, plastic gardening pots they were then considered extinct and removed from the network . This cycle continued until all plant and pollinator species were left with an interaction sum greater than 0 at which point the simulation moved on to the next pollinator species knockout. We carried out the extinction simulations separately for each of the aforementioned 600 network configurations and each of the three extinction orders.We evaluated network robustness via two response variables: R – this is a quantitative measure of robustness of a network following a species knockout . R is a simple calculation of the sum of the remaining plant species at each time step along the extinction simulation. R is standardized by its maximum value which equals the starting number of plants * the starting number of pollinators . R was calculated for each of the 50 simulations per order and proportion negative for all three networks.
Extinction cascades – the number of higher order extinction cycles that take place after a single pollinator species knockout.Cascade length is defined as the higher order extinctions that occurred beyond the induced pollinator knockout and the resulting plant extinction. A cascade of length 1 results when such plant extinctions lead directly to subsequent pollinator extinction, while a cascade of length 2 indicates additional subsequent plant extinction. We calculated the total number of cascade events that occurred across the entire knockout sequence for each of the 50 replicate network configurations for each set of starting networks using GLMs with Poisson errors and a log link function. This analysis directly mirrors the modeling approach for robustness discussed above, comprising two sets of models. The first set compared the effect of negative interactions, extinction order, and their interaction within each network , while the second set of models compared the effect of negative interactions, network ID, and their interaction, within each extinction order .Our study examined how both the incorporation of negative interactions into networks as well as order of extinction impacted robustness and total number of extinction cascades in three empirical networks. As expected, we found that incorporating negative interactions leads to lower network robustness via an increased rate of plant species loss in all three of the networks. Furthermore, when compared to random extinction order, simulations with generalist removed first show the lowest overall robustness whereas the removal of specialists first has the least impact on lowering network robustness. This is true for all three networks and followed our expectations based on previous network extinction simulations . While some of the results from our simulations were predictable or even mathematical inevitabilities , not all of our results could be predicted a priori. We did not expect the networks to behave idiosyncratically with respect to how negative interactions and extinction order impacted both R and the total number of extinction cascades. Specifically, we found that in the smallest of the networks , extinction order did not impact the magnitude of the effect of negative interactions on network robustness. The effect of removing generalist-first from the two larger networks seemed to supersede the impact of negative interactions, leading us to conclude that the impact of losing generalists can,in some cases, be so detrimental so as to make inclusion of negative interactions irrelevant. While extinction cascades can only take place in networks that incorporate negative interactions, the impact of negative interactions on total cascade length was unpredictable. Neither increasing negative interactions nor extinction order were a good predictor for how many extinction cascades networks would take place in the simulations. Total number of extinction cascades is likely relate to structural properties unique to each network and warrant further exploration. It difficult to draw conclusions as to why these distinct differences between networks were seen, as this study did not include an exhaustive exploration of other network properties that may influence network robustness and total extinction cascades. Future studies should focus on selecting networks with systematically varying properties such as; network size, nestedness, and connectance. These properties each have the potential to influence the impact that negative interactions have on network robustness. Nestedness is a network property that has been identified in nearly all empirical networks. It is the tendency of specialists to interact with generalists in the network . We would expect that an increase in nestedness could make the networks more robust to extinctions due to the redundancy in the number of pollinators available per plant. Still, Campbell et al. found that high values of nestedness actually can have the opposite effect, and can decrease robustness after the loss of a single species, in some extreme cases lead to the total collapse of the highly nested community. In our simulations, networks with more generalists will be inherently more vulnerable because true specialists were excluded from assignment of negative interactions . While we do not expect this limitation to impact our results dramatically—as true specialists that only interact with one or two plant species are uncommon—to fully explore the role of nestedness one would need to develop a method of assigning negative interactions that distributes the negatives evenly among the specialists and generalists. Connectance is simply the proportion of realized links in a network . In this study we, by chance, selected a range of network size and connectance.