Transient dynamics in plant-pollinator networks: Fewer but higher quality of pollinator visits determines plant invasion success

Invasive plants often use mutualisms to establish in their new habitats and tend to be visited by resident pollinators similarly or more frequently than native plants. The quality and resulting reproductive success of those visits, however, have rarely been studied in a network context. Here, we use a dynamic model to evaluate the invasion success and impacts on natives of various types of non-native plant species introduced into thousands of plant-pollinator networks of varying structure. We found that network structure properties did not predict invasion success, but non-native traits and interactions did. Specifically, non-native plants producing high amounts of floral rewards but visited by few pollinators at the moment of their introduction were the only plant species able to invade the networks. This result is determined by the transient dynamics occurring right after the plant introduction. Successful invasions increased the abundance of pollinators that visited the invader, but the reallocation of the pollinators’ foraging effort from native plants to the invader reduced the quantity and quality of visits received by native plants and made the networks slightly more modular and nested. The positive and negative effects of the invader on pollinator and plant abundance, respectively, were buffered by plant richness. Our results call for evaluating the impact of invasive plants not only on visitation rates and network structure, but also on processes beyond pollination including seed production and recruitment of native plants.

Here, we use a dynamic plant-pollinator network model to evaluate the efficiency of 78 pollinator visits non-native plants receive and their resulting reproductive success at the critical 79 early stages of invasion. In addition, we determine their impact on native species' reproductive 80 success at equilibrium. In terms of non-native traits, we focus on rewards production, pollen 81 attachability, and level of generality (i.e., number of pollinator species visiting them) because 82 these are highly variable traits that influence the reproductive success of pollinator-dependent biological processes encapsulated in the model and its assumptions in Seed production ∈ Only a fraction of the total pollination events become seeds, determined by the seed production efficiency of the plant species (parameter ).
Seed recruitment ∈ Only a fraction of seeds produced recruit to adults, determined by the competition among plants (function ).

Consumption of rewards
In each visit, pollinators consume a fraction of the floral rewards offered by the plant individual ( / ) at a rate .
Recruitment to adult pollinators ∈ Floral rewards consumed by the pollinator species summed over all the plant species the pollinator species visits (set ) are converted into new pollinator adults at a rate .

Production of rewards
Floral rewards of a plant population increase with its population density in a saturating manner, with rewards production decelerating as rewards increase up to the maximum of / when the rewards production stops.

Adaptive foraging Equation (4)
A pollinator increases its foraging effort to plants with more rewards, by reassigning its efforts from plants with fewer rewards. Foraging efforts are fractions that can take a maximum value of 1 (the pollinator assigns all its effort to that plant) and they sum to 1 over all plants the pollinator visits.
Efforts of a fixed forager 1/k aj Pollinators without adaptive foraging are assumed to have fixed foraging efforts across all the plants they visit equal to one over the number of plant species the pollinator visits 140 We ran the model for 10,000 timesteps prior to the plant introductions and another 10,000 150 timesteps after the introduction. We analyzed both the transient dynamics immediately after the 151 plant introduction (during the first 2,000 timesteps after the introduction) and the equilibrated 152 dynamics (at 10,000 timesteps after the introduction). The simulations generally equilibrated at 153 around 3,000 timesteps, so running them longer ensured we captured the dynamics at 154 equilibrium.

156
Non-native introductions 157 We introduced 8 types of plant species to each network (one per simulation) based on all 158 combinations of two levels of three properties (see Table 3) at t = 10,000, with density equal to 159 the plant extinction threshold, 0.02, and reward density 0.02 times that of the average native at  Table 3. Properties of the non-native plants introduced. 177

Factor (property) Description of level 1 Description of level 2 Generality (# links)
Specialist (average # links of 30% most specialist natives) Generalist (average # links of 30% most generalist natives) Pollen attachability ( ) Same as average native Four times higher than average native* Rewards production ( Same as average native Four times higher than average native* *We chose the high levels of pollen attachability and rewards production to be four times higher than  Table S1).

206
How does higher reward production, pollen attachability, and number of pollinator visitors 207 affect the reproductive success of non-native plants? 208 All introduced plant species either went extinct or dramatically increased their density 209 compared to that of native plants. Thus, we characterized the result of an introduction as either 210 invasion failure or success. We found that specialist plants with high rewards production and 211 high pollen attachability were the most successful invaders (see "Spec High R&P" in Fig. 1), 212 These plants invaded 95% of the times they were introduced into the networks, while the same 213 plant type except for being generalist invaded only 15% of the times (see "Gen High R&P" in 214 Fig. 1A). Specialist plants with high production of rewards but average pollen attachability had 215 an invasion success of 13% (see "Spec High R" in Fig. 1A). All other plant types never invaded.

216
Our CART analyses (Table 4, Table S1) confirm these results, showing that among the 21 217 factors analyzed (17 network structure properties and 4 non-native traits, see Methods), high 218 production of rewards contributed the most to the variation in invasion success, followed by 219 being a specialist, and finally by having high pollen attachability. Interestingly, our CART 220 analyses ranked the contribution of network structure to invasion success very low, with less 221 than 5% of predictive power (Table S1). invaded the networks, that is, specialist plant species with high production of rewards (Spec High R), 231 specialist plant species with high production of rewards and pollen attachability (Spec High R&P), and 232 generalist plant species with high production of rewards and pollen attachability (Gen High R&P), 233 respectively. Black and light gray bars represent successful and unsuccessful invasion, respectively, while 234 medium gray indicates where those two bar types overlap. 235 their invasion success? 237 We found that plants visited by fewer pollinators (in terms of abundance) at the moment 238 of their introduction were most likely to invade (Fig. 1B-C). Therefore, we conducted a second 239 (refined, see Table 4) CART analysis in which we incorporated the initial pollinator abundance

Initial analysis
Refined analysis* Five fold R 2 0.82 0.87

Main Contributions
High reward producer (34%) More specialized (25%) High pollen attachability (22%) Linkage algorithm (5%) High reward producer (36%) *Initial pollinator abundance connected to non-native (33%) High pollen attachability (31%) 247 The initial analysis followed the simulation design (see Methods). The asterisk indicates that the refined 248 analysis (as opposed to the initial) included the initial pollinator abundance connected to the non-native 249 plant as a new contributor for the CART analysis, which better predicted the plant invasion success than 250 the trait of being more specialized (i.e., visited by fewer pollinator species). We only listed the factors that 251 contributed 5% or more to the predictive power of the analysis, which excluded network structure 252 properties (see Table S1).

254
The explanation for introduced plants visited by fewer pollinators being more likely to 255 invade resides in the reward threshold determining whether a plant species attracts sustained 256 visitation or not (hereafter "reward threshold" ; Fig 2, Appendix S1, Fig. S2). When the reward Appendix S1, R* in Fig S2), as a result of the "ideal-free distribution" caused by pollinators  goes extinct (see Fig S2). In the successful invasion, the introduced plant species is able to attract the 290 pollinators' foraging effort fast enough during the transient dynamics that it obtains enough quality of 291 visits to persist before the threshold is met. The second peak observed in panel A corresponds to the 292 increased floral rewards due to the increase in abundance of the introduced species that successfully 293 invades, but then get depleted again to the reward density determining the system's equilibrium (see Eq.

294
S2 in Appendix S1). All successful and failed invasions look qualitatively the same as these figures. 295 296 297

How do plant invasions impact network structure and the reproduction success of native
298 plants? 299 We found that the native plants that shared pollinator species with the successful invaders invasion, which is explained by pollinators re-assigning their foraging efforts from the native to 302 the invasive plant species (Fig. 4D). However, the native plants only slightly decreased their 303 density (Fig. 4C) and never went extinct (data not shown) as a consequence of the invasion. The 304 magnitude of this negative effect on the density of native plants was reduced by the number of 305 plant species in the network (Fig. 4G). Conversely, the plant invasions increased the density of 306 native pollinators (Fig. 4F), an effect that was also attenuated by the number of plant species in 307 the network (Fig. 4H). Finally, the plant invasions slightly increased the networks' weighted 308 nestedness (Fig. 3C) and modularity (Fig. 3D). See Table S1 for all the statistics of the Welch 309 Two Sample t-test comparing weighted nestedness and modularity for all networks, groups of 310 networks, and by the plant types introduced. Table S2 conceptually summarizes Table S1 for 311 easy understanding of the trends. before (at 10,000 timesteps) and after (at 20,000 timesteps) the plant introduction for all the networks 316 with 40 species and connectance 0.25 that were invaded by the three plant types that successfully invaded 317 the networks (see Fig 1A). The middle bar, box, and error bars represent the mean, interquartile range, 318 and standard deviations of each distribution. Welch Two Sample t-test for A, B, C, and D show 319 significant differences between the variable means before and after invasion, all of which generated p-320 values less than 10 -7 (see Table S2). We found a negative correlation between weighted nestedness and 321 modularity ( Fig. S5A; correlation coefficient -0.17 by Pearson's test) -consistent with previous analysis 322 on binary structure (Fortuna et al. 2010) -which became more negative after the invasion ( Fig. S5B;  323 correlation coefficient -0.50). See Fig. S6 showing the same qualitative results of panels C and D but 324 when the invader and their interactions are removed from the analyses of network structure after the 325 invasion. That is, keeping network size and species composition constant before and after the invasion did 326 not change our results. 327  (Appendix S1) so they need to produce more rewards than the natives to attract pollinators. beyond visitation (i.e., successful pollination events, seed production, recruitment), a decrease in 397 quantity or quality of visits does not necessarily translate into a decrease in plant reproduction or 398 reduction of plant growth. 399 We found no extinction caused by the plant invaders, which is explained by: 1) plants 400 only needing a few high-quality visits to produce enough seeds, and 2) seed recruitment being 401 dependent on competition among plants for resources other than pollinators, with intraspecific 402 stronger than interspecific competition (see Table 1). Native plants receive enough high-quality increasing their initial abundance 10 times -as mentioned above -allowed all generalist types to 419 invade (Fig. S4A). Our results suggest that the common finding of invasive species often 420 exhibiting "highly generalized floral traits" (e.g., radial symmetry; reviewed in Parra-Tabla and 421 Arceo-Gómez 2021) might be explained by those taxa being introduced several times and at 422 larger numbers than those we simulated here.

423
Finally, to our knowledge, ours is the first study suggesting that the cost of too many