Parsing propagule pressure: Simulated and experimental disentanglement of introduction 1 size and number of introductions for colonizing individuals 2

Colonization of novel habitats is more likely with increasing propagule pressure— the total 21 number of individuals introduced to a site. Two key components of propagule pressure are the 22 number of introduction events and the size of those introduction events. It is unclear which of 23 these components is more important for colonization success, or under what environmental 24 conditions their relative importance might shift. Using demographic simulations paired with a 25 Tribolium flour beetle microcosm experiment, we introduced 20 total individuals into replicated 26 novel habitats of stable or fluctuating quality and manipulated the number and size of 27 introduction events used to distribute them through time. After seven generations, we evaluated how different combinations of the number and size of introductions affected establishment 29 probability, size of established populations, and whether effects depended on the variability of 30 the recipient environment. We found no effect of biologically realistic environmental 31 stochasticity on establishment probability or size of established populations in the demographic 32 simulations. However, there was strong evidence that establishment probability was enhanced 33 with more, smaller introductions. In the microcosm, we similarly found no effect of 34 environmental stochasticity on establishment probability, but unlike the simulations found that 35 populations that established were larger in the stable environment, especially with more 36 introduction events. The microcosm experiment yielded greater overall establishment probability 37 and larger populations compared to the demographic simulations. Genetic mechanisms likely 38 underlie these differences in results and thus deserve more attention in efforts to parse propagule 39 pressure. Our results highlight the importance of preventing further introductions of undesirable 40 species to invaded sites, and suggest conservation efforts should focus on increasing the number 41 of introductions or re-introductions of desirable species rather than increasing the size of those 42 introduction events.

the recipient environment. We found no effect of biologically realistic environmental 31 stochasticity on establishment probability or size of established populations in the demographic 32 simulations. However, there was strong evidence that establishment probability was enhanced 33 with more, smaller introductions. In the microcosm, we similarly found no effect of 34 environmental stochasticity on establishment probability, but unlike the simulations found that 35 populations that established were larger in the stable environment, especially with more 36 introduction events. The microcosm experiment yielded greater overall establishment probability 37 and larger populations compared to the demographic simulations. Genetic mechanisms likely 38 underlie these differences in results and thus deserve more attention in efforts to parse propagule 39 pressure. Our results highlight the importance of preventing further introductions of undesirable 40 species to invaded sites, and suggest conservation efforts should focus on increasing the number 41 of introductions or re-introductions of desirable species rather than increasing the size of those 42 introduction events. 43

INTRODUCTION 46
Colonization is the ecologically fundamental process of population establishment in an 47 unoccupied site, and it underlies the past, present, and future distributions of species. 48 Colonization occurs naturally, but is increasingly prevalent due to anthropogenic influences 49 (Sakai et al. 2001, Ricciardi 2007). Incipient populations often face 50 environments that are entirely novel, which is especially likely in the case of anthropogenic 51 colonization , Ricciardi 2007). Regardless of whether colonization events to 52 novel habitats are natural (e.g., range expansion) or human-mediated (e.g., biological invasions, 53 reintroductions of rare species, release of biological control agents), their successes or failures 54 have significant implications for natural resource managers and society (Mack et al. 2000). 55 Most introductions to novel habitats fail, and colonization success can be difficult to predict 56 (Lockwood et al. 2005, Zenni and Nuñez 2013). Incipient populations are commonly small, and 57 face threats from environmental, demographic, and genetic stochasticity (Lande 1988, 58 Fauvergue et al. 2012). Furthermore, the success of any given population can be idiosyncratic 59 with respect to taxonomy and geography (Lodge 1993, Lockwood et al. 2005. Thus, it is crucial 60 to understand more general features of the colonization process beyond the particular invading 61 organism or the particular invaded environment (Lockwood et al. 2005). Propagule pressure is 62 one such general feature that is the only known consistent predictor of colonization success in 63 novel habitats (Lockwood et al. 2005, Colautti et al. 2006, Simberloff 2009). 64 seeds, vegetative material) introduced to an area (Novak 2007). It is often described in this broad 66 sense, which belies its complexity. Two important components of propagule pressure are the 67 number of introduction events-sometimes termed propagule number, and the number of 2012). Models that hold the total propagule pressure constant agree that multiple, small 84 introductions distributed across space will lead to greater establishment probability compared to 85 a single, large introduction when Allee effects are weak (Haccou andIwasa 1996, Grevstad 1999, 86 generated conflicting views on how an introduction regime affects colonization success when 88 introductions are distributed through time and total propagule pressure is constant. 89 There is evidence from both models and experiments that colonization success can increase with 90 more, smaller introduction events through time. Branching process models show that, in the long 91 run, several, small introductions will always be more likely to successfully establish a population 92 than a single, large introduction (Haccou andIwasa 1996, Haccou andVatutin 2003). This propagule pressure. In a more recent experiment, several, small introductions led to a 65% 101 increase in abundance of successfully colonizing invasive Pacific Oyster (Crassostrea gigas) 102 compared to a single, large introduction (Hedge et al. 2012). 103 There is also evidence from both models and experiments that colonization success increases 104 with fewer, larger introduction events through time. In simulations of bird invasions, a single, 105 large introduction event always led to the greatest establishment probability (Cassey et al. 2014). 106 6 better predictor of establishment success than the number of introduction events (Memmott et al. 111 2005). In this case however, the introduction regimes with the most individuals per event also 112 had the highest total propagule pressure (Memmott et al. 2005). In an experiment that controlled 113 total propagule pressure, a single, large introduction of the non-native mysid, Hemimysis 114 anomala, led to larger populations and greater survival probabilities compared to several, small 115 introductions through time (Sinclair and Arnott 2015). 116 Environmental stochasticity in the recipient environment may also affect which introduction 117 regime is optimal for colonization. Branching process models show that a more variable The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/108324 doi: bioRxiv preprint Where N t+1,i is the size of population i at time t+1, k D represents stochasticity due to 177 demographic heterogeneity, µ i is the expectation of the size of population i in the next time step, 178 F mated(t,i) is the latent number of mated females in population i at time t, p is the probability of an 179 individual being female, R Ei is the latent density-independent population growth rate for 180 environment E, α is the egg cannibalism rate, N t,i is the total size of population i at time t, k E 181 represents environmental stochasticity, R 0 is the density-independent population growth rate for 182 the average environment, N migrants(t,i) is the total number of migrants to population i at time t, and 183 N residents(t,i) is the total number of residents in population i at time t. 184 We imposed a mating function such that a population would deterministically go extinct if it 185 comprised only non-migrant females. In cases with an all female population and a mixture of 186 . CC-BY 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/108324 doi: bioRxiv preprint residents and migrants, we only included the number of migrant females in the density-187 dependent effect of the demographic heterogeneity term k D *F mated(t,i) because this effect 188 manifests via the number of eggs laid by females and only migrant females, being pre-mated, 189 would lay eggs. Weakly regularizing gamma priors were taken from Melbourne and Hastings 190 (2008). The expected equilibrium population size for the model is: 191 For each combination of the 4 introduction regimes and 2 recipient environment types (described The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/108324 doi: bioRxiv preprint combination of demographic and environmental stochasticity for populations in the fluctuating 254 environment, and that demographic stochasticity was the sole contributor to total stochasticity 255 for populations in the stable environment. Total stochasticity (demographic plus environmental) 256 of each population that did not experience extinction (n=667) was calculated as the variance of 257 the natural logarithms of its population growth rates through 7 generations: 258 where, for a particular population, !"!#$ is its total stochasticity, !"#$%&'(!!" is its demographic 259 stochasticity, !"#$%&"'!"()* is its environmental stochasticity (assumed to be 0 for populations 260 in the stable environment), and ! is its per capita population growth rate between generation t-1 261 and generation t (t=1, 2, … , 7). We only calculated total stochasticity for populations that did 262 not experience any extinction in order to capture the full temporal extent of environmental 263 fluctuations and because extinctions would have an infinite effect on this measure of 264 stochasticity. 265

Statistical analyses 266
We evaluated how our environment treatment affected variability in population growth rate (total 267 stochasticity from Eq. 3) using a linear mixed effects model with environment (stable or 268 fluctuating) as a fixed effect and block as a random intercept effect. 269 We used a mixed effects logistic regression with a logit link to predict the binary response of 270 establishment, and a mixed effects Poisson regression with a log link to analyze population size. 271 In both models, introduction regime, environment treatment, and their interaction were treated as 272 fixed effects, and block was treated as a random intercept effect. 273 . CC-BY 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/108324 doi: bioRxiv preprint population size by fitting the generalized linear mixed effects models described above to data 275 from the multiple introduction regimes (i.e. not the 20x1 regime) and with additional predictor 276 variables. To assess the effect of the presence of a temporary extinction, we included an 277 additional Boolean predictor for whether a population went temporarily extinct or not. To assess 278 the role of the total propagule pressure, we included a numeric predictor representing the number 279 of beetles introduced after the latest temporary extinction. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/108324 doi: bioRxiv preprint they should have deterministically gone extinct, so we manually edited those population 295 trajectories such that they went extinct in the generation after having only 1 individual. 296

RESULTS 297
Simulations 298 Summary statistics for the posterior distributions of the four NBBg model parameters are given 299 in Supplementary Table 2. 300 Our simulations showed introduction regimes with more introduction events were more likely  We found no evidence that the probability of establishment was affected by a main effect of 313 environment (χ 2 =0.72, df=1, p=0.40), nor by an interaction between environment and 314 . CC-BY 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/108324 doi: bioRxiv preprint introduction regime (χ 2 =3.49, df=3, p=0.32). However, there was strong support for an effect of 315 introduction regime on establishment probability (χ2=59.76, df=3, p<0.0001). Pairwise 316 comparisons of the different introduction regimes averaged across the environment treatments 317 revealed that the 4x5 regime was the most likely to establish populations, with a probability of 318 about 0.98, whereas the 20x1 and 10x2 regimes were the least likely to establish populations, 319 with a probability reduced to about 0.8 (Figure 1). 320 The mean size of populations that persisted until generation 7 was shaped by significant effects The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/108324 doi: bioRxiv preprint (difference = -1.13 on logit scale, 95% CI = -0.22 to -2.04, χ 2 = 5.44, df = 1, p = 0.020) and mean 337 population size from 47.8 to 45.4 (difference = -0.052 on log scale, 95% CI = -0.02 to -0.09, χ 2 = 338 9.42, df = 1, p=0.0021). Each additional colonist contributing to a population after the latest 339 temporary extinction significantly increased the mean population size (estimate = 0.005 on the 340 log scale, 95% CI = 6.4e-05 to 0.01, χ 2 = 3.94, df = 1, p=0.047). 341 Results from the simulations are expected to represent the dynamics in the microcosm 342 experiment if the assumption of the model on which the simulations were built holds-that only 343 demographic processes are responsible for the dynamics observed in the experiment. However, 344 establishment probability at generation 7 was equal to or greater than that expected from the 345 simulations ( Figure 1) and mean population sizes were much larger in the experiment than in the 346 simulations (Figure 2), together suggesting an influence of non-demographic mechanisms. 347

DISCUSSION 348
We assessed how the number and size of introduction events through time drive colonization 349 success in a novel environment when the total number of individuals introduced to a site is fixed. 350 We considered novel environments that were either stable or randomly fluctuating in quality 351 through time, and evaluated populations through 7 discrete generations. We approached this 352 question in two ways: 1) stochastic simulations of a demographic population dynamics model 353 parameterized with empirical data, and 2) a highly replicated laboratory microcosm experiment. 354 By coupling these approaches, we were able to expand and test the theoretical understanding of 355 how the introduction regime affects colonization in stable and fluctuating environments as well 356 as to develop new avenues for research when observations did not align with predictions. We 357 . CC-BY 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/108324 doi: bioRxiv preprint found that several, small introductions increase colonization success and that demographic 358 processes alone are insufficient to explain the dynamics observed in the experiment. 359 We found minimal to no effect of a biologically realistic level of environmental stochasticity on 360 establishment probability in demographic simulations. This finding is inconsistent with the 361 prediction made by Grevstad (1999) who found with simulations that several, small introductions 362 would produce an especially high establishment probability compared to a single, large 363 introduction in a variable environment. The difference in findings is perhaps due to a difference 364 in the kinds of introduction regimes modeled: Grevstad (1999)  The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/108324 doi: bioRxiv preprint magnify the benefit of several, small introductions through time in the same way that Grevstad 380 (1999) found with several, small introductions across space. 381 There also did not appear to be a strong effect of environmental stochasticity on population size 382 in the demographic simulations. All treatments in the simulations reached similar mean 383 population size by generation 7, which was slightly higher than the equilibrium size due to our 384 measure only including extant populations. This suggests that strong density dependence in the 385 demographic simulations was the primary influence on population size. 386 We observed striking differences in the measures of colonization success between the 387 demographic simulations and the microcosm experiment. We found that establishment 388 probability increased with the number of introduction events (as in the simulations), but that all 389 microcosm establishment probabilities equaled or exceeded expectations from simulations. In the 390 microcosm, mean population size in stable environments was greater than in fluctuating 391 environments. There was also an interaction between environment and introduction regime, The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/108324 doi: bioRxiv preprint (Brown and Kodric-Brown 1977). Certainly, demographic rescue played a critical role for the 403 104 populations that went extinct temporarily until another introduction event revived them. 404 Those temporary extinctions had lasting effects on colonization success. Colonization success 405 declined for populations that experienced a temporary extinction, and the mean population size 406 significantly increased if more colonists contributed to the population after a temporary 407 extinction. These results reflect the overarching importance of total propagule pressure 408 regardless of introduction regime. 409 The rescue effect can also act genetically by increasing the fitness of populations (Brown and  The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/108324 doi: bioRxiv preprint The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/108324 doi: bioRxiv preprint The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/108324 doi: bioRxiv preprint