Dissecting the null model for biological invasions: A meta-analysis of the propagule pressure effect

Abstract

A consistent determinant of the establishment success of alien species appears to be the number of individuals that are introduced to found a population (propagule pressure), yet variation in the form of this relationship has been largely unexplored. Here, we present the first quantitative systematic review of this form, using Bayesian meta-analytical methods. The relationship between propagule pressure and establishment success has been evaluated for a broad range of taxa and life histories, including invertebrates, herbaceous plants and long-lived trees, and terrestrial and aquatic vertebrates. We found a positive mean effect of propagule pressure on establishment success to be a feature of every hypothesis we tested. However, establishment success most critically depended on propagule pressures in the range of 10-100 individuals. Heterogeneity in effect size was associated primarily with different analytical approaches, with some evidence of larger effect sizes in animal rather than plant introductions. Conversely, no variation was accounted for in any analysis by the scale of study (field to global) or methodology (observational, experimental, or proxy) used. Our analyses reveal remarkable consistency in the form of the relationship between propagule pressure and alien population establishment success.

Fig 1. Differences in the effect size (Zr) for levels of the most influential moderator variable (‘Number of predictors’) in explaining heterogeneity in the complete dataset (n = 96; Δ_LOO-IC relative to Intercept-only model = 3.4; Table A in S1 Text).

The dashed line shows the mean population-level effect size (0.47), and the grey bands show the 95% CI (0.34–0.59). CI, credible interval; LOO-IC, leave-one-out cross-validation information criterion; Zr, Fisher’s z-transformed correlation coefficient.

Fig 2. Differences in the effect size for levels of the most influential moderator variables in explaining heterogeneity in the ‘Propagule size’ dataset (n = 56; Δ_LOO-IC relative to Intercept-only model = 2.81; Table C in S1 Text).

Transform (A) is the form of the propagule pressure variable in its measured relationship with establishment success, and Propagule size (B) is the number of individuals in log₁₀ increments. Effect size estimates are conditional on the other moderators. The dashed line shows the mean population-level effect size (0.51) for the ‘Propagule size’ dataset, and the grey bands show the 95% CI (0.33–0.68). CI, credible interval; LOO-IC, leave-one-out cross-validation information criterion; Zr, Fisher’s z-transformed correlation coefficient.

Fig 3. Estimated relationship of establishment success with propagule pressure and 95% CI (shaded).

Dashed lines are individual experimental relationships based on a logistic model with random variation in the intercept and slope among individual experiments. Note, there was no statistical evidence for (i) the model with random intercept and slopes performing better than the random Intercept-only model nor for (ii) different slopes between invertebrates and vertebrates (taxon [= n]; invertebrate = 9, vertebrate = 5; slope difference = 0.13, 95% CI = -0.9–1.2). Data points are raw data from 14 relationships from 11 studies (see S2 Text) that experimentally tested associations between propagule size and establishment probability (see Materials and methods for more details). CI, credible interval.