Electronic Supplementary Material 1 Do animals generally flush early and avoid the rush? A meta-analysis

We identified 97 species effect sizes that we compiled from 25 different studies. From this, 87 effect sizes were estimated from relationship between flight initiation distance (FID) and starting distance (SD), and 10 from relationship between FID and alert distance (AD). A considerable amount of work has been conducted on birds; an observation reflected in the taxonomic distribution of effect size estimates: 82% birds, 7% mammals, 6% lizards approached slowly, 3% lizards approached rapidly, 1% snakes, and 1% arthropods (table S1). However, because insufficient sample sizes (N = 1), we excluded snakes and arthropods from analysis (table S1).

With the exception of one lizard species (Callisaurus draconoides) that reported zero effect size, all relationship between SD or AD and FID were positive (table S1). Following Cohen’s criteria [1], 3.1% of effect sizes were nearly zero (r from 0 to 0.09), 9.3% were low (r from 0.1 to 0.29), 27.8% were medium (r from 0.3 to 0.49), and 58.8% were large (r > 0.5).

Closely related species are more likely to have similar phenotypes than those more distantly related. The existence of a phylogenetic structure on animal responses makes observations not statistically independent. So, in our study we fitted a random-model phylogenetic meta-analysis; a framework that permits meta-analysis to explicitly account for any non-independence of taxa by including a covariance matrix that contains phylogenetic relatedness [2]. Random effects within groups are appropriate since we expect that some variation in FID depends on species, individual’s sex and age, as well as methodological differences between studies [3]. For analysis, r-values were transformed to Fisher’s z.

To reconstruct the phylogeny of birds to species of our dataset, we used the most recent avian phylogeny [4]. However, as it is not a consensus phylogeny, we randomly choose ten tree hypotheses from those available at the avian phylogeny website--http://birdtree.org/--and we ran the analysis with each tree. The inclusion of any phylogenetic hypotheses resulted in very similar results. Thus, we conservatively used those that yielded the least overall mean effect size (difference between results were in decimal scales). Composite phylogenies were also available for mammals [5], and lizards [6]. Phylogenies are shown in figure S1.

We used two metrics to indicate if “flush early” response has a phylogenetic signal. The first, Blomberg’s K, is a descriptive metric that indicate the strength of phylogenetic signal in a trait [7]. As many others, it assumes underlying Brownian model of evolution, which more closely related species are more similar to each other [8,9]. K-values less than one (limited to zero) implies that relatives resemble each other less than expected under Brownian motion. In turn, the second metric is a Monte Carlo based test that make no assumption about model of evolution underling data. This test gives the probability of the observed variance of the phylogenetically independent contrasts (PIC; [8]) be obtained by random [7]. Importantly, low variance of PIC means that related species have similar values of a given trait [8]. Thus, P-values > 0.05 indicate that observed variance of PIC is not statisticaly significant (i.e. have no evidence of phylogenetic signal). We used R package Picante 1.5 [10] to calculate both metrics. Due inefficiency of the metrics to deal with so few species [7], mammals and lizards were not investigated. Both metrics indicated, respectively, a weak and no significant phylogenetic signal in “flush early” response in birds (K = 0.29; PIC P = 0.174).

However, similarity of results between a phylogenetic and ordinary meta-analysis (i.e. one that ignored phylogenetic structure) suggests that there is a limited phylogenetic signal on effect size estimated for mammals and lizards too. All z-tests comparing results of same groups had P > 0.4 (table S2, S3).

Birds and mammals were quite variable in the relationship between SD and FID (respectively, I² = 96.6% and 98.4%), whereas lizards approached rapidly had low variability (I² = 10.7%), and lizards approached slowly were extremely homogeneous (I² = 0%). An examination of the dendrograms from the cluster analysis was not revealing beyond showing that there were no obvious taxonomic clusters (figure S2).

A global effect size could not be calculated in the phylogenetic meta-analysis because some species appeared more than once (some lizards were included in the ‘fast lizard’ and ‘slow lizard’ groups), and such data structure is not permitted in the analysis [2]. However, the traditional meta-analysis permits us to estimate the global effect size of the relationship between FID and SD or AD (which also includes snakes and the arthropod that we previously excluded). Our results from this non-phylogenetic analysis suggest that the global effect is large.

There is a tendency for studies with small sample sizes but with large effect sizes to be more likely to be published than those with small effect sizes [3]. A significantly negative correlation between effect size and sample size indicates a publication bias [3]. However, the rank correlation test (based on Kendall’s tau; [11]) does not indicate a publication bias (table S4). Likewise, the visual evaluation of funnel plot also does not indicate this kind of bias in the data (figure S3). From this we infer that our results should be somewhat generalizable.

Logically, FID must be less than SD and AD (an animal can not flush or look at a person before a person starts walking towards it). Thus, when we plot all possible FIDs under a given range of SD or AD values, we typically obtain a shape that approximates a right triangle. This constraint has implications on traditional null hypothesis testing because it violates the homoscedasticity assumption of linear regression (because the variance increases with increases in SD or AD) [12]. Consequently, it is possible that there may be potentially spurious relationships between FID and SD or AD [12,13]. If so, some of the estimates of effect size that we compiled may not reflect a real biological effect and that, because better sampled studies are given greater weight, large effect sizes could inflate our estimates of average effects.

Two recent works proposed null models to test statistical significance of the FID-SD (or AD) correlation [12,13]. Importantly, one of these [13] showed that the relationship may indeed be real in several species. Unfortunately for a meta-analysis, both methods require large amounts of raw data for their calculation and we were unable to obtain such data for our study.

We propose an alternative method to eliminate the effect of potentially spurious results using a null model based on observed effect sizes. Our goal was to create a null model that more realistically reflected the data used to estimate the observed correlation between variables. To do so, we extracted from papers information about the mean and standard deviation of a species’ FID, and the maximum starting distance (SDmax). For 11 species for which data were missing, we inferred parameters using average values from its taxonomic group (see table S1).

The null model generated N random numbers (N = species sample size) extracted from a uniform distribution to simulate SD (SD ~ U(FID mean, SD max)) and N random numbers from a normal distribution to simulate FID (FID ~ N(FID mean, FID standard deviation)). To truncate FID (so that FID ≤ SD), we wrote an algorithm (in ESM 2) in which normally distributed numbers were generated until all points of FID fell within the constrained range. We then calculated the correlation coefficient (r) for these simulated numbers and repeated this 9999 times. From these simulation results, we calculated the probability that the observed r-values used as an effect size in meta-analysis were created by a spurious relationship by dividing the number of r-values ≥ observed by the number of iterations. Overall, we generated a vector of P-values for effect sizes of species. P-values < 0.05 were considered significant (i.e. unlikely to have been yielded by a spurious relationship). The simulation routine was written in R [14].

Note that we explicitly used a species’ mean FID as the lower limit to SD rather than minimum SD that was in a given data set. We did so to reduce the chance of simulating immediate flight (i.e. where SD = FID) caused by SD being below the optimum FID. Moreover, had we done so, it would have included unrealistic data since experimenters used a relatively standardized FID protocol [15] where observations of immediate flight were excluded. Thus, to be conservative we also excluded from meta-analysis correlations that explicitly included immediate flight data (e.g. [16,17]). Using the mean FID as the lower limit to SD also make our model more parsimonious by prevent the inclusion of additional parameters to control immediate flight (like λ used in [13]). We justify this because introducing λ (which must be estimated by simulation) adds complexity to our null model and we felt that it did not, in this case, add value to our desire to understand the relationship between SD and FID.

Ultimately, we conducted a sensitivity analysis [3] by re-analyzing our dataset when we excluded the potentially artifactal effect sizes.
Results and Discussion

From 95 species effect sizes included in the phylogenetic meta-analysis, 17 had P-values ≥ 0.05 (table S1). However, it is important to highlight that 10 of 17 not significant r_s were those that were nearly zero or were otherwise classified as small [1]. Remember that what motivated our developing of a null model was the concern about heterogeneous variance. Yet, even under a traditional null hypothesis test that meets all of the assumptions of linear regression, we would expect that values with a small r_s (and sample size similar to that observed) would have a P > 0.05 simply because of its small effect size [18]. Thus, perhaps we should not be that concerned about potentially spurious effects. The potentially artifactual effect sizes of the remaining seven species were medium in magnitude. Finally, there was no evidence that high effect sizes were spurious; a problem, that if present, could have an effect on our conclusions about overall magnitude.

In conclusion, even after conservatively excluding all effect sizes that might have come from a spurious relationship, our results remained roughly the same as in previous analysis with entire data (table S5, S6). In brief, our analyses show that the small numbers of potentially artifactual effect sizes were not sufficient to significantly change the inferences drawn from our phylogenetic meta-analysis results.

Table S1. Parameters of all species surveyed in meta-analysis to test the flush early and avoid the rush hypothesis. Species were grouped into birds (B), mammals (M), lizards approached slowly (LS), lizards approached rapidly (LF), snakes (S), and arthropods (A). SD (max), maximum starting distance used by experimenter to approach species; FID (mean), mean FID; and FID (StDev), FID standard deviation; N, sample size; r, correlation coefficient from relationship between predator’s starting distance or alert distance, and flight initiation distance (FID) used as effect size; P (null), P-value yielded by a null model where FID is constrained to FID ≤ SD (see details in text). SD (max), FID (mean) and FID (StDev) values in bold indicates that were inferred from average values of its respective taxa group because such information is missing in source study. Effect sizes (r) in bold were estimated from relationship between FID and alert distance; the remainder effect sizes were all estimated from relationship between FID and starting distance. P-values in red indicates that effect size were significant under the null model (<0.05).