Statistical Analyses
All counts were first standardised to colony-forming-units (cfu) per mL.
Invasion success (relative invader fitness) was calculated as
proportional change, v , of the proportion of invader to resident,
calculated as: v = x2. (1 -
x1 )/x1. (1 -
x2 ), where x1 is the initial
invader proportion and x2 the final
(Ross-Gillespie et al. 2007). Initial invader proportion
(x1 ) was calculated as the average frequency of
the introduced invader:
\(x_{1}\ =\ E\left[\frac{I_{t}}{I_{t}\ +\ R_{t}}\right]\ =\ \frac{1}{3}\sum_{t\ =\ \left\{4,\ 8,\ 12\right\}}\frac{I_{t}}{I_{t}\ +\ R_{t}}\)(1)
where It is the density of the invader introduced
on day t and Rt is the density of the
residents getting invaded on day t . We could not measure resident
density on days 8 and 12, because it would require destructive sampling
of undisturbed treatments. We therefore used the resident density on day
4 and assumed that R4, R8 andR12 were equal for 1-, 2-, and 4-days disturbance
treatments.
We sampled R4 for 1-, 2-, and 4-days disturbance
treatments during their transfers, but we could not sampleR4 for 8- and 16-days disturbance treatments as
it is a destructive process. The disturbance history up to day 4 for 8-
and 16-days treatments is identical to that for 4-days treatment. We
therefore assumed the resident community dynamics are the same for these
three treatments, and used R4 for 4-days
treatment (before the disturbance) to calculateR4 for 8- and 16-days treatments:
\(R_{4,\ 8-days}\ =\ R_{4,\ 16-days}\ =\ \frac{R_{4,\ 4-days}}{\text{Disturbance\ mortality\ rate}}=\ \frac{R_{4,\ 4-days}}{0.01}\)(2)
where Ri,j is the density of the resident on dayi under j- days disturbance treatment. Based on this
calculation, we further assumed that R8,16-days =
R12,16-days = R4,16-days for 16-days
disturbance treatment, where R8,16-days =R on day 8 in the 16-day disturbance treatment and so forth. For
8-days disturbance treatment, we assumedR12,8-days = R4,8-days andR8,8-days = 0.01 R4,8-days to
account for the disturbance event on day 8.
In order to eliminate zero inflation, one was added to the final invader
density v (post volume standardisation) and was transformed to
log(v +1) to normalise the residuals. A value greater than 0.69
(log(1+1)) would indicate that the invader increased in proportion
throughout the experiment, whereas a value below this would suggest that
invasion was unsuccessful.
To analyse the effect of disturbance and resource abundance on invasion
success, v, a linear model was used to test effects of
disturbance, resource abundance, and invader morphotype, with all
two-way and three-way interactions. As the different morphotypes have
distinct growth strategies, we expected their invasion success to be
markedly different. Given a significant three-way interaction in the
most complex model, we did all further analysis on each invader
morphotype (SM & WS) separately.
For each invader morph, separate linear models were used to investigate
treatment (disturbance frequency and resource abundance) effects on
invasion success, evolved biodiversity (calculated using Simpson’s index
(Simpson 1949)) and total resident density (log10(cfu+1
mL-1). Disturbance frequency was treated as a
continuous predictor, whereas resource abundance was treated as
categorical due to only having three levels. Model selection was done
using likelihood ratio tests.
We then tested whether treatments indirectly affected invasion success
through changes in resident populations. To do this we first used a
model with resident biodiversity and total resident density, plus their
interaction, as predictors of invasion success. We then included
treatment (disturbance, resource abundance, and their interaction),
alongside resident population effects as predictors of success. The
models with both treatment and resident population effects were
initially tested using an ANOVA with type III sums of squares, then with
type II if no significant interactions were found to account for
differences in the ordering of predictors on significance testing.
Post-hoc model comparisons were used to look at significant differences
between levels of resource abundances and disturbance. For pairwise
comparisons of single treatments (e.g. between high, medium and low
resource abundances), model estimates were averaged over other
predictors in the model. Where multiple pairwise comparisons were used,
p values were adjusted using Bonferroni adjustments. When comparing
slopes to 0, confidence intervals overlapping zero indicated no
significant effect. All statistical analyses were carried out in R
version 4.0.3 (R Core Team).