study that suggests
otherwise. Sterile tissue was added to bags as necessary in order to
bring the total biomass to 350 g. Reproductive and sterile tissue was
mixed in the bags so that the reproductive tissue was well distributed
throughout. This experimental manipulation mimics the level of
propagule input that would occur in an incipient invasion or if a
drifting plant became tangled with attached algae and subsequently
released its propagules.
Recruitment of
S. muticum
was quantified by counting the
number of
S. muticum
juveniles that were present in the plots
5 months after the experimental invasion, which is the earliest
they can reliably be seen in the field. We resurveyed the plots to
count the number of
S. muticum
adults present 11 months after the
invasion ( just prior to reproductive season) and then removed all
S. muticum
from the experimental plots in order to prevent it from
spreading.
S T A T I S T I C A L
A N A L Y S I S
We analysed the
S. muticum
recruitment data using a two-way
anova
followed by separate regression analyses on each disturbance
treatment. For the control treatment, we performed a multiple
regression to determine what proportion of recruitment variation
was explained by propagule input and space availability. For the
disturbed plots, which did not vary in the amount of available space,
we carried out a simple linear regression to determine the impact of
propagule input on recruitment. We used the results of these analy-
ses to inform the construction of mechanistic candidate functions
for the relationship between propagule input, space availability
and recruitment. These candidate functions were compared using
differences in the Akaike’s information criteria (AIC differences;
Burnham & Anderson 2002). We then used model averaging, a form
of multimodel inference in which parameter estimates from more
than one candidate function are used jointly to describe the data,
in order to select a parameterized recruitment function for the
S. muticum
spread model.
The
S. muticum
survivorship data did not conform to the assump-
tions of
anova
(even after a number of different transformations)
so we used a non-parametric Kruskal–Wallis test to ask whether
S. muticum
survivorship differed in the disturbed and control
treatments. We then fitted five different survivorship functions,
assuming binomial error, to the data to test whether
S. muticum
survivorship (number of adults per recruit) was density-dependent.
Because the Kruskal–Wallis test suggested that survivorship differed
significantly between the two disturbance treatments (see Results)
we chose to fit the models to those two treatments separately to test
for density dependence. In addition to type 1 (linear), type 2 (saturating),
and type 3 (sigmoidal) functions, we also fitted a constant survivor-
ship model. These candidate functions were compared using the
Akaike’s information criterion (AIC differences; Burnham &
Anderson 2002).
The numbers of adult
S. muticum
(after 11 months) also violated
the assumptions of
anova
(despite transformations), so we used
non-parametric statistics to test two hypotheses: (i) adult density is
independent of disturbance treatment (Wilcoxon Signed Ranks
Test), and (ii) adult density is independent of propagule pressure
treatment (Kruskal–Wallis Test).
M O D E L
We used an integrodifference equation (IDE) model to describe the
spatial spread of an
S
.
muticum
population. IDE models assume
that the habitat is continuous in space, and that reproduction and
dispersal occur in discrete bouts. The depths inhabited by
S
.
muti- cum
comprise a relatively narrow vertical band, so the spread of the
population was assumed to occur in a one-dimensional habitat. The
model follows two state variables through time.
N t
(
x
) is the density
of
S. muticum
at a location
x
along this habitat at time
t
, and
Z t
(
x
)
is the amount of bare rock at
x
during
t
. The values for these state
variables are determined by functions representing the important
ecological processes in this system.
Sargassum muticum
density is
determined by the production and recruitment of propagules and by
adult survival. Bare rock is created by benthic herbivore distur-
bances, since herbivores consume native algae and thus alleviate
space limitation. The form of our model is then
N t
