Journal of Vegetation Science 19: 417-424, 2008
doi: 10.3170/2008-8-18384, published online 14 March 2008
© IAVS; Opulus Press Uppsala.
- Testing the intermediate disturbance
hypothesis in species-poor systems -
417
Testing the intermediate disturbance hypothesis in species-poor
systems: A simulation experiment for mangrove forests
Piou, Cyril1,2*; Berger, Uta1,2,3; Hildenbrandt, Hanno1,4 & Feller, Ilka C.5
1Center
for Tropical Marine Ecology, Fahrenheitstrasse 6, 23859 Bremen, Germany;
address: Institute of Forest Growth and Forest Computer Sciences, Technical University Dresden, Postfach 1117,
01735 Tharandt, Germany; 3E-mail uta.berger@forst.tu-dresden.de
4Present address: Theoretical Biology, Centre for Ecological and Evolutionary Studies, University of Groningen, Biological Centre, Kerklaan 30, 9751 NN Haren, The Netherlands; E-mail h.hildenbrandt@rug.nl;
5Smithsonian Environmental Research Center, PO Box 28, Edgewater, MD 21037, USA; E-mail felleri@si.edu;
* Corresponding author; E-mail cyril.piou@forst.tu-dresden.de
2Present
Abstract
Questions: What factors inluence tree species diversity of
mangrove forests, an example of species-poor systems? What
are the respective importance and interactions of these factors? Is the intermediate disturbance hypothesis applicable to
such systems?
Methods: We used the spatially explicit individual-based model
KiWi to investigate the effects on species diversity of perturbation frequency and intensity, different abiotic conditions, and
interspeciic competition simulated at the individual level. The
simulation system considered the three dominant Caribbean
mangrove species: Rhizophora mangle, Avicennia germinans and Laguncularia racemosa, applying species-speciic
growth and mortality characteristics. Firstly, effects on species
dominance of the abiotic conditions nutrient availability and
porewater salinity were tested with two competition scenarios.
Secondly, the effect of perturbation frequency and intensity
were investigated with selected abiotic conditions.
Results: Abiotic conditions inluenced species dominance and,
in extreme cases, excluded one or two species. Abiotic and
competition settings controlled the successional dynamics and
the response of species dominance to perturbation regimes. A
response consistent with the intermediate disturbance hypothesis was observed only with a coniguration of plant interaction
in which one species behaved as a pioneer so that succession
occurred by competitive exclusion.
Conclusions: We suggest that successional dynamics interact
with the intensity and timing of perturbations and determine
whether or not mangrove tree diversity conforms to predictions
of the intermediate disturbance hypothesis. For mangroves,
these successional dynamics are site-speciic depending on
abiotic conditions and species conigurations.
Keywords: Individual-based modeling; Interspeciic competition; KiWi model; Perturbation regime; Species dominance;
Succession.
Abbreviations: FON = Field of Neighbourhood; IDH =
Intermediate disturbance hypothesis; ISDH = Index of species
dominance heterogeneity; psu = Practical salinity units; RNA
= Relative nutrient availability.
Introduction
For several decades, plant ecologists have tried to understand the processes implicated in variations in species
diversity (e.g. Chust et al. 2006 see reviews by Loreau et
al. 2001; Barot & Gignoux 2004; Vellend & Geber 2005).
Among these processes, perturbations have been considered
of high importance and have led to an ongoing debate on
the intermediate disturbance hypothesis, which states that
species richness is maximized at intermediate levels of
disturbance (Grime 1973; Connell 1978; see reviews by
Mackey & Currie 2001; Sheil & Burslem 2003; Shea
et al. 2004). The situation of mangroves along tropical
coastlines favours potential damage by major destruction
events such as hurricanes or tropical storms (Imbert et al.
1998). Smith & Duke (1987) addressed the question of
disturbance effects on mangrove tree diversity in Northern
Australia. They showed that species richness decreased
with increasing hurricane frequency. However, very
few studies have analysed changes in mangrove species
composition in relation to perturbation regime (Baldwin
et al. 2001; Piou et al. 2006), and none have evaluated
the implicated processes behind these effects. A straightforward explanation for this lack of consideration is the
low number of tree species on mangrove systems. For
example, in the Caribbean region, which is a hot spot of
hurricane activity, only three to four true mangrove species are found. Thus, studies on tree species diversity are
mostly seen as superluous in this system.
However, considering species diversity as an expression
of species richness and evenness (Kempton 1979), systems
with only three species could also vary in species diversity.
Piou et al. (2006) used an adaptation of the Simpson’s reciprocal index of species diversity (Simpson 1949; Hill 1973)
to determine that the destruction intensity at different mangrove sites in Belize had an effect on the heterogeneity of
species dominance. Although the patterns in Belize differed
from other situations (e.g. Baldwin et al. 2001), it indicated
418
Piou, C. et al.
that the effects of large destruction on species diversity also
exist for species-poor mangrove systems. Based on these
indings, we chose to use the Caribbean mangrove system as
an example for analysing factors and processes inluencing
species diversity in species-poor systems.
Our irst hypothesis was that the succession of species
dominance depends on both the interspeciic competition
coniguration and the abiotic conditions. The second and
more general hypothesis was that the resulting succession
trajectories determine the type of response of the system to
perturbations, and the eventual production of a bell-shape
pattern of species diversity with intermediate perturbation
regime. To test these hypotheses, we investigated the effects
on species diversity of perturbation frequency, perturbation
intensity, different abiotic conditions, and interspeciic
competition by means of simulation experiments with an
individual-based model.
Methods
KiWi model: General settings
The experiments were carried out with the spatially
explicit mangrove model KiWi (Berger & Hildenbrandt
2000, 2003), developed as dynamic library software written
in C++ and using an interface in Microsoft ® Visual Basic
® (DLL and examples available from the corresponding
author). The KiWi model describes resource competition on the level of individuals and simulated growth of
mangrove stands composed of the three main Caribbean
species, Rhizophora mangle, Avicennia germinans and
Laguncularia racemosa. The gap model FORMAN (Chen
& Twilley 1998) provided the growth formulas, multipliers
for nutrient and salinity effects and respective parameters. It
is important to note that the KiWi model is not a gap model
since it describes trees individually and is spatially explicit.
We used Berger & Hildenbrandt’s (2000) innovation of the
ield of neighbourhood (FON) approach, which simulated
inter-individual competition for space and resources. We
assumed that the FON described the area where a tree inluenced its neighbours and was inluenced by them by sharing
limiting resources such as light or nutrients. The FON was
deined as a circular intensity ield that decreased from the
center (stem position) out to the boundary. It speciied the
intensity of competition exerted by a tree at any position
within its neighbourhood.
The growth of each individual tree was calculated with
the following formula (Berger & Hildenbrandt 2000):
DBH × H
G × DBH × 1 −
DBH max × H max
∆DBH
=
× fs (SALT ) × fn ( RNA) × fc ( FA ) (1)
274 + 3 × b2 × DBH − 4 × b3 × DBH 2
∆t
where: DBH was the stem diameter at breast height (cm);
H was tree height (cm); DBHmax and Hmax were maximum
values of diameter and height for a given tree species;
G, b2 and b3 were species-speciic growth constants and
the three f-functions were growth multipliers (see App.
1 for details or Chen & Twilley 1998). The growth multipliers fs(SALT) and fn(RNA) considered the effects of
the porewater salinity and relative nutrient availability,
respectively (Chen & Twilley 1998). The function fc(FA)
was the growth multiplier for the FON effect on growth
(Berger & Hildenbrandt 2000):
1
fc ( FA ) = max {0 ; 1 − ϕ × FA } = max 0 ; 1 − ϕ × ∑ ∫ FON n ( x, y ) do
A n≠ k O
(2)
where: ϕ was an arbitrary maximum value of effect of
competition simulating resource sharing capacity, A was
the FON area of the focus tree k, n were the neighbours
of k, belonging to the focal and neighbour tree n, and
the FONn function was the intensity of competition of
the neighbour n at each point of O. The FON function
was calculated as:
for 0 ≤ r < RBH
1
ln ( Fminn )
FON n ( r ) = exp −
× ( r − RBH ) for RBH ≤ r ≤ R
R
RBH
−
for R < r
0
(3)
where: RBH was the radius of the stem at breast height
of n, r was a distance from the stem position of n, and
Fmin was the minimum intensity of the FON (0.1, Berger
& Hildenbrandt 2000) at the FON radius (R). This FON
radius (R) depended on the size of the tree:
(4)
R = a × RBH b
where: a and b were scaling parameters (cf. ‘setting
interspeciic competition’ and App. 2). The value of b
determined inversely the competition intensity of individuals (see Berger & Hildenbrandt 2003 for variations of
model behavior depending on these two parameters).
According to the assumption of Chen & Twilley
(1998), an overall availability of recruits was considered
as RNtot = 18 saplings.100m–2.yr–1 (Chen & Twilley
1998). However, the annual number of recruits varied
randomly, and the number from each species (RNi) was
proportionally set according to the occurrence of mature
trees (height >5m) of each species:
RN i = int ( rnd1 × pi × RN tot + rnd2 × RN tot )
(5)
where: rnd1 was a uniform random number between 0.5
and 1.5; rnd2 a uniform random number between 0.1 and
0.3; and pi the proportion of mature trees of species i over
the total number of mature trees in the plot. The range of
variation of rnd1 was chosen to describe a natural luctuation in the availability of recruits per species (+/-50%).
The range of variation of the rnd2 provided an occasional
reappearance of an already excluded species. These two
- Testing the intermediate disturbance hypothesis in species-poor systems ranges of variations were set arbitrarily, but a sensitivity
analysis showed a low effect of these parameters on the main
results (App. 3). The recruits were installed randomly on
the simulation area, but were removed if the FON intensity
(sum of FON(x,y) of all trees at the point of installation x, y)
was higher than the species-speciic threshold (FAmax). This
threshold was set to FAmax = 0.5 for R. mangle (Berger &
Hildenbrandt 2000) and assumed as FAmax = 0.0 for the two
other species to simulate the shade intolerance of seedlings
of L. racemosa and A. germinans (Ball 1980; McKee 1993).
Mortality of individual trees not due to external perturbations was growth-rate dependent as described by Berger &
Hildenbrandt (2000).
Settings of interspeciic competition parameters
The growth parameters and effects of salinity and nutrient availability (DBHmax, Hmax, G, b2, b3, fs and fn, Eq.
A1.1, see App. 1) created species-speciic differences in
growth response at the stand level. For additional variation
in interspeciic competition, we considered two ways of
simulating spatial competition at the individual level. The
irst considered an equal effect of neighbouring competition
for trees of the same size for the three species. Thus, they
had the same resource sharing tolerance ( ϕ = 2.000, Berger
& Hildenbrandt 2000) and identical a and b parameters
(11.0, 0.64, respectively, cf. App. 2, Fig. A2.1). Since the
interspeciic competition in this parameterization was only
through the relative growth rate of each species, it is hereafter
referred to as species homogeneous spatial competition.
The second parameterization considered that each species
had spatially-speciic competition strength. Particularly, L.
racemosa, which was described as heliophilic (Wadsworth
1959; Ball 1980; Roth 1992) was set to have a lower sharing
tolerance ( ϕ = 2.222, assuming that the maximum FA was
10% lower than the other species, i.e., maximum FA = 0.45).
Additionally, species-speciic a and b parameters (App. 1,
Table A1.1) were used to describe the canopy and rootsystem differences for the three species. These parameters
were tuned (App. 2, Fig. A2.1) to reproduce ield data of
monospeciic stands of tree size / density relationships from
Belizean offshore mangroves, and to set L. racemosa as less
competitive than the two other species. This lower competition capacity of L. racemosa was at DBH < 80 cm; while
the a and b values also determined that A. germinans was
more competitive than R. mangle at DBH > 20 cm. This
second parameterization is hereafter referred to as species
heterogeneous spatial competition.
Effects of abiotic conditions
Our irst exercise was set to analyse the effect of
abiotic conditions on species diversity without any perturbations. We also investigated the effect of interspeciic
419
competition on succession of species dominance in this
exercise. Five salinities (0, 20, 40, 50 and 60 psu) and
four relative nutrient availabilities (RNA) (100%, 80%,
60% and 40%) were considered. Ten replicates of all
possible salinity/RNA scenarios on the two competition
parameterizations were simulated on a 6000-m² plot and
over 1000 years.
The number of trees and basal area per species were
used to calculate relative abundance and dominance for
each time step and transformed into importance values (IV)
according to Cintrón & Schaeffer-Novelli (1984):
IVi =
100 × Densi
q
∑ Dens j
+
100 × BAi
q
∑ BA
j =1
j
(6)
j =1
where: IVi , BAi and Densi were the importance values,
basal area and density of trees of the species i, and q was
the number of species. As a measure of species diversity,
we used the index of species dominance heterogeneity
(ISDH) from Piou et al. (2006). It was adapted from the
reciprocal index of Simpson (Hill 1973) and computed
as follows:
q
q
∑ IV × ∑ IV − 1
i
i
I SDH =
i =1
q
i =1
∑ ( IV × ( IV − 1))
i
(7)
i
i =1
This index indicated relative species dominance in our
three-species system and was given a value of 0 if no trees
could grow because of harsh abiotic settings. If trees could
grow, the ISDH were given values from 1 (only one species
present on the plot) to 3 (the three species representing
each 33% of importance on the plot). Since this index was
not mathematically independent from species richness, we
decided not to use the term ‘evenness’ to avoid confusion
with its calculations in community studies (Smith & Wilson
1996). However, through the variation of relative species
dominance, this index could indicate if different threespecies conigurations of our system were relatively rich
or not in term of species diversity. As indicators of salinity/
RNA effect on species diversity, the median, 1st. and 3rd.
quartiles of ISDH for each scenario over the last 400 yr of
simulations were calculated.
Effects of perturbation regimes
The second exercise was set to analyse the effects of
perturbation regimes on species diversity. Massive killing
events, which simulated mortality induced by a tropical
storm or hurricane, were applied at different mortality
rates (intensity) and frequencies. Because there is inconsistency in the literature on the way authors described
storm resistance capacity according to species or tree size
(e.g. Vermeer 1963; Stoddart 1963; Bardsley 1984; Roth
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Piou, C. et al.
1992, 1997; Smith et al. 1994; Imbert et al. 1998; Sherman & Fahey 2001; Baldwin et al. 2001; Imbert 2002),
we could not consider the mortality events related to
size or species in our simulations. The applied intensities
were probabilities of 30%, 50%, 70%, 90% and 99% of
mortality for each tree at the event times. The perturbation frequencies (1 /100 yr, 1 /80 yr, 1 /60 yr, 1 /40 yr,
1 /20 yr and 1 /10 yr) determined the exact number of
years between two events.
To achieve a stabilized system in term of number of
trees, we excluded the irst 400 simulation years. Perturbations were applied only on the following 400 years so
that the total simulated time was 800 years. The role of
abiotic conditions on system response to perturbation was
considered by selecting scenarios from the results of the
previous exercise. Benign (salinity 0 psu and 100% RNA)
and medium (salinity 50 psu and 80% RNA) conditions
were analysed, but extreme ones were not considered
because they resulted in a system overwhelmed by one
species. Ten replicates were simulated for each abiotic
scenario (benign or medium) for each competition parameterization (homogeneous or heterogeneous spatial
competition) and all mortality rate/perturbation frequency
scenarios. Similar to the previous exercise, the median
of ISDH was calculated over the last 400 yr for all cases.
To analyse the signiicance of perturbation intensity
with selected perturbation frequency, Kruskal-Wallis
non-parametric analysis of variance (ANOVA) by ranks
were applied on the last ISDH values of each simulation.
To analyse the effect of perturbation frequency with
selected perturbation intensity, identical non-parametric
ANOVAs were done considering all the ISDH values of
the simulated perturbation time. Mann-Whitney U tests
were used to assess signiicant differences of extremes
and intermediate ISDH values in order to validate disturbance effect patterns such as U-shaped, linear increase
or decrease, irregular or bell-shaped.
Results
First exercise: effects of abiotic conditions
Extremely low relative nutrient availabilities (40%
RNA) and extremely high salinities (60 psu) decreased
signiicantly the index of species dominance heterogeneity (ISDH) for both spatial competition parameterizations
(App. 4, Fig. A4.1). These extreme abiotic conditions
caused species exclusion through the parameterization
of R. mangle and A. germinans growth characteristics to
be non-adapted to high salinities and low nutrient availabilities, respectively. At the worst condition (salinity 60
psu and 40% RNA), no species grew at all, resulting in
ISDH = 0. Considering the rest of the abiotic scenarios,
Fig. 1. Dynamical variations of the two competition parameterizations with selected abiotic scenarios (medium = Salinity
50 psu and RNA 80%) in species relative importance (IV) and
ISDH (thin lines = respective irst and third quartiles).
highest ISDH values in both spatial competition parameterizations were found at intermediate levels of salinity
and RNA. The median ISDH values over the last 400yr were
relatively similar between the two spatial competition
parameterizations. However, ISDH and species importance
values varied more importantly during the irst 400yr for
all abiotic scenarios. For medium abiotic scenario (e.g.,
salinity 50 psu and 80% RNA), variations of species importance values showed a cycling of species dominance
(Fig. 1). The species heterogeneous spatial competition
parameterization created a quick succession from L.
racemosa to A. germinans (Fig. 1b) during the irst 50yr
of simulations. With homogeneous spatial competition,
the dominance of L. racemosa varied but stayed always
higher than the two other species (Fig. 1a). Identically,
for benign abiotic scenarios, the species heterogeneous
spatial competition created species succession, while the
homogeneous spatial competition showed importance
values variation without shift of species dominating.
- Testing the intermediate disturbance hypothesis in species-poor systems -
Fig. 2. Dynamical variations in species relative importance (IV)
and ISDH for the heterospeciic competition parameterization and
medium case of abiotic scenario (salinity 50psu, 80% RNA),
for different perturbation regimes. a. frequency= 1 / 100 yr,
intensity = 30% mortality; b. frequency = 1 / 60 yr, intensity =
70% mortality; c. frequency = 1 / 10 yr intensity = 99% mortality). (thin lines = respective irst and third quartiles).
Second exercise: effects of perturbation regimes
For the analysis of phenomena explaining the
response pattern, we concentrated only on the medium
abiotic scenario. Massive mortality altered the temporal
dynamic of ISDH (Fig. 2). The low perturbation regime
(Fig. 2a) did not modify the general trend of variation
of species importance values and ISDH compared to
non-disturbed dynamics (Fig. 1b). With an intermediate perturbation regime (more frequent and stronger
disturbances, Fig. 2b compared to 2a), L. racemosa
gained in importance although still less important than
the two other species. This reduced the difference in
relative importance of the three species and thus led to
an overall higher ISDH than with the low perturbation
regime. The most frequent and destructive perturbation
regime (Fig. 2c) switched the system quickly from A.
germinans to L. racemosa dominance. At this level of
perturbation regime, each disturbance had an effect of
421
Fig. 3. Median ISDH variations according to perturbation frequency and intensity for the two competition parameterizations
(a and b) with medium abiotic scenario (Salinity 50 psu and
80% RNA). Dashed lines represent selected pattern illustration
for Fig. A4.2-2 (App. 4).
keeping L. racemosa as the most important species on the
plot. This corresponds to the original succession situation
at the beginning (irst 10 years) of the simulations, as
if L. racemosa were the pioneer species of the system.
However, this change of dominance did not modify
signiicantly the ISDH values compared to low or absent
perturbations because the ratios of species importance
values were conserved. In this case, the high frequencies
stabilized these ratios and ISDH values over time.
Variations in perturbation regimes always had an effect
on the species dominance heterogeneity of the simulated
stands (Fig. 3). However, the overall patterns of simulation results depended on the different competition parameterization. The species homogeneous spatial competition
parameterization (Fig. 3a) showed lower ISDH values at
intermediate perturbation regimes than at lower and higher
perturbation frequencies and intensities. This U-shaped
curve pattern was clearly observable as to the inluence
of frequency regime with a selected perturbation intensity
(following line on Fig. 3a or App. 4, Fig. A4.2a), although
the values showed high variation among simulations (1st.
and 3rd. quartile variations). The species heterogeneous
spatial competition parameterization resulted in an overall
increase in ISDH values with increasing disturbance regimes
until non-extreme intensity and frequency followed then
by a small decrease (Fig. 3b). Thus, this trend led to an
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Piou, C. et al.
overall bell-shaped pattern, which was also more visible for the inluence of frequency regime with selected
perturbation intensity (following line on Fig. 3b or App.
4, Fig. A4.2b).
Analysing the patterns for all scenarios, we found
a clear difference of patterns between the two spatial
competition parameterizations. The homogeneous
spatial competition parameterization led to some cases
of U-shaped patterns while the heterogeneous spatial
competition on the contrary showed bell-shaped patterns.
However, not all perturbation regimes led to these U- or
bell-shaped patterns, but also included cases of linear
increasing or decreasing patterns or even non-signiicant
or irregular patterns. These trends were repeated with the
two selected abiotic conditions (cf. App. 4, Fig. A4.3 for
detailed results).
Discussion
This study illustrated that even for species-poor
systems, the dynamics and the processes that could
explain variations in species diversity are diverse and
interconnected. The interplay of abiotic conditions and
interspeciic competition produces a set of potential vegetation dynamics. Depending on the perturbation regime,
a system will follow a particular trajectory of this set,
and eventually test the expectations of the intermediate
disturbance hypothesis pattern.
Our simulations integrate the actual knowledge on
Caribbean mangrove species of species-speciic parameterization of growth, adaptations to abiotic conditions,
settlement, and spatial competitive strength. The results
of the irst exercise illustrate that abiotic conditions
inluence the dominance distribution of these species,
up to eventually excluding one or more species. On the
contrary, intermediate conditions of porewater salinity
and nutrient availability favorable to all three species
lead to higher coexistence. The setting of species-speciic
growth parameters of our model is thus able to re-create
the diversity of species dominance observed in the Caribbean. Other factors that were not considered in this study,
such as tidal regime, temperature, soil physico-chemical
properties (e.g., redox potential or sulide contents), could
have similar effects on species richness and dominance in
mangrove systems (Ball 1980; McKee 1993).
The results of the irst exercise also show that changes
in the characteristics of species-speciic spatial competition
do not modify signiicantly the overall measure of species
diversity. However, at a given abiotic condition, a change
in the settings for spatial competition drastically alters the
temporal variations of relative species dominance. Our
parameterization of homogeneous spatial competition leads
to a cycling dynamic but with L. racemosa dominating all
the time because of its faster growth rate. The hypothesis
behind this parameterization is that species differ in their
resource use capacity but not in a spatially explicit way. For
example, trees of the same size would have the same spatial
extent of resource use disregarding their species. In contrast,
the heterogeneous spatial competition parameterization is
derived from the hypothesis that individuals of L. racemosa
are less competitive for spatially distributed resources than
individuals of other species (Wadsworth 1959; Ball 1980;
Roth 1992). The reduction of resource-sharing tolerance
for the L. racemosa trees increased the effects of neighbours on their growth rates. Additionally, species-speciic
changes in the FON radius inluenced species interactions
by conferring lower competitive strength to L. racemosa
individuals than equal-sized A. germinans or R. mangle
trees. Thus, after the irst years of fast growth of L. racemosa
trees this heterogeneous spatial competition parameterization produced a shift in dominance. Thus, this succession
resulted from the switch in the importance of two forces:
(a) the primary growth rate of L. racemosa, which is known
to be faster than for the other species under low salinity
conditions, high nutrient, and light availability (McKee
1995; Sherman et al. 1998; Lovelock & Feller 2003); and
(b) the low strength of spatial interspeciic competition
of L. racemosa (as hypothesized by Berger et al. 2006).
These characteristics are typical of pioneer-like species in
any plant system. In mangrove forests, such successions
were described in some secondary recovery areas (Ball
1980; Berger et al. 2006), which suggests that our second
spatial competition parameterization is supported by ield
observations. These differences in the dynamics between
the two parameterizations become especially important
when considering the effects of perturbations.
The simulations with perturbations illustrated that species dominance of our system depended on the frequency
of the destruction events and their intensities. However,
we have seen that the pattern of response changed mainly
depending on the competition parameterization and thereby
the successional dynamic. Perturbations created gaps that
would take the same trajectory as the system’s dynamics
observed without perturbations. For each gap recovery,
the seedling availability depended on the dominant species in the rest of the stand. In the case of homogeneous
spatial competition parameterization, if the system was
perturbed each time when the majority of gaps were in the
cycling phase of highest dominance of L. racemosa, the
dominance of this species would increase more and more,
as in a resonance phenomenon. This situation was created
at intermediate perturbations regimes, leading to the lowest
ISDH values. With extreme disturbance regime, the system
would achieve the cycling phases earlier and, thus, would
return to a more even species distribution. This scenario led
to higher ISDH values, and overall created the observed Ushaped patterns. With the heterogeneous spatial competition
- Testing the intermediate disturbance hypothesis in species-poor systems parameterization, perturbations caused the system to return
reiteratively to conditions seen during the initial succession
phases. Since L. racemosa was the most pioneer-like of the
three species, it obtained higher importance with stronger
and more frequent perturbations, which created a more
homogeneous species dominance. Eventually, with extreme
perturbation regimes, L. racemosa dominated completely,
reducing the index of species dominance heterogeneity.
In mangrove forests, it is therefore possible to observe the
bell-shaped pattern typically described by the intermediate
disturbance hypothesis (IDH) (Connell 1978) if we have
a biotic coniguration where L. racemosa is pioneer and
succession happens during stand recovery or establishment.
However, in addition to bell-shaped or U-shaped patterns,
our results also revealed many cases of linear increases or
decreases due to perturbation regimes not itting exactly
the resonance of the recovery dynamics.
This diversity of responses to perturbation its the
observations of Mackey & Currie (2001) and the prediction of the IDH axioms detailed by Sheil & Burslem
(2003). Speciically, to have an IDH pattern one needs:
(1) a dominance successional sequence when no perturbations occur; (2) succession due to competitive exclusion
of fastest growing trees; and (3) perturbations that bring
the system back to earlier successional stages. The results
of our individual-based model simulating competition at
individual-level conirm these axioms. The homogeneous
competition parameterization of our study did not create
succession and therefore did not exhibit a pattern predicted
by the IDH. However, this dynamic is possible in nature
(e.g. in understorey species systems as in Beckage & Stout
2000) and in mangrove ecosystems particularly. Only few
studies have observed a real species succession in mangrove forests (e.g., Ball 1980; Berger et al. 2006). Lugo
(1980) concluded that zonation was a steady state result
of abiotic conditions and refuted Davis’ (1940) hypothesis
that zonation was the result of succession and land building
processes. Since Lugo’s paper, succession in mangroves has
been cautiously attributed to changes in abiotic conditions
because of external factors, but rarely to species-induced
modiications of abiotic conditions (e.g., Bertrand 1999).
Because the IDH pattern is the expression of the dynamics
of species succession, it can be used to compare species
succession at different disturbance levels, or conversely,
to compare the recovery dynamics of sites that exhibit different succession dynamics. Both aspects have never been
considered in mangrove ecology. Such studies could support
our simulation results that in some cases succession could
be due to plant-plant interactions and not always exclusively
to changes in abiotic conditions.
Finally, our study at the individual level demonstrates
that even if abiotic conditions strongly inluence species
composition in mangrove forests, spatial plant-plant interactions also play an important role. We showed that the
423
successional dynamic is dependent on the capacities of
individuals of different species to compete spatially for resources, and that these dynamics determine the way species
diversity will increase or decrease in case of perturbations.
Thus, we demonstrate that variations of mangrove species
diversity due to perturbation regime will depend on a series
of interacting factors, including succession coniguration,
actual dynamic phases, plant spatial interactions, and abiotic settings. Additionally, ield studies show that changes
of abiotic settings after perturbations (e.g., Cahoon et al.
2003), recruitment patterns (e.g. Baldwin et al. 2001; Clarke
2004; Piou et al. 2006) and also differences of resistance
of species to the considered perturbations (Baldwin et al.
2001; Imbert 2002) could inluence species composition of
mangroves. Hence, forecasting a general trend of evolution
of species diversity of mangrove forests only considering the
perturbation regime seems risky. It could be possible only in
a site-speciic case, knowing not only the abiotic conditions
of a particular site, but also the type of species interactions
and succession phenomenon that could occur.
Acknowledgements. The authors are very grateful to Volker
Grimm, Martha Liliana Fontalvo-Herazo, Elizaveta Pachepsky
and an anonymous reviewer for valuable comments on an
earlier version of this manuscript. This study was inanced in
the frame of the MADAM project, a cooperation between the
ZMT, Bremen, Germany and the UfPa and MPEG, both Belém,
Brazil, inanced by the German Ministry of Education, Science,
Research and Technology (BMBF) [MADAM – Mangrove
Dynamics and Management (Project number: 03F0154A)],
and the Conselho Nacional de Pesquisa e Tecnologia (CNPq).
This is MADAM contribution number 116.
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Received 15 February 2007;
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For App. 1-4, see below (online version)
also available at JVS/AVS Electronic Archives;
www.opuluspress.se/
I
App. 1. Details on growth multipliers and parameters.
In this appendix, we give the details of the growth multipliers and parameters (Table A1.1) entering in Eq. A1.1. The
function fs(SALT) was the growth multiplier considering the effect of the pore water salinity on growth (Chen & Twilley 1998):
1
fs ( SALT ) =
(A1.1)
1 + exp ( d × ( S0.5 − S ))
where: S was the salinity at tree position and S0.5 and d were species speciic constants (Table A1.1). The function
fn(RNA) was the growth multiplier considering the effect of the relative nutrient availability (RNA) on growth (Chen
& Twilley 1998):
fn ( RNA ) = c1 + c2 × RNA + c3 × RNA 2
(A1.2)
where: c1, c2 and c3 were species speciic constants (Table A1.1).
Table A1.1. Growth and spatial competition species-speciic parameters used in the KiWi model. Sources: (1) Chen & Twilley
1998, (2) see App. 2.
Parameter
Description
DBHmax
Hmax
G
b2
b3
d
S0.5
c1
c2
c3
a
b
Maximum diameter at breast height
Maximum height
Growth constant
Constant in height to dbh relationship
Constant in height to dbh relationship
Salinity effect constant
Salinity effect constant
RNA effect constant
RNA effect constant
RNA effect constant
FON radius scaling parameter for heterospeciic competition parameterization
FON radius scaling parameter for heterospeciic competition parameterization
Apps. 1-4. Internet supplement to: Piou, C. et al. 2008.
Testing the intermediate disturbance hypothesis in species-poor systems:
A simulation experiment for mangrove forests
Journal of Vegetation Science 19: 417-424; doi: 10.3170/2008-8-18384
A. germinans
L. racemosa
R. mangle
140
3500
162
48.04
0.172
-0.18
72.0
-0.50
2.88
-1.66
13.7
0.72
80
3000
243
71.58
0.447
-0.20
65.0
-1.00
4.42
-2.50
17.0
0.95
100
4000
267
77.26
0.396
-0.25
58.0
0.00
1.33
-0.72
18.0
0.83
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(2)
(2)
II
App. 2. Parameterization of the FON radius calculation.
In the KiWi model, the FON radius R of a tree depends on its size:
(A2.1)
where: a and b are scaling parameters. The parameterization of a and b can be effectuated to reproduce the DBHdensity trajectories of a self-thinning phenomenon.
R = a × RBH b
Demonstration:
In equation A2.1, the RBH is half the DBH, so A2.1 becomes:
1
R = a × b × DBH b
(A2.2)
2
The FON approach has been seen as reproducing the self-thinning trajectory very well (Berger & Hildenbrandt
2003). During the self-thinning in KiWi model, because of the mortality function, the total FON area of all individuals
can be considered as constant since the dead individuals are replaced by growth of the remnant. This corresponds to a
constant maximum resource use. Let assume this constant be FONtot. We could simplify its calculation as:
(A2.3)
FONtot = N × FONind
where FONind is the mean area of the FON area of the individuals deined as:
1
× DBH 2 b
(A2.4)
22b
where R and DBH are respective mean values assuming they represent the entire community. Assuming that during
self-thinning we have the relationship of the DBH-density trajectory:
FON ind = π × R 2 = π × a 2 ×
log ( N ) = α + β´log ( DBH )
(A2.5)
or
N = exp (α ) + DBH β
Interchanging Equation A2.4 in A2.3 and comparing to A2.5 we get:
N = exp (α ) + DBH β =
22b
FON tot
× DBH −2 b
= FON tot ×
FON ind
π × a 2
(A2.6)
22b
Since exp (α) and FON tot ×
are not dependents on DBH, we can link the β parameter directly to the FON
π × a 2
b parameter:
β = –2b
(A2.7)
Identically we can derive the value of a:
a=
2 2 b × FON tot
π × exp (α )
(A2.8)
We determined with the KiWi model that FONtot is constant ~215% and not depending on a nor b. These relationships
are conirmed by simulation experiments with monospeciic stands (Fig. A2.1).
Apps. 1-4. Internet supplement to: Piou, C. et al. 2008.
Testing the intermediate disturbance hypothesis in species-poor systems:
A simulation experiment for mangrove forests
Journal of Vegetation Science 19: 417-424; doi: 10.3170/2008-8-18384
III
Parameterization of species-speciic values
Data from monospeciic stands of Belizean mangroves (I.C. Feller, F. Chi and C. Piou unpubl.) at different density
were used to create regressions and calculate the parameters a and b for Rhizophora mangle and Avicennia germinans.
Fig. A2.1 shows the ield data, linear regression and results of monospeciic simulation without recruitment with the
corresponding FON a and b.
Fig. A2.1. Field DBH-density (cm and stem/ha) data on natural
logarithmic scale with corresponding linear regression (plain
lines) and simulation results (dashed lines) of monospeciic
stand of Rhizophora mangle (black) and Avicennia germinans
(grey) without recruitment.
Fig. A2.2. CARICOMP DBH-density (cm and stem/ha) data of
mixed forests on natural logarithmic scale with corresponding
linear regression (plain line).
For Laguncularia racemosa, not enough monospeciic ield data were available, so we estimated that this species
was less competitive in Belize in terms of spatially distributed resources such as light. This was then considered in
the a and b parameter giving a larger b-value (0.95) and smaller a-value (17.0) than for R. mangle (e.g. Berger &
Hildenbrandt 2003).
Parameterization of species-identical values
To use the same approach for the tuning of the a and b parameter in the irst parameterization (species homogeneous
spatial competition), data of density and mean diameter from mixed stands of the three species were considered. We
used the data from plots of the CARICOMP program (CARICOMP 2002, http://www.ccdc.org.jm/mangrove_data.
html) over the entire Caribbean region to create the regression and calculate the parameters a and b considering all
three species (Fig. A2.2).
Apps. 1-4. Internet supplement to: Piou, C. et al. 2008.
Testing the intermediate disturbance hypothesis in species-poor systems:
A simulation experiment for mangrove forests
Journal of Vegetation Science 19: 417-424; doi: 10.3170/2008-8-18384
IV
App. 3. Sensitivity analysis on random variables affecting recruitments
Since there are no solid data on the variation of sapling numbers, the ranges of the two random variables rnd1 and
rnd2 (Eq.5) were arbitrarily chosen (respectively [0.5 to 1.5] and [0.1 to 0.3]). They described a natural luctuation and
occasional reappearance of saplings in the plot respectively. In order to analyze the suitability of these parameterizations,
a sensitivity analysis was conducted to test the effect of the variation of these ranges on the variation of the median
values of index of species dominance heterogeneity (ISDH).
For this analysis, we selected simulations with the species heterogeneous spatial competition parameterization,
the intermediate abiotic conditions and three selected cases of perturbation regimes that should present the so-called
bell-shape pattern characteristic of the intermediate disturbance hypothesis. For each case, we tested 11 different new
ranges for each random variables by multiplying the limit values of these 2 ranges by variation factors of Δrnd = 0.5 to
1.5. We measured the median ISDH results over the last 400 years for each new range (ISDH-new) and analyzed the variation
comparing it to the original value (ΔISDH= ISDH-new /ISDH-0).
The results of this sensitivity analysis are presented in Fig. A3.1. Variations of up to 10% of the ranges of rnd1 and
rnd2 change with less than 10% the ISDH results and not generally the original pattern of system answer to perturbation
regime. Actually, only with the extreme perturbation regime the rnd2 variation lead to variations of ISDH higher than 5%
but increasing then the trend of bell-shape answer of the system to perturbation regime.
Based on these results, we considered the selected ranges of rnd1 and rnd2 adequate for our study.
Fig. A3.1. Results of sensitivity analysis of rnd1 and rnd2 on ISDH variations, (a) with low perturbation regime (intensity = 30%,
frequency = 1 / 100 yr), (b) with intermediate perturbation regime (intensity = 50%, frequency = 1 / 40 yr) and (c) with extreme
perturbation regime (intensity = 99%, frequency = 1 /10 yr) (original values of ISDH: 2.551, 2.781 and 2.766 respectively). All
sensitivity analysis simulations were done with the species heterogeneous spatial competition parameterization and intermediate
abiotic conditions.
Apps. 1-4. Internet supplement to: Piou, C. et al. 2008.
Testing the intermediate disturbance hypothesis in species-poor systems:
A simulation experiment for mangrove forests
Journal of Vegetation Science 19: 417-424; doi: 10.3170/2008-8-18384
V
App. 4. Complementary results
In this appendix we present complementary results of the simulation exercises. Fig. A4.1 shows the general results
of the irst analysis: relative nutrient availability and salinity conditions on species dominance heterogeneity.
Fig. A4.2 shows speciic results of the second analysis: effects of perturbation regimes on species dominance heterogeneity with selected abiotic scenarios.
Fig. A4.1. ISDH variations according to salinity and relative nutrient availability (RNA) conditions for the two competition parameterizations. Points are median values of replicate simulations, error bars represent irst and third quartiles.
Fig. A4.2. Median ISDH variations following perturbation frequency for the two competition parameterizations (a and b) with selected
mortality intensity (70%) and medium abiotic scenario (Salinity 50 and RNA 80) (N = 30 for each point, boxes represent irst and
third quartiles, error bars represent minimum and maximum).
Apps. 1-4. Internet supplement to: Piou, C. et al. 2008.
Testing the intermediate disturbance hypothesis in species-poor systems:
A simulation experiment for mangrove forests
Journal of Vegetation Science 19: 417-424; doi: 10.3170/2008-8-18384
VI
The analysis of variations in species diversity (ISDH) of the system depending on the perturbation regime showed
different type of patterns for the different parameterizations (Fig A4.3). The homogeneous spatial competition parameterization with benign abiotic conditions led to 4 U-shaped patterns out of 11 analyses. The heterogeneous spatial
competition parameterization with benign abiotic conditions led to 4 bell-shaped patterns out of 11 analyses. In both
cases, the rest of the analyses showed irregular, increasing or decreasing pattern of ISDH variations. With medium abiotic
conditions the patterns were more often U-shaped or bell-shaped, but with an identical trend: the homogeneous spatial
competition parameterization led to 6 U-shaped patterns and the heterogeneous spatial competition led to 7 bell-shaped
patterns out of 11 analyses in both cases.
Fig. A4.3. Patterns of system response in median ISDH variations according to frequency effect with selected intensity of disturbance
(a) or according to intensity effect with selected frequency of disturbance (b).
Apps. 1-4. Internet supplement to: Piou, C. et al. 2008.
Testing the intermediate disturbance hypothesis in species-poor systems:
A simulation experiment for mangrove forests
Journal of Vegetation Science 19: 417-424; doi: 10.3170/2008-8-18384