Aquatic Botany 95 (2011) 173–181

Contents lists available at ScienceDirect

Aquatic Botany
journal homepage: www.elsevier.com/locate/aquabot

Desynchronizing effects of lightning strike disturbances on cyclic forest
dynamics in mangrove plantations
Markus Kautz a,∗ , Uta Berger b , Dietrich Stoyan c , Juliane Vogt b , Nabiul Islam Khan b , Karen Diele d ,
Ulrich Saint-Paul d , Tran Triet e , Vien Ngoc Nam f
a

TU München, Hans-Carl-von-Carlowitz-Platz 2, 85354 Freising, Germany
TU Dresden, Pienner Str. 8, 01737 Tharandt, Germany
c
TU Bergakademie Freiberg, Prüferstr. 9, 99596 Freiberg, Germany
d
Leibniz Center for Tropical Marine Ecology, Fahrenheitstr. 6, 28359 Bremen, Germany
e
Vietnam National University, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Viet Nam
f
Nong Lam University, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Viet Nam
b

a r t i c l e

i n f o

Article history:
Received 2 August 2010


1. Introduction
The occurrence of cyclic dynamics in populations of annual
plants, perennial plants and forests has attracted considerable
attention over the last few decades (e.g. Mueller-Dombois, 1991;
Franco and Silvertown, 2004; Caplat et al., 2008). Both empirical
studies (Pacala and Silander, 1990; Franco and Silvertown, 2004)
and modelling approaches (Bauer et al., 2002; Caplat et al., 2008)
revealed that oscillations in species abundance and biomass occur
when factors that synchronize mortality and establishment at stand
level predominate factors that desynchronize dynamics such as fire
disturbances and storms (Remmert, 1991).
Several factors including seed dormancy, germination success,
plant fertility, or soil fertility can promote oscillations (e.g. Pacala
and Silander, 1990). Recent studies highlight the importance of spatial constellations (namely the spatial arrangement of neighbouring

∗ Corresponding author. Tel.: +49 8161 714592; fax: +49 8161 714598.
E-mail addresses: [email protected], [email protected] (M. Kautz).
0304-3770/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.aquabot.2011.05.005

trees) and the resulting neighbourhood interactions (Bauer et al.,
2002; Caplat et al., 2008) and reveal that variability of plant vitality can alter both the rate with which a population converges to a
stable size and the average duration of related oscillations (Franco
and Silvertown, 2004).
Mangrove forests serve as extraordinary examples of both synchronization and desynchronization effects. On the one hand,
sedimentation and storms frequently create new areas for colonization or secondary succession, maintaining the cyclic dynamics
mentioned above (Fromard et al., 1998). On the other hand, individual tree mortality is comparatively high (e.g. due to the static
instability of larger trees in soft sediments or due to frequent lightning strikes) suppressing the development of senescent cohorts
(Duke, 2001), and thus desynchronizing potential oscillations.

whether the frequency and intensity of these disturbances are sufficient to remix the regular cohort structure of the plantation, to
accelerate its transformation into a more natural forest structure
and thus to prevent cyclic dynamics of the vegetation cover.
The aim of our study was threefold: (1) to analyse the lightning pattern in Can Gio and to mimic it using a statistical model,
(2) to simulate the dynamics of the Can Gio mangrove plantation
by means of an individual-based model that includes the lightning
model, and (3) to investigate whether canopy disturbances induced
by lightning strikes can significantly affect expected oscillations in
tree density.
We expected our analyses and experiments to reveal that
the cohort structure of this plantation induces oscillations in
forest development as known from terrestrial forests (e.g. MuellerDombois, 1987; Itow and Mueller-Dombois, 1988; Elias and Dias,
2009). Furthermore it was hypothesized that canopy disturbances

caused by lightning strikes have a damping effect on transient oscillation, accelerating the forest’s transition to a more natural and
stable state.

2. Methods
2.1. Identification of lightning gaps
In order to quantify canopy disturbances induced by lightning strikes in the study site, we used both satellite images and
ground truth data. The satellite images were selected according to
image quality parameters (e.g. high spatial resolution, low ratio
of cloud coverage, sufficient spectral contrast) and availability of
recent, multi-temporal data (time series) highly representative of
the study area. Based on these criteria, we used panchromatic SPOT
images (time series: 2003/2005/2007 with a 2.5 m × 2.5 m pixel
size) representing 86% of the reserve above minimum sea level
including the entire core zone. All three images were taken at
similar tidal levels, which minimized the error when identifying
the coastline. The analysis was based on reference points obtained

around the thunderstorm centre. Remote sensing analysis (Fig. 2)
revealed spatio-temporal clustering, which was also reported by
Vietnamese foresters (pers. comm.). We applied a Matern cluster process (see Illian et al., 2008, p. 376) for the description of
the spatial distribution of the lightning in a given time interval.
This model includes parent points (=thunderstorms), which form
a planar Poisson process of intensity p (= thund ·T, where T is the
length of the time interval). A random number of daughter points
(=lightning) are scattered around each parent point. This number
has a Poisson distribution of mean c¯ . The locations of the daughter
points are uniform and random within a disc of radius R centred at
the parent point. The intensity of the point process of lightning is
¯ · thund .
light = c
The parameters thund , c¯ and R had to be estimated based on the
remote sensing data. Statistically, this posed a challenge since lightning leaves traces in forest canopies, but not in tidal channels or
creeks, on mudflats, and in shrub zones (Fig. 2). Hence, the window
of observation W for the lightning patterns only comprised the forest area within the 4 km × 4 km plots, rather than the entire square.
This area W, however, is so irregular that even the best software for
point process statistics could not be applied. Therefore, we applied
the interrupted-point-process approach (Stoyan et al., 1995).
This approach assumes that there is an original point process
˘ true in the whole area (=lightning strikes) and a random set X (=W),
both of which are independent of each other. Only those points of
˘ true that fall into X are visible, while all other points of ˘ true are
removed. The remaining point process ˘ obs is the interrupted point
process. To simplify the calculation, the random set X was assumed
to be spatially homogeneous and isotropic. Such a random set is
characterized by two fundamental characteristics:

Fig. 2. Subplot 1 (a) and 2 (b) chosen for the identification of lightning gaps (red


(1)

and its pair correlation function gobs (r) is
gobs (r) =

C(r)
· gtrue (r).
f2

(2)

Eqs. (1) and (2) enable determination of true and gtrue (r), when f,
C(r), obs and gobs (r) are known. true can be used to estimate thund ,
and gtrue (r) leads to estimates of c¯ and R.
A basic assumption of the interrupted point process model is
independence of ˘ true and X. Since ˘ true is unobservable, we tested
an aspect of this independence property by means of a Monte
Carlo test as described in Illian et al. (2008, Section 6.11.3). For this
test, the channels were approximated by a point pattern with the
result that we obtained a bivariate point pattern, with two types of
points, where 1 = channel point and 2 = gap. The test checked spatial


176

M. Kautz et al. / Aquatic Botany 95 (2011) 173–181

Table 1
Model description following the ODD protocol.

Trees “sense” the distance, size and explicit location of their neighbours by their overlapping FONs.

Stochasticity

Saplings establish randomly, depending on local conditions (not in the initialization of the plantation). Tree mortality due to
disturbances (here: lightning) is described by random functions.

Observations

The model provides yearly tracking of all state variables and derived parameters for all trees.

Details
Initialization
Input

Submodels
Description of a single tree

Empty plots of 1 km × 1 km were established as a plantation with a tree-to-tree distance of 1 m. New trees colonizing canopy gaps
were considered as saplings once they had reached a minimum height of 1.27 m.
Yearly recruitment rates define the establishment of new saplings. Abiotic factors such as topography, inundation height,
inundation frequency, pore water salinity and nutrient availability can be addressed explicitly by user-supplied maps corresponding
to the simulated forest stand; but for the purpose of this study they were considered to be optimal for the whole forest.

A tree is described by its stem position (x,y), stem diameter (dbh), and field-of-neighbourhood (FON). The latter describes the area
which a tree influences its neighbours and is influenced by its neighbours. The radius R of the FON increases with dbh:
within √
R = a · 0.5 · dbh. The intensity of competition is calculated as FON(r) = e−c(r−(0.5·dbh))

Recruitment and establishment

conditions improve, e.g. when a neighbouring tree dies.
(2) Due to lightning: For its description, we fitted a spatio-temporal point process model to the gap data observed at the study site.
The implementation of the lightning process comprises five steps: (1) choice of a random location of a thunderstorm centre within
the forest; (2) choice of cluster type: small cluster (probability p1 ) or large cluster (probability p2 = 1 − p1 ); (3) choice of the number
of lightning strikes within the cluster according to a Poisson distribution with mean c¯ 1 and c¯ 2 respectively; (4) choice of the random
position of each lightning strike in a radius R1 or R2 around the centre of the cluster; (5) removing all trees in the gap radius RGap
surrounding the chosen position. The value for RGap was chosen from 4 size classes, according to the frequency of their occurrence
measured for Can Gio (see Table 2). The gap shape was assumed to be circular.

correlations between the 1- and 2-point positions. The bivariate Lfunction L12 (r) was estimated for the data and then compared with
L12 (r)-functions of randomly generated bivariate patterns, where
the 1-points were the original ones while the 2-points were randomly shifted, with the same shift vector for all points.
2.2. Analysis of the impact of canopy disturbances on plantation
structure
In order to understand the influence of canopy disturbances on
the dynamics of the mangrove forest plantation, the individualbased mangrove model KiWi, developed for simulating neotropical

mangrove forests (Berger and Hildenbrandt, 2000), was parameterized to the Asian mangrove species R. apiculata and combined with
the lightning process model. The KiWi model provides a spatially
explicit description of a virtual mangrove forest. Each individual
tree is characterized by its stem position, stem diameter (dbh) and
a circular field-of-neighbourhood (FON) which specifies both the
zone of interaction with neighbouring trees and the strength of
competition exerted by the tree at each location inside its FON
(Berger and Hildenbrandt, 2000). The size of the FON increases with
dbh. The annual increment of dbh depends on the current size (dbh
and height) of the tree, the competition strength of neighbouring
trees, pore water salinity and nutrient availability. For the simu-



p1
Probability of small lightning clusters
p2
Probability of large lightning clusters
c¯ 1
Mean number of gaps within a small cluster
c¯ 2
Mean number of gaps within a large cluster
R1
Radius of small lightning cluster (m)
R2
Radius of large lightning cluster (m)
RGap
Radius of lightning gaps (m), and corresponding
probabilities of occurrence

Value

0.0176
0.0075
0.38
0.62
2.01
2.56
62
380
6 ≤ 9 (0.11)
9 ≤ 14 (0.53)
14 ≤ 18 (0.26)
18 ≤ 23 (0.10)


= ln

,

(3)

t

.

General information
Location (xy coordinates of the NW
corner; UTM/WGS ‘84)
Total area

Subplot 1

Subplot 2

699000/1165000

704000/1168000

4 km × 4 km
(1600 ha)
71% (1137 ha)
116

4 km × 4 km

10,622
0.016
0.047

To determine whether lightning regimes have different effects
on the development of the simulated forests, a Kruskal–Wallis test
was carried out for selected time steps. In the case of significance,
a Post Hoc test according to Siegel and Castellan (1988) revealed
which scenarios differ from each other.
The satellite images were analysed using ArcGIS 9.0 (ESRI
Inc., 2004). All statistical analyses were carried out with R (R
Development Core Team, 2011): we used the R package SpatStat
(Baddeley and Turner, 2005) for point pattern analyses and the
R packages EMD (Donghoh and Hee-Seok, 2009) and pgirmess
(Giraudoux, 2010) for the analysis of the simulated tree density
time series.
2.3. Sensitivity analysis
To trace the contribution of uncertain model parameters to the
forest dynamics, a sensitivity analysis was performed using the
extended Fourier amplitude sensitivity test (eFAST), a variancebased global sensitivity method (Cukier et al., 1978; Saltelli et al.,
1999, 2000). It quantifies the contribution of the individual input
parameters to the variance of the output variables. It reveals both
the main effect of each parameter on the model output and the
sum of the effects resulting from higher-order interactions of each
parameter with the other parameters (Saltelli et al., 2000; Saloranta
and Andersen, 2007). The model output was analysed based on discrete Fourier transformation using the software package SimLab
(2011). The eFAST sensitivity analysis was performed using R (R
Development Core Team, 2011). Following its specific sampling
procedure, different parameter sets were estimated with a −10%
to +10% range for each parameter described in Table 2. The parameters of the lightning submodel were not considered here in order

Disturbed area 2003–2005 (%
year−1 )

5
0.654
0.1
281.25
80
3000
71.575
0.44734
0.2

177

(4)

Table 3 summarizes the lightning gap characteristics obtained
in both subplots via the analyses of the satellite images. Both


178

M. Kautz et al. / Aquatic Botany 95 (2011) 173–181

Fig. 3. The empirical bivariate L12 (r)-function demonstrating the independence of
lightning gaps and channels in subplot 1 with the 95% confidence bands (dashed).

subplots include comparable portions of mangrove vegetation
but differ slightly in number of gaps and gap sizes. A comparison of gap frequencies between the two time steps 2003–2005

Fig. 4. (a) Pair correlation functions of the lightning gaps in subplot 1, calculated
for the whole 4 km × 4 km area gtrue (r) (solid), and corrected by an observation window specified by the forest matrix gobs (r) (dashed). (b) Empirical function gmean (r)
(solid) representing the aggregated pair correlation function of the gaps observed
in both subplots, and the derived model function gmodel (r) (dashed). Values above 1
(horizontal line) indicate clustering.

regime into the mangrove forest simulations. The aggregated pair
correlation function gmean (r) appears to consist of two components:
one representing small, highly concentrated clusters (the large values of gmean (r) for r < 100 m) and the other representing larger,
thinner clusters (values above one in the range of 100 m < r < 300 m)
(Fig. 4b). Therefore, the statistical model assumes that there are two
classes of clusters: large and small. Both cluster classes are characterized by their radii R1 and R2 , their mean numbers per cluster c¯ 1
and c¯ 2 , and their probabilities p1 and p2 (Table 2). These parameters
were estimated by a least squares estimation based on the theoretical pair correlation function of the generalized Matern cluster
process and gmean (r) (Illian et al., 2008, p. 371).
Finally, we estimated the space-time intensity thund of the
Poisson process of thunderstorm centres. The data used for this
purpose are the numbers of lightning gaps in the four-year period
2003–2007 within both subplots. These are 78 and 80, respectively.
This yielded an estimate for the intensity light of lightning:
light

=

78 + 80
= 1.76 km−2 year−1 = 0.0176 ha−1 year−1 .
2 · 4 × 4 · 4 · 0.7


M. Kautz et al. / Aquatic Botany 95 (2011) 173–181

27.27
72.75
4.67


down, finally leading to a de-synchronization of the senescence
and re-colonization process. Consequently, the ranges between
the maxima–minima values of the tree density decrease with
increasing lightning frequency. The Kruskal–Wallis test reveals that
lightning initially has a significant damping effect on the oscillation amplitude but this difference gets lost over the course of time
(Table 4). After 25 simulation years, the tree densities differ significantly between all three scenarios. After 120 years, there is a
difference between the scenario without lightning and both scenarios with lightning. However, the lightning scenarios (Can Gio
and Florida) cannot be distinguished from each other. After 400
years, no significant difference in the lightning effect is detectable.
The damping coefficient (measured as the ratio between consecutive maxima of the tree density oscillation and normalized by
the time span between the occurrence of two consecutive maxima)
increases with lightning frequencies: from approx. 0.006 (“Without”), 0.007 (“Can Gio”) to 0.008 (“Florida”). In contrast, the time

3000

Lightning Frequency
Without
Can Gio
Florida

2500

IV

2000

I
II

1500

Our results demonstrated transient oscillation behaviour of tree
density. The damping coefficient (i.e. strength of damping effect)
increased with lightning frequency but the period of the oscillations
remained constant. The fact that damping factors do influence the
oscillation amplitude but not its period is already known from classical mechanical systems. Interestingly, both the cyclic behaviour
and the damping characteristics were not imposed by the KiWi
model itself but rather appear as emergent properties resulting
from local interactions among the trees.
The mangrove plantations in Can Gio can be seen as ideal for
canopy disturbance analyses because lightning strikes typically
kill several neighbouring trees simultaneously, rather than killing
individual trees, creating relatively large gaps that can be easily detected in satellite images. The dead trees shed their leaves,
but do not burn and thus remain standing for some time. Nevertheless, the certainty of detection of lightning gaps in mangroves
depends strongly on the spatial resolution and quality of the satellite images, influencing the signature recognition. While the spatial
resolution of the SPOT images used in this study (2.5 m) is acceptable, the variable quality of the consecutive images (shadowing,
reduced contrasts in closing gaps) as well as the lack of colour channels meant that the power of the automatic gap classification was
reduced. The additional use of the Quickbird image (©Google Earth,
2008) as a reference, however, improved manual identification. The
mean gap size measured for Can Gio is similar to those documented
for other mangrove areas (e.g. 506 m2 in Sherman et al., 2000;
202 m2 in Whelan, 2005), but the lightning frequency is probably
lower than elsewhere (0.05–0.09 ha−1 year−1 in Florida, Huffines
and Orville, 1999; Shafer and Fuelberg, 2006). Consequently, the
percentage of disturbed plantation area in Can Gio is also relatively
low (0.23%, in comparison to 1.1–1.9% in Florida, Zhang et al., 2008).
The analysis showed that the frequency of lightning gaps varies
strongly between years, a fact also observed in other studies (e.g.
Sherman et al., 2000). Therefore, while the results from the time
series of the present study (2003–2007) may not be representative
for previous decades, they still provide valuable information for the

all three available individual-based mangrove forest models (KiWi,
FORMAN, and MANGRO, see Berger et al., 2008 for a review) are
parameterized to neotropical mangrove species only. The actual
parameterization for R. apiculata is based on species-specific biological data (Gong and Ong, 1990, 1995) and is discussed in detail
by Fontalvo-Herazo et al. (submitted for publication).
The combination of the forest simulation model with the Matern
cluster process model allows a sound analysis of transient oscillation in a real forest system by means of simulation experiments. Our
results complement earlier theoretical studies of cyclic behaviour
on plant populations by Bauer et al. (2002) and Caplat et al. (2008).
The study presented here confirms the findings of Bauer et al.
(2002) that nonlinear population dynamics can emerge, provided
that neighbourhood competition is the main source of plant mortality and that the establishment of recruits depends on light
availability. Due to the chosen parameterization of the field-ofneighbourhood approach, tree-to-tree competition is asymmetric
in the KiWi model and larger trees exert higher competition
strength against smaller trees than vice versa, as this is the case
in competition for light. This results in a strong damping effect
down to a stage where vegetation dynamics shows only fluctuating
patterns as already shown by Caplat et al. (2008).
Returning to our initial research questions our results revealed
that (i) a cycling of tree density and related values such as biomass
and vegetation cover can be expected on the stand level. (ii) The
plantation structure emphasizes this nonlinear behaviour. (iii) The
present lightning regime in Can Gio damps the amplitude of the
transient oscillation but is not sufficient to prevent it.
Acknowledgements
We thank Felix Ballani (TU Bergakademie Freiberg) for the calculation of the bivariate L-functions. Furthermore, we are grateful to
Jan Vermaat and an anonymous reviewer for their useful comments
to an earlier proof of this article.
The study was part of a project funded by the German Research
Foundation (DFG, SA 622/12-3); Juliane Vogt was funded by a DFG

imagery (IKONOS). Syst. Biodivers. 2, 113–119.
Dijksma, R., van Loon, A.F., van Mensvoort, M.E.F., van Huijgevoort, M.H.J., te Brake,
B., 2010. An extended hydrological classification for mangrove rehabilitation
projects: a case study in Vietnam. In: Hoanh, C.T., Szuster, B.W., Suan-Pheng,
K., Ismail, A.M., Noble, A.D. (Eds.), Tropical Deltas and Coastal Zones—Food Production, Communities and Environment at the Land–water Interface. , ISBN 978
184593618-1, pp. 384–397, doi:10.1079/9781845936181.0000.
Donghoh, K., Hee-Seok, O., 2009. EMD: a package for empirical mode decomposition
and Hilbert spectrum. R Journal 1, 40–46.
Duke, N.C., 2001. Gap creation and regenerative processes driving diversity and
structure of mangrove ecosystems. Wetl. Ecol. Manag. 9, 257–269.
Elias, R., Dias, E., 2009. Cyclic patch dynamics in a Macaronesian island forest. Commun. Ecol. 10, 25–34.
FAO, 1993. Mangrove for production and protection. A changing resource system:
case study in Can Gio District, South Vietnam. Bangkok, Thailand.
Fontalvo-Herazo, M.L., Piou, C., Vogt, J., Saint-Paul, U., Berger, U. Simulating harvesting scenarios towards the sustainable use of mangrove forest plantations. Wetl.
Ecol. Manag., submitted for publication.
Franco, M., Silvertown, J., 2004. A comparative demography of plants based upon
elasticities of vital rates. Ecology 85, 531–538.
Fromard, F., Puig, H., Mougin, E., Marty, G., Betoulle, J.L., Cadamuro, L., 1998. Structure, above-ground biomass and dynamics of mangrove ecosystems: new data
from French Guiana. Oecologia 115, 39–53.
Giraudoux, P., 2010. pgirmess: Data Analysis in Ecology. R Package Version 1.4.9.,
http://CRAN.R-project.org/package=pgirmess.
Gong, W.K., Ong, J.E., 1990. Plant biomass and nutrient flux in a managed mangrove
forest in Malaysia. Estuar. Coast. Shelf Sci. 31, 519–530.
Gong, W.K., Ong, J.E., 1995. The use of demographic studies in mangrove silviculture.
Hydrobiologia 295, 255–261.
Grimm, V., Berger, U., Bastiansen, F., Eliassen, S., Ginot, V., Giske, J., Goss-Custard, J.,
Grand, T., Heinz, S.K., Huse, G., Huth, A., Jepsen, J.U., Jørgensen, C., Mooij, W.M.,
Müller, B., Peer, G., Piou, C., Railsback, S.F., Robbins, A.M., Robbins, M.M., Rossmanith, E., Rüger, N., Strand, E., Souissi, S., Stillman, R.A., Vabø, R., Visser, U.,
DeAngelis, D.L., 2006. A standard protocol for describing individual-based and
agent-based models. Ecol. Model. 196, 115–126.

Saloranta, T.M., Andersen, T., 2007. MyLake—a multi-year lake simulation model
code suitable for uncertainty and sensitivity analysis simulations. Ecol. Model.
207, 45–60.
Saltelli, A., Tarantola, S., Chan, K.P-S., 1999. A quantitative model-independent
method for global sensitivity analysis of model output. Technometrics 41, 39–
56.
Saltelli, A., Chan, K., Scott, E.M. (Eds.), 2000. Sensitivity Analysis. John Wiley & Sons,
Chichester.
Shafer, P., Fuelberg, H., 2006. A statistical procedure to forecast warm season
lightning over portions of the Florida peninsula. Weather Forecast. 21, 851–
868.
Sherman, R.E., Fahey, T.J., Battles, J.J., 2000. Small-scale disturbance and regeneration
dynamics in a neotropical mangrove forest. J. Ecol. 88, 165–178.
Siegel, S., Castellan Jr., N.J., 1988. Nonparametric Statistics for the Behavioural Sciences. MacGraw Hill Int., New York, pp. 213–214.
SimLab, 2011. Software Package for Uncertainty and Sensitivity Analysis. Joint
Research Centre of the European Commission, Downloadable free of charge at:
http://simlab.jrc.ec.europa.eu.
Stoyan, D., Kendall, W.S., Mecke, J., 1995. Stochastic Geometry and its Applications.
Wiley, Chichester.
Tran, T., Barzen, J., Le Cong, K., Moore, D., 2004. War-time herbicides in the Mekong
delta and their implications on post-war wetland conservation. In: Furukawa,
H., Nishibuchi, M., Kono, Y., Kaida, Y. (Eds.), Ecological Destruction, Health and
Development Advancing Asian Paradigms. Kyoto University Press/Trans Pacific
Press, pp. 199–211.
Whelan, K.R.T., 2005. The successional dynamics of lightning-initiated canopy gaps
in the mangrove forests of Shark River, Everglades National Park, USA. Ph.D.
Dissertation. Florida International University, Miami, FL, USA.
Zhang, K., Simard, M., Ross, M., Rivera-Monroy, V.H., Houle, P., Ruiz, P.L., Twilley,
R.R., Whelan, K.R.T., 2008. Airborne laser scanning quantification of disturbances
from hurricanes and lightning strikes to mangrove forests in Everglades National