Using Lidar Bathymetry and Boosted Regression Trees to Predict the Diversity and Abundance of Fish and Corals

Abstract

Coral reef ecosystems are topographically complex environments and this structural heterogeneity influences the distribution, abundance and behavior of marine organisms. Airborne hydrographic lidar (Light Detection and Ranging) provides high resolution digital bathymetry from which topographic complexity can be quantified at multiple spatial scales. To assess the utility of lidar data as a predictor of fish and coral diversity and abundance, seven different morphometrics were applied to a 4 m resolution bathymetry grid and then quantified at multiple spatial scales (i.e., 15, 25, 50, 100, 200 and 300 m radii) using a circular moving window analysis. Predictive models for nineteen fish metrics and two coral metrics were developed using the new statistical learning technique of stochastic gradient boosting applied to regression trees. Predictive models explained 72% of the variance in herbivore biomass, 68% of parrotfish biomass, 65% of coral species richness and 64% of fish species richness. Slope of the slope (a measure of the magnitude of slope change) at relatively local spatial scales (15-100 m radii) emerged as the single best predictor. Herbivorous fish responded to topographic complexity at spatial scales of 15 and 25 m radii, whereas broader spatial scales of between 25 and 300 m radii were relevant for piscivorous fish. This study demonstrates great utility for lidar-derived bathymetry in the future development of benthic habitat maps and faunal distribution maps to support ecosystem based management and marine spatial planning.

Full text

Journal of Coastal Research SI 53 27–38 West Palm Beach, Florida Fall 2009
DOI: 10.2112/SI53-004.1
§
National Oceanic and Atmospheric Administration
NOS/CCMA Biogeography Branch
1305 East-West Highway
Silver Spring, MD 20910
simon.pittman@noaa.gov
†
University of the Virgin Islands
Marine Science Center, 2 John Brewer’s Bay
St. Thomas 00802, U.S. Virgin Islands
Using Lidar Bathymetry and Boosted Regression Trees to Predict the
Diversity and Abundance of Fish and Corals
Simon J. Pittman
§†
, Bryan M. Costa
§
and Tim A. Battista
§
Coral reef ecosystems are topographically complex environments and this structural heterogeneity inuences the distribution,
abundance and behavior of marine organisms. Airborne hydrographic lidar (Light Detection and Ranging) provides high resolution
digital bathymetry from which topographic complexity can be quantied at multiple spatial scales. To assess the utility of lidar data
as a predictor of sh and coral diversity and abundance, seven different morphometrics were applied to a 4 m resolution bathymetry
grid and then quantied at multiple spatial scales (i.e., 15, 25, 50, 100, 200 and 300 m radii) using a circular moving window analysis.
Predictive models for nineteen sh metrics and two coral metrics were developed using the new statistical learning technique of
stochastic gradient boosting applied to regression trees. Predictive models explained 72% of the variance in herbivore biomass, 68%
of parrotsh biomass, 65% of coral species richness and 64% of sh species richness. Slope of the slope (a measure of the magnitude
of slope change) at relatively local spatial scales (15-100 m radii) emerged as the single best predictor. Herbivorous sh responded
to topographic complexity at spatial scales of 15 and 25 m radii, whereas broader spatial scales of between 25 and 300 m radii were
relevant for piscivorous sh. This study demonstrates great utility for lidar-derived bathymetry in the future development of benthic
habitat maps and faunal distribution maps to support ecosystem-based management and marine spatial planning.
ADDITIONAL INDEX WORDS: Topographic complexity, terrain morphometrics, seascapes, predictive modeling, sh species
richness, spatial scale, Puerto Rico
Pittman, S.J.; Costa, B.M., and Battista, T.A., 2009. Using lidar bathymetry and boosted regression trees to predict the diversity and
abundance of sh and corals. Journal of Coastal Research, SI(53), 27–38.
INTRODUCTION
A coral reef ecosystem often exists as a spatially complex mosaic
of patches, including coral reefs, seagrasses and unvegetated
sediments. Each distinct habitat type exhibits highly variable within-
patch structural heterogeneity at a range of spatial scales (Hatcher,
1997; Pittman, McAlpine, and Pittman, 2004; Pittman et al., 2007a).
Structural heterogeneity interacts with and is modied by marine
fauna through its impact on key ecological processes including
predation, competition and recruitment (Caley and St. John, 1996;
Hixon and Beets, 1993). Many studies of shes on coral reefs
have demonstrated a strong positive correlation between structural
heterogeneity of the substratum and sh species richness, abundance
and biomass (Friedlander and Parrish, 1998; Gratwicke and Speight,
2005a and b; Luckhurst and Luckhurst, 1978; Roberts and Ormond,
1987). Frequently, in situ structural heterogeneity is measured as
topographic complexity using techniques such as prole gauges,
stereophotos, and most commonly, the chain-and-tape method
(Frost et al., 2005; McCormick, 1994; Risk, 1972; Walker, Jordan,
and Spieler, 2009). The chain-and-tape method measures surface
rugosity as the ratio of contoured surface distance to linear distance.
These measurements, however, are conducted at relatively ne spatial
scales (i.e., grain of 1-10 cm and extent of 3-10 m), usually with
only a single scale of measurement (representing two-dimensional
structure) and typically conned to a single habitat type or even a
single patch (Knudby, LeDrew, and Newman, 2007). This limits
the scope of inference and provides very little useful information for
the development of spatially explicit predictive models, which are
urgently needed to support ecologically meaningful decision making
in resource management (Mellin, Andréfouët, and Ponton, 2007;
Miller et al., 2004; Pittman et al., 2007a).
The ability to accurately predict continuous patterns in marine
species distributions and identify hotspots of species richness,
abundance and biomass across broad extents of the marine
environment (including previously unsurveyed areas) is considerably
more valuable. Consequently, there is great interest in remote sensing
techniques such as lidar (Light Detection and Ranging), which is
capable of capturing spatially continuous high resolution bathymetry
over broad spatial scales (Brock et al., 2004; Brock et al., 2006). If
ecologically meaningful bathymetric structure can be captured, then
lidar methods have many advantages over in situ techniques.
The utility of lidar data as a predictor of faunal diversity and
abundance, however, remains uncertain. To date, only two published
studies have examined lidar-faunal relationships in the marine
environment (but see also Walker, Jordan, and Spieler, 2009).
Kuffner et al. (2007) found that EAARL-derived (Experimental
Advanced Airborne Research Lidar) rugosity of Florida patch reefs
was only weakly correlated with in situ chain-and-tape rugosity
and explained very little of the variability in sh species richness
and abundance. In contrast, Wedding et al. (2008) used SHOALS-
derived (Scanning Hydrographic Operational Airborne Lidar
ABSTRACT

Journal of Coastal Research, Special Issue No. 53, 2009
Pittman, Costa, and Battista
28
Survey) rugosity of Hawaiian coral reef ecosystems and found
strong correlations with both in situ chain-and-tape rugosity and sh
species richness, abundance and biomass. These studies differed
substantially in the number of habitat types and depth range sampled
and sh-habitat relationships were modeled using simple linear
statistical techniques with only a single derivative of bathymetry as
a predictor (i.e., surface rugosity).
A wide range of metrics now exist for quantifying complex
structure in continuously varying surfaces and could have great utility
in spatial ecology (McGarigal and Cushman, 2005). The elds
of digital terrain modeling (or geomorphometry in geology) and
industrial surface metrology in product engineering have developed
and applied a wide range of morphometrics for investigating
geomorphological surface features and irregularities or roughness
in engineered surfaces (Pike, 2001a, 2001b). Very little is known
about their performance as predictors for marine fauna.
The majority of studies linking marine fauna to benthic structure
have utilized categorical or thematic benthic habitat maps, which
represent benthic structure as two-dimensional horizontal surfaces
composed of mosaics of internally homogeneous patches with
discrete patch boundaries. In landscape ecology, this is known
as the patch mosaic model of environmental structure (Forman,
1995). Patch mosaic structure has proved to be important for
many species, but often subsumes ecologically meaningful within-
patch heterogeneity and does not usually incorporate topographic
variability. Lidar data, however, can represent seascape structure
as a continuously varying three-dimensional surface. This model
of the environment is known as the spatial gradient perspective or
the continuum model of environmental structure (Austin and Smith,
1989; McGarigal and Cushman, 2005), which is thought to be
more realistic for some species (Fischer and Lindenmayer, 2006).
Much of this previous work has focused on terrestrial species and
their responses to spatial patterning in the environment, although
Pittman et al. (2007a) used nonlinear modeling techniques and
found that bathymetric complexity explained more of the variance
in sh species richness than did measures of categorical seascape
composition (i.e., amount and diversity of benthic habitat types).
In this paper, we conduct an extensive nonlinear exploratory
analysis to assess the performance of a suite of lidar derivatives as
faunal predictors and to identify the best predictors at multiple scales
across a coral reef ecosystem in southwestern Puerto Rico. We
extend the range of morphometrics applied to lidar beyond surface
rugosity by including plan curvature, fractal dimensions, slope, slope
of the slope and standard deviation of water depth. The primary
analytical challenge was to determine if lidar-derived predictors
were capable of explaining a large proportion of the variability in
sh and coral species richness and abundance.
Three specic questions were addressed:
1) Are different surface morphometrics and in situ measures of
topographic complexity correlated?
2 ) Is lidar-derived bathymetry a useful predictor of sh and coral
diversity and abundance?
3) Which morphometric(s) are the best predictors of sh and coral
metrics and at which spatial scales?
METHODS
Study Area
The continental shelf of southwestern Puerto Rico supports a
complex mosaic of benthic habitat types (e.g., coral reefs, seagrasses,
sand, mangroves), collectively referred to as a coral reef ecosystem
(Figure 1). Much of the study region is within the La Parguera
Nature Reserve and is managed by the Government of Puerto Rico’s
Department of Natural Resources and Environment. Benthic habitat
types in the region have been mapped at the spatial resolution of 1
acre to depths of approximately 33 meters, using visual interpretation
of high resolution aerial photography (Kendall et al., 2002). Large
areas of the study region, however, were unclassied due to poor
water column clarity that precluded the interpretation of seaoor
structure. The integration of benthic habitat maps and newly
acquired lidar bathymetry in a Geographical Information System
(GIS) highlighted substantially more of the benthic complexity
across the region (Figure 2).
Field data
Underwater visual surveys of sh and benthic habitat were
conducted semi-annually (Jan/Feb and Sept/Oct) between 2001
and 2007. Survey sites were selected using a spatially stratied
random sampling design incorporating two strata (i.e., hardbottom
and softbottom) derived from National Oceanic and Atmospheric
Administration’s nearshore benthic habitat map (Menza et al., 2006).
Hardbottom habitat types included colonized pavement, patch reef,
linear reef, colonized pavement with sand channels, spur and groove,
scattered coral/rock in unconsolidated sediments and reef rubble
(Kendall et al., 2002). Softbottom habitat types included seagrass,
macroalgae, sand, and mud. Fish surveys were conducted within
Figure 1. La Parguera study area in southwestern Puerto Rico showing the 4
m resolution lidar bathymetry data extending across shallow water (<60 m)
coral reef ecosystems of the continental shelf.
Puerto Rico
La Parguera
67°0'0"W67°5'0"W
17°55'0"N
0 5 km
Bathymetry
Meters
45
<1
Fish & coral surveys

Journal of Coastal Research, Special Issue No. 53, 2009
Lidar Bathymetry for Predicting Fish and Corals
29
To conduct benthic habitat surveys and collect percentage cover
and species richness data on scleractinian corals, an observer placed
a 1 m
2
quadrat at ve random locations along the sh transect. The
quadrat was divided into 100 smaller squares (10 x 10 cm). Corals
were identied to genus (and species where possible) and percent
cover was estimated to the nearest 0.1 %.
Variance (σ
2
) in depth along each sh transect was calculated
from depths measured by a SCUBA diver at each (n=5) random
benthic quadrat location using a digital depth gauge. Rugosity was
measured with a six meter chain (1.3 cm chain link) draped over the
contoured surface at two positions along the transect. The straight-
line horizontal distance was measured with a tape. An index of
rugosity was calculated as the ratio of contoured surface distance
to linear distance, using R = 1-d/l, where d is the contoured distance
and l is the horizontal distance (6 m). Chain-and-tape rugosity was
only measured at hardbottom sites in the study area.
A total of 506 underwater survey transects were used to develop
models of faunal-bathymetric relationships, including 301 faunal
samples from hardbottom and 205 from softbottom habitat types.
Where in situ chain-and-tape data were included in analyses, only
data from hardbottom survey sites were used. Transects at the edges
of the mapped area (n=21) were excluded to avoid confounding by
map edge artifacts. GIS scripts were used to create a center point
or “centroid” for each transect, based on transect length and the
directional bearing of the survey, with which to extract underlying
values from the lidar bathymetric surfaces.
Hydrographic lidar data collection
Bathymetry and reectivity data were collected for southwestern
Puerto Rico between 7
th
and 15
th
May 2006 using a lidar LADS Mk II
Airborne System operated by Tenix LADS Incorporated. The laser
system was mounted on a DeHavilland Dash 8-200 aircaft ying at
survey speeds of 72-90 meters per second and at an altitude of 366-
671 meters above the sea surface. A 900 Hertz (1064 nm) Nd:Yag
laser acquired spot data at a rate of 900 pulses per second, with swath
widths of 192 meters. This provided post-processing spot data with
a 4 x 4 meter spacing. The surveys also achieved 200% seabed
coverage in waters up to 50 m depth. Water depth was calculated
by comparing the return times from a green laser reected off the
substratum and an infrared laser reected off the sea surface to form
a height datum, together with information on aircraft altitude and
heading and GPS surface height data.
Quantifying surface morphology
The depth pulses were weighted by uncertainty, averaged
and gridded at a 4 x 4 meter spatial resolution in CARIS BASE
Editor (Stephenson and Sinclair, 2006). Erroneous lidar returns
were removed and a seamless bathymetric surface was exported
as a GeoTIFF. In ArcGIS 9.2 (Environmental Systems Research
Institute, Inc.), negative values (i.e., land) and mangroves were
removed from the bathymetric surface. Gaps or “holidays” in the
data were lled using a nearest neighbor resampling technique that
assigned “NoData” cells the value of their nearest neighbor based on
Euclidean distance.
Seven morphometrics were calculated (i.e., mean water depth,
standard deviation of water depth, rugosity, slope, slope of the slope,
plan curvature and fractal dimension) (Table 1) from the bathymetric
surface in order to quantify a range of structural attributes from the
benthic terrain of southwestern Puerto Rico. These metrics included
a 25 m long and 4 m wide (100 m
2
) belt transect deployed along a
randomly selected bearing (0-360
o
). Constant swimming speed was
maintained for a xed duration of fteen minutes, which standardized
the sampling and enabled comparison between sites. The number
of individuals per species was recorded in 5 cm class increments.
Weight (W, referred to herein as biomass) was calculated from fork
length (FL) using equation W= aFL
b
, where a and b are constants for
the allometric growth equation derived from data in Bohnsack and
Bannerot. (1986) and FishBase (Froese and Pauly, 2008). Species
richness was calculated as the number of species per transect (100
m
2
) and abundance was calculated as the total count of individuals
for each species or group per transect. Species were considered
herbivorous if their diet was dominated by plants and piscivorous if
they included any sh in their diet, based on information in Randall
(1967) and FishBase (Froese and Pauly, 2008). Three individual
species were selected: an abundant piscivore (coney, Cephalopholis
fulva), an abundant herbivore (blue tang, Acanthurus coeruleus), and
a specialist damselsh (threespot damselsh, Stegastes planifrons),
which is known to exhibit a strong positive relationship with several
scleractinian coral species (Booth and Beretta, 1994; Gratwicke and
Speight, 2005a).
Figure 2. A transparent subset of the 2001 NOAA benthic habitat map of
Puerto Rico (La Parguera region) overlaying airborne lidar bathymetry. Sig-
nicant within-patch structural heterogeneity was revealed by lidar for both
classied (i.e., “colonized pavement”) and “unclassied” habitat types. The
lidar data will contribute to a future remapping of coral reef ecosystems in
southwestern Puerto Rico.

Journal of Coastal Research, Special Issue No. 53, 2009
Pittman, Costa, and Battista
30
the major classes of terrain parameters as dened by Evans (1980).
To explore the inuence of spatial scale on predictive performance,
the mean morphometric value of the surrounding seascape was
calculated at six spatial scales (Table 2) using a circular moving
window within the focal statistics geoprocessing function of
ArcGIS’s Spatial Analyst (Environmental Systems Research
Institute, Inc.).
To better illustrate and compare the similarities and differences
between morphometrics, cell values were plotted for each
morphometric along the same 500 m horizontal prole. A polyline
was converted into 1 m interval points and intersected with each of
the morphometric surfaces at three spatial scales (4, 50 and 200 m
radius windows) to extract a value for each point along the transect.
These proles were then graphed and visually compared.
In addition, a slope of slope surface (2
nd
derivative of bathymetric
height) was reclassied as high, medium and low relief (Figure
3). To examine congruence in benthic patterns between the slope
of slope map classes and benthic habitat types in NOAA’s benthic
habitat map, the area and proportion of high, medium and low slope
of slope classes was quantied for each habitat type. To test for
Morphometric Unit Description Formula Analytical Tool
Mean
water depth
Meters Average water depth
Σ depth / n grid cells
Focal statistic in ArcGIS
Spatial Analyst
Standard deviation of water
depth
Meters Dispersion of water depth values
about the mean
σ =
Focal statistic in ArcGIS
Spatial Analyst
Surface rugosity
Ratio value Ratio of surface area to planar
area
See Jenness (2002, 2004) Benthic Terrain Mapper
toolbox
http://www.csc.noaa.gov/
products/btm
Slope
Degrees Maximum rate of change in slope
between cell and eight neighbors
tan θ = rise / distance ArcGIS Spatial Analyst’s
slope function
Slope of the slope
Degrees of degrees Maximum rate of maximum slope
change between cell and eight
neighbors
tan θ′ = θ / distance ArcGIS Spatial Analyst’s
slope function
Plan
curvature
1/100 z units
– = convex
+ = concave
Rate of change in curvature
across the surface highlighting
ridges, crests and valleys
-2(D + E) * 100
Where:
D is [(Z4 + Z6)/2 - Z5]/ L
2
E is [(Z2 + Z8)/2 - Z5]/ L
2
Curvature function in
ArcGIS 3D Analyst
Fractal
dimension
(D)
Unitless A measure of surface roughness
with values between 2 and 3
-[log(n1/n2) /
log(L1/L2)] + 1
Where:
n1; n2 is number of
elements
L1; L2 is linear size
FocalD script in LandSerf
2.2 (Wood, 2005)
Table 1. Descriptions and formulae for terrain morphometrics applied to a lidar bathymetry grid for southwestern Puerto Rico.

Journal of Coastal Research, Special Issue No. 53, 2009
Lidar Bathymetry for Predicting Fish and Corals
31
statistical relevance to sh and corals, faunal samples located in the
same slope of slope class were grouped (i.e., high, medium and low)
and tested for signicant difference using Tukey’s HSD (Honestly
Signicant Difference) pairwise comparisons test (Sokal and Rohlf,
1995).
Spatial data management and data availability
The quality of all sh and benthic habitat survey data were assessed
and all survey data were attributed with a unique identication
number and a geographical coordinate to facilitate spatial analyses.
The database includes metadata on eld methods and is available
from the Center for Coastal Monitoring and Assessment (2007).
The lidar bathymetry and reectivity data are also available from
the Center for Coastal Monitoring and Assessment (2008).
Statistical analyses
The distribution of data for each metric was examined and
transformed as necessary to approximate normality for parametric
statistical techniques. In general, species richness data were normally
distributed requiring no data transformation, but abundance and
biomass were skewed toward a higher frequency of low values and
were log transformed to approximate a normal distribution. Pearson
product moment correlation (Sokal and Rohlf, 1995) was used to
examine the strength and direction of association between every pair
of metrics, with emphasis on the magnitude of the coefcient value
rather than hypothesis testing.
Exploration of relative variable importance and development of
predictive models was carried out using a nonparametric statistical
machine learning technique called Stochastic Gradient Boosting
(TreeNet™, Salford Systems, Inc.) (De’ath, 2007; Elith, Leathwick
and Hastie, 2008; Friedman, 2001, 2002). This variant of boosted
regression trees (BRT) optimizes predictive performance through
the iterative development of a large ensemble of small regression
trees constructed from random subsets of the data. Each successive
tree predicts the residuals from the previous tree to gradually
boost the predictive performance of the overall model (Friedman,
2002). Variable selection with TreeNet™ is robust to colinearity
amongst predictors and the presence of irrelevant predictors and
therefore does not require prior variable selection or data reduction.
The procedure was parameterized using default settings, with the
exception that least squares was used as the regression loss function.
A random 20% of the data was assigned for testing model accuracy
and a maximum of 1000 trees was used to nd the best model. The
relative contribution of the predictor variables to the overall patterns
of sh and coral richness and abundance was determined using the
variable importance score generated by TreeNet™. This is based
on the improvements of all splits associated with a given variable
across all trees in the model, then rescaled across all trees so that the
most important variable always gets a score of 100. Other variables
receive scores that were relative to their contribution to the model’s
predictive power. Only variables contributing >70% were recorded.
RESULTS
Associations among lidar-derived and in situ
bathymetrics
Four lidar-derived surface morphometrics (SD of water depth,
mean rugosity, slope and slope of slope) were signicantly (p<0.01)
correlated with chain-and-tape rugosity for hardbottom areas,
although the maximum correlations were relatively weak (max. r =
0.31 - 0.41) (Table 3). Chain-and-tape rugosity was most strongly
correlated with slope of slope. The same four colinear lidar-derived
morphometrics were more strongly correlated (max. r = 0.54 - 0.62,
p<0.01) with variance of quadrat depth (Table 3). In contrast, plan
curvature was negatively correlated with all metrics except mean
water depth. Associations between fractal dimension and other
metrics were highly variable. The directionality and strength of
correlations between metrics were inuenced by the spatial scale at
which the morphometrics were calculated. For example, the strong
association between slope and SD of water depth at relatively ne
spatial scales (<50 m) decoupled progressively with increasing scale
(r = 0.98 at 15 m and r = 0.42 at 300 m). In contrast, rugosity and
slope remained highly correlated (r = 0.89 to 0.9) across all scales.
The majority of the strongest pairwise correlations occurred at the 15
Figure 3. Reclassed 100 m slope of slope raster map using Jenks optimization
(Jenks, 1967) to dene three classes of low (<10), medium (10-20) and high
(>20) slope of slope (unit=degrees of degrees). This resulted in 256 surveys
sites in the low slope of slope areas, 171 in the medium slope of slope areas,
and 79 in the highest slope of slope areas.
Window size
(radius, m)
Area of window
(m²)
15 707
25 1,963
50 7,854
100 31,416
200 125,664
300 282,743
Table 2. Size of circular analysis windows and corresponding sample
unit area (surrounding each faunal survey point) within which surface
heterogeneity was averaged for each morphometric to create multi-scale
derivative surfaces. Cell size of grids = 4 m x 4m or 16 sq. m.

Journal of Coastal Research, Special Issue No. 53, 2009
Pittman, Costa, and Battista
32
m window size (Table 3) and the majority of decouplings occurred
at scales greater than 100 m. Plots of morphometric values along a
single 500 m prole illustrated that morphometric patterns differed
widely across the same highly variable benthic terrain (Figure 4).
Prole similarity was greatest between rugosity, slope, and slope
of the slope and most different for fractal dimension. Slope of the
slope, however, revealed more cell to cell variability and intricacy
along the prole than did slope and rugosity even for the relatively
at sandy areas between 180 and 320 meters along the transect
(Figure 4). The plots also illustrate the effect of increasing the scale
of the moving window, which was to reduce the variability along
a scale gradient, or in other words, to smooth out the values with
increasing scale.
Lidar-derived morphometrics as predictors of sh and
coral distributions
The highest performing boosted regression tree models were for
herbivore biomass (r
2
= 0.72), parrotsh biomass (r
2
= 0.68), coral
species richness (r
2
= 0.65), herbivore richness (r
2
= 0.64) and sh
species richness (r
2
= 0.64) (Table 4). Weakest predictive models
were for coney, grouper and piscivores.
Slope of slope was the single best predictor, with local variability
in the surrounding seascape contributing more to models than the
broadest spatial scales. For instance, the 25 m radius (1,963 m
2
)
slope of slope was an important predictor (>70 % contribution)
in nine of nineteen models; 15 m radius (707 m
2
) slope of slope
was an important predictor in eight of nineteen models; and 100
m (31,416 m
2
) was important in six of nineteen models (Table 4).
Overall, herbivore species richness, abundance and biomass were
best predicted by morphometrics quantied at relatively ne spatial
scales (15 and 25 m radii) and piscivores at broader spatial scales
(25-300 m radii).
Chain-and-tape rugosity as a model predictor
When in situ chain-and-tape rugosity was added to boosted
regression tree models as a predictor, using a subset of all hardbottom
samples only (NB: chain-and-tape rugosity was only measured in
hardbottom areas), it contributed more to the nal model than any
of the lidar metrics for fourteen of nineteen faunal metrics. These
metrics included sh and coral species richness, sh assemblage
biomass and abundance, coral cover, piscivore and herbivore
richness, biomass and abundance, parrotsh biomass, and blue
tang biomass and abundance. For threespot damselsh (Stegastes
planifrons), however, lidar rugosity was a stronger predictor than
chain rugosity at relatively ne spatial scales (≤ 50 m radius). The
partial-dependence plot (Figure 5) generated within TreeNet™
presents a visual interpretation of the dependency between the
response and a single predictor (50 m lidar rugosity), revealing a
nonlinear increase in threespot damselsh abundance with increase
in rugosity.
Mapping slope of slope to predict sh and coral richness
and abundance
When faunal metrics were grouped into high, medium and
low thematic map classes using a reclassed 100 m scale (i.e.,
intermediate scale) slope of slope surface, all faunal metrics were
signicantly higher in areas with medium slope of slope than in
areas with low slope of slope (Table 5). Fish species richness,
coral cover and abundance, and the biomass of threespot damselsh
(Stegastes planifrons) showed progressively higher values (p<0.05),
with increasing slope of slope values (Figure 6 and 7; Table 5). In
contrast, biomass of piscivores, groupers, and coney (Cephalopholis
fulva) were higher in areas with medium slope of slope than in areas
with high slope of slope (Figure 6).
When the area of each slope of slope class was quantied for each
benthic habitat type (Table 6), data showed that 80-92% of softbottom
areas (e.g., mud, sand, and seagrasses) contained low slope of slope.
Hardbottom areas were more topographically heterogeneous, with
some habitat types containing a large proportion of low slope of slope
substrata (i.e., linear reef with 26% low slope of slope and colonized
pavement with 44 % low slope of slope). In contrast, almost 50%
of aggregated patch reefs were high slope of slope. Nine percent of
the previously unclassied area was composed of high slope of slope
and 17% of the area was medium slope of slope (Table 6).
DISCUSSION
Hydrographic lidar data offer great utility in marine ecology
and resource management by providing a detailed and spatially
Table 3. The maximum strength of linear association among pairs of morphometrics applied to lidar bathymetry. Statistically signicance correlations (Pearson,
p<0.01) are shown in bold. The window size (radius in meters) is shown in parentheses.
Lidar surface metrics
Mean
water depth
SD
water depth
Mean
rugosity Slope
Slope
of slope
Plan
curvature
Fractal
dimension
Mean water depth
SD water depth -0.39 (300)
Mean rugosity -0.1 0.93 (15)
Slope -0.09 0.98 (15) 0.91 (all)
Slope of slope 0.07 0.89 (15) 0.86 (200) 0.95 (100)
Plan curvature 0.09 -0.31 (15) -0.67 (300) -0.54 (300) -0.49 (25)
Fractal dimension 0.42 (300) -0.53 (300) -0.20 (25) 0.23 (25) 0.16 (300) -0.39 (200)
In-situ metrics
Chain-tape rugosity 0.07 0.33 (25) 0.31 (100) 0.38 (25) 0.41 (25) -0.17 0.09
Quadrat depth variance -0.04 0.61 (15) 0.54 (25) 0.61 (15) 0.62 (15) -0.25 (25) -0.09

Journal of Coastal Research, Special Issue No. 53, 2009
Lidar Bathymetry for Predicting Fish and Corals
33
continuous representation of benthic structure across broad spatial
scales. This study has shown that morphometric patterns derived
from lidar bathymetry function as good predictors of several
high priority sh and coral metrics commonly used in resource
management planning. By including a wide range of morphometics
we were able to quantitatively compare metric performance and
determine that the slope of slope, a second derivative of bathymetry,
outperformed surface rugosity and all other morphometrics. Slope
of slope demonstrated an ability to capture more of the ecologically
meaningful intricacies that exist in the topographic surface of a
coral reef ecosystem. Furthermore, boosted regression trees are
an appropriate analytical technique for modeling nonlinear faunal-
habitat relationships with interactions between predictors, thus
highlighting the complex ecology that operates across the seascape.
Associations among surface morphometrics and the
inuence of scale
The surface morphometrics selected for this study included
representatives from three of the four major classes of terrain metric
(only aspect was omitted) as dened by Evans (1980). Each class of
metric provided important information on the structure of the benthic
terrain, however, such studies are novel in marine ecology and their
relevance had not previously been evaluated. Our study found
0
5
10
15
20
25
5004003002001000
Slope (degrees)
1.5
2.0
2.5
3.0
5004003002001000
Fractal surface (D)
-20
-16
-12
-8
5004003002001000
Distance along transect (m)
Water depth (m
)
4 m
50 m
200 m
1.00
1.05
1.10
1.15
5004003002001000
Rugosity (planar:surface area
)
-15
-5
5
15
25
5004003002001000
Convexity< > Concavit
y
0
20
40
60
80
5004003002001000
Slope of the slope (degrees of degrees)
0
1
2
3
4
5
500400300200100
SD depth (m)
SD not calculated for 4 m
Figure 4. Proles for individual morphometrics at 1 m intervals along a 500 m transect in the La Parguera region.

Journal of Coastal Research, Special Issue No. 53, 2009
Pittman, Costa, and Battista
34
strong colinearity among several terrain morphometrics, but also
across metric classes (i.e., slope and rugosity), usually indicative of
metric redundancy (Pike, 2001a). Multicolinearity has important
implications for the choice of statistical technique and variable
selection. For example, interpretation of variable importance
in conventional multiple regression models is confounded
by multicolinearity. Multivariate ordination (e.g., principal
components analysis, multidimensional scaling, factor analysis)
can be used to reduce the suite of metrics into a few orthogonal
predictors (McGarigal and McComb, 1995). Alternatively, here
we advocate the use of innovative machine learning algorithms
that employ boosting to optimize variable selection (see De’ath,
2007). As an effective data mining tool, boosted regression trees
were designed to be immune to many of the assumptions that exist
with more conventional regression techniques, including statistical
independence and absence of colinearity, and are particularly good
at nding clear relationships in large and complex ecological data
sets (Elith, Leathwick, and Hastie, 2008, Leathwick et al., 2006).
Interestingly, some pair-wise correlations were only strong at
the nest spatial scales, with colinearity declining with increasing
spatial scale. This is important since scale-dependence in the
behavior of metrics is likely to inuence their contribution to a
model and ultimately the interpretation of results. The majority of
de-couplings occurred at scales greater than 100 m radius, suggesting
a possible threshold effect at the 100 m spatial scale and highlighting
the importance of considering scale. Similarly, Schmidt and
Andrew (2005) found that the scale effect in terrestrial terrain
analysis was non-uniform across space and sometimes anisotropic
(i.e., directionally dependent). These results further emphasize the
importance of a multi-scale exploratory approach in predictive
modeling.
Associations between lidar surfaces and in situ
bathymetric measurements
Lidar surface morphometrics were signicantly and positively
Table 4. The best predictors for models of sh and coral metrics developed using stochastic gradient boosted regression trees (TreeNet™). Maximum number of
trees was set at 1000. Only predictors contributing more than 70 % to the model are shown and are listed in order of their importance.
Response variables
No. trees
used
Best predictor / spatial scale (m radius) Best model r
2
Fish metrics (100 m
2
)
Assemblage
Species richness 875 slope of slope (15, 25 & 100) 0.64
Biomass (g) 593 slope of slope (25, 200 & 15) 0.46
Abundance 614 slope of slope (15) 0.27
Trophic group
Piscivore abundance 174 slope of slope (25), water depth (300),
slope (25)
0.16
Piscivore biomass (g) 195 slope of slope (200), plan curv. (25), SD
depth (100)
0.18
Piscivore richness 277 slope of slope (200), slope of slope
(100), rugosity (25)
0.32
Herbivore abundance 586 slope of slope (15 & 25) 0.57
Herbivore biomass (g) 1000 slope of slope (25 & 15) 0.72
Herbivore richness 485 slope of slope (15 & 25) 0.64
Family/Species groups
Grouper biomass (g) 173 plan curv. (25), slope of slope (100),
water depth (300)
0.22
Parrotsh biomass (g) 613 slope of slope (25 & 15) 0.68
Species
Coney abundance 1000 plan curv. (300) 0.21
Coney biomass (g) 993 plan curv. (300), fractal dimension (200) 0.12
Threespot damselsh abundance 904 rugosity (50), slope (50), slope of slope
(100)
0.48
Threespot damselsh biomass (g) 943 slope of slope (100), rugosity (50), slope
(50)
0.41
Blue tang abundance 871 slope of slope (25), water depth (15),
plan curv. (25)
0.24
Blue tang biomass (g) 694 slope of slope (25, 15 & 100) 0.24
Coral metrics (5 m
2
)
Scleractinian coral species richness 917 slope of slope (25) 0.65
Scleractinian coral cover 258 slope of slope (200) 0.54

Journal of Coastal Research, Special Issue No. 53, 2009
Lidar Bathymetry for Predicting Fish and Corals
35
correlated with in situ measures of topographic complexity, although
most of these correlations were relatively weak. Differences between
the two data capture techniques, particularly the spatial grain and
extent of sampling (centimeters versus meters) may explain the
relatively weak correlations in the present study. A closer concordance
in measurement scale may explain why a stronger linear correlation
was found between lidar morphometrics and quadrat depth variance
than with chain-and-tape rugosity. Water depth measured at each of
ve randomly positioned quadrats along a 25 m long survey transect
likely sampled depth at scales more similar to lidar pulses than did
the chain-and-tape rugosity technique. Interestingly, chain-and-tape
rugosity was most strongly correlated with slope of slope, which
may help to explain the success of this lidar-derived predictor, since
chain-and-tape rugosity is also strongly correlated with a range of
sh metrics (Friedlander and Parrish, 1998; Gratwicke and Speight,
2005a; Wedding et al., 2008).
Utility of lidar metrics for predicting sh and coral
metrics
At local scales, slope of slope in the surrounding seascape was the
most important individual nonlinear predictor in TreeNet™ models
for thirteen of seventeen sh metrics, as well as species richness
and abundance of scleractinian corals. Areas with high slope of
slope indicated high topographic complexity through the measure
of the magnitude of change in slope across an area. Ardron (2002)
measured a similar component of topographic complexity that
quantied the density of slope change and this was also considered
to be ecologically meaningful for sh species richness, although
Ardron’s metric did not account for the steepness of changes in
slope. Prediction strength was higher for community metrics and
herbivores and lower for piscivores and groupers suggesting that
additional environmental variables may inuence their ecological
relationships. Furthermore, the biomass of piscivores and groupers
decreased unexpectedly from areas of medium slope of slope to areas
of high slope of slope. We hypothesize that heavy shing pressure has
removed many large-bodied piscivores (e.g., snappers, groupers and
sharks), thus disrupting the sh distribution patterns. Comparative
studies that include data from regions with lower shing pressure
and more intact piscivore populations are now required.
Overall, herbivorous sh responded to topographic variability at
relatively ne scales and piscivores at broader spatial scales. The
size of a sh, its home range size, and resource requirements will
determine the spatial scales at which species sample their environment
and this information can be used to determine a characteristic scale of
response (Holland, Bert, and Fahrig, 2004; Pittman and McAlpine,
2003; Pittman et al., 2007b). More information is needed to determine
the home range sizes for a range of herbivorous and piscivorous sh
species to examine differences between trophic groups. Fish species
richness was best explained by topographic complexity at scales of
between 15 to 100 m radii (i.e., approximately 700 m
2
to 31,416 m
2
).
Similarly, other studies in the Caribbean have found that benthic
Response variables
Signicant difference amongst
100 m slope of slope classes
√= (p<0.05)
Fish metrics (100 m
2
)
Low & High Low & Medium Medium & High
Assemblage
Species richness
√ √ √
Biomass (g)
√ √
Abundance
√ √
Trophic group
Piscivore abundance
√ √
Piscivore biomass (g)
√ √
Piscivore richness
√ √
Herbivore abundance
√ √
Herbivore biomass (g)
√ √
Herbivore richness
√ √
Family/Species groups
√ √
Grouper biomass (g)
√ √
Parrotsh biomass (g)
√ √
Species
Coney abundance
√ √
Coney biomass (g)
√ √
Threespot damselsh
abundance
√ √ √
Threespot damselsh
biomass (g)
√ √ √
Blue tang abundance
√ √
Blue tang biomass (g)
√ √
Coral metrics (5 m
2
)
Scleractinian coral
species richness
√ √
Scleractinian coral
cover
√ √ √
Table 5. Signicant difference (Tukey HSD, p<0.05) for all faunal metrics
amongst slope of slope map classes (low <10, medium 10-20 and high >20
degrees of degrees).
Log density S. planifrons
0.00
0.02
0.04
0.06
0.08
0.10
0.12
1.02 1.03 1.04 1.05 1.06
LiDAR derived rugosity (50 m radius)
1.01
Figure 5. Partial dependency plot generated from a TreeNet™ boosted regres-
sion tree model showing the pattern of dependence for threespot damselsh
abundance on a single lidar predictor (mean surface rugosity at 50 m radius
scale). A substantial increase in damselsh abundance can be seen with only
a slight increase in rugosity beyond 1 (a at surface) and then a more gradual
increase and non-linear response to areas with moderate to high rugosity.

Journal of Coastal Research, Special Issue No. 53, 2009
Pittman, Costa, and Battista
36
structure within the surrounding 100 m radius (31,416 m
2
) strongly
inuences the distribution patterns for sh species richness and
abundance (Grober-Dunsmore et al., 2008; Pittman et al., 2007a,
b). In a remote region of the Indian Ocean, Purkis, Graham, and
Riegl (2008) found statistically signicant relationships between sh
species richness and surrounding surface rugosity at ≤ 20 m radii.
Although lidar-derived predictors performed well, our preliminary
results for hardbottom areas revealed that chain-and-tape rugosity
outperformed lidar-derived morphometrics for fourteen of the
nineteen faunal metrics. This result corroborates ndings from a
similar studies in Hawaii (Wedding et al., 2008) and Florida (Walker,
Jordan, and Spieler, 2009) that found chain-and-tape rugosity more
0
50
100
150
200
0-10 >10-20 >20
Slope of slope (100 m radius) map class
Mean fish biomass (g/100 m
2
)
Blue tang
Thre espot damse lfish
Groupe r
Cone y
0
5
10
15
20
25
0-10 >10-20 >20
Slope of slope (100 m radius) map class
Mean fish species richness (100 m
2
)
Assemblages
Piscivores
Herbivores
0
1000
2000
3000
4000
5000
0-10 >10-20 >20
Slope of slope (100 m radius) map class
Mean fish biomass (g/100 m
2
)
Assemblages
Piscivores
Herbivores
Parrotfis h
Figure 6. Mean (± SE) for all sh metrics grouped by low (<10), medium
(10-20) and high (>20) slope of slope (unit=degrees of degrees) thematic map
classes derived from lidar bathymetry. Signicant differences between all
class pairs are shown in Table 4.
Type
Slope-Slope
Type
Area (sq m)
Percent
(%)
High 36,104 7.11
Medium 250,204 49.27
Low 221,512 43.62
High 3,583,638 19.00
Medium 7,007,332 37.16
Low 8,268,397 43.84
High 4,463,106 13.46
Medium 15,939,183 48.06
Low 12,763,441 38.48
High 1,214,033 10.68
Medium 7,226,616 63.59
Low 2,923,559 25.73
High 806,210 14.56
Medium 937,227 16.92
Low 3,795,112 68.52
High 9,982 1.62
Medium 111,422 18.12
Low 493,426 80.25
High 603,802 47.27
Medium 437,681 34.26
Low 235,882 18.47
High 463,898 27.60
Medium 941,580 56.02
Low 275,317 16.38
High 174 0.06
Medium 92,293 34.06
Low 178,513 65.88
High 2,509 0.05
Medium 494,853 8.90
Low 5,065,270 91.06
High 982,596 9.01
Medium 3,541,403 32.46
Low 6,386,437 58.54
High 251,961 0.49
Medium 3,545,821 6.96
Low 47,147,023 92.55
High 21,290 28.89
Medium 51,598 70.01
Low 812 1.10
High 5,100,625 9.27
Medium 9,476,059 17.21
Low 40,475,841 73.52
Patch Reef
(Individual)
Colonized
Pavement
Colonized
Pavement with
Sand Channels
Linear Reef
Spur and Groove
Reef
Unknown
Colonized
Bedrock
Reef Rubble
Sand
Scattered
Coral/Rock in
Unconsolidated
Sediment
Seagrass
Macroalgae
Mud
Patch Reef
(Aggregated)
Table 6. Summary data on the amount and proportion of low, medium and
high slope of slope area inside each of the NOAA benthic habitat types.

Journal of Coastal Research, Special Issue No. 53, 2009
Lidar Bathymetry for Predicting Fish and Corals
37
highly correlated with sh species richness and abundance than
lidar-derived rugosity. Therefore, the acquisition of ner scale (<
4 m resolution) continuous bathymetry may facilitate development
of more accurate predictions. Lidar is capable of acquiring higher
resolution bathymetry than used in the present study, although lidar
data are usually obtained for purposes other than ecology (but see
Brock et al., 2004; Brock et al., 2006). For instance, data used here
were collected primarily for the purpose of updating navigational
charts and not specically collected for predicting sh and coral
distributions. Another possible limitation, with respect to sampling
coral abundance and species richness, was that only a 5 m
2
area (5
x 1 m
2
quadrats) was sampled at each site. Higher sample size may
inuence the modeled relationship and hence predictive power; this
component of the coral reef ecosystem monitoring protocol requires
further analyses to determine optimal sample size and sample unit
area.
Lidar bathymetry has clear advantages over conventional thematic
benthic habitat maps since it represents three-dimensional complexity
rather than a two-dimensional patch mosaic. A key disadvantage,
however, is that lidar data are typically used independently of direct
and spatially continuous information on biological community
structure, although it is possible that bathymetric patterns may
function as proxies for biological patterns. Future predictive
modeling studies may benet from an integration of both high
resolution bathymetry and correspondingly high resolution benthic
habitat maps. The signicance of slope of slope as a measure of
topographic complexity for predicting both sh and coral metrics
suggests that incorporating lidar-derived topographic complexity
into benthic habitat maps will not only reveal substantial within-
patch structural heterogeneity, but when combined with nonlinear
modeling techniques and GIS, will help us to identify and map a wide
range of the dominant organisms that exist in coral reef ecosystems.
CONCLUSIONS
This study was an exploratory precursor to the development
and evaluation of spatial predictions for sh and corals. We have
identied a parsimonious set of multi-scale environmental predictors,
readily acquired with a single remote sensing device, and capable of
explaining a large proportion (60-72 %) of the spatial variability in
marine faunal diversity and abundance across a coral reef ecosystem.
Lidar-derived measures of topographic complexity were not strongly
correlated with in situ measures of topographic complexity, but
nevertheless performed very well as predictors for species richness
of sh and scleractinian corals and for the abundance and biomass
of herbivorous sh, including parrotsh. The slope of the slope
outperformed rugosity and emerged as the single best predictor, due
to its ability to capture more of the ne scale topographic complexity
that existed across the coral reef ecosystem. Boosted regression
trees provided an appropriate statistical technique to select the most
ecologically meaningful predictors and to model complex nonlinear
relationships including interactions between predictors.
Future efforts should be directed at the development and
evaluation of spatial predictions through the coupling of lidar
data, boosted regression trees and GIS. Accurate predictive maps
depicting the spatial patterns in sh and coral species richness and
abundance provide valuable baseline data on resource distributions
even for unsurveyed regions. However, since our models left much
variation in faunal metrics unexplained, additional predictors may be
required in order to build a more complex spatial environment with
which to statistically link species and community patterns. Benthic
terrain analysis is a relatively new eld in marine science and will
benet greatly from the integration of concepts and analytical
developments from related elds that have existing expertise and
tools for the analysis of surface structure. Furthermore, a greater
understanding of how continuously varying spatial structure in the
marine environment modies ecological processes may facilitate the
eventual mapping of pattern-process interactions such as hotspots
and cold spots for predation, prey refuge, competition, settlement,
breeding success and size distributions. Supported by judicious eld
and computer simulation experiments, such efforts may provide
many new insights on the ecological signicance of structural
heterogeneity in the marine environment.
ACKNOWLEDGEMENTS
We thank the many scientists that contributed to faunal surveys
in the La Parguera region of southwestern Puerto Rico as part of
NOAA’s National Coral Reef Ecosystem Monitoring Program. We
also thank J. Brock, S. Purkis, K.M. Pittman and two anonymous
reviewers for their helpful comments. This research was funded by
NOAA’s Coral Reef Conservation Program.
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