Predictive mapping of fish species richness across shallow-water seascapes in the Caribbean

Abstract

Effective management of coral reef ecosystems requires accurate, quantitative and spatially explicit information on patterns of species richness at spatial scales relevant to the management process. We combined empirical modelling techniques, remotely sensed data, field observations and GIS to develop a novel multi-scale approach for predicting fish species richness across a compositionally and topographically complex mosaic of marine habitat types in the U.S. Caribbean. First, the performance of three different modelling techniques (multiple linear regression, neural networks and regression trees) was compared using data from southwestern Puerto Rico and evaluated using multiple measures of predictive accuracy. Second, the best performing model was selected. Third, the generality of the best performing model was assessed through application to two geographically distinct coral reef ecosystems in the neighbouring U.S. Virgin Islands. Overall, regression trees outperformed multiple linear regression and neural networks. The best performing regression tree model of fish species richness (high, medium, low classes) in southwestern Puerto Rico exhibited an overall map accuracy of 75%; 83.4% when only high and low species richness areas were evaluated. In agreement with well recognised ecological relationships, areas of high fish species richness were predicted for the most bathymetrically complex areas with high mean rugosity and high bathymetric variance quantified at two different spatial extents (≤0.01 km2). Water depth and the amount of seagrasses and hard-bottom habitat in the seascape were of secondary importance. This model also provided good predictions in two geographically distinct regions indicating a high level of generality in the habitat variables selected. Results indicated that accurate predictions of fish species richness could be achieved in future studies using remotely sensed measures of topographic complexity alone. This integration of empirical modelling techniques with spatial technologies provides an important new tool in support of ecosystem-based management for coral reef ecosystems.

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ecological modelling 20 4 (2007) 9–21
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Predictive mapping of fish species richness across
shallow-water seascapes in the Caribbean
S.J. Pittman∗, J.D. Christensen, C. Caldow, C. Menza, M.E. Monaco
NOAA/NCCOS/CCMA Biogeography Team, 1305 East-West Highway, Silver Spring, MD 20910, USA
article info
Article history:
Received 20 June 2006
Received in revised form
30 November 2006
Accepted 11 December 2006
Published on line 2 February 2007
Keywords:
Bathymetric complexity
Coral reef ecosystems
Caribbean
Fish species richness
Predictive modelling
Seascape structure
abstract
Effective management of coral reef ecosystems requires accurate, quantitative and spa-
tially explicit information on patterns of species richness at spatial scales relevant to the
management process. We combined empirical modelling techniques, remotely sensed data,
field observations and GIS to develop a novel multi-scale approach for predicting fish species
richness across a compositionally and topographically complex mosaic of marine habitat
types in the U.S. Caribbean. First, the performance of three different modelling techniques
(multiple linear regression, neural networks and regression trees) was compared using data
from southwestern Puerto Rico and evaluated using multiple measures of predictive accu-
racy. Second, the best performing model was selected. Third, the generality of the best
performing model was assessed through application to two geographically distinct coral reef
ecosystems in the neighbouring U.S. Virgin Islands. Overall, regression trees outperformed
multiple linear regression and neural networks. The best performing regression tree model
of fish species richness (high, medium, low classes) in southwestern Puerto Rico exhibited an
overall map accuracyof 75%; 83.4% when only high and low species richness areas were eval-
uated. In agreement with well recognised ecological relationships, areas of high fish species
richness were predicted for the most bathymetrically complex areas with high mean rugos-
ity and high bathymetric variance quantified at two different spatial extents (≤0.01km2).
Water depth and the amount of seagrasses and hard-bottom habitat in the seascape were
of secondary importance. This model also provided good predictions in two geographically
distinct regions indicating a high level of generality in the habitat variables selected. Results
indicated that accurate predictions of fish species richness could be achieved in future stud-
ies using remotely sensed measures of topographic complexity alone. This integration of
empirical modelling techniques with spatial technologies provides an important new tool
in support of ecosystem-based management for coral reef ecosystems.
© 2006 Elsevier B.V. All rights reserved.
1. Introduction
In the Caribbean Sea, as in many regions worldwide, human
activity is having adverse impacts on the structure and func-
tion of coral reef ecosystems (Bellwood et al., 2004; Burke and
Maidens, 2004; Wilkinson, 2004; Waddell, 2005). In response,
∗Corresponding author. Tel.: +1 301 713 3028; fax: +1 301 4384.
E-mail address: simon.pittman@noaa.gov (S.J. Pittman).
many initiatives are underway to identify, prioritise and delin-
eate areas of special importance in an effort to mitigate human
impacts. An initial step in this process often involves the
determination of seascapes and biological communities that
are “representative” or “distinctive” (e.g., biodiversity anoma-
lies) or function as “surrogates” for biodiversity (e.g., habitat
0304-3800/$ – see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolmodel.2006.12.017

10 ecological modelling 20 4 (2007) 9–21
types and indicator taxa) (Ward et al., 1999; Roberts et al.,
2002). Areas that support high species richness are usually
given highest priority, particularly when the maintenance and
enhancement of biodiversity is the central goal of the man-
agement strategy (Myers et al., 2000; Roberts et al., 2002).
To support such initiatives, ecologists are increasingly called
upon to provide accurate, quantitative and spatially explicit
information on patterns of species richness at scales rele-
vant to the management process (Vanderklift and Ward, 2000;
Lourie and Vincent, 2004).
For terrestrial environments, ecologists have routinely
developed spatial models based on animal–environment rela-
tionships to predict the diversity and abundance of plants
and animals across the landscape using a wide variety
of linear and non-linear modelling techniques integrated
with a Geographical Information System (GIS) (Guisan and
Zimmermann, 2000; Miller et al., 2004). Modelling tech-
niques have included, but are not limited to, multivariate
ordination (e.g., canonical correspondence analysis), gener-
alised linear models (GLMs), generalised additive models
(GAMs), classification and regression trees (CART), genetic
algorithms, and artificial neural networks (ANNs) (Guisan
and Zimmermann, 2000). Spatial predictive models and
their derivative map products have greatly enhanced the
ability to undertake broad-scale ecological assessments,
prioritise areas for enhanced protection, develop zon-
ing plans, and better understand species-habitat linkages
(Ferrier, 2002; Mac Nally and Fleishman, 2004; Miller et al.,
2004).
In contrast, far fewer attempts have been made to develop
spatial predictions for the diversity and abundance of marine
organisms. The major constraints are related to the acquisi-
tion of environmental data at spatial extents and resolutions
that capture ecologically meaningful habitat structure. For
instance, predicting fish species richness across coral reef
ecosystems presents several logistical and technological chal-
lenges. First, coral reef ecosystems are largely submerged by
water of varying clarity and depth. Second, they are char-
acterised by a mosaic of habitat types that exhibit complex
spatial patterns in vertical and horizontal structure (Robbins
and Bell, 1994; Hatcher, 1997). Third, the fish community of
coral reef ecosystems is exceptionally diverse, varying widely
between habitat types, but with many species using multiple
habitat types through daily home range movements, ontoge-
netic shifts, spawning and non-spawning migrations (Ogden
and Gladfelter, 1983; Parrish, 1989; Christensen et al., 2003;
Pittman and McAlpine, 2003). Finally, relatively little is known
about the influence of seascape structure on either individual
species or multi-species assemblages (Robbins and Bell, 1994).
Recent conceptual and technological developments, how-
ever, have led to an increased availability of remotely sensed
data for coral reef ecosystems (Andr´
efou¨
et et al., 2003; Mumby
et al., 2004a; Riegl and Purkis, 2005; Brock et al., 2006). In addi-
tion, accurate benthic habitat maps and extensive spatially
referenced faunal survey data now provide an unprecedented
opportunity to develop spatial predictive models for coral reef
ecosystems (Monaco et al., 2001; Battista and Monaco, 2004;
Mumby, 2006). In conjunction with the application of advanced
spatial technologies to marine environments, studies from
the emerging field of seascape ecology have provided new
insights into the influence of multi-scale benthic structure on
marine fauna (Turner et al., 1999; Kendall et al., 2003; Pittman
et al., 2004). Field experiments indicate that the composition
and spatial arrangement of the benthic seascape influences
animal movements (Irlandi and Crawford, 1997; Micheli and
Peterson, 1999) and predator–prey interactions (Irlandi, 1994;
Irlandi et al., 1995; Micheli and Peterson, 1999; Hovell and
Fonseca, 2005) and ultimately the distribution and abundance
of species (Turner et al., 1999; Kendall et al., 2003; Pittman et
al., 2004). Such studies suggest that it is possible to predict
spatial patterns of fish species richness with empirical mod-
els based on a relatively small suite of environmental variables
quantified at multiple spatial scales.
In this study, we evaluate the performance of three
empirical modelling techniques (linear multiple regression,
regression trees and artificial neural networks) applied to link
fish species richness data (quantified within 100 m2units) with
benthic habitat structure in the surrounding seascape at mul-
tiple spatial scales (approx. 200–400,000 m2). We then use a GIS
to spatially extend the fish–environment relationship across
mosaics of habitat types (coral reefs, seagrasses, mangroves
and unvegetated sandy sediments) in southwestern Puerto
Rico. This provides a spatially continuous prediction of fish
species richness (presented as high, medium and low number
of species). The generality of the best performing model was
then measured by applying it to two geographically distinct
regions in the neighboring U.S. Virgin Islands.
The key research questions were:
(1) Can we produce useful and accurate predictions for fish
species richness (number of species) using a limited suite
of easily quantified environmental variables?
(2) Which modelling techniques result in the most accurate
spatial predictions?
(3) Can we develop a model with sufficient accuracy and gen-
erality to be applicable to coral reef ecosystems elsewhere
in the region?
2. Methods
2.1. Study area
Three study areas across nearshore waters of the U.S.
Caribbean (Fig. 1) were selected due to their local and national
importance as marine resources: (1) La Parguera, southwest-
ern Puerto Rico (322 km2); (2) Buck Island National Monument,
St. Croix, U.S. Virgin Islands (157 km2); (3) St. John, U.S. Virgin
Islands (206 km2). All three areas exhibit a complex mosaic of
habitat types (coral reefs and other hard substrate, seagrasses,
mangroves and soft sediments), with varying depthand bathy-
metric complexity. In addition, fish communities have been
surveyed extensively across all three sites and accurate ben-
thic habitat maps and bathymetric data are also available for
the region.
2.2. Fish surveys
Fish were identified and counted using daytime underwa-
ter visual surveys along a 25m long ×4 m wide belt transect

ecological modelling 20 4 (2007) 9–21 11
Fig. 1 – Location of the study region within the Caribbean Sea. Study areas are: (1) La Parguera region, southwestern Puerto
Rico (322 km2); (2) Buck Island, St. Croix, U.S. Virgin Islands (157km2); (3) St. John, U.S. Virgin Islands (206 km2).
(100 m2). Survey sites were selected using a stratified ran-
dom sampling design incorporating two strata; hard and soft
benthic habitat types derived from NOAA’s nearshore ben-
thic habitat maps (Kendall et al., 2002). These maps defined
the offshore extent of the sampled area, which corresponds
approximately to the 33 m isobath. A total of 2130 surveys were
conducted between 2000 and 2005, as part of an ongoing mon-
itoring project, with 894 surveys in Puerto Rico, 902 in St. Croix,
U.S. Virgin Islands and 423 in St. John, U.S. Virgin Islands.
2.3. Environmental predictors
Multiple scales of variability in benthic structure represented
by bathymetric variance, mean rugosity and the area and
number of habitat types that surround each fish survey site
were quantified using a GIS. To quantify topographic or bathy-
metric variance, we first constructed bathymetric models
using triangulated interpolated networks (TINs) within a GIS
using depth data acquired from NOAA’s Geophysical Data Sys-
tem (GEODAS) supplemented by depths recorded by SCUBA
divers (NOAA’s Biogeography Team). Vertical accuracy of TIN
models was validated (mean vertical error< 0.3 m) using an
independent set of bathymetric data and then converted
into raster maps (spatial resolution=5m×5m). The standard
deviation (!) of depth was calculated within multiple geomet-
rically increasing spatial extents (cells= 3 ×3 [225 m2]; 5 ×5
[625 m2]; 9 ×9 [2025 m2]; 17 ×17 [7225 m2]; 33 ×33 [27,225 m2];
65 ×65 [105,625 m2]; 129 ×129 [416,025 m2]) within a GIS. This
exploratory multi-scale approach, analogous to a moving-
window calculation (McGarigal and Cushman, 2005), created
a set of raster grids, each with a mosaic of spatial gradients
(Fig. 2). Gradients created using broader spatial extents were
longer and less intense than gradients created using finer spa-
tial extents.
Fig. 2 – Subset from the raster grid of mean rugosity
quantified in the surrounding 7225 m2spatial extent.
Overlaying of the benthic habitat map (black lines) revealed
that spatial gradients of values were created across mosaics
of hard and soft substrata. In this subset, patch reefs with
high rugosity are surrounded by seagrasses with low
rugosity. Raster cell values decrease from the interior of
patch reefs (high rugosity) to the interior of seagrass beds
(low rugosity), with areas of seagrass in close proximity to
patch reefs having elevated values that increase with
increasing proximity to the patch reefs (edge-interior
effects).

12 ecological modelling 20 4 (2007) 9–21
2.3.1. Assigning rugosity to the benthic habitat map
To create a spatial layer that represented differences in
finer-scale topographic complexity between habitat types,
we reclassified NOAA’s nearshore benthic habitat maps with
mean rugosity values measured in situ using an adaptation of
the “chain link method” (Risk, 1972). A six metre chain was laid
over the substratum at two randomly selected positions along
the fish survey transect at all hard-bottom sites. An index of
rugosity [R] was calculated as the ratio of contoured surface
distance to linear distance using R=1−d/l, where dis the con-
toured distance and lis the horizontal distance (6 m) above
the substratum. The maps were then converted into a raster
grid (5 m ×5 m cells) and the distribution of mean values at
multiple spatial extents were quantified with the same spatial
extents as used for bathymetric variance.
2.3.2. Quantifying amount of habitat types
The amount of hard substratum, amount of seagrass and the
number of habitat types in the seascapes surrounding each
sample site were calculated from raster versions of NOAA’s
nearshore benthic habitat maps, with the same spatial res-
olution and extents as used for bathymetric variance and
mean rugosity.These maps were constructed with a minimum
mapping unit (MMU) of 4000 m2and provided a hierarchical
classification system from which the “Type” level provided a
maximum of 13 habitat classes. For each fish survey site, an
environmental variable that represented water depth was also
created by extracting intersecting data from the bathymetric
model.
2.4. Development of predictive models
Multiple linear regression, regression trees and artificial
neural networks were used to model animal–environment
relationships. These techniques have been widely demon-
strated to have great utility in predicting animal–environment
relationships in both aquatic and terrestrial systems. Com-
parisons of modelling techniques, however, have often led
to equivocal results regarding the suitability of a single tech-
nique, occasionally with only very slight differences in overall
predictive accuracy (Moisen and Frescino, 2002). Multiple
linear regression is an extensively tested and widely under-
stood technique that has often performed well in modelling
ecological relationships, but is limited to a global linear fit
and assumptions of normality and homoscedasticity in the
response data (Guisan and Zimmermann, 2000). In contrast,
artificial neural networks are capable of detecting complex
non-linear relationships, can outperform linear regression,
but are more complex making the relative importance of indi-
vidual predictors more difficult to assess (Lek et al., 1996).
Regression trees have also been demonstrated to be an effec-
tive technique for uncovering linear and non-linear structure
in data and are more simple to interpret than artificial neu-
ral networks since they provide a set of binary decision rules
(De’ath and Fabricius, 2000).
2.4.1. Multiple linear regression
To reduce skewness and kurtosis the response data were first
square-root transformed. To ensure parsimony in model con-
struction, the strongest linear predictors that were also the
least co-linear were selected by first using a forward stepwise
procedure and by then constructing a separate correlation
matrix to determine multi-colinearity amongst predictors.
Models with the highest adjusted R2and lowest Akaike’s
Information Criterion (AIC) were selected and the formulae
describing the relationships between the response variable
(fish species richness) and the predictor variables (benthic
habitat structure) were applied in a GIS to generate a spatially
continuous prediction of fish species richness.
2.4.2. Artificial neural networks
Feed-forward neural networks with a supervised learning
algorithm for the backward propagation of errors were applied
to untransformed response and predictor variables. This type
of neural network is the most frequently used in ecology (see
algorithm in Lek and Gu´
egan, 1999). We used a single hidden
layer and limited the number of hidden nodes to between 1
and 15 in order to minimise over-fit and maximise our gen-
eralisation performance. An over-fit penalty of either 0.01 or
0.001 was used, with variable number of tours (20–40) and
variable number of iterations (50–100) on each tour. Different
random starting values were used to avoid local minima. In
addition, 10-fold cross-validation was used to find models that
generalised well (Efron and Tibshirani, 1993). This procedure
involves subdividing the data into 10 groups, 9 of which train
the algorithm with the other being used as a validation data
set. The process is then repeated so that every data point acts
as both training data and validation data. The true error is
calculated as the average error from all trials. Formulae and
predictions were saved for the best fitting model based on the
highest adjusted R2, combined with a low over-fit penalty and
the smallest generalisation error (root mean squared error).
2.4.3. Regression trees
The regression tree procedure was applied within S-PLUS v7
(Insightful Corp.) using untransformed response and predictor
variables. Regression trees are built through binary recur-
sive partitioning (Breiman et al., 1984) using an algorithm
that repeatedly splits the response data into two indepen-
dent groups based on the association with individual predictor
variables. The process creates a hierarchical tree of decision
rules useful for predicting a continuous response variable. To
find the optimal tree size and to compensate for over-fitting,
a sequence of trees of differing complexity were generated
using 10-fold cross-validation. The smallest tree that was also
within one standard error of the tree with the minimum error
rate was selected as the final model (Venables and Ripley,
2002). This ensured that the final model neither fitted pre-
cisely to the specific data set, nor was so general as to render
its predictions meaningless. To create the spatial predictive
model of fish species richness, the final regression tree model
was applied to the spatial data layers within a GIS using Stat-
Mod Zone (Garrard, 2002), a custom-built GIS extension that
interfaces with S-PLUS.
2.5. Spatial autocorrelation
Spatial autocorrelation of the response variable was tested
using Moran’s IIndex for both the raw values and the eco-
logical model residuals. The Moran’s IIndex ranges from −1

ecological modelling 20 4 (2007) 9–21 13
(indicating strong negative spatial autocorrelation) to +1 (indi-
cating strong positive spatial autocorrelation). In addition,
semi-variograms were examined to assess the relationship
between species richness covariance and increasing distance
between survey points (lag distance).
2.6. Assessment of model accuracy
Predictive accuracy of the models of fish species richness
for southwestern Puerto Rico produced from multiple lin-
ear regression, artificial neural networks and regression trees
were assessed using a random 20% of all fish surveys (162
samples) and four widely used performance measures. First,
coefficients of determination (R2) were used to measure the
strength of the linear association between raw observed data
and raw predicted data. Second, predictive maps were re-
classed by terciles (equal interval thirds) to produce three
ordered mutually exclusive map classes (high, medium and
low) of fish species richness. Receiver-operating characteris-
tic curves (ROC) were constructed for each class, and the area
under the curve (AUC) was used to compare prediction perfor-
mance (Fielding and Bell, 1997). We adopted the interpretation
offered by Hosmer and Lemeshow (2000), whereby an AUC
value of 0.7–0.8 is considered an acceptable prediction; 0.8–0.9
is excellent and >0.9 is outstanding. A value of 0.5 is defined as
the predictive ability that could be achieved by chance alone.
Third, we used Cohen’s Kappa statistic "(Cohen, 1960)
to measure the degree of agreement between predicted and
observed data and to test whether the prediction exceeded
one that could be produced by chance alone. "=1 if perfect
agreement; "= 0 if no more agreement than by chance alone.
Landis and Koch (1977) offer the following ranges of agreement
for the Kappa statistic: poor = "< 0.4; good = "> 0.4–0.75; excel-
lent = "> 0.75. Finally, error or confusion matrices were used to
compare “Users Accuracy” and “Producers Accuracy” for each
mapped tercile of the response variable, as well as forming
an additional measure of the total accuracy of the predictive
maps (Lillesand and Kiefer, 1994). Models were then assessed
based not only on overall prediction accuracy using all per-
formance measures, but also on their ability to discriminate
areas of high, medium and low fish species richness.
2.7. Assessment of model generality
The generality of the best model for predicting fish species
richness was tested through its application to geographi-
cally distinct shallow-water coral reef ecosystems in the U.S.
Caribbean. The same suite of model performance measures
was used to evaluate generality. For each region, a random
20% of all available fish surveys were set aside for accuracy
assessment (182 from Buck Island, St. Croix, U.S.V.I. and 78 for
St. John, U.S.V.I.).
2.8. Prediction error by habitat type
In order to understand the pattern of errors (direction and
magnitude) and the relationship between error and habitat
heterogeneity in the study area, we examined the results of
model validation for each of the main habitat types includ-
ing: (1) the proportion of validation data that were correctly
classified (high, medium or low fish species richness); (2) the
proportion of validation data that were either underestimated
by one or two classes or overestimated by one or two classes.
3. Results
3.1. Spatial autocorrelation
Species richness data exhibited statistically significant spa-
tial autocorrelation (Moran’s IIndex = 0.5, p< 0.05), although
visual assessment of semi-variograms indicated that spatial
autocorrelation was relatively low, with high variance at small
distances. Analysis of the residuals from the final regression
tree model, however, showed that spatial autocorrelation was
non-significant in the residuals (Moran’s IIndex = 0.15, p> 0.1)
and therefore the spatial autocorrelation that was present
appears unlikely to have significantly biased the model results.
3.2. Assessment of model accuracy
All modelling techniques performed significantly better than
random ("≥0, AUC ≥0.5). Only regression trees and neural
networks, however, provided fish species richness models
with “good” overall performance ("≥0.4) (Table 1). Regres-
sion trees outperformed neural networks, with the final tree
model having a total map accuracy of 74.7% and an AUC value
indicative of a borderline “excellent” prediction (AUC = 0.79).
Regression trees also predicted the spatial distribution of both
high fish species richness and low fish species richness classes
with high accuracy. However, the ability to accurately pre-
dict the spatial patterns of high fish species richness and low
fish species richness areas varied widely amongst all mod-
elling techniques. Neural networks performed well for low
fish species richness, but poorly for high species richness. For
multiple linear regression, the opposite occurred, with high
Table 1 – Model performance indicators for predictive models of fish species richness for southwestern Puerto Rico
Models Performance measures
R2"AUC Map accuracy (%) Mean
Linear regression 0.39 0.30 0.73 54.3 0.49
Regression trees 0.55 0.54 0.79 74.7 0.64
Neural network 0.52 0.43 0.78 66.7 0.60
Total map accuracy> 70% is bold.

14 ecological modelling 20 4 (2007) 9–21
Table 2 – Model performance indicators by map class for predictive models of fish species richness for southwestern
Puerto Rico
Linear regression
(map class)
Regression trees
(map class)
Neural network
(map class)
Low Medium High Low Medium High Low Medium High
AUC value 0.73 0.61 0.89 0.86 0.65 0.85 0.85 0.71 0.79
Users accuracy (%) 60.3 33.3 87.185.713.6 81 87.530.5 52.6
Users accuracy> 70% is bold. AUC > 0.8 is bold.
accuracy for low species richness and lower accuracy for high
fish species richness areas (Table 2). When the medium fish
species richness class was excluded from the accuracy assess-
ment (using low and high fish species richness classes only),
the overall map accuracy was higher for all regions (Puerto
Rico 83.4%; St. John 86.7%; St. Croix 76.4%).
3.3. Attributes of the final model
The initial regression tree contained 12 terminal nodes and
used 7 of the 36 available predictors including mean rugos-
ity at intermediate (∼7000 m2) and broad spatial extents
(∼400,000 m2), bathymetric variance at two relatively fine spa-
tial extents (225 m2and ∼2000 m2), water depth; the amount
of seagrass and hard-bottom habitat types quantified at the
broadest spatial extents (∼400,000 m2). Mean rugosity quan-
tified at an intermediate scale (∼7000 m2) and bathymetric
variance quantified at a more local scale (∼2000 m2) explained
the largest proportion of variance in fish species richness
(Fig. 3). Water depth contributed approximately 5% to the
explained variance. The amount of all hard-bottom habitat
types and the amount of seagrasses in the seascape were
most influential at the broadest spatial extents, although both
contributed very little to the total explained variance. The
remaining 28 predictors each explained less than 2% of the
variance and were not selected for tree construction by the
recursive partitioning algorithm.
Pruning of the original regression tree through cross-
validation produced a final tree consisting of the two most
important predictors and four terminal nodes that were used
to predict the response variable (Fig.4). The final tree explained
55.1% of the total variation in fish species richness for south-
western Puerto Rico. The first split was based on mean rugosity
quantified at an intermediate spatial extent (∼7000 m2). The
algorithm calculated a threshold value of 11.8 (index of rugos-
ity) to separate less rugose soft-bottom areas (seagrass, sand,
mud and scattered coral) from more rugose hard-bottom areas
(colonized pavement with sand channels, linear reef, colo-
nized pavement and patch reefs). The low and high rugosity
habitat types were then each split into two groups with higher
fish species richness predicted for the more bathymetrically
variable areas. Mean rugosity alone accounted for 64.1% of the
explained variation in the final model.
3.4. Association between mean rugosity and fish
species richness
Fish species richness exhibited a strong positive correla-
tion with mean rugosity (Spearman rank correlation r= 0.73,
p≤0.001). All soft sediment habitat types (seagrass, sand,
Fig. 3 – Contribution of predictor variables to overall predictive power for the original regression tree (before pruning) for
Puerto Rico. Mean rugosity quantified at a 7225 m2spatial extent and bathymetric variance quantified at a spatial extent of
2025 m2explained the largest proportion of variation in fish species richness. Variables that contributed less than 2% to
explained deviance are not shown.

ecological modelling 20 4 (2007) 9–21 15
Fig. 4 – Final regression tree model for fish species richness
across coral reef ecosystems of southwestern Puerto Rico.
This model was also used to predict fish species richness
for Buck Island, St. Croix (U.S. Virgin Islands) and St. John
(U.S. Virgin Island). The splitting variable and its threshold
value are shown for each branch (horizontal lines). The four
terminal nodes show the predicted values.
mud/macroalgae and scattered coral in sandy sediments) had
significantly lower rugosity than hard-bottom habitat types
(colonised pavement and sand channels, colonized pavement,
linear reef and patch reef) (Kruskal–Wallis F= 356.8, p≤0.0001)
(Fig. 5). Similarly, all soft sediment habitat types, except
scattered coral in sand, had significantly lower species rich-
ness than hard-bottom habitat types (Kruskal–Wallis F= 475.9,
p≤0.0001). Pairs of habitat types within soft and hard cat-
egories, however, were not significantly different in mean
rugosity or fish species richness (p≥0.05).
3.5. Assessment of model generality
The predictive maps provided a visual and spatially explicit
application of the model outputs (Figs. 6 and 7). Comparison
of predictive maps with benthic habitat maps revealed that
predictions supported the observed relationship between the
main benthic habitat types and fish species richness. That is,
generally, hard-bottom habitats had higher species richness
than vegetated habitats or soft sediments. Results suggest,
however, that fish species richness is highly variable across
the region, even within a single habitat type, although this
heterogeneity is not represented by patterns of substratum
variability captured by the benthic habitat map. Instead, the
predictions show gradients in fish species richness across
habitat boundaries. Furthermore, mangrove edges were also
elevated in regions within close proximity to topographically
complex hard-bottom substratum.
Application of the final regression tree model developed
for southwestern Puerto Rico to Buck Island, St. Croix and St.
John produced two additional predictive maps of fish species
richness (Fig. 7). The Puerto Rico model provided “good” pre-
dictions for both St. Croix and St. John, with an overall map
accuracy of 70.5% for St. John and 67.6% for Buck Island, St.
Croix (Table 3). The mean value of all performance measures
for St. John equaled that for Puerto Rico, but accuracy exceeded
the Puerto Rico model for prediction of both high and low
species richness areas that were considered “outstanding”
based on AUC values (>0.9) (Table 4). For St. Croix, predic-
tion of low species richness areas exceeded Puerto Rico, but
prediction of high species richness areas was less accurate
(Table 4).
3.6. Prediction error by habitat type
Between 60 and 100% of the validation data collected from
almost all habitat types from Puerto Rico, St. Croix and St.
John were classified correctly (Fig. 8). In Puerto Rico, however,
fish species richness predictions for the map class of scattered
coral and sand was equally likely to be correctly classified as
underestimated or overestimated. The largest magnitude of
errors in the Puerto Rico model occurred in mangroves, with
fish species richness markedly underestimated. For St. Croix,
fish species richness was overestimated at a cluster of six sites
over sand and for St. John, fish species richness was underes-
timated for the majority of reef rubble sites.
Fig. 5 – Means and standard errors for (A) index of rugosity,
and (B) mean fish species richness for the most abundant
habitat types mapped in southwestern Puerto Rico. NB: no
rugosity recorded for mangroves.

16 ecological modelling 20 4 (2007) 9–21
Fig. 6 – Map (A) predicted fish species richness model for southwestern Puerto Rico derived from the final regression tree. (1)
Margarita Reef; (2) Media Luna; (3) La Parguera are shown. Inset area shows (B) the benthic habitat map classes, and (C) a
close up of the fish species richness prediction with validation data indicating either a correct classification or a
misclassification. Markedly more heterogeneity is represented in the prediction than is present in the benthic habitat map.
Table 3 – Model performance for fish species richness predictions using the highest performing model (regression trees)
from Puerto Rico applied to the U.S. Virgin Island data
Regions Performance measures
R2"AUC Map accuracy (%) Mean
St. John 0.56 0.53 0.79 70.5 64.6
St. Croix 0.48 0.46 0.76 67.6 59.4
Total map accuracy> 70% is bold.
Table 4 – Model performance by map class for fish species richness predictions using the highest performing model from
Puerto Rico applied to the U.S. Virgin Island
St. John (map class) St. Croix (map class)
Low Medium High Low Medium High
AUC value 0.91 0.56 0.90 0.81 0.68 0.79
Users accuracy (%) 87 16.7 86.587 20 65.9
Users accuracy> 70% is bold. AUC > 0.8 is bold.

ecological modelling 20 4 (2007) 9–21 17
Fig. 7 – Map (A) predicted fish species richness model for
Buck Island, St. Croix, U.S. Virgin Islands derived from the
final regression tree model developed for southwestern
Puerto Rico. (1) Buck Island; (2) Green Cay Marina; (3) Tague
Bay are shown. Map (B) Predicted fish species richness
model for nearshore St. John, U.S. Virgin Islands derived
from the final regression tree model developed for
southwestern Puerto Rico. (1) Cruz Bay; (2) Reef Bay; (3)
Coral Bay are shown.
4. Discussion
This study demonstrates that good spatial predictions of
fish species richness for coral reef ecosystems can be pro-
duced using just two components of topographic complexity
(bathymetric variance and habitat rugosity) quantified in the
surrounding seascape at different spatial scales.
4.1. Linking fish to their environment at multiple
spatial scales
The positive relationship between topographic complexity
and species richness has been attributed to the increase in
surface area of the substratum and usually an increase in the
availability of refuge and the variety of microhabitats avail-
able to marine fauna, thereby allowing for enhanced niche
partitioning (MacArthur and Levins, 1964). The importance of
surface topography or rugosity in supporting high fish species
richness in coral reef ecosystems has been well documented
at relatively fine spatial scales (<25m) (e.g., Luckhurst and
Luckhurst, 1978; Friedlander and Parrish, 1998; Lirman, 1999;
Gratwicke and Speight, 2005). Using multiple linear regression,
Gratwicke and Speight (2005) were able to explain 71% of vari-
ation in fish species richness using a simple index of habitat
complexity composed of relatively fine-scale measurements
Fig. 8 – Proportion of correctly predicted cells and the
proportion and magnitude of misclassified cells for (A)
Southwestern Puerto Rico; (B) Buck Island, St. Croix (U.S.
Virgin Islands); (C) St. John, U.S. Virgin Islands. Data are
shown only for habitat types with three or more validation
samples. Grey, correctly classified; black, underestimated
species richness by 2 classes; diagonal lines, overestimated
species richness by two classes; white, underestimated
species richness by 1 class; horizontal lines, overestimated
species richness by 1 class.

18 ecological modelling 20 4 (2007) 9–21
of structural attributes, with rugosity alone explaining 52%.
Few studies, however, have quantified topographic complexity
at multiple and broad spatial scales (hundreds to thousands
metres) (Ardron, 2002).
In the absence of any a priori information to determine
which spatial scales were most important, we developed
an exploratory approach by measuring environmental het-
erogeneity at a number of scales and then let the form of
the relationship between predictor and response determine
which scales were most influential. The application of a multi-
scale “moving-window” approach resulted in the creation of
mosaics of spatial gradients that were used as predictors
of fish species richness. These gradients did not represent
physical structure as actually observed across the coral reef
ecosystem, but instead, represented the influence that phys-
ical structure has on the seascape and species distributions
beyond the boundaries of the patches delineated in the ben-
thic habitat maps. For the quantification of mean rugosity,
our approach incorporated spatial patterns within the benthic
habitat map, but was not confined to the inherent categorical
boundary structure (see Fig. 2). For instance, the intermedi-
ate scale mean rugosity grid (∼7000 m2) provided gradients
that extended approximately 50–100 m around patches (Fig. 2),
which represented the transition of one habitat type into
another, and thus captured the steep gradient in fish species
richness that can occur as a result of an edge effect. Field
studies confirm the existence of gradients and edge effects
particularly for species of benthic feeding fish utilising coral
reef ecosystems. Several species which utilise the reef for
refuge, often are observed foraging on adjacent soft-bottom
habitats (Parrish, 1989; Kendall et al., 2003). Furthermore,
Dorenbosch et al. (2005) suggested that changes in density
of several reef-associated fish observed at increasing distance
from a patch reef represented an edge effect, with densities
on seagrass beds near patch reef edges higher than on the
seagrass beds farther away. The creation of gradient structure
presents an important advance beyond the simple use of a
categorical map in landscape ecology and incorporates mean-
ingful environmental variability that is not usually considered
in the construction of categorical habitat maps. In addition,
our model of fish species richness for southwestern Puerto
Rico also predicted elevated fish species richness for the edges
of mangroves that were in close proximity to topographically
complex areas (coral reefs). This may result from an increase
in multi-habitat using fish species that use mangroves as part
of an series of ontogenetic habitat shifts between seagrasses
and coral reefs (Mumby et al., 2004b).
Another potentially important form of heterogeneity
is habitat richness, which in terrestrial landscapes has
often been linked to species richness (e.g., MacArthur and
MacArthur, 1961; Ricklefs and Schluter, 1993; Kerr, 2001). In
marine systems, however, habitat richness as a landscape
attribute has rarely been quantified or linked to species
richness (Pittman et al., 2004). Regardless of this dearth of
information, habitat richness has been considered as a poten-
tially useful criterion in the selection of MPA’s (Ward et al.,
1999), although our results indicate that habitat richness was
not a relevant predictor of fish species richness. This may be a
scale dependent result or related to the relatively coarse reso-
lution of the benthic habitat map. Alternatively, it may relate
to the fact that habitat richness, defined as a simple tally of
number of habitat types does not account for the variation in
the type of habitat present and functional linkages between
habitat types such as complementation or supplementation
effects (sensu Dunning et al., 1992). New measures of diversity
such as taxonomic diversity (Izs´
ak and Papp, 2000) may allow
us to quantify the diversity of mosaics based on differentiation
of more functionally different habitat types.
4.2. Evaluation of modelling methods
Regression trees effectively modelled much of the spatial
variability in fish species richness and outperformed other
methods as this method was able to both select a relevant
set of predictor variables and to make accurate predictions
based on judicious subdivision of the data space. The split-
ting rules developed by the recursive partitioning algorithm
split the data at values that were ecologically meaningful
with regard to the demonstrated thresholds in the relation-
ship between fish species richness and habitat rugosity. For
instance, the first split separated hard-bottom habitat types
with significantly higher rugosity and fish species richness
from soft-bottom types with lower rugosity and fish species
richness. Analysis of the model residuals showed that errors
from the final regression tree models were spatially random,
which provided an additional measure of model goodness-of-
fit. This further demonstrates the utility of regression trees
combined with GIS as a powerful exploratory modelling tool
for developing spatial predictions in ecology. The compari-
son of performance between modelling methods suggested
that relationships between fish species richness and environ-
mental variability across a spatially heterogeneous habitat
mosaic likely encompasses components of both linearity and
non-linearity. Multiple linear regression provided the most
accurate predictions for the high species richness class, but
performed poorly for the low and medium species richness
class. It appears that significantly more non-linearity is added
when modelling across mosaics of soft and hard substratum
types and overall, the more flexible techniques that can han-
dle non-linearity performed better. Non-linearity may occur
due to the interaction between bathymetric complexity and
other variables including water depth. Modelling techniques
that can incorporate multiple interactions between predictor
variables may reveal additional non-linear complexity in the
relationship between fish species richness and the surround-
ing environment.
4.3. Applications to marine resource management
Marine resource managers are often faced with limited and
uncertain ecological information on which to base their deci-
sions. For coral reef ecosystems, few geographic regions have
sufficient spatial data on the distribution of species, commu-
nities and habitat types to adequately identify and prioritise
sites for MPA designation or to re-evaluate existing MPA
boundaries. Even less is known about the ecological processes
that maintain biological diversity and the extent of connec-
tivity across habitat mosaics and at broader spatial scales
between regions (Vanderklift and Ward, 2000). Spatial predic-
tions of species richness provide a proactive conservation tool

ecological modelling 20 4 (2007) 9–21 19
that contributes to a more informed process in MPA site selec-
tion and evaluation and provides a cost-effective addition to
the rapidly growing toolbox in support of ecosystem-based
management.
The strength of the relationship between fish species
richness and topographic complexity suggests that in the
absence of benthic habitat maps, topographic complexity may
be a useful surrogate for predicting spatial patterns of fish
species richness. Work is currently underway that will deter-
mine whether useful predictors for fish communities can be
developed using only high resolution in-water acoustic sen-
sors (multi-beam, side-scan sensors, etc.) and airborne laser
altimetry (lidar-light detection and ranging) (Kuffner et al., in
press). This would facilitate predictive modelling over broad
spatial scales for even remote areas in a rapid and cost-
effective way.
The methods and results presented here allow for the iden-
tification of species richness hotspot and coldspots, which can
be used in the decision-making process for MPA site selec-
tion and evaluation of existing management areas. Overlaying
boundaries of designated or potential sites would allow com-
parison between the proportion of high, low and medium
species richness areas that exist within and outside the
MPA. Furthermore, if high diversity areas for fish species
coincide with high diversity areas for other phyla, predic-
tions of fish species richness may function as surrogates for
broader ecosystem biodiversity. The spatial coincidence of
high species richness across phyla has been documented in
some terrestrial regions (Prendergast et al., 1993), yet little
is known about the performance of fish as indicator taxon
for ecosystem diversity. However, caution is advised when
developing management strategies based solely on the most
popular selection criteria (i.e., species richness), and using
only one of a limited number of taxa (i.e., fish) (Ward et
al., 1999). Furthermore, when applying diversity “hotspot”
maps, it is important to understand that many fish are highly
mobile and may use multiple habitats, such that “hotspots”
are likely to be maintained through functional interactions
with adjacent resources in the surrounding seascape. Selec-
tion of spatial scales for management, therefore, should focus
on spatial extents that are functionally meaningful and these
units may be determined by the study of movement patterns
and functional connectivity across the seascape (Pittman
and McAlpine, 2003). Community composition also provides
important information that may support decision-making for
placement of MPA’s, but was not incorporated in our mod-
els. For example, protection of two areas of equally high fish
species richness, but with identical species composition (high
assemblage similarity) may not necessarily protect the highest
regional species diversity.
4.4. Limitations of the approach and sources of error
Analysis of the model residuals indicated that the models
were not fully able to fit the interactions between local species
richness and the environment. This could be due to the
high structural heterogeneity that existed, but that was not
captured by our variables of topographic complexity, habitat
richness and the amount of seagrasses and hard-bottom habi-
tat types in the seascape. For instance, a patch reef may have
high topographic complexity, but may be comprised of a sin-
gle species of coral or many species, that can be either living
or dead or some combination of these variables. For seagrass
beds, blade height, seagrass species composition and patch-
iness of the bed are all important attributes (Pittman et al.,
2004) that may be used to refine future predictions.
Errors in both the response variable and the environ-
mental predictors are likely to account for some of the
misclassifications that occurred. Bathymetric standard devi-
ation represented the amount of variation about the mean
for a defined spatial extent, but was limited to depth sound-
ing data (GEODAS) captured by a variety of different methods
with varying geo-positional accuracies. The spatial resolution
of the environmental data may also have resulted in prediction
error. For instance, the habitat map with a minimum map-
ping unit of 4000 m2may have resulted in some patches being
unrepresented or instead classified as sand or some other
habitat type. Benthic habitat maps are rarely constructed
specifically to capture the multiple scales of functional het-
erogeneity for fish communities and their utility in linking to
spatial patterns in fish assemblages must be carefully eval-
uated. Several of these errors can now be easily overcome
or at least minimised with improvements in geo-positioning
technologies, advances in remote sensing such as lidar and
new information generated from studies with a multi-scale
seascape ecology perspective. By developing a multi-scale
analytical approach, evaluatingthe sources of error and identi-
fying the most influential variables (and the relevant scales of
influence), this study provides an important first step towards
the development of future spatial predictions of species rich-
ness that can incorporate higher resolution data for coral reef
ecosystems.
Acknowledgements
We thank the many scientists that contributed to the collec-
tion of NOAA field data and extend gratitude to our partners
including NOAA’s Coral Reef Conservation Program; National
Park Service; U.S. Geological Survey and the University of
Puerto Rico. Comments from Christopher Jeffrey, Matthew
Kendall and two anonymous reviewers helped improve the
manuscript.
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