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\begin{document}

\title{Predicting Ecosystem Pattern across Landscapes}



\author[1]{Sean Basquill}%
\author[1]{Shawn Leroux}%
\affil[1]{Memorial University of Newfoundland}%


\vspace{-1em}



  
  \date{May 21, 2024}


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\selectlanguage{english}
\begin{abstract}
Predictive modelling is fundamental to ecology and essential for
objective biodiversity assessment. However, while predictive
biodiversity models are generally well-developed, models for predicting
patterns within and among ecosystems have not been adequately
operationalized. We contend the scarcity of such models marks a
concerning gap in the scientific community's ability to make ecosystem
predictions across landscapes, and more broadly for supporting the
conservation of biodiversity and ecosystem functions. We propose
ecosystem spatial pattern models (ESPM) to fill this gap in modelling
capacity. Under our approach to ESPM, spatial patterns of ecosystem
properties are the basis for resolving ecosystem organization at local
and landscape extents. Our integrative modelling framework differs from
others in that it accords biotic and abiotic constituents equally, based
on with their joint mechanistic influence on ecosystem dynamics.
Development of ESPM is especially timely for ecosystem assessment is
undergoing a contemporary groundswell, as scientists and conservation
groups propose ambitious targets for ecosystem conservation and
restoration.%
\end{abstract}%



\sloppy


\emph{Abstract}

Predictive modelling is fundamental to ecology and essential for
objective biodiversity assessment. However, while predictive
biodiversity models are generally well-developed, models for predicting
patterns within and among ecosystems have not been adequately
operationalized. We contend the scarcity of such models marks a
concerning gap in the scientific community's ability to make ecosystem
predictions across landscapes, and more broadly for supporting the
conservation of biodiversity and ecosystem functions. We propose
ecosystem spatial pattern models (ESPM) to fill this gap in modelling
capacity. Under our approach to ESPM, spatial patterns of ecosystem
properties are the basis for resolving ecosystem organization at local
and landscape extents. Our integrative modelling framework differs from
others in that it accords biotic and abiotic constituents equally, based
on with their joint mechanistic influence on ecosystem dynamics.
Development of ESPM is especially timely for ecosystem assessment is
undergoing a contemporary groundswell, as scientists and conservation
groups propose ambitious targets for ecosystem conservation and
restoration.

\emph{}

\emph{Introduction}

Predictive modelling is essential for understanding the natural world
and for making informed decisions about current and future states.
Dramatic biodiversity shifts, compounded with the poorly understood
ecological consequences of emerging climatic regimes, have served as a
clarion call for more predictive conservation science. These shifts have
also helped to reaffirm the broader role of prediction in basic and
applied ecology (Houlahan et al. 2017). However, while predictive
biodiversity models (e.g., species or community distribution models) are
generally well developed, and frequently employed to inform conservation
decision-making, these advancements have not been fully realized in
predictive spatial models of ecosystems (Fulton et al 2019, Geary et al
2020, Halvorsen et al 2020, Simensen et al 2020). Spatially explicit
models are required for predicting intra- (e.g., structure, composition,
function, spatial properties) and inter-ecosystem (e.g., identity,
spatial properties) patterns across landscapes. The scarcity of such
models hinders the scientific community's ability to make objective
ecosystem predictions and near-term forecasts at sub-global scales.

Predictive spatial models have emerged as the principal tool to
understand biodiversity patterns, and to forecast the effects of
ecological change (Ara\selectlanguage{ngerman}újo et al 2019). While the scope of these models
has progressively broadened to address multiple components of
biodiversity, biotic predictions are by far the most common application
(Pollock et al 2020). In their review of spatially explicit biodiversity
models, Zurell et al (2022) report 80\% of published models are focused
on species distributions. A smaller percentage of predictive spatial
models address higher order (e.g., communities) components of
biodiversity but these too are, almost exclusively, biotic entities
(Pollock et al 2020, Zurell et al 2022). For example, joint distribution
and generalized dissimilarity models of communities (e.g., community
distribution, diversity, or interactions) are common extensions of
predictive species distribution models (Zurell et al 2020, Wilkinson et
al 2021, Mokany et al 2022). In sharp contrast, comparable spatial
models of ecosystem pattern -- and more specifically those models that
integrate biotic and abiotic variables and system-level properties
(Table S1) -- are extremely rare (Dor-Haim et al 2019, Halvorsen et al
2020, Simensen et al 2020). This gap in modelling capacity is
remarkable. To fill this gap, new spatial modelling approaches are
needed for modelling ecosystem patterns across landscapes. Development
of suitable models is especially timely for ecosystem assessment (e.g.,
Keith et al 2022) has undergone a contemporary groundswell, as the
scientific community (e.g., Watson et al 2020, Bullock et al 2022)
propose ambitious targets for ecosystem conservation and restoration.

Conservation practitioners and regulatory authorities rely on spatial
models to ensure decisions are informed by robust predictions and
related measures of statistical uncertainty. Most conservation decisions
are realized in geographic space and selecting the appropriate spatial
scale to maximize success is imperative (Di Minin et al 2022). Trend
analyses show the ecosystem concept is frequently employed to structure
spatially based conservation plans and to mitigate stressors including
climate change (Anderson et al 2021). The most prominent commitments to
ecosystem conservation have been established in global agreements (e.g.,
Convention on Biological Diversity 2021), while implementation falls to
national signatories and to sub-national governments and conservation
organizations (Perino et al 2022). In Canada, for example, standardized
spatial data of significant `key biodiversity areas' including
threatened ecosystems, have been recommended to inform national
conservation planning (Shea et al 2018). However, achieving this
ecosystem objective presents a challenge in Canada that is shared
elsewhere. The challenge is that spatially explicit ecosystem prediction
is recognized as an essential tool to inform regional (i.e.,
continental, national, sub-national) commitments to global conservation
initiatives but very few fully integrated spatial models of ecosystem
pattern, at regional landscape scales, are available. Some members of
the scientific community have raised this as a problematic issue (Fulton
et al 2019, Geary et al 2020), but it is seldom acknowledged,
particularly in the applied literature (Halvorsen et al 2020).

In this Forum, we propose a novel framework for spatially explicit
modelling of ecosystem pattern. Our framework differs from other spatial
ecosystem models in that it accords biotic and abiotic components
equally, commensurate with their joint influence on ecosystem assembly
(sensu Keith et al 2022). Under this approach, the ecosystem is modelled
as a spatially explicit place demarcated by the strength of concordance
among constituent biotic and abiotic variables (Box 1). Different
ecosystems are in turn discriminated by relatively unique combinations
of biotic and abiotic variables that recur along spatial gradients
(Figure 1E, 1F). Under our approach, groups of local ecosystems scale up
to form the heterogenous landscapes within which they occur (Figure 1F).
The bounds of an ecosystem's local extent can only be determined by
considering both the extent and identity of proximate ecosystems.
Consequently, the spatial organization of ecosystems, comprising a
particular landscape, can be predicted by identifying spatially
structured differences among constituent ecosystem types. Our framework
offers a quantitative strategy for modelling the range-wide occurrence,
identity, and characteristic properties of individual ecosystems.
Furthermore, it provides an approach for determining regional patterns
of ecosystem spatial organization, and related changes in biotic-abiotic
relationships, across heterogenous landscapes.

This Forum includes four primary components. First, we briefly review
existing ecosystem modelling approaches, with a focus on models
formulated to predict ecosystem or meta-ecosystem spatial patterns at
regional landscape extents -- the spatial extent where most terrestrial
environmental decisions are made. Second, we demonstrate how a
limitation in predictive modeling capacity occurs because of disparate
scientific traditions and related conventions of modelling practice.
Third, we outline a novel conceptual framework for predictive ecosystem
spatial pattern modelling at regional landscape extents. Our framework
includes an analytical workflow illustrated with a case study. Lastly,
we conclude with a perspective where we propose future research
directions and opportunities.

\emph{Spatial Ecosystem Models -- a Brief Overview}

Most ecosystem models lie on a continuum of basic to applied objectives
with related modelling trade offs (DeAngelis and Yurek 2016). Basic
ecosystem models are often mathematical models, primarily intended to
develop, test, and formalize ecosystem theory (Jørgensen 2016). Most of
these models have been aspatial, spatially implicit, or limited to few
geographic sites and ecosystems (DeAngelis and Yurek 2016). The other
end of the spectrum is marked by applied ecosystem models, which are
usually fit to empirical data (Evans 2012) or derived using expert-based
protocols (Halvorsen et al 2020). Applied models are normally intended
for description or prediction of ecosystem conditions, including their
specific arrangement in geographic space (Pickett and Candenasso 2002,
Evans 2012, Geary et al 2020). Recently though, increasing awareness of
the importance of space in shaping ecosystem pattern and process has
prompted appeals to extend spatially explicit ecosystem modelling more
evenly across scientific domains (e.g., DeAngelis and Yurek 2016, Fulton
et al 2019). Spatially explicit approaches are not necessary in all
ecosystem models, but they are indispensable for models intended for
making predictions of ecosystems across landscapes (Evans 2012). We
highlight the importance of spatially explicit modelling approaches as a
strategy to help bridge theoretical and applied branches of ecosystem
science. Furthermore, we demonstrate their use for contemporary and
near-future ecosystem predictions, at local to regional landscape
extents.

Ecosystems occur in geographic space (Pickett and Candenasso 2002) and
space has long been recognized as a fundamental property mediating the
expression of ecosystem heterogeneity (Rowe 1961, Holling 1992). Yet
until recently, advances in spatially explicit ecosystem modelling have
occurred under the somewhat independent auspices of ecosystem and
landscape ecology (Loreau et al 2003). The latter discipline has
commonly considered ecosystems and ecosystem processes as landscape
components, focusing on their contributions to spatial heterogeneity
(Pickett and Cadenasso 1995). Ecosystem ecologists have, in turn, mainly
concentrated their attention on the exchange of organisms, energy,
materials -- particularly resources such as inorganic nutrients -- along
continuous geographic gradients or discretized landscape mosaics (Massol
et al 2011, Gounand et al 2018). Their burgeoning approach -- sometimes
called `\emph{spatial or landscape ecosystem ecology} ' (sensu Loreau et
al 2003) -- often uses the meta-ecosystem as an analytical construct
(Massol et al 2011) and frequently relies on mathematical models (e.g.,
Harvey et al 2021). However, current perspectives in spatial ecosystem
ecology (e.g., Leroux et al 2017, Gounand et al 2018, Harvey et al 2021)
call for improved integration of ecosystem and meta-ecosystem models
with real-world landscape contexts to inform conservation policy. Thus
far, this synthesis of landscape and ecosystem ecology has predominantly
been championed through spatially explicit models of ecosystem
functional properties (e.g., Leroux and Loreau 2012, Gounand et al 2018,
Soranno et al 2019). We contend further synthesis is needed to predict
other spatially structured aspects of ecosystem variation, including
common pools of biotic and abiotic complexity at local and regional
landscape extents. Furthermore, those biotic and abiotic factors
interacting in a particular time and place, influence location-specific
patterns of ecosystem compositional, structural, and functional
properties (Nash et al 2014). The spatially explicit ecosystem modelling
strategy presented in this forum is structured to illustrate these
interdependent aspects of intra- and inter-ecosystem organization and
variation.

\emph{Scientific Traditions in Ecosystem Ecology}

Ecosystems are complex and may include hundreds or even thousands of
biotic and abiotic components (Loreau 2010). Studying or modelling all
aspects of ecosystem complexity is not possible or desirable. To
represent ecosystem variation, one needs a basis for simplification and
this simplification comes with trade-off (Geary et al 2020). In the
basic ecosystem sciences, the customary emphasis on ecological function
(Box 2), has come at the expense of detailed information on biotic
properties (Loreau 2010, Mokany et al 2016) and on the contributing
roles of abiotic complexity (Johnson and Martin 2016, Richter and
Billings 2015, Dor-Haim et al 2019, Hjort et al 2022). Many of these
traditions are long-standing and mirrored across general ecology (Loreau
2010). Loreau (2010) attributes them to a divergence of practice between
community and ecosystem ecologists. Species interactions and patterns
are largely studied by community ecologists. Ecosystem ecologists
instead emphasize interactions between species and their abiotic
environments, particularly those interactions that give rise to fluxes
of materials. These latter functions (Box 1) are widely considered the
fundamental foci for basic modelling and empirical inquiry at the
ecosystem level. While biota and biotic processes are considered
ecosystem components, they are normally relegated to the community
(Loreau 2010) and generally interpreted as components of biodiversity.
These enduring traditions of practice are also echoed across the
spectrum of basic and applied ecosystem ecology, and their recognition
within this broader scope of ecosystem science is not new (e.g., Rowe
1961, Blew 1996).

Blew (1996) outlined three major traditions of ecosystem science each
rooted in relatively distinct perceptions of the ecosystem concept and
its salient features (Box 2). The three traditions place differing
levels of emphasis on biotic, abiotic, or functional ecosystem features
(Table S1). While Blew's (1996) summary has not been updated to include
modern theory and modelling approaches, some of which strive for
improved integration (e.g., Geary et al 2020), similar conventions in
ecosystem science exist today (Baveye et al 2018, Zarnetske et al 2019,
Alahuhta et al 2020). Blew (1996) attributes such divergence of
scientific practice to controversies surrounding the ecosystem concept
itself, which Loreau (2020) shows have pervaded since its inception.
Many of the debates originate because the ecosystem concept is at once
both comprehensive and flexible (Pickett and Candenasso 2002, Currie
2011). The ecosystem concept's inherent flexibility lends itself to
different approaches for modelling wholeness and integration among key
unit components (Pickett and Candenasso 2002, Gignoux et al. 2011,
Jørgensen 2016). However, part of the debate with past modelling efforts
have been discussions over which system-level properties (Table S1) best
exemplify wholeness, adequately represent complexity, and underpin
quantifications of variation (Currie 2011). We concur with Jørgensen
(2016) and suggest there are many departure points for simplifying the
ecosystem, as an object for modelling, to help address these
considerations, and to advance understanding of ecosystem patterns.
Furthermore, we highlight the importance of spatially explicit
approaches as a distinct strategy for bridging different analytical
traditions, and for producing predictive models needed for ecosystem
forecasts. These ecosystem modelling trade-offs will necessarily vary
according to purpose. And while research to distinguish ecosystem
modelling strategies and to assess their relative merits are on-going
(e.g., Geary et al 2020), our novel approach falls outside the scope of
recent efforts and related recommendations.

In the next section, we present a framework for ecosystem
conceptualization and spatial pattern modelling. The framework
integrates elements of the ecosystem science traditions outlined above
and presented in Box 2. It does not emphasize biotic, abiotic, or
functional features of ecosystem variation. Instead, our framework
focuses on the causes and consequences of these features' concordance
(Box 1) in space and time. Additionally, we show how that spatial
concordance shapes patterns of ecosystem heterogeneity at local and
regional landscape extents.

\emph{Integrative Ecosystem Spatial Pattern Modelling}

Our strategy for ecosystem spatial pattern modelling is summarized as a
conceptual framework. We draw concepts from ecosystem, community, and
landscape ecology, seeking to demonstrate an integrative basis for
predicting the drivers and outcomes of ecosystem assembly. To illustrate
practical application of our framework, we provide a workflow (Figure 1)
based on a case study from Cape Breton, Nova Scotia, Canada. We showcase
data, analytical procedures, and interpretive guidelines required for
framework operationalization, as they relate to the case study. These
operational considerations are applicable to any predictive spatial
model of regional ecosystem pattern. In that regard, an overarching
objective of our framework is to help catalyze new perspectives and
statistical methods for obtaining general insight into the origin and
implications of ecosystem spatial organization. We begin by summarizing
the conceptual foundation of our framework.

Conceptual foundation

The premise of our modelling strategy is that ecosystems can be
predicted by resolving patterns of relative spatial concordance (Box 1)
among biotic and abiotic features (Table S1). The particular combination
of features found along a geographic gradient, and the spatial
relationships among them (Figure 2), provide an integrated basis for
distinguishing conterminous ecosystems and their respective boundaries
(Figure 2). Such distinguishing properties are not absolute, for
ecosystems intergrade and vary continuously in space and time (Leroux
and Loreau 2012, Newman et al 2019, Soranno et al 2019). These
gradations occur because individual biotic-abiotic features, intrinsic
to a particular ecosystem, may transcend boundaries of locally adjacent
ecosystems. However, ecosystem-level organizational patterns can be
identified by relative differences in the collective strength of
concordance among constituent features. For example, in boreal
landscapes, tree species composition may be relatively concordant across
adjacent upland forest and treed bog ecosystems. Here, key differences
are expressed in lower vegetation layers, and in soil, organic matter,
hydrology, and topographic properties. Under this approach, different
ecosystems can be discriminated by relatively unique and consistent
combinations of features, that recur predictably across landscapes.
Landscapes of heterogeneous ecosystems are composed of these different
ecosystems. Here, each ecosystem manifests at characteristic spatial
scales (Massol et al 2011, Soranno et al 2019, Bullock et al 2022) and
has characteristic levels of integration (Rowe 1961, Loreau 2020),
uniformity (Pickett and Candenasso 1995, Halvorsen et al 2021), and
distinction (Dor-haim et al 2019, Simensen et al 2020).

A nuance of our interpretation is that we do not seek a means to
reconcile patterns of low spatial concordance between or among biotic
and abiotic ecosystem constituents. Instead, we emphasize levels of
collective spatial concordance within and across biotic-abiotic domains
(Box 1). Furthermore, we suggest collective levels of concordance are a
relative, continuous, and changeable ecosystem property\emph{.} Some
ecosystems have inherently higher concordance, whereas others are
characterized by lower relative levels of this emergent ecosystem
property (Loreau 2020). Holling (1992) attributed differences in overall
concordance to keystone variables. Keystone variables are individual
ecological processes or constituents with a disproportionate influence
on ecosystem spatial organization and variation (Holling 1992). Over
time, these variables, many of which operate across scales, can catalyze
developmental changes in other aspects of ecosystem structure,
composition, and function (Nash 2014, Newman et al 2019). Such changes
often lead to more consistent expressions of landscape pattern and
spatial grain (Peterson 2002), and potentially to higher levels of
ecosystem integration (Rowe 1961, Loreau 2020).

Case Study

\emph{Overview}

We define ecosystem spatial pattern models (ESPM) as statistical models
formulated to predict spatially structured dimensions of intra- and
inter-ecosystem variation. We adapt elements of community-level spatial
models (see review in D'Amen et al 2017) to configure our analytical
strategy for ESPM. Community-level models are multi-species extensions
of species distribution models (Norberg et al 2019, Zurell et al 2020),
formulated to simultaneously model the presence or abundance of species
comprising communities, or to model patterns of species compositional
dissimilarity among sites, at various scales of resolution
(Nieto-Lugilde et al 2018). These models are also commonly applied to
predict community-level properties (e.g., species richness and
composition -- Norberg et al 2019) and or assemblages (e.g., community
type -- Pinto-Ledezma and Cavender-Bares 2021) across geographic
gradients. Ecosystem spatial pattern models differ from community-level
distribution models in three main respects: modeled response variables,
prerequisite test and predictor data, and the specific assembly
determinants underpinning model prediction. We briefly summarize these
features below in the workflow applied in our case study.

To build our strategy for ESPM, we focus on one of the three main
strategies to community-level modelling (see Ferrier and Guisan 2006).
This approach, referred to as \emph{assemble and predict together} ,
models species-environmental relationships concurrently with spatial
predictions of community-level properties and or entities (Ferrier and
Guisan 2006, D'Amen et al 2017). Our analytical approach most closely
mirrors joint-species distribution modelling, a strategy to predict the
responses of multiple species occurring throughout a study space (see
review in Warton et al 2015). We extend this to model ecosystem spatial
patterns.

Under our approach to ESPM, spatially concordant patterns of
biotic-abiotic co-occurrence and or abundance are the basis for
identifying ecosystems at local and landscape extents. To illustrate
implementation of an ESPM, we outline a typical modelling workflow
(Figure 1) and provide an overview of key procedures. Key components
include aspects of ecosystem survey (Figure 1A); ESPM training and
predictor data compilation and refinement (Figure 1B), and finalization
(Figure 1C); model building (Figure 1D); spatial prediction of
individual ecosystem constituents and their properties (Figure 1E); and
lastly, prediction of ecosystem-level patterns and properties at local
(i.e., within individual ecosystems ) and landscape (i.e., among
ecosystems or ecosystem types)(Figure 1F) extents. Below we summarize
these ESPM components as they relate to our case study. We also provide
a detailed overview of the more prominent challenges (see Table 1 for
complete list) encountered during model implementation, offering
practical solutions to address these obstacles. Our overall intent is
not to report on ESPM outcomes, as they relate to our case study, but to
illustrate key aspects of model set-up, operationalization, and problem
resolution.

\emph{Ecosystem Survey}

Field data employed in our case study (Figure 1A) were obtained from
ecosystem surveys of 1004 plots across Cape Breton (10,311 square
kilometers), Nova Scotia, Canada (see general overview of ecosystem
survey methods in section S2). Ecosystem survey protocols incorporate
different methods for biotic and abiotic variables. These methods may
also be applied across multiple spatial extents and grains. Survey
methods have a strong influence on the properties and structure of
resulting data, with implications for how these data are used in
modelling spatial ecosystem patterns. These implications are discussed
below in our overview of ESPM training and predictor data.

\emph{Data Compilation and Refinement}

\emph{Training Data}

Data required for ESPM include training and predictor datasets. Training
(sometimes called test or response) data (Figure 1B) are derived from
ecosystem field surveys, as described above. These data must undergo
similar preparations, refinements, and partitioning recommended for
species (see Guisan et al 2017) and community-level modelling (see
Ovaskainen and Abrego 2020, Mokany et al 2022), as applicable. A notable
distinction is that ecosystem training data include both biotic and
abiotic variables. Differences among these respective survey variables
introduce incompatible data structures in the training pool, with a
bearing on predictive model outputs. We provide a brief overview of
these issues and suggest options to address them. Last, we introduce
measures to finalize training data selected for model fitting.

Different measurement scales and units are typically employed for
quantifying biotic and abiotic phenomena in field surveys. In our study,
vascular plant, bryophyte, and lichen taxa were measured by estimating
areal cover by individual species. These estimates were expressed as a
percent of total cover for individual vertical vegetation strata (e.g.,
canopy tree, woody shrub, tree sapling and seedling, herbaceous, lichen,
and bryophyte). In contrast, abiotic attributes were recorded using a
variety of measurement scales and units, depending on the attribute.
These abiotic records include measures in linear (e.g., humus depth in
centimeters), categorical (e.g., landform type), concentration (e.g.,
milligrams/kilogram of calcium in soil), volume (e.g., above-ground
woody biomass in cubic meters), ratio (e.g., percent slope), or
logarithmic (e.g., pH) units. Pooling ecological variables with
disparate measurement scales, units, and limits misrepresents their
statistical relationships to one another, and introduces interoperable
dimensions into a training dataset (König et al 2019). One possible
means to alleviate this problem is to convert all variables to
presence/absence records. This method was particularly effective for the
types of categorical variables we have in our data (e.g., species
identity and abiotic attributes such as humus, soil, and bedrock type)
but less appropriate for continuous measures, particularly those which
were present at all surveys locations (e.g., vegetation height). To
address this latter problem, ubiquitous variables can be eliminated from
the data pool, a procedure implemented on biotic training data employed
in community-level modelling (e.g., Ovaskainen and Abrego 2020).
Alternatively, some continuous data (e.g., pH) could be converted to
categorical classes, employing empirically supported class intervals.
Given the diverse data types in our case study, we excluded ubiquitous
variables and fit a hurdle model (see Ovaskainen and Abrego 2020) with
and without abundance data.

A second challenge arising in training data compilation is the
disproportionate ratio of biotic to abiotic variables recorded in field
surveys. Tens or hundred of species are frequently documented from
individual ecosystem plots, whereas the number of abiotic attributes
assessed (Figure 1A) is rarely comparable. Our case study plot data are
comprised of abundance records of over 900 vascular plant, lichen, and
bryophyte species, coupled with only 20 abiotic variables recorded at
the site-level and 10 to 30 additional abiotic measurements taken from
soil profiles at each survey location (see section S2). Imbalanced
numbers of biotic and abiotic data survey variables unduly weights biota
in training data pools, with implications for the relative influence
these variables have on predictions of joint concordance among biotic
and abiotic ecosystem constituents. One option to address this imbalance
is to aggregate species into groups based on common ecological traits
(i.e., life history, morphological, or physiological characteristic of
an individual) and to employ the resulting trait groups to represent
biota in a test data pool. Incorporating species traits into predictive
spatial biodiversity models has been shown to greatly improve model
performance (Regos et al 2019). Traits can also be invaluable for
understanding species response to their environment and their ecological
roles in communities and ecosystems (Kissling et al 2018). One solution
we implemented in our case study was to aggregate species with common
traits to the genus level; an example was \emph{Sphagnum} , a
species-rich genus commonly found on moister soils.

Methods outlined above can be applied with different subsets of training
data. This approach can help reveal ecosystems at different scales, and
to determine whether separate models, with distinct pools of training
data, are required for predicting sub-components of total ecosystem
diversity in a study landscape. Variations in training data structure
and origin can strongly shape spatial biodiversity model predictive
performance (Guillera\selectlanguage{english}-Arroita et al 2015, Mod et al 2020). In our case
study, pools of test data were scaled across levels of ecological
complexity to determine how variations in training data dimensionality
affected model performance. For example, differences in growth-form
(tree, shrub, herb) dominance, surficial origin (glacial, aeolian,
marine, lithic), soil properties (upland, wetland soils), and
biogeoclimatic regionality (alpine, boreal, temperate) were employed to
parse training data into less complex subsets.

\emph{Predictor Data}

While training data employed in spatial biodiversity modelling are
typically obtained from field surveys, predictor (sometimes called
environmental, explanatory, or covariate) data are derived from remotely
sensed, or modelled, spatial data extending completely across a study
region (Bryn et al 2021). These data are required to model ecosystems
continuously in space (Figure 1B). Very few studies have evaluated the
suitability of predictor data for this type of predictive modelling
(Dor-Haim et al 2019, Halvorsen 2020, Simensen 2020). We suggest
suitable predictors should encompass spatial data on biotic and abiotic
variables, which are independent from survey records (i.e., training
data). They may also include spatial data on functional ecosystem
properties (e.g., productivity), physiognomic structure (e.g., dominate
growth form), and on regular or episodic disturbance (e.g., flooding,
forestry, fire). Potential predictor datasets must be refined to address
the same limitations (e.g., correlation, collinearity, and variance
inflation) presented in modelling species and communities; we do not
review these measures (see Guisan et al 2017 for guidance). Here we
focus on the factors considered to finalize the selection of predictors
(Figure 1C) employed in our case study, and the implications of these
factors for modelling ecosystem pattern.

To assemble our pool of candidate predictors, we considered three
factors -- ecological response, assembly mechanisms, and spatial
scale(s) of influence. In general, we sought predictors deemed important
for shaping variations in the distribution or prominence of those
ecosystem features (Table S1) which scale up to drive spatial ecosystem
patterns. This approach is analogous to the basis of joint species
distribution modelling, which assumes species respond mutually to both
their physical environment, and to one another (D'Amen et al 2017,
Ovaskainen and Abrego 2020). We extend this idea to encompass reciprocal
influences among biotic and abiotic variables and sought covariates
(Table S3) to predict singular and joint biotic-abiotic responses.

Many ecological assembly drivers (e.g., climate, topography, surficial
geology) affect both biotic and abiotic ecosystem constituents and
facilitate interactions between them. In our study region, a challenge
we encountered is that some predictors are only available at relatively
coarse-grains (e.g., climate - approximately 1 kilometer resolution)
precluding their use in our compilation of finer-grained predictors. Our
initial approach was to seek predictors with spatial grains similar to
our survey grain (between 25 and 400 m\textsuperscript{2}, depending on
the ecosystem). Ecosystem surveys were structured around ecologically
conspicuous breaks in topographically controlled gradients (e.g., local
vegetation), so we employed direct (e.g., remotely sensed vegetation
indices) and indirect predictors (e.g., terrain) of those gradients to
compile our pool of fine-grained (50 m resolution) candidate predictors
(Table S3). Predictor data can be subsequently upscaled to coarser
spatial resolutions (e.g., 100, 250, 500, 1000 m) to test the influence
of varying spatial grains on predictive model performance. Konig et al
(2021), for instance, have demonstrated how joint species distribution
model performance varies at different spatial grains. Lastly,
investigating the effect of scope, defined as the ratio of spatial
extent to grain (Frazier 2022), could provide insights into scaling
relationships and their role in predictions of ecosystem pattern.

The combination of predictor data employed in a spatial biodiversity
model can be finalized (Figure 1C) before or with model fitting. Where
model fitting is used to assist with data selection, selection criteria
can be conceptual, theoretical, and or statistical (Guisan et al 2017).
Several ecologists (e.g., Araujo and Guisan 2006) have suggested that
many biodiversity distribution models do not adequately consider
relevant theory to guide predictor data selection (e.g., Poggiato et
2021). Araujo and Guisan (2006) further suggest that greater attention
needs to be given to the explanatory value of each predictor, and to its
relevance as a causal determinant of ecological pattern. We employed an
iterative approach based on model performance, and drew on theoretical
and conceptual criteria, to finalize predictor variables employed in our
case study (Table S3).

\emph{Model Building and Assessment}

Model building includes technical aspects of model algorithm selection,
managing statistical assumptions, model fitting, and translating model
outputs to mapped summaries, among related considerations (Guisan et al
2017, Araujo et al 2019, Zurell et al 2020). In this section we provide
an overview of key factors relevant for ESPM algorithm selection.
Additional issues, pertaining to ESPM building, are outlined in Table 1.

\emph{Algorithm Selection}

Previous efforts to model ecosystems in space have largely emphasized
biotic, abiotic, \emph{or} functional response variables (Box 1, Table
S1) to predict ecosystem-level variation (Table S2). Our case study
goals differ as we emphasize biotic \emph{and} abiotic variables
equally. Furthermore, we aim to ``assemble and predict together'' (sensu
Ferrier and Guisan 2006) (see case study overview). Given these
conditions, we sought candidate ESPM algorithms which could model biotic
and abiotic ecosystem constituents simultaneously and predict individual
and shared responses of each variable. In addition, we fit ESPM with in
situ (i.e., recorded in the field) training data, thereby better
capturing the range of biotic and abiotic complexity characterizing
ecosystems. By applying this integrative strategy for ESPM, ecosystems
are treated as an \emph{emergent function} (sensu Nieto-Lugilde et al
2018) of biotic-abiotic co-occurrence and patterns of local concordance.

Our initial challenge was defining criteria to select an algorithm from
the numerous examples (Table 2) applied for spatial biodiversity
modelling. Following our evaluation, we screened algorithms according to
their flexibility (e.g., regarding data inputs), implementation (e.g.,
ease of application), analytical properties, and performance (Table 3).
Overall, we emphasized algorithms with the capacity to accommodate pools
of presence/absence, or abundance, records of both biotic and abiotic
variables as training data; employ species traits; and to allow for
interactions among predictors. We also prioritized algorithms which
could predict individual and joint responses in space. To assist with
our selection, we drew on recent review articles (Nieto-Lugilde et al
2018, Norberg et al 2019) and individual model algorithm assessments
(e.g., Warton et al 2015, Wilkinson et al 2021) to identify spatial
algorithms with relatively high predictive power. Candidate algorithms
that met our requirements include joint species distribution modelling
(implemented with Hierarchical Modelling of Species Communities (HMSC))
(Ovaskainen et al 2017), generalized dissimilarity modelling (Mokany et
al 2022) and probabilistic bioregion modelling (Hill et al 2020). Of
these three algorithms, we selected HMSC for our case study as recent
reviews demonstrate its overall flexibility and moderate to high
predictive performance for spatial biodiversity modelling (Warton et al
2015, Zhang et al 2018, Norberg et al 2019). Furthermore, availability
of a comprehensive methodological guide with tutorials in R (Ovaskainen
and Abrego 2020), training modules, and communication (Ovaskainen,
Tikhonov pers comm) facilitated implementation for our purpose.

\emph{Prediction of Intrinsic Ecosystem Constituents and Properties}

Separating individual (Figure 1E, e.g., biotic or abiotic features --
Table S1) and shared (Figure 1F, i.e., two or more ecosystem features)
responses provides a means to predict both intra- and inter-ecosystem
patterns. This approach also improves understanding of commonalities,
potential interactions, and properties (e.g., traits) among those biotic
and abiotic variables characterizing specific ecosystems or sites. Joint
distribution models, such as Hierarchical Modelling of Species
Communities (HMSC), assume that responses to environmental circumstances
are shared; as such, these models are structured to predict both
individual and joint responses among test variables (Ovaskainen and
Abrego 2020). Furthermore, HMSC is specifically designed so models of
individual response variables are statistically connected, so that
information from lower-order (i.e., individual biota and abiotic
features) predictions informs higher-order (i.e., aggregate)
predictions.

\emph{Ecosystem-level Prediction}

The ultimate purpose of ESPM is to make ecosystem predictions at both
local and regional extents (Figure 1F). A key assumption of this
objective is that disparate local ecosystems can be resolved, and that
the arrangement and spatial properties of those individual ecosystems
determine regional landscape structure and composition. Under these
interrelated premises, the diversity and spatial organization of
ecosystems, comprising a particular landscape, can be predicted by
determining spatially structured differences among constituent ecosystem
types. To achieve this ESPM objective, we propose analytical techniques
to identify statistical commonalities among groups of biotic and abiotic
variables co-responding in predicted geographic space (Table 1). These
techniques provide a basis to identify ecosystem types, which we define
as ecosystems that recur predictably across landscapes. Technical
conventions and methods employed for aspatial classification of
ecological units (e.g., community, habitat, landscape types) are
suitable for this purpose. A number of these methods, and other less
common techniques, have been applied to variables modelled in space (see
Table 1).

An issue we considered was how to define statistically defensible
thresholds of similarity or uniqueness among ecosystems. Ecosystems are
spatially continuous, so the issue centers on quantifying patterns of
relative discontinuity, arising from discordant patterns of abundance
and or occurrence among ecosystem features jointly modelled in space.
Outputs of spatial models are often continuous (e.g., probability of
occurrence or co-occurrence) and many modelling applications require the
identification of suitable thresholds for identifying ecological
meaningful levels of relative continuity or discontinuity across space
(Zurell et al 2020). For example, users may want to know if the
probability of occurrence, for a particular species, is high enough to
justify conservation actions (Bryn et al 2021). Thresholds have also
been applied for determining whether co-occurrence patterns among groups
of species reveal higher order levels of spatially structured
biodiversity (e.g., communities - Ferrier and Guisan 2006) or ecological
geography (e.g., bioregions - Hill et al 2020). For ESPM, and other
spatially structured models of ecological diversity and organization,
the challenge can be framed as discretizing multi-dimensional units from
ecological gradients that are inherently continuous (Halvorsen et al
2020). This challenge is common to all pattern resolution (Levin 1992)
but arguably amplified in ecosystem ecology. We do not propose a single
analytical solution to this challenge, for it is embodies aspects of
theory, philosophy, and pragmatism.

\emph{Perspective}

We frame ESPM as an outgrowth in the advancement of spatial ecosystem
ecology. As this latter branch of ecology continues to evolve, efforts
to model within- and cross-ecosystem patterns and processes are
increasingly being tested in complex real-world study landscapes. This
is where the potential to bridge theoretical and applied modelling
traditions is greatest. While most spatial ecosystem models, at this
frontier, are formulated to predict responses to ecosystem
heterogeneity, we focus on the origins and organization of that
heterogeneity. Our framework is intended to help encourage new strategic
directions in the type of integrative modelling needed to strengthen
conservation assessments of ecosystems, at those region-specific extents
relevant to environmental decision making (Perino et al 2022). While
forecasting ecosystem change in future scenarios is essential for
decision making, quantifying current ecosystem patterns is comparably
important (Watson et al 2020). Outputs of our framework can also help
catalyze efforts needed to improve basic understanding of structural,
compositional, and functional relationships across scales and among
extant ecosystems.

Our approach is not intended as an endpoint. Instead, we offer an
alternative analytical perspective to quantify emergent aspects of
ecosystems, and how they assemble across space. Patterns of
heterogeneity reflect past and present interactions among biotic and
abiotic elements. The unique combination of ecosystem elements and
processes, expressed at a specific time and place, is like a dynamic
blueprint. We do not model dynamic aspects of that blueprint, or
assembly processes themselves. Our focus is on the spatially structured
determinants and outcomes established by those processes. We do not view
this apparent divergence from the functional or mechanistic (often
referred to as process-based) emphasis typical in ecosystem and
meta-ecosystem ecology, as a disciplinary incongruency. Pattern and
process span all levels of organization in nature, including ecosystems.
Numerous spatial models have been formulated to predict and help
understand biodiversity distributional patterns (Araujo et al 2019), but
spatial models of ecosystem pattern are scarce (Geary et al 2020) and
frequently absent from broad-scoped thematic reviews. Even in extensive
reviews (e.g., Zurell et al 2021) of spatial biodiversity models, only
process-based spatial ecosystem models are sufficiently common for
consideration. These trends persist in general ecology almost twenty
years after Loreau et al (2003) highlighted the schism between models of
biotic (e.g., population, community) elements, and those built for
ecosystem prediction. Our approach is intended to help provide a common
basis for linking predictions across scales and levels of ecological
organization, including constituent facets of biotic and abiotic
complexity.

Recognition of the importance of abiotic pattern and process for
understanding ecosystems, and other components of biodiversity, has
largely originated within the geoscience community (Richter and Billings
2015). Here, biogeochemical elements are often emphasized, while other
physical and more strictly abiotic variables and processes are rarely
addressed as completely (Johnson and Martin 2016, Dor-Haim et al 2019).
This disparity in purview has affected perceptions of what an ecosystem
is, how it can be modelled, and which abiotic variables should be
considered in empirical ecosystem research (Richter and Billings 2015,
Johnson and Martin 2016). We suggest abiotic complexity is not
singularly important because biota rely on it -- it is fundamental to
ecosystem organization. Moreover, many abiotic variables and properties
originate, or are shaped by, from biotic processes (e.g., humus, water
chemistry, soil structure). Recognition of abiotic components of
ecosystem constitution and dynamics, and their influence on ecosystem
properties has begun to rise within the ecological research community
(van der Plas 2019). In addition, recent perspectives and methodological
guides (e.g., Zarnetske et al 2019, Alahuhta et al 2020, Hjort et al
2022) hold considerable promise for increasing broader awareness of
abiotic complexity, and for catalyzing new approaches for understanding
joint biotic-abiotic patterns and processes shaping ecosystems.

In what follows, we outline recommendations for moving forward. While
our case study includes the kind of detailed workflow deemed essential
to advance predictive ecology (McIntire et al 2022), much effort remains
to explore the strengths, and to identify and address the limitations,
of ESPM as an analytical template for predicting ecosystem organization.
We summarize three overarching issues required to refine our framework;
model data and testing, linking model and theory refinement, and
applying model outputs to support environmental decision making.

Data required for spatial modelling of species and communities are
generally well documented (Bryn et al 2021). The extraordinary
popularity of these models has also prompted development of new training
and predictor data, and investigations of the suitability these data
have for biodiversity modelling are on-going (e.g., Guillera-Arroita et
al 2015, Brodie et al 2020). However, comparable overviews of basic data
necessary for ESPM, and similar spatial ecosystem models, are rare and
standardized guidelines for data selection do not exist. Prominent
advances in spatial ecosystem modelling largely center on the
application of remote sensing data for predictions of individual
ecosystem components or properties, such as structure (e.g., topography,
vegetation physiognomy - D'Urban Jackson et al 2020) or function (e.g.,
productivity, disturbance -- Anderson 2018). For the most part, these
latter spatial models do not incorporate ground-derived field measures
of biotic and abiotic ecosystem compositional and structural complexity,
although recent efforts promote better integration across varied data
sources (e.g., Pasetto et al 2018,). Instead, such field data are
typically applied for independent spatial predictions of population,
community, or geophysical components of nature. Data prerequisite for
ESPM include both the detailed type of in situ ecosystem data collected
as part of ecosystem inventories, or long-term monitoring, coupled with
specific predictors, many of them remotely derived, necessary for
modelling ecosystem gradients. Environmental predictors employed for
spatial modelling of other components of biodiversity and geodiversity
can be adapted for this latter purpose (Simensen et al 2020).

To facilitate overall improvement of our framework, we suggest adoption
of standardized data compilation and processing protocols, comparable to
those recently established for spatial biodiversity models (Zurell et al
2020). Test and predictor data should be made available directly or via
data extraction pipelines provided in study documentation. These
provisions will not only help ensure model repeatability and
interoperability but facilitate efforts to transfer models to new
locations or times. These measures will be particularly helpful where
data are sparse or absent, or where environmental circumstances are
significantly dissimilar. Furthermore, records of data, metadata, and
data processing routines are necessary to determine the influence
spatial context has on predictive outcomes.

To make models useful, they must be reliable, flexible, and informative.
Many models are only applicable in specific circumstances, compromising
generality or predictive inference for accuracy. Predictive models are
usually improved by testing with different data, parameters, performance
metrics, and algorithms. And ultimately, the only way to improve
predictive capacity, and to refine modelling approaches, is to predict
frequently and to implement model assessment protocols (Dietze 2017,
McIntire et al 2022). We suggest ESPM models need to be tested in
different biomes, at different landscape extents, and with different
subsets of total regional ecosystem variation. As realistic ecosystem
models tend to be more complex (Evans 2012, Mouquet et al 2015), often
creating computational challenges, reduced datasets from smaller, less
complex, regions are recommended for initial model testing. Extending
predictions to unsurveyed areas, as part of testing routines, may be
informed by new methods intended to identify the area of applicability
for predictive spatial models (Meyer and Pebesma 2021). Lastly, running
modelling trials with simulated data can help simplify and expediate
testing scenarios before applying them to real data. Simulated data can
also be employed to help evaluate model performance, as part of
assessment trials (Gallagher et al 2021).

Theories established to explain ecosystem organization have been closely
tied with efforts to quantify pattern within and among ecosystems (Levin
1992). And while predictions typically accompany theory development,
they also serve to corroborate or refine theory (Houlahan et al 2017).
However, ecological theories are often incomplete and fragmented
(Mouquet et al 2015) and models may employ elements of multiple theories
with different origins. Our predictive framework draws from several
interrelated theories all coupling aspects of both static and dynamic
pattern resolution. Process-based approaches for predicting ecosystem
dynamics are essential, but they can be greatly strengthened by efforts
to resolve contemporary ecosystem organizational complexities, many of
which remain vague and inadequately understood. Moreover, process-based
(mechanistic) and static pattern-based (phenomenological or correlative)
models lie along a continuum, sharing many of the same theoretical
underpinnings and, in some cases, overlapping research objectives
(Mouquet et al 2015). We suggest any model along this continuum can
serve as a starting point to abstract complexity, further understanding,
and test theory. Such models are different representations of the same
ecological entity, and we posit greater effort is required to reconcile
and facilitate knowledge exchange among various ecosystem modelling
strategies. To help advance this synthesis, we further suggest ESPM
outputs could be applied as inputs in process-based (e.g., simulated)
spatial ecosystem models. This approach could help determine how spatial
ecosystem patterns respond under dynamic scenarios.

We close with a note on matching models to purpose. Part of our
motivation with this Forum has been to promote a novel predictive
approach for guiding ecosystem-based environmental decision making.
Regulatory authorities and conservation practitioners need reliable,
timely, and accessible evidence to inform and evaluate their actions.
Many decisions are made on short time horizons, tied to fluctuating
budgetary and political circumstances. To underpin these decisions,
tactical ecosystem predictions are required to determine which
individual ecosystems occur where and why; how ecosystems relate to one
another (i.e., spatially, functionally, biotically, and abiotically)
within their respective ranges; what environmental drivers are important
across varied spatial and temporal contexts; which ecosystems support
priority constituents (e.g., rare species, functional traits, carbon) or
properties (e.g., productivity); and which ecosystems are declining and
or otherwise vulnerable. These aspects of contemporary ecosystem
geography reflect past assembly pathways, including the consequences of
natural disturbances and human land use, and provide a basis to improve
strategic predictions of ecosystem change. Tools which facilitate
synthesis of ecosystem organization and dynamics are critical for
successful natural resource management because decision makers must be
mindful of both existing and projected circumstances when settling
trade-offs among conflicting land uses and societal pressures.

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\emph{Supporting Materials}

\textbf{Box 1. Spatial concordance -- a basis for resolving intra- and
inter-ecosystem patterns}

Ecosystems can be distinguished by predicting their component features
(Table S1) and the spatially structured relationships between them.
These complex relationships span biotic and abiotic domains, scales, and
levels of ecological organization. To resolve these complexities, and
how they vary across landscapes, we focus on variations in spatial
concordance within and among assemblages of biotic (B) and abiotic (A)
variables.

Spatial concordance is a condition where two or more ecosystem features
show similar scale-specific responses (e.g., presence, abundance) across
shared segments of a geographic gradient (plots A and B -- right panel).
Concordant spatial relationships can arise between individual biotic
(e.g., local species populations -- O'Neill 2001) and abiotic (e.g.,
inorganic elements -- Austin 2013) ecosystem constituents. Furthermore,
concordances can occur across structural (e.g., vegetation physiognomy
-- Yang et al 2017), compositional (e.g., community -- Pinto-Ledezma and
Cavender-Bares 2021), and functional (e.g., productivity -- O'Neill
2001) ecosystem features. Most studies have focused on concordance among
biotic properties (Soranno et al 2019) and particularly how they relate
to community variations (e.g., identity -- Austin 2013) or to landscape
heterogeneity (Pickett and Cadenasso 1995). Instead, we emphasize
spatial concordance within and between biotic and abiotic domains (plot
AB -- right panel). This integrative approach reflects the reciprocal
roles (Gignoux et al. 2011, Richter and Billings 2015, Halvorsen et al
2020) of biotic-abiotic constituents and processes in ecosystem assembly
(Keith et al 2022). It also provides a means to parse individual and
aggregate (Table S1) sources of ecosystem variation and to identify the
strongest co-varying biotic-abiotic relationships.

Variations in spatial concordance reveal relationships among ecosystem
features and how they scale up to form different ecosystems and the
boundaries separating them. To resolve these relationships and their
roles in shaping intra- and inter-ecosystem patterns, we distinguish
areas where spatial concordance levels are relatively uniform and
continuous, from adjacent areas where these collective properties show
pronounced change. The latter correspond with boundaries -- some narrow
and relatively discrete, others wider and more diffuse (Cadenasso et al
2003) -- between neighbouring ecosystems. Distinguishing adjacent
ecosystems and their common boundaries requires resolution of joint
distinctions in biotic-abiotic composition and structure.

To illustrate these patterns, random point occurrences of biotic and
abiotic variables were independently simulated across a categorical
landscape. The map (left panel) summarizes how these occurrences relate
to one another, showing landscape areas marked by: (1) high biotic and
abiotic; (2) moderately high abiotic, low biotic; (3) moderately high
biotic, low abiotic; and by; (4) low biotic, low abiotic patterns of
spatial concordance. These geographic areas are depicted in plots
showing individual (plots A and B -- right panel) and shared (plot AB --
right panel) biotic and abiotic responses (Y axes) along a spatial
gradient (X axis).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Box 2. Traditions in ecosystem conceptualization and their
influence on research and modelling}

A critical factor in ecosystem research is resolution on what an
ecosystem is. Many theoretical and practical examinations of the
ecosystem concept have been presented since its inception (e.g., O'Neill
et al 2001) and although all have improved use and understanding of the
term, disparities among the prevailing philosophic and scientific
traditions of ecosystem science persist (Loreau 2020). Blew (1996)
outlined three major traditions in ecology, each rooted in relatively
distinct perceptions of the ecosystem concept and its primary
definitional criteria (see Table S1). Similar traditions persist in
contemporary ecosystem science (Baveye et al 2018, Zarnetske et al 2019,
Alahuhta et al 2020). Modified after Blew (1996), the three major
traditions include:

\textbf{1) Biotic tradition.} The biotic approach to ecosystem science
is organism focused and typically emphasizes either species or, more
often, communities as the most important expression of ecosystem
organization. Abiotic constituents are ranked with lesser importance and
may be employed to model or describe biotic patterning. Spatial
properties may be explicitly, or implicitly, recognized, and functional
relationships are inferred (O'Neill 2001). Such units are sometimes
called bio-ecosystems, ecological communities, or community-ecosystems
(Rowe and Barnes 1994). A prominent example is the IUCN global ecosystem
red list, which emphasizes biotically defined units for its operational
definition (Keith et al 2013).

\textbf{2) Functional tradition.} Under the tenets of this approach to
ecosystem science, the singular representation of holism and complexity
are an ecosystem's functional features (Currie 2011). This approach
emphasizes the processes (e.g., respiration, decomposition, material
cycling), properties (e.g., energy balance, productivity, trophic
structuring), or products (e.g., biomass) resulting from interactions
between biotic and abiotic ecosystem components (Gignoux et al 2011).
Spatial properties may be explicitly or implicitly recognized (DeAngelis
and Yurek 2016), and biotic complexity is often generalized to trophic
levels, higher taxonomic ranks, or specific functional groups. Prominent
examples of this approach are process-based models of ecosystems at
local (e.g., Caron-Lormier \emph{et al.} 2009) and global extents (e.g.,
Bonan and Doney 2018); ecosystem simulation models (e.g., Xia et al
2017); and mathematical models of individual ecosystems (e.g., Svirezhev
et al 1984) or meta-ecosystems (e.g., Leroux and Loreau 2012).

\textbf{3) Abiotic tradition.} Following principles of the abiotic
tradition, which is sometimes called the \emph{enduring
features}approach, ecosystems are interpreted as ecologically homogenous
areas of terrestrial or marine geography (e.g., Zhao et al 2020). While
biotic variables may be employed to name, map, or describe ecosystems
defined through this tradition, biota are usually viewed as ephemeral
products of more enduring abiotic drivers, such as climate, landform,
soil, hydrology, and geology. These latter physical or marine
geodiversity features are considered the building blocks of ecosystems
(Sayre et al 2009). This approach deemphasizes ecosystem function and
dynamics, focusing on steady-state expressions of ecological
variability. Units developed through the abiotic tradition are sometimes
called geo-ecosystems (Rowe and Barnes 1994) and they are most applied
at broader spatial scales. Biomes, ecoregions, ecozones, ecosites, and
landscape ecosystems are prominent examples of units developed,
following this tradition, in the contemporary literature (e.g., Yang et
al 2017, Keith et al 2022).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 1.} Ecosystem spatial pattern modelling framework
components: (A). Ecosystem field surveys, encompassing measures of
biotic and abiotic variables. (B). Data Compilation and Refinement. (C)
Final model inputs including training and predictor data. (D). Model
Building and Assessment. (E). Spatial prediction of ecosystem
constituents and properties. (F) Spatial predictions of ecosystem
patterns and properties, at local (i.e., within individual ecosystems or
ecosystem types) and landscape (i.e., among ecosystems or ecosystem
types) extents. E and F adapted from Pollock et al 2020.

\textbf{Table 1.} Practical solutions for common challenges anticipated
during ESPM implementation, following workflow components outlined in
Figure 1.\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.30\columnwidth}\raggedright\strut
\textbf{Component}\strut
\end{minipage} & \begin{minipage}[b]{0.30\columnwidth}\raggedright\strut
\textbf{Challenge}\strut
\end{minipage} & \begin{minipage}[b]{0.30\columnwidth}\raggedright\strut
\textbf{Solution}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\textbf{Ecosystem survey (A)}\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Optimizing survey effort across disparate environmental gradients,
scales, and spatial contexts\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Implement stratified random survey design (e.g., Metzger et al
2013)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Fixed spatial grains may bias some survey data\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Explore utility of plotless survey methods (Cogbill et al 2018)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Subjective survey site selection may introduce spatial bias\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Coarse-grain (sensu Newman et al 2019) data to common raster grid cells
(Miller et al 2004)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
\textbf{Training Data Compilation (B) and} \textbf{Finalization
(C)}\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Measurement scales and units employed for biotic and abiotic field
survey variables differ markedly\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Convert survey measurements to presence/absence records (K\selectlanguage{ngerman}önig et al
2019)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Disproportionate ratios of biotic to abiotic variables\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Pool species by common ecological traits (Kissling et al 2018)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Adequacy of survey data\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Utilize rarefaction methods (Chao and Jost 2012)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Effects of spatial survey grain and extent on training data
structure\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Utilize rarefaction methods (Chao and Jost 2012); test for scale
dependencies using independent data sets with differing spatial grains
(Mod et al 2020)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Training data dimensionality impacts model performance\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Scale pools of test data across levels of ecological complexity; reduce
or eliminate disjunctions (sensu Miller et al 2004) in test data\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
\textbf{Predictor Data Compilation (B) and} \textbf{Finalization
(C)}\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Determining relevant conceptual, theoretical, and statistical criteria
for selecting predictor data\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Draw on key theory from relevant disciples. Select predictors to resolve
joint biotic-abiotic patterns and processes shaping ecosystems at
various scales\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Mismatched spatial resolution of predictors and response variables (Bryn
et al 2021)\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Coarse-grain training data to match predictor grain (Newman et al 2019);
assess effect of spatial scaling on model performance (K\selectlanguage{ngerman}önig et al
2021)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Unequal numbers of biotic and abiotic predictors\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Employ pilot models to test the effect varying ratios, and combinations,
of biotic and abiotic predictors has on ESPM performance (Brodie et al
2020)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Implications of pooling disparate predictors shaping ecosystem pattern
across spatial grains\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Determine whether modelled responses are shaped more by local and or
regional drivers (e.g., Soranno et al 2019), and whether responses vary
among ecosystems and ecosystem constituents\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Implications of grouping predictors of direct, indirect, and resource
gradients (Austin 2013)\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Clarify expected responses of individual and aggregate ecosystem
features (Table S1) to individual environmental gradients (Austin
2013)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Optimizing combinations of predictors\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Explore implications of co-variate trade-off (Brodie et al 2020)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\textbf{Model Building and Assessment (D)}\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Model algorithm selection\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Seek ESPM algorithms with adequate flexibility, functionality, and
predictive capacity. Candidate algorithms may be adapted from
community-level (e.g., Nieto-Lugilde et al 2018) or bioregion modelling
(e.g., Hill et al 2020) techniques.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Determining model settings\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Settings (e.g., cross-validation, latent variables, random effects,
residual associations) depend on selected algorithm and on results of
trial model implementations; consult published methodological guidelines
(e.g., Ovaskainen and Abrego 2020, Mokany et al 2022)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Evaluating model fit and performance\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Metrics for evaluating model fit and performance vary by algorithm and
modelling intent; consult appropriate guidelines (Ara\selectlanguage{ngerman}újo et al 2019,
Zurell et al 2020)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Translating model prediction to mapped spatial outputs\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Continuous (e.g., ordination) or discrete (e.g., region of common
profile) post-hoc analytical outputs can be mapped in YUV colour space
(e.g., Tikhonov et al 2020)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\textbf{Intrinsic Predictions (E)}\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Determine value of lower-order intrinsic (e.g., biotic and abiotic
ecosystem constituents and properties) predictions for informing
higher-order modelling objectives\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Improve understanding of commonalities, potential interactions, and
properties of individual variables characterizing ecosystems or sites;
disentangle the relative contributions of individual variables to
assembly mechanisms; relate model results to existing ecological
knowledge\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\textbf{Extrinsic Predictions (F)}\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Select method for resolving the identities, features, and distribution
of disparate ecosystems and ecosystem types\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Adapt classification methods and indices (e.g., similarity, clustering,
ordination) developed for community-level (Ferrier and Guisan 2006) or
bioregion modelling (Hill et al 2020)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Explore utility of less common tools: concordance analysis (e.g., Taranu
et al 2020), ecological uniqueness indices (e.g., Dansereau et al 2022),
or embedding techniques such as T-SNE (e.g., Sonnewald et al
2020).\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 2.} Different algorithms considered for predictive
ecosystem modelling.\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
\textbf{Modelling algorithm} & \textbf{Algorithm Notes} & \textbf{R
package(s)} & \textbf{References}\tabularnewline
\midrule
\endhead
Multivariate regression tree (MRT) & multiresponse extention of
classification and regression tree (CART) & mvpart (discont.) &
Nieto-Lugilde et al 2018, Norberg et al 2019\tabularnewline
Multiresponse multivariate adaptive regression splines (MMARS) &
multiresponse version of multivariate adaptive regression splines (MARS)
& MDA, EARTH & Nieto-Lugilde et al 2018, Norberg et al
2019\tabularnewline
Constrained linear ordination (CLO) & similar to generalized linear
model (GLM) & VGAM & Nieto-Lugilde et al 2018, Norberg et al
2019\tabularnewline
Constrained quadratic ordination (CQO) & generalized linear model (GLM)
with quadratic response & VGAM & Nieto-Lugilde et al 2018, Norberg et al
2019\tabularnewline
Constrained additive ordination (CAO) & similar to generalized additive
model (GAM) & VGAM & Nieto-Lugilde et al 2018, Norberg et al
2019\tabularnewline
Multiresponse artificial neural networks (MANN) & a type of machine
learning & NNET, neuralnet & Nieto-Lugilde et al 2018, Norberg et al
2019\tabularnewline
Multivariate stochastic neural network (MISTN) & a type of machine
learning & MISTNET & Harris 2015, Nieto-Lugilde et al 2018, Norberg et
al 2019, Zhang et al 2018\tabularnewline
Hierarchical Bayesian Modelling (HBM) & a relatively newer application
of Bayesian algorithms & spBayes, BayesComm, HMSC, boral, or rosalia &
D'Amen et al 2017, Nieto-Lugilde et al 2018, Norberg et al 2019,
Ovaskainen et al 2017, Warton et al (2015), Wilkenson et al 2019, Zhang
et al 2018\tabularnewline
Latent variable model (LVM) & Bayesian implementation; overlap with HBM
& R2jags, gllvm & Hui et al 2015, Warton et al 2015, Ovaskainen et al
2017\tabularnewline
Generalized dissimilarity modelling (GDM) & use continuous functions to
model community patterns by considering variation in species along
environmental gradients & gdm & D'Amen et al 2017, Nieto-Lugilde et al
2018, Norberg et al 2019\tabularnewline
Gradient forest (GF) & community level extension of Random Forest &
gradientForest & Nieto-Lugilde et al 2018, Norberg et al
2019\tabularnewline
Region of common profile (RCP) & Less frequently applied in ecology &
RCPmod & Lyons et al 2017\tabularnewline
Generalized joint attribute modelling (GJAM) & not commonly applied;
conflicting evidence on predictive performance (Zhang et al 2018) & gjam
& Zhang et al 2018, Norberg et al 2019\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 3.} Evaluation of different algorithms considered for
predictive ecosystem modelling. Features are drawn from recent reviews
(Nieto-Lugilde et al 2018, Norberg et al 2017), methodological guides
(Mokany et al 2022), personal communication (Ovaskainen 2021), and from
assessments of individual algorithms (e.g., Poggiato et al 2021).
Algorithms described in Table 2. A -- Multivariate regression tree, B --
Multiresponse multivariate adaptive regression splines, C -- Constrained
linear ordination, D -- Constrained quadratic ordination, E --
Constrained additive ordination, F -- Multiresponse artificial neural
networks, G -- Multivariate stochastic neural network, H - Hierarchical
Bayesian model / Latent variable model, I -- Generalized dissimilarity
modelling, J -- Gradient forest, K -- Region of common profile, L --
Generalized joint attribute modelling\selectlanguage{english}
\begin{longtable}[]{@{}llllllllllllll@{}}
\toprule
& & \textbf{Algorithm} & \textbf{Algorithm} & \textbf{Algorithm} &
\textbf{Algorithm} & \textbf{Algorithm} & \textbf{Algorithm} &
\textbf{Algorithm} & \textbf{Algorithm} & \textbf{Algorithm} &
\textbf{Algorithm} & \textbf{Algorithm} &
\textbf{Algorithm}\tabularnewline
\midrule
\endhead
\textbf{Features} & \textbf{Features} & \textbf{A} & \textbf{B} &
\textbf{C} & \textbf{D} & \textbf{E} & \textbf{F} & \textbf{G} &
\textbf{H} & \textbf{I} & \textbf{J} & \textbf{K} &
\textbf{L}\tabularnewline
\textbf{Data Inputs} & Abundance records can be employed as training
data & & & & & & \selectlanguage{ngerman}ü & & \selectlanguage{ngerman}ü & & & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü\tabularnewline
& Flexibility to accommodate pools of biotic and abiotic variables as
training data & & & & & & \selectlanguage{ngerman}ü & & \selectlanguage{ngerman}ü & & & \selectlanguage{ngerman}ü &\tabularnewline
& Categorical and continuous variables can be included as training data
& & & & & & \selectlanguage{ngerman}ü & & \selectlanguage{ngerman}ü & & & \selectlanguage{ngerman}ü &\tabularnewline
& Categorical and or continuous predictor data can be employed & \selectlanguage{ngerman}ü & & &
& & \selectlanguage{ngerman}ü & & & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & &\tabularnewline
& Large datasets efficiently handled & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & & & & & \selectlanguage{ngerman}ü & & & &
&\tabularnewline
& Traits, phylogeny, and other ancillary data can be incorporated & & &
& & & & & \selectlanguage{ngerman}ü & & & &\tabularnewline
\textbf{Implementation} & Model outputs easy to visualize, understand,
and interpret & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & & & & & & & & & &\tabularnewline
& Readily available tutorials and examples of code & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü &
& & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & & &\tabularnewline
& Technically challenging to implement and fit models & & & & & & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü
& \selectlanguage{ngerman}ü & & & &\tabularnewline
& Computationally demanding and time consuming to run & & & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü &
\selectlanguage{ngerman}ü & & \selectlanguage{ngerman}ü & & & &\tabularnewline
& Results can be challenging to interpret & & & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü &
& \selectlanguage{ngerman}ü & &\tabularnewline
& Inscrutable or ``black box'' approach & & & & & & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & & & &
&\tabularnewline
\textbf{Analytical Properties} & Allows for non-linear responses & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü
& & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü\tabularnewline
& Allows for interaction between predictor variables & \selectlanguage{ngerman}ü & & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü &
\selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & & & \selectlanguage{ngerman}ü &\tabularnewline
& Accounts for unexplained co-occurrences & & & & & & & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & & & &
\selectlanguage{ngerman}ü\tabularnewline
& Uncertainty can be explicitly quantified & & & & & & & & \selectlanguage{ngerman}ü & & & \selectlanguage{ngerman}ü &
\selectlanguage{ngerman}ü\tabularnewline
& Predicts compositional differences between locations as a continuous
function of environmental gradients & & & & & & & & & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü &
&\tabularnewline
& Dissimilarities between pairs of sites related to differences in
environmental conditions and geographic (distance) isolation & & & & & &
& & & \selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & &\tabularnewline
\textbf{Performance} & Moderate to high predictive power & & & & & & & &
\selectlanguage{ngerman}ü & \selectlanguage{ngerman}ü & & &\tabularnewline
\bottomrule
\end{longtable}

\selectlanguage{english}
\FloatBarrier
\end{document}

