A structural equation modeling approach for

Ecological Informatics 41 (2017) 74–90

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Ecological Informatics journal homepage: www.elsevier.com/locate/ecolinf

A structural equation modeling approach for formalizing and evaluating ecological integrity in terrestrial ecosystems

MARK

Franz Mora Sistema de Información Espacial para el Soporte de Decisiones sobre Impactos a la Biodiversidad (SIESDIB), Comisión Nacional para el Uso y Conservación de la Biodiversidad (CONABIO), Liga Periférico - Insurgentes Sur, Núm. 4903, Col. Parques del Pedregal, Delegación Tlalpan, 14010 Ciudad de México, Mexico

A R T I C L E I N F O

A B S T R A C T

Keywords: Ecological integrity Spatial indicators GIS SEMs Predator-prey interactions Apex predators

Ecological integrity is a functional property that integrates habitat functions and species information for maintaining key ecological interactions in predator-prey systems. As a functional property, ecological integrity can be modeled as a latent concept from observable spatial attributes that measure the ecosystem's capacity to provide suitable habitat conditions for apex predators. Ecological integrity is a tri-dimensional concept that stems from “stable”, “concurrent” and “intact” conditions. A theoretical framework and a methodology is presented here for modeling ecological integrity from observable attributes (as GIS layers) to obtain a spatial representation of the integrity condition. From a theoretical framework, the ecological integrity concept is obtained with a structural equation modeling approach, where several other latent variables are obtained for characterizing a hierarchical network of spatial information. Later on, these observable attributes, and several latent modeled variables are translated into sources of geographic information that can be used to monitor changes in the natural remnant areas due to human impacts. When examining the direct, indirect and total effects of habitat loss and fragmentation on ecological integrity, spatial intactness (e.g., the amount of remnant habitat and connectivity) and stability (resistance in the interaction network and mobile links) are the attributes more affected by the pathway effects. The balance of the formative parameters obtained for the model supports the idea that ecosystems that have a high degree of integrity should maintain a high level of stability, selforganization and naturalness. These attributes are achieved when spatial habitat intactness and species interactions are maintained.

1. Introduction The human transformation of natural landscapes is still the major contributing factor for loss and degradation of the complexity and condition of ecosystems, by promoting habitat fragmentation and species loss (Ewers et al., 2010; Jantz et al., 2015; Sih et al., 2000). As historical natural ecosystems become highly impacted by human activities, the capacity for recovering their self-organization and selfregulation towards stable conditions after impacts is greatly affected by the ecological integrity of surrounding natural areas. Due to habitat loss effects, changes in community assemblages and composition lead to a subsequent loss of species interactions, particularly disrupting functions at the top of ecological hierarchy (Valiente-Banuet et al., 2015). However, large carnivores, as top predators, are necessary for maintaining biodiversity and ecosystem function (Ripple et al., 2014). Habitat loss is the main process reducing ecological integrity for top predators by modifying key ecological processes (Haberl et al., 2007) and by producing negative effects on their habitats (Ripple et al., 2014; Theobald, 2013).

E-mail address: [email protected]. http://dx.doi.org/10.1016/j.ecoinf.2017.05.002 Received 12 October 2016; Received in revised form 4 May 2017; Accepted 6 May 2017 Available online 07 May 2017 1574-9541/ © 2017 Elsevier B.V. All rights reserved.

Ecological integrity is a key concept in natural resource management (Brown and Williams, 2016; Thompson, 1999; Tierney et al., 2009). With landscape transformation targeting remnant natural areas, ecological integrity is the primary feature that is highly at risk due to human impacts. Integrity in ecological systems has been defined as “the capacity of the ecosystem to support and maintain a balanced, integrated, adaptive biological system having the full range of elements and processes expected in the natural habitat of a region” (Angermeier and Karr, 1994; Karr, 1990; Parrish et al., 2003). The lack of ecological integrity in human transformed landscapes is directly linked to changes in ecosystem's structure and function, which result in degradation processes that lead to biodiversity loss (Millenium Ecosystem Assessment, 2005a,b). As a theoretical concept, ecological integrity is a latent, complex variable that stems from the complexity of ecological processes and from mechanisms that sustain ecological interactions resulting from the complexity of biodiversity (Farnsworth et al., 2012; Jax, 2010). Therefore, ecological integrity is a characteristic that emerges from the interaction of several ecological processes. These provide ecosystems

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effects that habitat loss and fragmentation may exert on ecosystem properties that sustain viable populations of apex predators. Spatial information regarding complex interaction of apex predators and their habitat, along with mapped effects of habitat loss and fragmentation on mammalian apex predators is used as a surrogate for ecological integrity manifestations. For a practical definition, structural equation modeling (SEM) is used here as the main methodological approach for describing and monitoring ecological integrity. SEM in natural systems is a methodological framework that has been previously used to analyze latent variables in complex relationships (Grace et al., 2010; Grace and Bollen, 2008). As a latent variable, ecological integrity has been modeled with SEM using habitat functions (Capmourteres and Anand, 2016); for evaluating agricultural impacts on aquatic biological integrity and health (Riseng et al., 2011; Sanchez et al., 2015); for evaluating habitat loss effects on ecological processes (Altamirano et al., 2016); soil ecology mapping (Angelini et al., 2016; Eisenhauer et al., 2015) patterns of species occurrence (Joseph et al., 2015); and for deriving environmental indicators for conservation strategies (Santibáñez-Andrade et al., 2015). Here, an approach suitable for a spatial analysis context is developed based on SEM. The methods rely on a framework that integrates the use of SEM and geographic information systems (GIS) as a way to model ecological integrity as a spatial latent variable. In addition, the SEM provides a framework for implementing an analysis to confirm the presence of latent variables from the interaction among spatial indicators of ecological integrity. The additional information derived from SEM is also useful for evaluation purposes when emerges from the theory that supports the formalization of the proposed ecological integrity concept. Later on, the set of spatial information derived from the modeling framework can be integrated into the spatial decision support system (SDSS) where is presented as a tool for monitoring changes in the ecological integrity condition for the remnant natural landscape.

with the ability to self-organize and maintain stability while remaining natural (without human influence). As observed throughout emergent properties, integrity is best described by characteristics associated with concepts of sustainability, naturalness, stability (Andreasen et al., 2001) and self-organization (Jax, 2010). For that reason, ecological integrity evaluations are increasingly being used for guiding and organizing ecological monitoring programs (Wurtzebach and Schultz, 2016). The main goal of this research is to present a set of concepts translated into spatial information that help to formalize the concept of ecological integrity for monitoring purposes. With a practical definition of ecological integrity, a hierarchical analysis framework can be developed using spatial information as primary source for decision making (Ferretti and Pomarico, 2013; Imam et al., 2011; Lin et al., 2009). Therefore, the ecological integrity concept is used here a main directive to define a set of spatial indicators (manifest and latent) that support an analysis that help to characterize the potential of remnant natural landscapes to sustain predator-prey interactions in Mexico. As observable indicators of ecological integrity, the spatial indicators developed here serve as a way to summarize and describe the status of predator and prey species and their habitat. They can serve to diagnose the current habitat conditions, and to monitor significant changes that jeopardize the sustainability of viable populations. Spatial indicators of ecological integrity also serve to create a structure in decision making, based on hierarchies and networks of relevant information (Saaty and Shih, 2009). 1.1. Ecological integrity and spatial decision support systems A spatial decision support system (SDSS) for top predators and their habitat conservation in the remnant landscape of Mexico is the goal for ecological integrity evaluations. A SDSS based on ecological integrity must combine spatial information, multicriteria decision analysis and optimizing models (Rushton, 2001), assuming that transformation of the natural landscape in the form of habitat loss and fragmentation directly affects the attributes and processes associated with naturalness, stability and self-organization in ecosystems. Ecological integrity becomes a practical concept for implementing a SDSS when the elements that shape the self-identity characteristics of the concept are clearly defined, and has a practical meaning when the concept of integrity is linked to human impacts. In order to develop a practical definition for a SDSS, the ecological integrity concept is first associated with a set of emergent properties, which are notions derived from the knowledge gained from analyses of the pattern and processes of biodiversity (Geneletti, 2008). Ecological integrity is considered here as a functional property that integrates habitat functions and the spatial requirements for species, that maintain key ecological interactions in predator-prey systems. The main concept is derived from a collection of several sub-concepts which formalize the procedure of data mining and knowledge discovery when exploring direct and indirect relationships among concepts and observed variables represented as geographic indicators. Then, a practical definition of ecological integrity is primarily sustained by spatial information, and a theoretical model help to establish a plausible ecological hypothesis on how ecosystems are impacted by human transformation. In addition, ecological integrity concepts are connected and interact with other information levels, forming an entire ecological hierarchy. Therefore, both vertical and horizontal connection among concepts and manifest variables come into play to define emergent properties (Jorgensen and Nielsen, 2013) that can be used in an ecological hierarchy framework for decision making (Lin et al., 2009). Once an operational definition is available, an evaluation and monitoring system of the integrity of predator-prey interactions and their habitat can be implemented. The evaluation system is constructed around spatial indicators that measure changes in ecological integrity attributes by monitoring landscape changes, and by describing the

2. Methods The methods used for building an ecological integrity model include: (a) spatial analysis to produce several spatial indicators, and (b) structural equation modeling for establishing a hypothetical link between structure and function in ecosystems, based on the interaction of the spatial variables used for defining several concepts. The indicators used as manifest variables of ecological integrity are obtained via cartographic models and spatial analysis. Later on, SEM is conducted with several diagnostic procedures that are used to produce and discuss latent variables as measures of ecological integrity. Finally, confirmatory analysis is implemented and supported by the implementation of a SEM based on ecological processes. Furthermore, SEM estimates the values of latent variables that are not observable, which are often referred as hypothesis variables. The latent variables and their relationships provide additional information that is used also as indicators of ecological integrity. This is useful for exploring the quantitative spatial representation of ecological integrity, especially when it is represented using qualitative reasoning (Nuttle et al., 2009). Here, ecological knowledge regarding integrity is directly derived from data describing information variables, which influence and depend on the hypothesis variables. Therefore, the main goal for the SEM framework is to obtain a theoretically based and statistically valid model for ecological integrity. 2.1. Spatial analysis for manifest variables The analysis framework for ecological integrity is theoretically based on species interaction information and evaluates the integrity of a landscape based on the interplay of predator-prey systems (or the lack thereof). The interaction networks (in this case, predator-prey interactions for 239 mammal species) are evaluated for all extant top predators 75

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Fig. 1. Manifest spatial indicators of ecological integrity. (a) Reference conditions for the spatial indicator (prey diversity); (b) current conditions for the spatial indicator (prey diversity); (c) integrity condition for the spatial indicator (prey diversity). Naturalness (predator and prey diversity, functional diversity, remnant habitat, habitat connectivity), self-organization (habitat selection, trophic connectivity), and stability (habitat specialization and network resistance).

expert knowledge associated with predator-prey interactions for terrestrial mammals in Mexico (see Fig. 1; Table 1). The indicators are “constructions” or “stacks” of geographical distributions of species and their possible interactions, which are summarized in geographical layers in a geographical information system (GIS). One widely used method to obtain “stacks of interactions” is to predict the distributions of individual species with niche-based species distribution models (SDMs), also called ecological niche models, ENMs (Guisan et al., 2013), and then to stack them to predict species assemblages based on

(viz., Puma concolor, Puma yagouaroundi, Panthera onca, Leopardus pardalis, Leopardus wieddi, Canis latrans, Ursus americanus and Lynx rufus); and one probably extinct predator in the wild (Canis lupus). The predator-prey interactions are analyzed based on the changes registered from their potential habitat distributions to current conditions. As manifest indicators of ecological integrity, spatial indicators developed here serve as a way to summarize and describe the status of predator and prey species and their habitat. These spatial indicators are based on geographic information and 76

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Table 1 Description of the metrics used for manifest ecological integrity indicators. Ecological metric

Formula

Functional diversity

FD =

Predator and prey diversity

Number of species (S)

Ecological (habitat) specialization

FG S

( ) H

1 2

SSI = ⎡ − 1⎤ ⎣ h ⎦ CSSI = ∑ SSI/S

Habitat selection

Description and interpretation

References

Functional diversity (FD) is a concept used to describe the variety of functional characters, complexity of food webs and functional groups present in a community. As used here, functional diversity indicates the number of species groups that perform different functions within ecosystem, or show similar responses to the environment. For predatorprey interactions all 239 mammal species were categorized in seventeen functional groups. The FD spatial indicator represents the spatial variation of the relationship between the number of functional groups, and the number of species within groups.

(Mason et al., 2005); (Gitay and Noble, 1997).

Predator and prey diversity is expressed as species richness (S). Prey richness is an indicator of the number of preys present from the species´ pool (239 mammal species identified in the interaction networks). Predator richness is the number of predators present as described by the stack-SDMs. Ecological specialization is a measure of the variety of ecological conditions (habitats) where species occur. Here, the term specialization is a manifestation of the tendency of species to occur in different landscapes composed of different species. As a spatial indicator, provides a similarity measure of the geographic co-occurrence of local species, as compared to large-scale occurrence data (SSI). The level of ecological specialization for predators and prey as they occur in the landscape was calculated as a compound of the specialization index for all species occurring in a location (CSSI).

(Vimal and Devictor, 2015); (Devictor et al., 2010; Julliard et al., 2006)

The habitat selection indicator integrates a measure of the species' ability to select all available habitats as a function of their spatial distribution. As such, is an indirect measure of the prevalence of species in the habitat. This indicator is calculated as the average proportion of habitats occupied by all species described in the interaction networks.

Remnant habitat

Amount of remnant habitat

The amount of remnant habitat is associated with the spatial requirements of species which allows a viable population to persist as a meta-population. Remnant habitat is defined here as the proportion (within species´ home range) of viable habitat that is not transformed from its natural condition. Therefore, the amount of remnant habitat is an inverse indication of habitat loss.

(Hendriks et al., 2009); (Riitters et al., 2002)

Habitat connectivity

Probability of habitat adjacency

Habitat connectivity is calculated as the probability of having similar adjacent habitat types within the home-range for all species in the interaction network. Therefore, along with the amount of remnant habitat, it is an indication of habitat fragmentation for top predators.

(Riitters et al., 2002)

Trophic connectivity

Probability of habitat adjacency (for apex predators)

Trophic connectivity is the mobility among different habitats for mobile (in this case trophic) links. Mobile links here are organisms that spread the predator function (apex predators). Trophic connectivity is defined here as the probability that a top predator can visit similar adjacent habitats and perform its ecological role within their surrounding landscape. Trophic connectivity is associated with predator's mobility by analyzing the spatial heterogeneity within its home range. The trophic connectivity is calculated as the probability of adjacency of similar habitats for apex predators, based on the model developed for evaluating habitat fragmentation at landscape scale.

(Lundberg and Moberg, 2003). (Riitters et al., 2002)

Network resistance

C=

Here, network resistance (within an species' interaction network) is an indicator that shows the capacity of the trophic network to resist changes due to species loss by measuring species connectivity (C) as an indirect measure of resistance (resistance increases as connectivity increases). Therefore, connectivity integrates the information about number of species (S), and number of interactions or links (L) within an interaction network

(Dunne et al., 2002)

L S2

ecological indicators (EIi) used here are obtained as spatial information that show the ecological condition resulting from the habitat loss relative to the reference conditions (Fig. 1a,b,c; Eq. (1)). As change indicators, the reference condition for each ecological characteristic (ECr); i.e., the integrity in their spatial patterns (without habitat loss effects) is established with the information that describe the potential distribution of species without human effects. This potential distribution is attained from species distribution models (SDMs) obtained from

hypothetical interactions (stacked-SDMs) (Dubuis et al., 2011). The stacked-SDM or “constructions” are used here as manifest variables to build the concepts used in the theoretical model. Subsequently, they are used in the structural equation model for hypothesis testing. The emergent properties that the ecological integrity concept conveys are often identified from a reference state or reference dynamics in the ecosystem, and therefore, ecological integrity is essentially a change indicator of reference conditions (Andreasen et al., 2001). Therefore, all 77

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included to complement the natural habitat condition. These variables included elevation and slope terrain derived from the global ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) DEM at 1 arc-second resolution (Earth Observing System Data and Information System (EOSDIS), 2009).

ecological niche modeling for all species associated with interaction networks (predator-prey interactions for 239 mammal species) and available in CONABIO's geolibrary of biodiversity information (SNIBCONABIO; http://www.conabio.gob.mx/informacion/gis/). The current condition (ECc) is established when the information of habitat loss and landscape transformation (INEGI series 4.0, 2010) is combined with the niche models to produce information about the current distribution of species. All spatial indicators are expressed as a deviation of reference conditions as:

EIi =

2.2. Structural equation modeling and latent variables The SEM is a framework that relies on a priori theoretical model to derive theoretical constructs (or concepts) from empirical data from which direct measurements are not available. The conceptual model used here to derive ecological integrity as a latent variable emerges from biodiversity information and interaction networks (Fig. 2). The model represents statistical dependencies or associations between observed and latent variables, based primarily on theoretical relationships which impose a model structure that is statistically tested for confirmatory purposes. A model fit test the validity of model structure; i.e., the proposed relationships among variables, based on the difference between the observed and calculated co-variance matrices, validating also the individual pathways proposed in the conceptual model. The link between ecological integrity and biodiversity is established when ecological processes (which vary geographically and ecologically) are maintained within an ecosystem throughout species interactions.

ECr − ECc ECr

(1)

where, EIi is the ecological integrity indicator for the ith ecological metric; ECr is the reference condition and ECc is the current condition. The indicator shows the proportion of change if ECr < ECc; otherwise the EIi = 1; when ECr = ECc. All reference and current conditions are evaluated from a set of ecological characteristics described in Table 1. When the human impact component is considered for the habitat of species, indicators of spatial intactness in the landscape (e.g., the inverse of habitat fragmentation) are included as manifest variables. These are the amount of remnant habitat and connectivity (Riitters et al., 2002) within the home range of apex predators. Additionally, two terrain variables that form the concept of landscape heterogeneity were

Fig. 2. Conceptual meta-model proposed for building the concept ecological integrity using manifest variables developed in this approach.

78

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processes involved in this balancing process are convergence and divergence (Phillips, 1999). Furthermore, self-organization is a natural tendency in ecosystem development that coordinates, regulates and controls all of the ecosystem components involved in the natural process (Anderson, 1991), which in turn reflects a certain level of complexity reached after an impact through mechanisms of ecological memory (diversity and trophic connectivity). Throughout the self-organization process, a maturity state can be reached (Levin, 2005; Odum, 1988) in which species interactions promote an evolutionary strategy (such as ecological specialization) for habitat selection and adaptation, allowing habitat occupation for species and their corresponding strategies. On the other hand, stability is a generic term for a whole series of properties in an ecosystem (Grimm et al., 1992). Stability can be defined as the tendency of the ecosystem to maintain itself without structure or function changes due to environmental variability or perturbations by balancing resilience and resistance (Vallina and Le Quéré, 2011). Stable conditions maintain all of the relationships established by the self-organization process at equilibrium (or when there exists a the balance between divergence and convergence) and therefore produce a structure and function that are characteristic of a steady state. A stable condition integrates the concurrent self-organization properties of ecosystems, including, the persistence of all components (particularly species and interactions) under constant conditions via self-stabilization, where the probability of persistence is at a maximum for all occurring species (Oldfield, 1983). All of these components interact simultaneously at a particular ecological domain to sustain ecological integrity. A human modification of the natural state of ecosystems has direct effects on naturalness and indirect effects on self-organization and stability and therefore on ecological integrity (Fig. 2). Possible negative impacts (arrows 6–8 in Fig. 2) directly result from modification of the natural landscape when human activities promote habitat loss and habitat fragmentation, which in turn increase the extinction probability of species and the loss of their interactions and decrease their viability. Naturalness, self-organization and stability all have positive effects on ecological integrity by maintaining the conditions that allow self-regulatory and evolutionary processes to occur (as indicated by arrows 1–5, Fig. 2). When evaluating ecological integrity via predator-prey interactions, these regulatory and evolutionary processes are associated with stability and are linked with the interaction resistance of trophic interactions (as a result of predator and prey richness) and functional diversity (indirectly measured as the number of functional groups) as observed variables (as indicated by squares in Fig. 2). Self-organization also has a positive effect on ecological integrity (arrow 3) when mobile links and ecological memory allow an ecosystem to recover from human impacts. Self-organization is indirectly observed by the presence of trophic connectivity and habitat specialization and selection, which are all indirect, observed measures of mechanisms that promote unity, cohesion and ecological memory.

Table 2 Definition of variables used in the SEM for ecological integrity. Spatial indicator

Variable type

Ecological integrity Naturalness Stability Self-organization Biodiversity Spatial intactness Mobile links

Endogenous latent

Landscape heterogeneity

Exogenous latent

Prey richness Predator richness Trophic connectivity Functional diversity Habitat specialization Habitat selection Interaction resistance Remnant habitat Habitat connectivity

Endogenous manifest

Elevation Slope

Exogenous manifest

Due to the importance of predator-prey interactions for ecosystem functioning, they are used here in a SEM for ecological integrity. In this model, the main top-down process that describes the importance of key species in maintaining ecological integrity is the predator-prey interaction. Predator-prey interactions have a positive effect on ecosystem functions when greater predator diversity improves herbivore suppression, indirectly impacting plant biomass (Finke and Snyder, 2010). Additional effects include niche complementarity, functional facilitation, sampling and dilution effects and intra-guild predation, all of which impact the stability of ecological rates or stocks over time (Finke and Snyder, 2010). The negative effects of losing predator diversity within ecosystems include cascading effects (O'Connor et al., 2013) and prey suppression (Finke and Snyder, 2010). 2.3. A theoretical framework for an ecological integrity model From ecological theory, the ecological integrity concept emerges as a complex construction of several ecological principles (Fig. 2). The interaction among naturalness, stability, and self-organization conform the core of the concept. Naturalness is frequently associated with human impacts in ecosystems. Then, it is sometimes defined as an alternative state (which is, in turn, self-organized and stable) resulting from self-regulatory processes, which reflects a condition without any human influence (Anderson, 1991). A natural or intact state is mostly characterized by the presence of native biodiversity, and the corresponding species interactions result in a certain level of ecological complexity, without which the ecosystem would increase in fragility according to human impacts, which would result in a consequent loss of coherence. Additionally, a natural state can be defined, as the degree to which an ecosystem would change towards a steady-state without human presence, after being impacted or modified by human activity (as a measure of environmental impact). In this approach, a direct way to evaluate a natural condition is to determine how the natural habitat for species is transformed and the degree of human impact that is observed as habitat loss and fragmentation. Self-organization is a process that causes macroscopic order (regionally) from microscopic disorder (through process operating at small scales) and is therefore an emergent property that results from the balance of external forcing and internal constraints (Oldfield, 1983). As such, self-organization is an inferred condition that is manifested when several ecological processes reach a state of balance. The ecological

2.4. Structural equation model estimation and evaluation After developing a conceptual model, the meta-model assisted the modeling process, identifying all possible (hypothetical) path relationships (arrows in Fig. 2). For model evaluation and parameter estimation, a set of 1,937,913 cases (which represent the total number of pixels contained in a spatial indicator raster map at 1 km2 resolution) and 19 variables (8 latent and 11 manifest) were used for the model (Table 2). For the development of the structural equation model, all latent variables were defined in the meta-model as a combination of several manifest variables. The application of the SEM framework allowed the estimation of latent variables, assuming that all are reflective; i.e., they are assumed as the cause of co-variation in all their manifest variables. Therefore, the purpose of confirmatory factor analysis is to gain an understanding of the internal structure that produces multiple 79

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the maximum-likelihood method (Table 3). Additional measures of fitness showed agreement between the model-implied and the observed covariance matrices, particularly with the comparative fit index associated with the agreement between the model-implied covariance (CFI = 0.916) and the Standardized Root Mean Square Residual for covariance matrices (SRMR = 0.04), presenting favorable values for fit assessment (Bagozzi and Yi, 1988; Hooper et al., 2008; SchermellehEngel et al., 2003). The standardized path coefficients for manifest variables (which show the magnitude of the variable effects on each latent variable) were statistically significant (Table 4) and had similar values, which indicates a good fit and stable structure that is a reliable representation of the latent variables obtained (Grace and Bollen, 2008). The estimated model effects (indirect, direct, and total) on endogenous and latent variables, are presented as standardized path coefficients (Table 5). The latent variables obtained with the model have a good representation and are able to define the emergent concepts, as depicted by their spatial values (Fig. 4). Here, landscape heterogeneity is a concept that is mainly derived from a combination of the slope (0.18; pvalue < 0.05) and elevation (0.08; p-value < 0.01), which suggests that terrain with high steepness at higher elevations is more complex. Spatial intactness is the result of the two variables that determine habitat fragmentation in a combination that suggests that a large amount of remnant habitat (1.0; p-value < 0.01) with a high connectivity (0.93; p-value < 0.01) provides the results of an intact landscape. The concept of biodiversity expresses a combination of both predator (0.85; p-value < 0.01) and prey (1.0; p-value < 0.01) richness. Formative latent variables for ecological integrity are also consistent with their reflective variables. The pattern of variation due to error in ecological integrity is < 15% (R2 = 0.86). Naturalness integrates the positive effects of two latent factors (biodiversity and spatial intactness) and a negative effect of landscape heterogeneity (−0.76; Table 3; Fig. 3). Stability is reached when the interaction resistance (or species' connectivity) is combined with two other latent concepts; mobile links and naturalness. Pattern of variation due to error in stability is ~20% (R2 = 0.80). Self-organization is a manifestation of habitat selection (0.9; p-value < 0.01) and specialization (0.9; p-value < 0.01) and affected by naturalness and stability. The variation due to error in selforganization is ~14% (R2 = 0.86). The interaction among latent variables forms the path-sequence of interactions that compose the main latent ecological integrity, and therefore, these latent variables are considered to be the causes of variations in integrity (Table 5). Therefore, ecological integrity is itself an effect variable formed by latent changes that are produced by exogenous manifest variables (e.g., landscape) and spatial intactness as a result of habitat loss. The loss of ecological integrity (as an effect of habitat loss and fragmentation) is also considered to be the cause of the co-variation of manifest variables, which allows the model of ecological integrity to be a combination of direct and indirect causes of species and habitat losses (as measured in the manifest variables). Overall, the model confirms that naturalness (0.37; Fig. 3), self-organization (0.37; Fig. 3) and stability (0.23; Fig. 3) have significant positive and direct formative effects on ecological integrity. When the strength of the compound path is considered, the greatest total effect on ecological integrity is from stability (0.535; Table 3; Fig. 3), which is greater than naturalness (0.389; Table 3; Fig. 3) and self-organization (0.370; Table 3; Fig. 3). These positive formative effects mainly occur because spatial intactness (0.82; Table 3; Fig. 3) and biodiversity (0.69; Table 3; Fig. 3) have, in turn, strong total effects on naturalness, which supports the idea that a natural landscape condition is the direct result of a suitable and connected remnant habitat with high values for both predator and prey richness. Mobile links (0.083; Table 3; Fig. 3) has the greatest total effect on stability and lesser indirect effects on self-organization and ecological integrity, which indicates that the functional spatial role of predators (trophic links) has a moderate stabilizing effect, more than organizational effects (on self-organization). However,

relationships in the observed variables, which form an implied covariance matrix. In other words, a hypothesis is established in which all latent variables are the causal factors of all co-variations in the spatial indicators. Additionally, all latent variables were represented (or conceptually formed) by a small number of indicators within each latent domain, in which each latent variable has a direct influence on their observables and, as a consequence, the relationships described produce the observed co-variances (Alexander, 2014). Evaluation and assessment of the ecological integrity SEM were based on an adequate overall model fit and the relative stability of the parameter estimates. External validity, as defined by Bollen (2011), was tested as a consistent relationship to other variables and ecological theory. The validity is assessed based on standardized, unstandardized parameters and unique variance estimates (Bollen, 2011). The overall model fit was evaluated by determining the Chi-square (χ2) and other fit indexes, including the Run Mean Square Error of Approximation (RMSEA) and the Standardized Root Mean Square Residual (SRMR) as well as the corresponding significance values. The estimation of the SEM was obtained using a maximum likelihood procedure in the Onyx software (1.0–872 versions, July 2014), which is graphical software that is used to create and estimate SEMs (von Oertzen et al., 2015). Hypothesis tests for model-data consistency were performed using the Chi-square test (χ2) and its associated confidence levels (p-values) as a measure of correspondence between the observed and model-implied covariance matrix. Additional statistical indicators were used to test the model fit. These included the root mean square error approximation (RMSEA, Eq. (2)) and the Standardized Root Mean Square Residual for covariance matrices (SRMR, Eq. (3)) to test for significant differences between the observed covariance and those implied by the model. The overall fit analysis (external validation) used the meta-model presented as a reference (Fig. 2). All of the results and interpretations presented in the results section are based on the judgments of better data; information representation contained within spatial indicators and fit tests obtained for the model.

RMSEA= max[((χ2 df − 1) (N − 1)] , 0)

(2)

where χ is the chi-square value, df is its degrees of freedom and N is the sample size. 2

SRMR=

2

P i ⎡ (sij − σij) ⎤ ⎫ 2∑∑⎢ ⎨ i=1 j=1 (siis jj) ⎥ ⎬ ⎣ ⎦⎭ ⎩

⎧

p(p + 1) (3)

where p = number of observed variables; sij = observed covariances; σij = reproduced variances; Sii and Sjj are the observed standard deviations (Hu and Bentler, 1999). 3. Results 3.1. SEMs of ecological integrity The structural equation model of ecological integrity obtained by the maximum likelihood method is shown in Fig. 3. Several parameters are presented, including (1) the proportion of variation explained by each latent concept (R2); (2) loadings of indicators on latent variables (from latent variables to manifest variables); and (3) path coefficients, both of unstandardized and standardized (in parenthesis) estimates. The incoming paths (from latent variables to ecological integrity) are represented by partial regression coefficients as the change expected if a predictor is varied (in standard deviation units). Therefore, partial coefficients measure the predicted sensitivity of each latent concept to ecological integrity. All latent variables have a reliable representation since all loadings had relatively similar magnitudes and were statistically significant. The structural model showed a good fit (null hypothesis not rejected at 0.05 confidence level) between the concept and model obtained with 80

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Fig. 3. A SEM for ecological integrity in predator-prey interaction networks with parameters describing direct and indirect relationships and interaction effects among latent variables. Ellipses signify latent variables used to represent ecological integrity concepts, while boxes represent observed (manifested) variables. Numbers associated with paths from latent to observed variables represent exploratory factor analysis loadings, while numbers associated with paths between latent variables represent path coefficients. Standardized values for path coefficients are in parenthesis (*p < 0.05; **p < 0.01).

4. Discussion

Table 3 Structural equation modeling (SEM) fit statistics for the structural equation model (SEM) of ecological integrity. The Chi-square statistic (χ2) indicates the overall fit for the structural model to the structure of the data. A good fit shows no significant difference between the data and model (p > 0.05). A root mean square error approximation (RMSEA) estimates approximation errors and tests for causality in model specification. A good fit (RMSEA < 0.06 and SRMR < 0.05) shows that no significant differences occur between the data and model. The comparative fit index (CFI) is a type 3 index based on a non-central χ2 distribution, which is recommended for a small sample size and a non-normal distribution in the data (Tomer and Pugesek, 2003). The Tucker-Lewis index (TLI) is a relative fit index that compares a chi-square for the model tested and from a null model (baseline). CFI and TLI values > 0.9 show a good data-model fit. Statistic

Value

Degrees of freedom χ2 Kulback-Leibler to saturated RMSEA (classic) SRMR (covariances only) CFI (to independent model) TLI (to independent model)

43 1,952,761.6 1.01 0.15 0.04 0.92 0.89

4.1. A definition of ecological integrity from the SEM framework The analytical framework provided by the SEM formalizes ecological concepts that are generally vaguely defined by incorporating specific manifest (observable) variables when building complex ideas that can be quantitatively represented as spatial information. Additionally, all indicators are constructed to show human impact on species interactions and their relationship with habitat loss. The SEM analysis framework sustains the idea that ecological integrity is an emergent property with self-identity characteristics; and clearly supports the idea that land cover transformation and habitat fragmentation have strong effects on the integrity of predator-prey interactions within ecosystems. All of these effects have strong repercussions by reducing the capacity of the ecosystem to sustain the occurrence of apex predators and impact their population viability. Landscape modifications are observed as major impacts when the landscape natural condition is highly modified towards a deteriorated or impacted state. The concept of ecological integrity stemmed directly from the interaction of naturalness, stability and self-organization, as suggested by the conceptual model. This was later confirmed by the structural equation model. As the theory suggested, the ecological integrity concept is tri-dimensional and requires the other three latent variables (sub-concepts) to analyze their formative effects. The model showed external validity, i.e., based on a theoretical framework, sensu (Bollen, 2011), when all three formative latent variables had a positive effect on

naturalness has the greatest formative effect on stability (0.87; Table 3; Fig. 3). Similarly, the greatest indirect effect is observed for naturalness on self-organization (0.365 Table 3; Fig. 3).

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path coefficients), but naturalness and self-organization contribute similarly to the results expected from the theoretical model. Spatial intactness is also an important formative variable that positively and directly affects the notion of naturalness and indirectly affects self-organization. The model of ecological integrity seems to be valid, according to ecological theory and validity assessment (Bollen, 2011; Grace and Bollen, 2008). As a major component of ecological integrity, stability is described here as a state of organization in ecosystems, in which all structural and functional elements remains unchanged due to perturbations and human impact. Unstable conditions show a lack of key elements in maintaining species interactions as a result of trophic downgrading or biotic homogenization (by losing specialist or generalist species) and the disruption of habitat occupation mechanisms (such as habitat selection), all of which produce potential non-desirable effects, such as the loss of horizontal biodiversity and “cascade” effects (Duffy et al., 2007). The components of stability in trophic interactions that are considered here are the mobile links (in a latent form, including trophic links) and interaction resistance in the trophic networks. Then, stability indicators describe the consistency in predator-prey interactions. For trophic relationships, ecological integrity assumes the presence of key components for species interactions (apex predators, mesopredators and prey species), which are in turn organized hierarchically as interaction networks. As manifest variables for structural equation modeling, indicators of naturalness reflect the ecosystem's capacity to maintain species interactions and ecological complexity, as well as the habitat condition to support viable populations of apex predators. The spatial intactness of habitats (or conversely, habitat fragmentation) is an indicator that is based on the combination of two measures that, first, evaluate the amount of remnant habitat, and second, evaluate the habitat adjacency or continuity for top predators. Here, the combination of both measures provides an evaluation of the inverse of the fragmentation condition based on a model developed in landscape ecology research (Riitters et al., 2002). The inverse of the habitat fragmentation of remnant natural areas is calculated within the potential habitat distribution using species' spatial habitat requirements (fragmentation within a home range). The condition of the remnant habitat in the spatial intactness indicator is then evaluated for extant top predators based on changes registered from their potential habitat distribution to current conditions. With the loss of spatial intactness, the natural condition has serious effects on self-organization and stability. As suggested by the structural equation model, spatial intactness has

Table 4 Unstandardized parameter estimates for path coefficients, standard error and associated p-values. Paths

Unst. estimate

Self-organization → ecological integrity Stability → ecological integrity Naturalness → ecological integrity Naturalness → stability Naturalness → self-organization Stability → self-organization Mobile link → stability Biodiversity → naturalness Landscape → biodiversity Landscape → naturalness Landscape → self-organization Landscape → mobile link Spatial intactness → naturalness Biodiversity → predator richness Biodiversity → prey richness Landscape → elevation Landscape → slope Self-organization → habitat selection Self-organization → trophic connectivity Self-organization → habitat specialization Stability → prey richness Stability → interaction resistance Spatial intactness → spatial habitat Spatial intactness → spatial connectivity

S.E.

Z-score

P(> |z|)

1.201

0.08

14.45

< 0.001

1.032 2.158 1.126 0.683 0.587 2.155 0.248 0.836 − 0.298 0.156 0.015 0.333 0.308 0.370 0.071 0.106 0.273

0.08 1.09 0.02 0.04 0.17 1.20 0.01 0.07 0.05 − 0.06 0.01 0.03 0.04 0.08 0.01 0.07 0.01

12.87 1.98 60.53 15.95 3.52 1.79 38.79 12.66 − 6.62 − 2.46 1.49 13.3 7.89 4.62 12.76 1.44 27.28

< 0.001 < 0.001 < 0.001 < 0.001 0.045 0.037 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 0.034 < 0.001

0.483

0.01

40.28

< 0.001

0.452

0.02

21.54

< 0.001

− 0.104 0.810 0.390 0.340

0.09 0.04 0.06 0.09

− 1.22 21.89 6.84 3.82

0.027 < 0.001 < 0.001 < 0.001

ecological integrity, as theoretically formulated. The balance of the formative parameters obtained for the model supports the idea that ecosystems that have a high degree of integrity should maintain a high level of these properties. This indicates that a “high” ecological integrity can occur only as a consequence of “stable”, “concurrent” and “intact” conditions for stability, self-organization and naturalness, respectively (as indicated in Fig. 4). Additionally, the SEM suggested that the natural properties that are associated with biodiversity (predator and prey richness), as well as mobile links, are necessary elements for maintaining a stable and natural condition. Substantive significance can be attributed to stability and spatial intactness as main reflective concepts of integrity (as indicated by the

Table 5 Estimated model effects on endogenous and conceptual variables in SEM model for ecological integrity. Estimates are standardized path coefficients of direct, indirect and total effects of endogenous latent variables. Variable

Effect

Mobile links

Direct Indirect Total Direct Indirect Total Direct Indirect Total Direct Indirect Total Direct Indirect Total Direct Indirect Total

Spatial intactness

Biodiversity

Naturalness

Stability

Self-organization

Naturalness

Stability

Self-organization

Ecological integrity

0.083

0.035 0.035

0.013 0.013

0.713 0.713

0.114 0.114

0.006 0.587

0.600 0.600 0.870

0.096 0.096 0.380 0.365 0.745 0.420

0.005 0.005 0.370 0.019 0.389 0.380 0.155 0.535 0.370

0.083

0.820 0.820 0.690

0.870

0.420

0.370

Bold values represent the latent variables with the highest total effect on ecological integrity.

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Fig. 4. Latent variables as spatial quantitative indicators of ecological integrity obtained with the SEM. (a) Ecological integrity; (b) Naturalness; (c) Stability; (d) Self-organization, (e) Biodiversity; (f) Mobile links; (g) Spatial intactness; and (h) Landscape heterogeneity.

formative effects on concepts other than naturalness, reinforcing the idea that human impact has substantial effects on the properties of all latent concepts, particularly on stability. A strong positive influence of

the remnant habitat and connectivity in forming the concept of stability, in addition to naturalness, sustains the perception that natural landscapes are a necessary condition for stability and self-organization. 83

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Fig. 5. The ecological integrity hierarchy framework for evaluating the condition in natural ecosystems based on landscape characteristics to sustain predator-prey interactions.

of predator-prey relationships, in general, and apex-predators, in particular, shape the natural landscape, conferring to it myriad characteristics and properties (Beschta and Ripple, 2009; Brook et al., 2012; Ripple et al., 2014). Several of these characteristics are manifested here as spatial indicators and are identified as emergent properties with the SEM. Apex predators confer integrity properties to ecosystems via topdown effects (Ripple and Beschta, 2004). Some of these are identified as latent variables, such as mobile links, by integrating trophic connectivity with landscape heterogeneity, and naturalness, by integrating functional diversity as a form of horizontal diversity, sensu (Duffy, 2002; Duffy et al., 2007), and biodiversity in predator and prey. Mobile links can be associated with some other properties, including predation risk (as trait-mediated effects), and control effects in prey and mesopredators (as density-mediated effects). When these top-down effects are removed, the loss of apex predators may produce several cascade effects (Beschta and Ripple, 2009; Murray et al., 2011; Terborgh and Estes, 2010). Here, the effects of land cover transformation and integrity loss in the form of species-interaction loss can also be amplified directed towards habitat selection and interaction resistance (especially when there is a negative relationship between prey density and stability, as identified by the model) by reducing the habitat available for mesopredators. When cascade effects occur, herbivore irruption and mesopredator release could result in a loss of integrity of predator-prey interactions (Galetti et al., 2015a, b).

Spatial intactness has direct repercussions on naturalness and indirect effects on stability and self-organization by modifying the mechanisms of ecological memory (e.g., trophic connectivity) and predator-prey richness. Furthermore, mobile links play a direct role in stability and indirectly in self-organization by maintaining stability through landscape pattern coherence, which organizes and regulates trophic interactions (Peterson, 2002). On the other hand, self-organization indicators are a manifestation of ecosystem's ability to self-regulate and self-maintain the organization of apex predators and their occurrence in the landscape. As an integrity characteristic, self-organization describes ecosystem conditions from a divergent to a concurrent condition. A divergent condition shows that human impact has removed some or all possible elements for habitat occupancy and distribution (e.g., top predators or prey connectivity) in such a way that the ecosystem reflects a loss of the functional balance of trophic connectivity and ecological memory. A concurrent condition shows that all elements that allow a balance between convergence and divergence processes are maintained throughout evolutionary and ecological processes; i.e., by maintaining the presence of apex predators regulates prey patterns in addition to other bottom-up effects. Therefore, the components of self-organization used here describe the trophic connectivity (as a result of trophic mobile links) and habitat selection (as a result of habitat preference or specialization). Self-organization (as defined here) is associated with spatial coherence as an indirect measure of both predators and prey moving freely among habitats by measuring how well they remain distributed after habitat loss. As established in the correspondent path model sequence, stability is an indirect indication of connectivity within trophic networks since it is directly affected by mobile links and is also related to the possible responses of predator and prey losses (e.g., biodiversity loss). Usually, prey and mesopredator irruptions emerge when strong connections exist among top predators and prey (Elmhagen and Rushton, 2007; Ripple et al., 2013; Wang et al., 2015). Mesopredators, in particular, are released when top predators exert strong densitymediated effects. A loss of stability (as defined here) may indicate where possible effects occur for prey and mesopredator irruptions. As confirmed by the structural equation model, the ecological integrity concept, which is related to the function of apex predators within ecosystems, is formed according to the self-identity properties defined by the manifest variables used in the model. In particular, the SEM confirms the importance of self-organization in the landscape and species interactions that maintain stability. It is unarguable that ecosystems without top predators could be considered to be completely integral. A natural landscape without top predators is most likely to degrade ecologically. Therefore, a major consequence of top predator loss is trophic downgrading (Estes et al., 2011) and some forms of ecological degradation, such as extinction debt, as a result of cascade effects (Cardillo et al., 2005; Kuussaari et al., 2009). As suggested, predator-prey relationships play a fundamental role within an ecosystem in maintaining ecological integrity. The presence

4.2. Ecological integrity within a hierarchy network framework The results obtained with SEM define ecological integrity as a function of landscape attributes that describe functional and structural characteristics that sustain predator-prey interactions. The results obtained with the SEM also provide a new set of (latent) indicators that offer a simplified indication of the complexity in ecological conditions. In addition, these indicators suggest a network framework that may be used to test causal interactions between anthropogenic pressures (such as habitat loss and fragmentation) and the current state of ecological integrity. Besides describing the complexity in a causal network, latent indicators also reflect changes taking place at various levels in an ecological hierarchy. The ecological integrity hierarchy includes functional (naturalness, stability, self-organization, mobile links, ecological specialization) compositional (prey diversity, predator diversity and functional diversity) and structural elements (habitat selection, remnant habitat and habitat connectivity) all of which, when combined at different levels, defined the integrity condition in ecological systems. This tri-dimensional representation of the ecological integrity concept is similar to the triangular representation that shows hierarchy in ecosystems (Dale and Beyeler, 2001). The inter-relationship among ecological indicators forms an ecological integrity hierarchy network (EIHN) framework (Fig. 5). Here, the EIHN integrate the relevant ecological indicators that support the information contained at each hierarchy level. The different 84

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Fig. 6. Ecological integrity status for selected landscapes (Biosphere Reserves). Top predator occurrence locations are from 1990 to date (SNIB, CONABIO).

levels show relevant ecological information that goes from the basic or manifested information, to subsequent levels in the hierarchy (1st and 2nd order latent indicators) that support an ecological evaluation. At

the top of the framework are the synthetic or general information that support the notion of a general indicator at the top of the hierarchy (Fig. 5). Therefore, a EIHN framework provides an integrative view of

Table 6 Photographic and indirect historical records for selected landscapes of ecological integrity in Mexico.

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Fig. 7. Top predators and preys in the “Tehuacán-Cuicatlán Biosphere Reserve”. Photograph records for top predators and preys date from 2011 to 2015.

several biosphere reserves are examples of maintaining predator-prey interactions at almost pristine conditions. This can be observed in the mapped landscape condition, and supported by the occurrence of species associated to predator-prey interactions (Fig. 6; Table 6) (delaTorre et al., 2017; Briones-Salas et al., 2016; Carrera-Treviño et al., 2016a; Carrera-Treviño et al., 2016b; Hendriks et al., 2016; Monroy-Vilchis et al., 2016; Ramirez-Reyes et al., 2016; Urrea-Galeano et al., 2016; Cruz-Jácome et al., 2015; Dueñas-López et al., 2015; Farias et al., 2015; Charre-Medellin et al., 2014; Ramírez-Martínez et al., 2014; AhumadaCarrillo et al., 2013; Almazán-Catalán et al., 2013; Botello et al., 2013; Hernández-SaintMartin et al., 2013; Juárez-Casillas and Varas, 2013;

all relevant elements that contribute to sustain integrity in predatorprey interactions in the landscape, covering key elements and offering an overall measure of status (with the general indicator) and a status quantification that can be monitored by observable manifestations of ecological integrity. 4.3. Spatial patterns of ecological integrity in Mexico Spatial distribution of extant top predators and preys are highly associated with the spatial pattern of ecological integrity throughout the country (Fig. 6). With a high ecological integrity landscape status, 86

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Fig. 8. Top predators in the “Sierra de Guerrero”. Photograph records date from 2015 to 2017.

interactions. The set of spatial indicators that form the ecological integrity concept can be then used for characterizing significant differences among selected landscapes, and evaluate their current capacity to sustain ecological integrity. For example, within the “Tehuacán-Cuicatlán” biosphere reserve, the presence of large top predators such as pumas, jaguarondi, bobcats and coyotes (Puma concolor, Puma yagouaroundi, Lynx rufus and Canis latrans) as well as meso-predators like grey foxes (Urocyon cinereoargentus) and their preys like white-tailed deer and collared peccary

Peña-Mondragon and Castillo, 2013; Rojas-Martinez et al., 2013; Towns et al., 2013). In addition, the mapping pattern of ecological integrity also helps to identify surrounding areas with similar values to those observed in protected areas (Fig. 8). The ecosystem condition can be evaluated based upon ecological integrity values alone, and serves to compare the overall status of different landscape units and the specific condition due to landscape changes (habitat loss and fragmentation). Spatial indicators can be used for a further characterization that allows a complete evaluation of ecosystems' integrity to support predator-prey

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predators in the “Sierra de Guerrero”. Also, I would like to thank Dr. Esther Quintero (CONABIO), Dr. Miguel Equihua (INECOL) and an anonymous reviewer for insightful comments that greatly improved previous manuscripts. This research was supported by CONABIO and is part of the Spatial Decision Support System for Evaluating Human Impacts on Biodiversity (SIESDIB).

(Odocoileus virginianus and Pecari tajacu) are often registered (Fig. 7). The presence of all these species indicates an ecosystem functioning able to support viability in their natural populations, which have maintained the integrity in predator-prey interactions within the reserve. As an indication of the ecological status, photograph records recurrently report most of these species, which is also a current situation for all landscapes selected as examples (Table 6). Usually, the larger predators (e.g., puma, jaguars and bobcats) occur at sites with higher ecological integrity. Smaller predators such as jaguarondi and coyotes can exist at intermediate levels of ecological integrity, especially if prey species are present, as shown in the co-occurrence patterns (Fig. 6). Similarly, good ecological integrity conditions can be observed in landscapes where a scheme of natural protected areas does not exit (Fig. 8). Nevertheless, the presence of large predators in the “Sierra de Guerrero” such as pumas and jaguars (Panthera onca), along with some meso-predator species such as coyotes, and their preys, are also reported in these non-protected areas. This is also a clear indication that ecosystem functioning supports viable populations and the predatorprey interaction in the “Sierra de Guerrero” landscape. As observed, the ecological integrity map is a strong tool for evaluating areas with a high potential for conservation actions, and more importantly, as a tool for monitoring purposes when spatial indicators are used for evaluating spatio-temporal trends of the ecological integrity components. Manifest and latent indicators can be used for developing indexes of intactness and degradation to orient practical decisions for conservation and restoration of habitats.

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5. Conclusions Ecological integrity is a powerful concept that evaluates ecosystems conditions and changes. However, to use it successfully in a decisionmaking context, a solid, non-vague definition is necessary. Ecological integrity, as defined here, is a functional property that integrates habitat functions and species information for maintaining key ecological interactions in predator-prey systems. Manifest variables of ecological integrity attributes describe the current status of the remnant habitat for maintaining population viability and preserving key predator-prey interactions in the landscape. When integrated as a model, the information system implemented through the ecological integrity concept is retrospective, by providing the information to analyze the current status of ecosystems, and prospective, by providing elements to identify negative tendencies when habitat loss and fragmentation are analyzed. As a mapping tool, the model of ecological integrity has shown that habitat loss and fragmentation have a negative effect on the ecological integrity of areas supporting top predators in Mexico. Due to an extensive natural landscape transformation, the remnant areas to support predator-prey interactions have been considerably reduced. The imperiled condition that remains for large predators in Mexico threatens the integrity of several ecosystems, particularly when habitat loss and fragmentation directly affect the natural condition of remnant landscapes, indirectly affecting stability and self-organization. Nevertheless, ecological integrity can be defined and mapped from manifest geographic information depicting the spatial distribution of species, which is related to the trophic interaction of the major predators that are still present. The geographical information derived from this analysis may help to elucidate the patterns of apex predator distributions and evaluate the remnant conditions. Acknowledgements I would like to thank Dr. Salvador Mandujano Rodriguez and M.S. Eva López-Tello (INECOL) for providing the evidence of predators and preys collected with photo traps in the “Tehuacán-Cuicatlán” Biosphere Reserve (project CONACYT CB-2009-01-130702). I would like to thank also M.S. Fernando Ruiz for providing photographic evidence of apex 88

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