Introduction

Mangrove forests are recognized as providing various ecosystem goods and services to people. These include protection from floods, provision of various plant and animal products for fuel, food and health, water quality improvement, storm surge buffering, and others. Mangroves are essential sediment traps where nutrients are actively uptake and transformed (Lee et al., 2014). Despite the well-established understanding of mangrove importance, the destruction of these forests is persistent. Rotich et al. (2016) pointed out that the lack of effective mangrove management across multiple countries has led to the degradation of these ecosystems. This is largely due to ambiguous jurisdiction and insufficient collaboration between different agencies, which often leads to conflicting interests. Globally, more than 50% of mangroves have been lost, with Mexico being one of the top ten countries removing mangroves considering the high degradation rates and loss of these ecosystems (Atwood et al., 2017; Bryan-Brown et al., 2020). Hamilton & Casey (2016) estimated a global annual rate of mangrove cover loss of 0.39% from 173 067 km² in 2000 to 163 925 km² in 2014. The main drivers of mangrove deforestation and degradation are urban and industrial encroaching, agricultural and aquacultural conversion, and logging for timber and fuelwood (Chowdhury et al., 2017). Given the growing awareness of the linkages between human wellbeing and ecosystems, the mangrove forest loss prompts the development of assessment tools to help resource managers detect changes in mangrove conditions and improve preservation criteria.

Ecosystem integrity (EI) is often used as a framework for assessing the health of ecosystems and thus informs on ecological management effectiveness. The EI concept refers to the ability of an ecosystem to function and selfregulate despite external disturbances or stressors. This implies that the ecosystem has a specific composition and structure that interacts to maintain its unity (Kandziora et al., 2013). According to Parrish et al. (2003), ecosystem integrity is defined as the capacity of an ecological system to sustain and maintain a community of organisms with similar species composition, diversity, and functional organization compared to those found in natural undisturbed habitats within a region. These authors also state that the ecosystem exhibits integrity when its dominant ecological characteristics, such as its compositional elements, structure and function, and ecological processes, vary within their natural ranges and can recover from most disturbances caused by natural environmental dynamics or human interference.

The concept of ecosystem integrity is widely implemented in the management of natural resources and environmental legislation, and it plays a central role in conservation policies and programs in many regions around the globe (Manuel-Navarrete et al., 2001; Kwak & Freeman, 2010). However, standardized methods are still needed to evaluate the integrity of ecosystems, and an operating conceptual framework is required (ManuelNavarrete et al., 2001).

We base our work on ecosystem integrity as defined by Equihua et al. (2016), who developed a framework to assess and guide ecosystem management actions for sustainable development. This approach is based on complex systems theory, which considers ecosystems as self-organizing entities that are limited in their structure (including biological diversity) and function as thermodynamic dissipative system properties (Kay, 1991; Regier, 1995; Manuel-Navarrete et al., 2007) and undergoing biological evolutionary processes (Levin, 2005).

In Mexico, the National System of Biodiversity Monitoring (SNMB, García-Alaníz et al., 2017) is a key player in collecting data on national biodiversity. In the realm of mangroves, the National Commission for the Knowledge and Use of Biodiversity (Conabio) has implemented the Mangrove Monitoring System (SMM). This system, a crucial tool in biodiversity monitoring, tracks qualitative and quantitative changes in mangrove forest distribution and function. It does so by employing remote sensing techniques and field surveys to collect data on plant biomass and other biophysical variables in situ. These data, when analyzed, can provide valuable insights into the evaluation of ecosystem conditions through a common framework of indicators. Equihua et al. (2016) suggested processing such ecosystem monitoring data using Bayesian networks (BN) to produce an index of ecosystem integrity (Fig. 1). A BN is a multivariate model that captures a pattern among a group of variables influenced by multiple factors. There are two main components comprising a BN: 1) A qualitative representation of the linkages among the variables and 2) a quantitative component at each node accounting for the conditional probabilities that define them. The qualitative component is a structure called, in mathematical graph theory, a directed acyclic graph (DAG) (Fig. 1), in which each vertex or node represents a random variable that can have two or more possible values or stages (Aguilera et al., 2011). The arcs linking the nodes indicate known or statistically presumed causal dependence between them (Pearl, 1988). The node from which an arc emerges is called a parent node, representing an independent variable.

Figure 1
Generic representation of the ecosystem integrity concept with an influence diagram or Bayesian Network (BN, from Equihua et al., 2016).
Integrity is considered a latent variable (not directly observable), although measurable with data that inform about its possible state. Intermediate nodes Sp refers to species; Nodes Str refers to structure and Proc, process. Grey nodes represent utility functions that allow the translation of integrity components into society’s values criteria.

In contrast, a node with an incoming arc is the child node, representing a dependent variable. The quantitative component in this pattern of influences assigns a linked matrix to each variable, which encompasses the conditional probabilities of all possible events in a node given the parents. In this way, a conditional probability table (CPT) is produced that describes the probability of each possible value of the child node (dependent variable), conditioned by each possible value of the parent nodes. The whole network is an expression of the joint probability distribution of the system considered. Bayes' theorem, combined with the rules of probability, allows updating the a priori probabilities as a result of new evidence in some node by propagating the conditional probabilities (Barber, 2013) and producing a posteriori value given the evidence provided. This propagation of probabilities makes the BN useful for diagnosis (top-down reasoning) or explicative purposes (bottom-up reasoning).

Thus, a BN can be used as a classifier to calculate the posterior probability of a node variable of interest (i.e., EI), given the values in other nodes. The modeling approach proposed in this work assumes that an environmental unit's ecosystem condition (Integrity) behaves as a latent variable, either not directly measurable or very difficult to do so. However, its effect generates concrete patterns of structural and functional attributes that can be observed and directly quantified. These patterns vary according to the environmental context and the surrounding species set in any location. Thus, given a context and based on the evidence provided by knowing the values of structural and functional attributes, it is possible to infer the integrity status of the ecosystem through probability propagation. The EI index of condition will have a maximum where an ecosystem is furthest from human intervention and a minimum where the most degradation occurs.

Objectives

In this paper, we aimed to develop a BN to assess an index of ecosystem integrity (EI) for mangrove ecosystems.

Materials and methods

Study area

The study area was the Tampamachoco mangrove located in the State of Veracruz, Mexico (21° 0.9′ N, 97° 47′ W). This mangrove area is part of the Ramsar site no. 1602 "Mangroves and wetlands of Tuxpan." The four most crucial mangrove species in Mexico are present, but our study focuses on a monospecific forest area of Avicennia germinans. This region is characterized by three seasons: rainy (June-October), winter windy (NovemberFebruary), and dry (March-May) (Day et al., 2004).

In approximately 20 ha of mangrove forest, there are areas of massive tree mortality where the mangrove is in a transitional or degraded state (Fig. 2). Mangrove degradation and mortality were possibly caused by the interruption of water flow due to the construction of three 500 to 700 m-long levees in the 1980s. The presence of the levees obstructed the flow of surface water, whereby the hydroperiod was altered, resulting in increased evaporation and accumulation of salts in the soil. This disturbance is higher in the upper zones, with less tidal influence and poor water circulation between the levees. The environment in most of the affected areas went from 65 ‰ to 140 ‰. (Vovides et al., 2011). Salinity increased to levels toxic for any plant; therefore, the mangrove trees had symptoms of "top dying", which is a phenomenon that slowly kills trees by stripping them of leaves, branches, and twigs (López-Portillo et al., 2014). Hydrological restoration of the site started in 2012 by digging 16 transversal channels through the embankments to allow water flow (López-Portillo et al., 2014).

Figure 2
Study site and sampling plots within the disturbed and undisturbed area of Tampamachoco mangrove.

Field survey

We selected five sampling plots of 10 m × 10 m located in the undisturbed and disturbed forests, respectively (Fig. 2). Plots were monitored annually for monthly productivity and forest structure as part of a national program to document mangrove dynamics across Veracruz, Mexico (López-Portillo et al., 2014). Additionally, we estimated the leaf area index (LAI) by analyzing digital hemispheric photographs (DHP). Pictures were taken in the three relevant seasons to capture the natural temporal variability of values in the system during the year: dry (March 2014), rainy (September 2014), and winter windy season (January 2015). Nine DHP directed towards the zenith were taken in each study plot with a Canon camera (model Rebel EOS TX5) equipped with a "fisheye" lens, according to Leblanc and Chapman (2004). The camera was horizontally leveled at standard breast height (1.30 m), and the camera top lay north. The shots were taken when the incidence of the sun was reduced (7 h 00 11 h 00 and 17 h 00 19 h 00) to avoid overexposure. The DHPs were analyzed using CANEYE free software.

Foliar nutrients

We collected 30 green leaves from three A. germinans trees selected at random in each of the 10 study plots to determine their concentration of total carbon (C), nitrogen (N), and phosphorus (P). Sample collection was conducted in the three seasons (dry, rainy, and winter windy). Leaves were collected from branches exposed to light incidence, facing east, without signs of herbivory or any other physical sign of damage. The leaves were stored at 4.0 °C while in transit to the laboratory.

Chemical analysis

We measured the leaf area of collected green leaves using a LI-COR area meter. Subsequently, leaves were dried in a stove at 75 °C to measure dry weight, and then we determined leaf mass per area (LMA). We milled the dry leaves and quantified the total C and N using a Leco Co. elementary multi-analyzer Model TruSpec CN. The concentration of total P was assessed by the vanadate/molybdate method by colorimetry.

Bayesian Network (BN) building

The BN was developed using the Netica software (Norsys Inc.), following the general guidelines suggested by Marcot et al. (2006). The first stage of construction was to define the qualitative structure of the BN, establishing system variables and the causal relationship between them. The structure was based on the general RB model developed by Equihua et al. (2016, Fig. 1), which was developed to infer the condition of ecosystems. The variables within this structure of our model were specifically adapted to assess the condition of mangrove ecosystems. Experts in our team, two in mangrove ecology and one in Bayesian network modeling, were explicitly inquired to obtain information on relevant ecological variables in mangrove dynamics and their interactions. Table 1 summarizes the selected relevant variables of the model to assess mangrove integrity classified by type of component (i.e., structure, function, and environment). The BN quantitative element required the range of values of the nodes to be discretized; thus, experts were also asked to define suitable ranges of values for the stage corresponding to each node.

Table 1
Summary of the model variables, including their states and corresponding discretization intervals.

Node	Discretization methodology	States (intervals)
	Structural
Holdridge Complexity Index (HCI)	Expert knowledge	High (0.031 – 0.1)
		Low (0.0 – 0.03)
Tree height (m)	Expert knowledge	High (4.1 – 8.0)
		Low (0.0 – 4.0)
Basal area (m2/ ha)	Expert knowledge	High (0.24 – 1.0)
		Low (0.0 – 24.0)
Tree density (ind / ha)	Expert knowledge	High (3000 5000)
		Low (0 – 3000)
Leaf area index (LAI)	Expert knowledge	High (1.1 – 4)
		Low (0 – 1)
	Functional
Litter production (g/m2/month)	Expert knowledge	High (10 – 50)
		Low (0 – 10)
Leaf total carbon (%)	Reference values in Méndez-Alonzo et al. (2008)	High (41 – 100)
		Low (0 – 40)
Leaf total nitrogen (%)	Reference values in Méndez-Alonzo et al. (2008)	High (2.1 – 10.0)
		Low (0 – 2)
Leaf total phosphorus (%)	Reference values in Méndez-Alonzo et al. (2008)	High (0.1 – 0.2)
		Low (0.0 – 0.1)
Leaf N: P ratio	Twilley & Day (2012)	High (3250)
		Low (0 – 32)
Leaf mass per area	Reference values in Méndez-Alonzo et al. (2008)	High (0.022 – 0.028)
		Low (0.0 – 0.021)
	Environmental
Salinity (‰)	Day et al. (1987)	High (50 – 90)
		Low (0 – 50)
Oxidation-reduction potential (Mv)	Reef et al. (2010)	High reduction (-389 to -101)
		Reductor (-100.9 to 20)
pH	Expert knowledge	Acid (0.0 6.5)
		Neutro (6.6 7.3)
		Basic (7.4 8)
Temperature (°C)	Expert knowledge	Low (0 – 11)
		Medium (11 – 29)
		High (29 – 33)
Flood level (cm)	Expert knowledge	Dry to saturated (-14 0)
		Low (0.1 – 10.0) High (10.1 – 35.0)

Since the target mangrove is monospecific, we excluded the number of species (diversity) as a significant variable. Other taxonomic groups relevant to the structure and functions of mangrove systems were not sampled and omitted due to the absence of pertinent data. The hydroperiod is the frequency, duration, and depth of water inundation (tide and precipitation) (Twilley & Rivera-Monroy, 2005). However, we only used the flood level because we had no data on the frequency and duration of water inundation. An intermediate latent node (named stress) was added, considering that its combined effect can account for the interaction among the three categories of environmental gradients (Fig. 3: resources, regulators, and hydroperiod; Twilley & Rivera-Monroy, 2005). According to the multigradient conceptual model, the interaction between these three gradients is a constraint that defines the structure and productivity of mangrove wetlands. At low-stress levels, such as low salinity, high light and nutrients, and intermediate flooding, mangrove wetlands will reach their maximum biomass and net ecosystem productivity (Twilley & Rivera-Monroy, 2005). Low stress correlates with low salinity in pore water, low Na ions in the soil, high soil nutrient content, and intermediate flooding. Contrariwise, high-stress levels correlate with high pore-water salinity, high soil Na+ and low nutrient concentrations, and extreme (very low or high) flood levels (Table 1).

Figure 3
Bayesian network proposed to evaluate the ecosystem integrity of the Tampamachoco mangrove.
Green node, output node; purple nodes, function variables; brown nodes, structure variables; blue nodes, stressors; orange node, season of the year.

Model parameterization

To train the model for the assignment of values to CPT within the nodes, we used the collected field data, as well as databases from the project "Hydraulic restoration in the Tampamachoco lagoon for the rehabilitation of the mangrove and its environmental services supported by Conabio" (López-Portillo et al., 2014). From these studies, we used the forest structure data registered in 2011 and monthly litter production recorded in 2014. In addition, we measured in situ pore water parameters during the dry, rainy (2014), and winter wind season (2015).

The CPT of the Bayesian model was calculated using the learning algorithm Expectation Maximization (EM), as implemented in Netica software. This algorithm was selected because it trains models with latent variables and databases with missing values. The algorithm works iteratively, searching for maximum likelihood (ML) through two repetitive steps that converge towards the estimation of parameters (Barber, 2013). Netica implements an algorithm to "soften" the CPT of the nodes to cope with overfitting. We applied this soften algorithm to the model CPT with degree one. We used this approach in training the model, allowing for uncertainty in the statistical relationships estimated by the algorithm (Marcot et al., 2006). In the case of this study, uncertainty was assumed since, in some cases, data acquisition did not have a precise match in location or time.

Model validation

Model review

External experts in mangrove ecology and Bayesian network modeling reviewed the network node influence arrangement. We discussed the proposed network with them through individual interviews. We inquired them about i) The suitability of the causal relationship represented in the BN structure, ii) the relevance of the critical variables considered estimating the ecosystem integrity of the mangrove, iii) the biological representativeness of the discretization intervals of variables, and iv) the accuracy/precision of the inference process, in the context of hypothetical cases in variable states. Their observations and suggestions were incorporated into the model structure and the ranges of node stages.

Regressions

We explored the relationship between the most critical variables of the model and the ecosystem integrity estimated for the mangrove using linear regression. We calculated the posterior probability that the ecosystem integrity would be high (P [ecosystem integrity] = High). Due to the evidence of a set of separated cases from the database to test the trained model, the estimates were calculated using the process cases option in Netica. This function reads each of the cases in the database as evidence. It updates the probabilities to produce the posterior probability associated with each state in the nodes that did not have findings in the given case.

Sensitivity analysis

We conducted a sensitivity analysis to explore how much influence a variable had in inferring the state of the node ecosystem integrity (target variable). This analysis also helped identify and fix errors in the BN's or CPT's structure (Pollino et al., 2007).

Performance measures

We evaluated the model's predictive capacity using a k-fold cross-validation (5 x 2 cv) (Korb & Nicholson, 2011). We took 80% of the data as a training set and 20% as a test set (80% 20% hold-out). The data was discretized by stratification, ensuring that the class distribution of the entire data set is represented in each. The mean square error (MSE) evaluated the model's accuracy.

Additionally, we calculated performance measures, including the confusion matrix, which test the accuracy of the BN by comparing the results predicted by the model with the known actual results. This test is based on the most probable outcome (Marcot et al., 2006). In the confusion matrix, the false positives (Error type I), false negatives (Error type II), and their sum are displayed; Spherical loss has a range of values that vary from [0, 1], with one being the value for the best model performance. It is calculated as follows (Marcot, 2012):

Where:

MOAC = mean probability value of a given state Averaged over all Cases

Pc = predicted probability for the correct state

Pj = predicted probability for state j

n = number of possible states.

The area under the ROC (Receiver Operating Characteristic) curve (AUC) uses prediction accuracy through a continuum of prediction thresholds rather than through an arbitrary cutoff of probability (such as 0.5), as the confusion matrix does. The AUC varies from 0 to 1 and represents the probability that a positive result has a higher predicted probability than a negative result. The diagnosis for a perfect model will have 0% false positives, so the closer AUC = 1 is, the better the performance. An AUC = 0.5 represents a random model, while an AUC = < 0.5 represents a model that consistently gives a wrong answer (Marcot et al., 2006).

Results

Forest structure, leaf traits, and pore water parameters

In general, the A. germinans forest in Tampamachoco has a very low complexity in structure. HCI varied from 0.01 to 0.7, and LAI values from 0.3 to 2.9. Stand height varied in a 3.5 m to 6.9 m range, basal area from 0.1 m² to 0.7 m², and tree density from 1525 ha^-1 to 4600 ha^-1. All these parameters were significantly higher in the undisturbed mangrove area (Table 2). Regarding leaf traits, the N:P ratio was significantly higher in disturbed areas and total C in green leaves, which ranged from 40.3% to 53.6 %.

Table 2
Forest attributes at the disturbed and undisturbed area of Tampamachoco mangrove forest.

Values are means ± standard deviation. Different lowercase letters indicate statistical differences at p < 0.05.

Parameter	Undisturbed area	Disturbed area
	Structure
HCI	0.05 ± 0.02 a	0.03 ± 0.0 b 3.8
Stand height (m)	5.3 ± 0.9 a	± 0.2 b
Basal area (m2/ ha)	0.4 ± 0.3 a	0.3 ± 0.2 a
Tree density (ind/ ha)	2850.0 ± 830.7 a	2955.0 ± 1115.0 a
Leaf area index (LAI)	1.1 ± 0.3 a	0.6 ± 0.2 b
	Functional
Leaf C (%)	42.8 ± 1.2 b	44.9 ± 2 a
Leaf N (%)	2.1 ± 0.1 a	2.3 ± 0.2 a
Leaf P (%)	0.07 ± 0.0 a	0.06 ± 0.0 b
Leaf N: P ratio	29.5 ± 1.8 b	38.8 ± 6.1 a
Leaf mass per area (LMA)	0.02 ± 0.0 a	0.02 ± 0.0 a
Litter productivity (g/m2/month)	4.1 ± 0.8 a	2.7 ± 1.5 b
	Environmental
Salinity (‰)	53.1 ± 7.7 b	64.8 ± 6.1 a
pH	6.9 ± 0.1 a	6.9 ± 0.1 a
Redox potential (mV)	-285.7 ± 21.9 a	-277.4 ± 13.0 a
Temperature (°C)	25.5 ± 3.5 a	25.8 ± 3.7 a
Flood level (cm)	2.5 ± 2.5 a	3.4 ± 0.9 a

On the contrary, foliar P was significantly higher in undisturbed area trees and ranged from 0.04% to 0.2% (Table 2). Nitrogen in green leaves ranged from 1.9% to 2.7%, and no statistical differences existed between areas with different conditions. Salinity was found in a range of 30.6‰ to 74.9 ‰ and was statistically higher in disturbed mangrove areas. The rest of the environmental parameters did not differ significantly between the disturbed and undisturbed areas (Table 2).

BN structure and parameters

The BN structure proposed to estimate the ecosystem integrity of the Tampamachoco mangrove is shown in figure 3. The upper node of the BN corresponds to the general indicator ecosystem integrity, being the variable of interest (Fig. 3, green node). The integrity node's child nodes comprise function variables and forest structure (Fig. 3, purple and brown nodes, respectively). These are considered evidence that input nodes infer probability distribution in integrity node states.

Sensitivity test

According to the sensitivity analysis for the node ecosystem integrity, the leaf N: P ratio node contributed most of the information to estimate the integrity of the mangroves (Table 3). Variables representing the forest structure (HCI, followed by tree height and LAI) were next important for estimating the mangroves' ecosystem integrity, with considerable variance reduction values (Table 3). HCI components showed a low sensitivity due to topology in the BN structure. That is, HCI functioned as an intermediate variable. Functional variables such as LMA, leaf P, and litter production were also shown to be essential variables by the sensitivity analysis. Leaf C and N nodes contributed very little information (Table 3).

Relationship of functional and structural variables with mangrove condition

Table 3
Sensitivity analysis for node Ecosystem integrity measured as mutual information or variance reduction (RV) expressed as a percentage.

Variables are in order according to their influence on the possible results of the ecosystem integrity node.

Variable or node	%
Leaf N:P ratio	11.0
Holdridge Complexity Index (HCI)	10.5
Leaf Area Index (LAI)	5.6
Leaf mass per area (g/cm2 )	3.1
Leaf phosphorus (%)	3.0
Litter production (g/month/m2 )	2.3
Basal area (cm2 / ha)	1.9
Tree density (ind / ha)	1.9
Leaf carbon (%)	1.7
Tree height (m)	0.9
Leaf nitrogen (%)	0.6

With regard to structural and functional variables versus the condition of the mangrove forest predicted by the model (P [Ecosystem integrity = High]), linear regressions were significant, except for the cases of tree density, basal area, LMA, and leaf N concentration (Fig. 4). LAI, HCI, and stand height had positive relationships with the integrity of the mangroves, with moderate observed r² values (Fig. 4). Litter production and green leaf P also had positive relationships, although they resulted in low r² values. By contrast, The N: P ratio and green leaf C had a negative relationship with the integrity of the mangrove and low values of r².

Figure 4
Linear regressions for the distribution of high integrity probability predicted (P [Ecosystem integrity = High]) concerning observed values for the structural and functional variables: A) Holdridge complexity index (HCI), B) Canopy height, C) Leaf litter production, D) Leaf area index (LAI), E) C in green leaves, F) P in green leaves and G) N:P ratio in live leaves.

Model performance

Table 3 shows the results of three performance metrics in the five tests carried out. The cross-validation yielded a minimum squared error (MSE) of 0.3.

Discussion

Model application

Our results suggest that the BN analysis is a suitable tool for evaluating the ecosystem integrity of a monospecific basin mangrove forest of black mangrove (Avicennia germinans) associated with the Tampamachoco lagoon. The model can be revised for other mangrove habitats with characteristic species composition and structure. We propose this model as a baseline for assessing the condition of mangroves in conjunction with monitoring and generating ecosystem information schemes in Mexico, specifically within the mangrove monitoring system (SMM). The model includes key forest structure, leaf trait variables, and environmental stressors that influence the structure and function of mangroves locally (Twilley & Rivera-Monroy, 2005). The probabilistic approach captures spatial and temporal influence patterns of physical, chemical, and biological variables, encompassing their complexity and stochastic behavior.

The use of BN analysis to assess the condition of ecosystems has gained interest in many areas, like investment, epidemiology, etc. We suggest they are also valuable for natural resource management and sustainability assessment (Aguilera et al., 2011; McCann et al., 2006). BN analysis is easily interpretable and efficient for synthesizing expert knowledge concerning other classification models, such as neural networks, that are difficult to understand and explain (Fernandes et al., 2010). The graphic representation explicitly shows the proposed causal relationships among the variables, with a holistic approach to assess the state of the ecosystem (as a joint multivariate probability distribution). The simplicity of the structure is also advantageous for communicating the model results to experts and other social actors unfamiliar with the models (McCann et al., 2006). This facilitates its interpretation and its possible use by experts and decision-makers. This approach can elucidate ecosystem integrity under different degradation conditions (Equihua et al., 2016).

Additionally, using learning algorithms allows the model to continue learning and updating the CPT from the data generated systematically in monitoring programs, increasing the model's accuracy in evaluating the ecosystem. In our case, this was also useful in processing data with a certain degree of complexity, given the diversity of sources of information (fieldwork and databases available) and the occurrence of missing data.

Relationship of forest structure and function variables with mangrove integrity

The HCI was the most influential structural variable, providing the highest percentage of information in estimating the integrity of the Tampamachoco mangroves (Table 3). It has been reported that this variable is significantly affected by human and natural disturbances (Kairo et al., 2002). This is confirmed in the case of the Tampamachoco mangrove forest, where low HCI values were observed in a condition of poor integrity (Fig. 4). In the disturbed area of the Tampamachoco mangrove, high salinity > 60 ‰ is the primary factor causing the apical death of the upper branches in the trees and, thus, the structure of the canopy (Vovides et al., 2011). Natural factors that can modify the structure, reducing both tree height and leaf size, include the incidence of strong winds and the frequency of extreme weather events such as hurricanes (Méndez-Alonzo et al., 2008). Compared to density and basal area, canopy height was the most affected component, which was not significantly affected by these perturbations (Krauss & Osland, 2020). LAI was the third most crucial variable for estimating the condition of the Tampamachoco mangrove according to the sensitivity test (Table 3). Results confirm that LAI is one of the most critical biophysical parameters for assessing the health of mangroves (Ishtiaque et al., 2016). The method implemented in this work, which takes digital hemispheric photos to measure LAI, has some advantages over other direct and indirect methods. Direct measurements through trees can be tedious, destructive, and expensive in terms of time and money (Weiss & Baret, 2014). Most studies using the LAI as an indicator of mangrove health have employed remote sensing methods (Kovacs et al., 2005; Kovacs et al., 2009; Ishtiaque et al., 2016). These methods are a viable option, although field observations must calibrate them. Taking digital hemispheric photos is a quick, inexpensive, readily available method and is a permanent record of the fraction of the canopy opening (Chianucci & Cutini, 2012).

Litter production had little importance in assessing mangrove integrity compared to the other functional variables such as N:P ratio, leaf P, and LMA. However, we observed that mangrove conditions affected litter production (Fig. 4). Litterfall production is a standard indicator of ecosystem health. A healthy system produces a stable amount (monthly or annually) of leaf litter since the old leaves are lost and replaced by new leaves. A decrease in litter production may indicate that the mangrove is stressed (Department of Environment and Science [DAS], 2018). In Tampamachoco, the degraded mangroves exposed to high salinity may be investing more energy to maintain the water balance so that their primary productivity can be diminished. López-Rosas et al. (2023) found that an increase of 10‰ in the average interstitial water values reduced litter production in various marsh plants and tree species. At the ecosystem level, the decrease in litter production triggered a lower generation of detritus, which likely alters food chains that depend on it as an energy source. On the other hand, litterfall can also be determined by the year's season, as it responds to environmental stresses such as salinity that increase the cost of maintaining photosynthetic tissue. In Mexico, the highest level of leaf fall occurs between April and August (López-Portillo & Ezcurra, 1985).

N:P ratio, LMA, and leaf P provided valuable information for mangrove integrity estimation (Table 3). Arrivabene et al. (2014) suggested that differences in environmental conditions can cause adaptive morphoanatomical changes in mangrove leaves, which can be used as evidence of alterations in their environment. They found that LMA is an essential indicator of the mangrove condition of Avicennia schaueriana and Laguncularia racemosa, which is higher in areas of high salinity. In this work, we found a decrease of LMA in the leaves of trees in the undisturbed area, possibly related to lower pore-water salinity (Fig. 4). N:P and P are indicators of P nutritional status of trees, which, according to evidence, were affected negatively in A. germinans trees by disturbance (Fig. 4). Nitrogen (N) and phosphorus (P) are important elements to form important leaf compounds. The quantity and ratio of these two plant elements indicate nutrient limitation and utilization efficiency. The LMA, in conjunction with leaf nutrients and stoichiometry, can be framed within the leaf economic spectrum (Wright et al., 2004), which defines physiological and anatomical strategies related to the use of resources. It has been found that the leaves of A. germinans have a high LMA and high C concentration when the tree grows in environments where water stress is high and nutrient resources are limited (Méndez-Alonzo et al., 2008). This means a more significant investment is required to produce leaves with greater longevity to accumulate nutrients or slow-synthesis compounds such as lignin or lipids. In contrast, plants that grow with high nutrient availability tend to have a low LMA and a low C content, which could indicate the accumulation of compounds such as water. However, most of the comparative studies of foliar attributes do not include mangroves, possibly due to the lack of quantitative information (Quadros & Zimmer, 2017).

It has already been suggested that assessing the condition of mangroves by only considering forest structure may be insufficient, so it is important to consider variables of ecosystem function (McKee & Faulkner, 2000). However, it must be recognized that obtaining the values of these variables is pricier than measuring only the structure. The loss of integrity affects the processes of the ecosystem, and modifying its functioning alters the forms of production and the services it provides. Thus, the management of ecosystem integrity should be aimed at understanding and conceiving possible scenarios of integrity alteration that could accommodate human use while preserving ecosystem services delivery capacity in the long term.

Model validation

The resulting average AUC (0.73) indicates that our model can reasonably classify the ecosystem integrity of mangroves (Table 4). Marcot et al. (2006) mention that models with an AUC < 0.5 tend to be wrong constantly, while a value of 1 would be a model with a perfect performance. Our spherical loss result also indicates that our model has a good classification performance (Dlamini, 2010; Pollino et al., 2007). Assessing the model's predictive capacity based on the data is essential to provide a reliable model. In this work, we evaluated the model's predictive capacity by splitting the training data, separating the training data from the test data set in the cross-validation permitted to avoid the overfitting of the model and minimize the possibility of optimistic estimates about its performance. Experts' review of our model was an important part of the validation since it allowed us to reduce the inherent (epistemic) uncertainty reflected in the causal relationships represented in the structure and the CPTs. The participation of experts in the parameterization process favors constructing more robust predictive models. That is, they generate stable and replicable results in response to changes in the available data (Dlamini, 2010). An additional advantage of incorporating expert judgment in the qualitative design of the model is that it avoids overfitting. Marcot et al. (2006) have found that BN's produced using data only (for both structure and conditional probabilities) tend to overfit the models, making them pertinent only for the specific data set in the training.

Table 4
Performance measures results for ecosystem integrity node, from a cross-validation fold, for five test samples.

Test no	Error rate (%)	AUC-ROC	Spherical loss
1	50.0	0.44	0.59
2	33.3	0.44	0.60
3	0.0	1.0	0.99
4	16.7	0.83	0.82
5	16.7	0.94	0.77
Mean	23.3 ± 18.9	0.73 ± 0.3	0.77 ± 0.2

Conclusions

The BN constructed in this work is a proposal that may serve as a reference for assessing the integrity of mangrove ecosystems nationwide. We suggest that the model work together with the data collection and analysis on biodiversity in the country, such as the SMM conducted by Conabio. The structural variables of the mangrove forest (HCI and LAI) are essential to evaluate the ecosystem integrity of the mangrove in terms of the contribution of information. However, the functional variables (litter production and leaf nutrients) provide relevant information to evaluate the condition of the mangrove, as we demonstrated here. Experts and users, in general, may update the BN to reflect advances in scientific understanding of mangrove ecosystems and the framework of environmental policy design.

Acknowledgments

To the Consejo Nacional de Humanidades, Ciencia y Tecnología (Conahcyt) for grant No. 300755 to A. Corona Salto. The logistic and economic support of the project "Hydraulic restoration in the Tampamachoco lagoon in the state of Veracruz for the rehabilitation of the mangrove and its environmental services" (SNIBConabio Project No. HH025). To the field technicians M. en C. Mauricio Hernández Sánchez and Biól. Moisés Rivera Rodríguez for their great help in the work in the study area and the laboratory to the chemists Ariadna Martínez Virues, Daniela Cela Cadena, and Sandra Rocha Ortiz for all their help in the nutrient determinations. To Carmen Martínez García for all her support in academic and personal aspects.

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Author notes

*Corresponding author: ana.lara@inecol.mx