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Ethics statement
The study complied with the existing rules and guidelines outlined by the Committee for the Purpose of Control and Supervision of Experiments on Animals (CPCSEA), Government of India, the Institutional Animal Ethics Committee’s (IAEC) and guidelines of Indian Institute of Science Education and Research (IISER) Kolkata. All experimental protocols followed here have been approved by the Institutional Animal Ethics Committee’s (IAEC) and guidelines of Indian Institute of Science Education and Research (IISER) Kolkata, Government of India. No animals were euthanized or sacrificed during any part of the study, and behavioral observations were conducted without any chemical treatment on the individuals. At the end of the experiments, all fish were returned to stock tanks and continued to be maintained in the laboratory.
Procuring subject animals and maintenance
We used wild-caught zebrafish (from Howrah district, West Bengal, India), bought from a commercial supplier. The fish were maintained in the laboratory in mixed-sex groups of approximately 60 individuals in well-aerated holding tanks (60 × 30 × 30 cm) filled with filtered water. The lighting in the laboratory was maintained at 14 hL:10 hD to mimic the natural LD cycle in zebrafish. They were fed commercially purchased freeze-dried blood worms once a day alternating with brine shrimp Artemia. The holding tanks were provided with standard corner filters for circulation. They were maintained in the laboratory for six months before experiments were conducted to ensure they were all adults and were reproductively mature. Holding room temperature was maintained between 23 and 25 °C.
Experimental setup
The experiments were conducted in a square glass arena (83 × 83 cm), with a half-diagonal of the square from the center that approximated ten fish standard body lengths (i.e. 40 cm, assuming one body length of adult zebrafish to be about 4 cm) (Fig. 1). Each corner of the arena was provided with a square chamber (of sides 10 cm) built from transparent mesh (using synthetic fish nets) for housing the females. This design allowed for the stimuli females to be localized in the patches and not escape into the arena while simultaneously ensuring that the test males can have visuo-chemical communication with the females. The center of the arena was provided with a removable chamber (with holes) for acclimation of the males prior to the trial.
Figure 1

Diagrammatic representation of the arena for the density experimental set-up. The central chamber (indicated by a circle) represents the area where the test males were released and the corner square chamber (separated by transparent mesh) contained females of varying density. The distance of each patch from the central chamber was 40 cm.

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Three sets of experiments were performed to test their association preferences under (1) only varying female densities (2) increasing female and vegetation densities and (3) increasing female densities with decreasing vegetation.
Association preference experiment with varying female densities
For this experiment, each small chamber within the arena housed two (low number), four (medium number), eight (high number) or no (blank) females. These chambers represented patches of varying female numbers. The position of the female-containing chambers, as well as the composition of females within each patch, was randomized between trials. A total of 20 males were tested for their association preferences. Details on the data collected are provided in Supplementary File S1.
Association preference experiment with vegetation
For this experiment, the female-housing chambers (patches) were provided with vegetation (using artificial plants) of varying density (Fig. 2). Each subject fish was tested under two experimental settings. In E1, the number of females was proportional to the density of associated vegetation cover. We used four different densities of females, each associated with different densities of plants
1.
one female + no plants (no vegetation—N)

2.
two females + two plants (low vegetation—L)

3.
four females + three plants (moderate vegetation—M) and

4.
eight females + five plants (high vegetation—H).

Figure 2

Diagrammatic representation of the arena the vegetation experimental set-up. The central chamber (indicated by a circle) represents the area where the test males were released and the corner square chambers (separated by transparent mesh) contained females of varying density and each patch was associated with variable number of plastic plants representing vegetation cover.

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For E2, we interchanged in the vegetation cover for the two and eight female patches. The patch composition in E2 set were as follows
1.
one female + no plants (no vegetation—N)

2.
two females + eight plants (high vegetation—H)

3.
four females + three plants (moderate vegetation—M) and

4.
eight females + two plants (low vegetation—L).

All test males were tested in E1 and E2 on consecutive days in no particular order. Details on the data collected are provided in Supplementary Files S2 and S3.
Experimental protocol
For the experiment involving association preferences with only varying female numbers a total of 20 males were tested, while 24 males were tested for experiments on the association preferences in varying female numbers combined with vegetation density gradients (E1 and E2 experiments). The experiments were performed two months’ apart to ensure the fish do not retain any memory from the first experiment, and thus they could be treated as two independent sets. We isolated subject males of comparable sizes and kept them in individual isolation in 500 ml jars for four days prior to experiments as that allowed us to keep track of individual fish and also stimulated mate-seeking behavior21,22. They were fed freeze-dried blood worms every day at constantly maintained feeding times. The gravid females that were used for the experiment as stimuli for association were isolated (about 22 females) in a small holding tank (30 × 20 × 20 cm) with a feeding regimen similar to the test males. Before the start of each trial, we introduced the females into each chamber (patch) randomly (according to the experimental setup described above) and left them there for 15 min. for acclimation. A single male individual was then gently introduced into the central cylindrical chamber (with a hand-net), open at both ends (made of transparent plastic and provided with holes). After a five-minute acclimation period, the chamber was slowly removed to allow the male to swim freely in the arena and video recording was commenced. Video recordings were done using a camera (Sony DCR-PJ5, Sony DCR-SX22) placed perpendicularly above the arena. The test fish (males and females) were fed only after the end of experimental trials, on each day of experiments. At the end of the trials, the fish were returned to their holding tanks. No subject male fish were tested more than once per experimental setup and trial. The females used for the patches, were housed together (but separate from their male counterparts) in a smaller tank. Before the trials the females were picked randomly and assigned into each patch. During the experiment, the position of females being used was randomized between trials from patch to patch, to avoid the possibility of bias among the subject males for any particular females in the patches.
We recorded the behavior of each test fish for 10 min. All videos were analyzed using the software BORIS23. A single visit to any of the patch was denoted when the male approaches within 6 cm (1.5 times their average body length) of the patch. We collected data on three parameters: total number of visits to each patch, the total amount of time spent in each patch and the mean time spent per visit within each patch. The same overall protocol was followed for all sets of experiments.
Statistical analyses
We noted the total number of visits to each patch, the total duration of time spent in each patch and mean time spent per visit per patch for the entire ten minutes duration of video recording for each test male. We calculated preference index (I) the total number of visits (I_visit) and total time spent (I_time) for each patch as proportion of the total visits made to all four patches24.

I_visit for patch A = No. of visit to patch A/(visit to patch A + visit to patch B + visit to patch C + visit to patch D).

I_time for patch A = time spent in patch A/(time spent in patch A + time spent in patch B + time spent in patch C + time spent in patch D).

All statistical analyses were performed in R studio (version 1.1.463)25. We developed generalized linear mixed models (GLMMs) using package glmmTMB (version 0.2.3)26 with ‘fish’ as the random factor and ‘Patches’ as the fixed factor, with four levels representing the four choices for the test (male) fish. Preference for total number of visits (I_visit) as well as total time spent (I_time) were found to fit beta distribution with values ranging between 0 and 1. For data fitting, we added 0.0001 to every value, to remove zeroes. Relevelled models were used to compare the parameters between the four patches. Link = logit was used under beta family to construct the GLMM models.
For analyzing the data for the second and third experiments involving varying female densities along with vegetation densities (E1 and E2), we followed a similar procedure of constructing a GLMM followed by post hoc tests. GLMM models were constructed with a single independent variable, “patch”, that had four levels, designated as H (high vegetation density), M (moderate vegetation density), L (low vegetation density) and N (no vegetation). More

Connectivity confers resilience
We observed inherently higher grazing performance in better-connected, unperturbed systems (Fig. 2a,f). The two better-connected systems (connectivity = 14.5; 21.6) had significantly higher grazing performance than the least-connected system (connectivity = 9.6), demonstrating a positive, non-linear, relationship between connectivity and ecosystem function in the controls (Fig. 2a,f; S1, S2). Physical disturbances, however, did not appear to dramatically alter this relationship at the system level (Fig. 2b,c), despite clear impacts on performance in the affected patch (Fig. 2g,h).
Figure 2

Grazing performance in response to ten experimental disturbance treatments at three connectivity levels. Grazing performance is algal consumption as a proportion of total algae available (mean ± SE). In d: both stressors were applied to the same patch (same). In e: stressors were applied to different patches (diff).

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Each disturbance regime resulted in a significant decrease in grazing performance within the affected patch (Fig. 2f:j; S2), but not always across the entire system (e.g. Fig. 2a:e; S1). Impacts within affected areas were sometimes offset at the whole system level by increases within unstressed patches because the stressors themselves triggered animal aggregations in unstressed regions. For example, the animals typically left heat-stressed areas, sometimes finding refuge in the unstressed patch. This meant that unstressed protected areas sometimes returned higher grazing performance than in the control scenarios, offsetting losses in the affected patch and resulting in no significant change in performance across the whole system (Fig. 2b,c).
Multiple stressor scenarios
Multiple stressors had variable effects on the shape of the connectivity-resilience relationship (Fig. 2; Extended data Fig. 2). When heat-stress and harvesting were applied to the same patch, grazing performance was heavily reduced under all connectivity scenarios, but the shape of the connectivity-resilience relationship remained positive (Fig. 2d,i). However, when applied to different patches, these effects were strongly antagonistic. Heat-stress offset the effect of harvesting, creating a slight negative relationship between connectivity and resilience. There was a loss in grazing performance at higher connectivity levels and, by contrast, a slight gain at the lowest connectivity (Fig. 2e,j). Heat-stress likely encouraged animals to move away from the hotter patch, into the harvesting patch. These patches were in closer proximity in better-connected systems, making animal congregations in the harvesting patch more likely, thus increasing the relative impact of harvesting and changing the shape of the connectivity-resilience relationship.
Disease interactions
We applied a 50% consumption penalty for infected individuals in disease simulations, representing a realistic simulation of real-world diseases that can hinder animal performance. White-spot disease, for example, affects shrimp consumption rates before causing mortality, allowing the disease to spread while also suppressing consumption rates27. Some diseases may have different magnitudes of effect on individuals. Thus, we also simulated stronger disease effects by reducing grazing rates for infected crabs by 100%. In general, the simulated disease infected more crabs at higher connectivity levels (Extended data Fig. 3), leading to higher consumption penalties with increasing connectivity in most scenarios (Fig. 3a,b). The 50% disease effect level did not negate the inherent benefits of connectivity observed in unperturbed systems (Fig. 2), but at a more strongly negative relationship between connectivity and grazing performance was observed under a 100% penalty (Fig. 3b). Thus, disease had a higher impact on ecosystem function in better-connected systems (Fig. 3; Extended data Fig. 4).
Figure 3

Box and violin plots of effect size for each of the (a) 50% and (b) 100% disease effect scenarios and (c) standard error plot of variation across all spatial scales and connectivity levels. Linear model (dashed line) in (a) and (b) provided as visual guide of direction of trend. Data in (c) are the grand-averages of within-treatment standard errors.

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There was also less variability in grazing performance with higher connectivity, but not significantly (Fig. 3c). The within-treatment standard error in grazing performance was empirically lowest in the best-connected systems across three spatial assessment levels (Fig. 3c), suggesting that grazing responses were more predictable in better-connected systems (Fig. 3c).
Conservation implications
Given the setting of reserves in complex spatial mosaics, with multiple stressors, it is necessary to have a better understanding of how connectivity can change the way ecosystems respond to stressors. We show that these relationships are complex, even in simplified, controlled systems. Despite the microcosm scale of our experiments, our results support real-world phenomena that have been linked with the benefits of connectivity and/or protected areas. Thus, we suggest these findings contribute valuable information to support the future design of research and management strategies for natural systems. For example, Marine Protected Areas (MPAs) can be considered analogous refuges to the unaffected patches in our harvesting scenarios. MPAs provide an offsetting service in natural ecosystems where, by excluding harvesting, they provide a refuge and source of animal resupply28 that supports fisheries and acts to maintain ecosystem function e.g.22. Our systems responded similarly to these real-world examples in that the number of animals available for harvest was highest at the edge of the simulated MPA, as observed in the best-connected systems (Extended data Fig. 5). This phenomenon was strongest in the multiple-stressor scenario that applied heat-stress to the patch that was protected from harvesting pressure. Heat-stressed animals vacated the hotter protected area, exposing them to possible capture.
Additionally, connectivity may provide a stabilising effect on ecosystem function, a phenomena that may partially contribute to previous findings that connectivity strengthens ecosystem resilience (e.g.29). Thus, when connectivity is low, ecosystems may experience greater variability in the performance of key ecosystem functions, potentially limiting capacity to resist or recover from disturbance.
We tested the role that connectivity plays in shaping animal functional responses to single and multiple disturbance events of different types. To do so, we quantified the effect that different combinations of stressors had on the grazing performance of a widespread mesograzer, the yellow-footed hermit crab (Clibanarius virescens), in purpose-built arenas at three levels of connectivity. Connectivity can be measured in many ways, with effects being difficult to quantify between systems with different numbers of redundant or complimentary routes, motifs such as triangular or circular clusters, or ‘hubs’ that connect multiple patches to one central node30. To minimise unintended effects of altering the number or place of connections, we altered system connectivity by varying the location of important patches (containing food) within a standard 4 × 3 node grid of approx. 42 × 32 cm (Fig. 1), rather than by adding or removing connections. We selected system configurations (habitat patch placements) that were symmetrical along both the x and y axes, minimising the risk of introducing unintentional confounding effects. This created a base system with 12 nodes and 14 edges in all cases.
Connectivity within each system was calculated using a modified measure of closeness31, as in Eq. (1):

$$text{Connectivity }= frac{1}{T+P+D}times 100$$
(1)

where; T = average shortest path length from food node 1 to all other nodes; P = average shortest path length from food node 2 to all other nodes; and D = shortest path length between both food nodes. All path lengths were counted as integer steps between nodes.
Standard experimental procedure for all treatments
We tested ten treatments at each connectivity level, resulting in N = 236 replications; between 73 and 82 at each connectivity level.
Each replication involved slowly warming crabs and arenas to the desired temperature (defined per treatment below) over a 4-h period, approximately mimicking daily warming cycles. One crab was then added to each patch (12 total in the system), and six 1 mg algal pellets were added to each of the two food patches (coloured patches in Fig. 1). Every 20 min, the number of pellets remaining was counted, and an additional six pellets were added to each patch. Each experimental replication lasted 1 h (3 × 20-min intervals), starting when crabs were first added to the arena. Thus, in all cases, 18 pellets were added to each patch; 36 total to the system. This was determined as the control level because an individual crab is expected to consume approximately three pellets per hour at an optimal temperature 29.5 °C25. Hence, by adding pellets equal to the mean consumption rate (one per crab per 20-min period), we simulated a stable system in which consumption was approximately equal to algal production in the absence of stressors. Any reduction in consumption (driven by stressors) below optimal rates implies that algal mass would increase over time, suggesting that the system is trending towards a phase shift. Thus, by our definition, lower consumption makes the system less resilient.
Treatment specifics
Control
The control treatments were run as per the standard experimental procedure described above with no stressor applied.
Heat-stress
For the temperature stressor treatment, the experiment was run as per the standard experimental procedure, but with a temperature stress applied to the half of the arena incorporating an affected patch ‘Zone B’). Water was heated using a combination of sous vide precision cookers and aquarium heaters, arranged in a way that ensured the stability of target temperatures for the duration of the experiment. The stressed half of the arena was set to 33.5 °C, and the unstressed half was set to optimal temperature (29.5 °C; as per24). The 4 °C increase in temperature is expected to decrease consumption rates by approx. 15–20%24, with an additional effect on movement expected to amplify this effect. This is intended to simulate a system with connected heat-stressed and refuge areas.
Harvesting pressure
A harvesting stressor was applied that simulated a fishery management scenario with a fixed bag limit. We designated one food patch as a protected area and resupply point (blue in Fig. 1), and the other as a harvesting area (red in Fig. 1). Because our systems included two distinct habitat patches, separated by different amounts of featureless habitat at different connectivity levels, we equate these to reef or vegetated habitat where fauna are likely to congregate near resources. Similarly, fishers are likely to congregate in the same areas, unless excluded. Thus, by restricting harvesting in one of the patches, we have simulated the broad dynamics of an enclosed bay that contains both protected and high harvesting pressure habitat areas, and some unprotected, but featureless areas in-between that would be expected to experience low harvesting pressure, which we did not attempt to simulate.
In this scenario, we set a bag-limit that allowed up to three crabs (or as many as were present under three) to be harvested from the affected patch at the end of each 20 min interval, and then the same number of crabs were added to the protected area, simulating a maximum sustainable yield management (MSY) scenario. Under the harvesting only stressor, all other experimental procedures were as per the standard scenario, with temperature set to optimal (29.5 °C) across the entire arena.
Heat-stress and harvesting
To investigate how multiple stressors interact with the connectivity-resilience relationship, we also applied both heat-stress and harvesting to the same arenas simultaneously in two ways. First, by applying both stressors to the same patch (same), and second by applying the heat-stress to the protected area and the harvesting pressure to the other (diff).
Disease
We applied a simulated effect of disease by recording interactions between individuals and applying a 50% and 100% (separately) consumption penalty for ‘infected’ crabs. Reduced consumption is a known effect observed in individuals infected by numerous diseases, including some that are known to affect crustacean mesograzers (e.g. white-spot disease27). We recorded all experimental treatments on video (GoPro models) and then extracted data on the movement and interactions between crabs from each video. Unique colour markers were used to track individual crabs, enabling data to be recorded for all occasions during which contact was made between crabs (including the total duration of each interaction). We also recorded the time that each crab entered and/or exited one of the designated habitat patches.
Disease spread scenarios were then modelled from interaction data, whereby we designated an individual crab as being the infection vector (starting with a disease) and then quantified how the disease spread through the system through crab-to-crab interactions. For each treatment replication, 12 sub-replications were assessed simulating each of the 12 different crabs starting with the disease. See Extended data Fig. 1 for example of infection pathways taken for each ‘starting crab’ during one physical replicate. Interaction and movement data were extracted from videos manually. Disease spread was then simulated from interaction data in R using customised code.
For each disease spread scenario we applied the stressor as a 50% reduction in consumption for diseased crabs as our primary test level, also testing the effect at a 100% reduction level to observe a worst-case scenario. The effect was calculated based on the total consumption within a period and time that crabs (both infected and uninfected) spent in close proximity to food using the below equations:
1.
Consumption after disease = 
Disease effect (as percentage) × observed consumption rate × cumulative infection time.

2.
Observed consumption rate = (frac{total ; consumption}{sum_{n=1}^{12} crab ; n ; total ; time ; in ; food ; patch})

3.
Cumulative infection time = (sum_{n=1}^{12}crab ; n ; time ; in ; food ; patch ; while ; infected)

See worked example in Extended data Table 1.
Statistical analyses
We assessed the effect of treatment (connectivity level and stressor(s)) with generalised linear models (glm). Effect was assessed at two levels: both at the whole system level, as total consumption across both habitat patches combined and, within the affected patch only (affected), tested in separate analyses. Treatments (as factors) were: Control; heat-stress, harvesting; heat-stress and harvesting (same); heat-stress and harvesting (diff). Noting that in the heat-stress and harvesting (diff) treatment there was no designated ‘unaffected’ patch because both patches were affected by at least one stressor. For consistency, we included the patch affected by harvesting in all affected patch analyses. Connectivity level was the system’s connectivity metric (9.6; 14.5; 21.6), also set as a factor.
To identify the best model, we started with the most complex model that included all possible interaction terms, and used a leave-one-out technique, exclude the most complex interaction term until a significant interaction was identified using Analysis of Deviance (ANOVA) with chi-squared test (detailed outputs in S1; S2). The final glm model was selected as the most complex equation (i.e. largest interaction term) that returned a significant interaction in this test, resulting in a final model for both system level and affected patch level of:
Consumption ~ Harvesting + Heat-stress + Connectivity + Disease + Harvesting:heat-stress + Harvesting:Connectivity + Heat-stress:Connectivity + Harvesting:Disease + Heat-stress:Disease + Connectivity:Disease + Harvesting:Heat-stress:Connectivity.
Mean ± SE plots presented were derived from outputs for this glm equation. Alpha was set to 0.05.
Treatment differences were assessed using model outputs, with significant differences defined as non-overlapping treatment values for model fit (mean) ± standard error.
Disease effect size was calculated as:

$$Effect;size , = , left( {diseased;consumption , {-} , replication;consumption} right)/replication;consumption$$ More

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Site selection
Hyrcanian temperate forests, dominated by old broadleaf trees, are located in the north of Iran adjacent to the Caspian Sea. We selected the Neka Zalemroud forest in Mazandaran province as the study area for this research (36° 26′ 09″ to 36° 30′ 47″ N latitude and 53° 20′ 34″ to 53° 31′ 51″ E longitude) as the boundaries of sampling area have been illustrated in Fig. 1 by the authors. This forest has been covered with 2533 hectares of old broadleaf trees such as Fagus orientalis, Carpinus betulus, Quercus castanafolia, Acer velutinum, Acer cappadocicum, Parrotia persica and some other species. This region is affected by permanent winds and the maximum wind speed is in the range of 10 to  > 30 m/s. The windstorms with more than 100 km/h cause damage forest trees, including uprooting or stem breakage. The windstorms cause many tree failures annually, which is in result of the tree harvesting and gap creation in forest stands. Hence, we aimed to identify the uprooted or stem broken trees using the sample plots data after the windstorm with 100 km/h (4 h) on 21 March 2018.
Figure 1

The location of study area and sample plots (QGIS 3.12.0, https://www.qgis.org/en/site/).

Full size image

Methods
Data from field measurement of 600 sample plots in the study area were summarized before and after the windstorm in March 2018. ARC MAP 9.3 software was used to spatially locate the sample plots on the forest map. Also, the slope of plots was defined by topography map (1:50,000) in this software. The permanent sample plots were created by Department of Natural Resources of Mazandaran Province (in the structure of the forest management plan) as a part of government-sponsored “permanent sample plot” protocol to monitor the changes in the number of trees and species48. In this protocol, the centers of these sample plots are marked with a metal rod and the geographical coordinates are recorded. The attributes of all trees in the sample plots are recorded consisting of species, diameter at the breast height, tree’s height, number of trees, distance to the center of the plot, crown diameter and land, soil and climate characteristics of the plot location. On average, in each plot, there are about 10 to 20 trees with a diameter of more than 7 cm (marketable size), and using the recorded data of the trees, it is possible to identify each tree in subsequent monitoring. As the protocol dictates, preliminary data were recorded on the stage of creating plots by experts from the Provincial Department of Natural Resources in 201649. After the windstorm on 21 March 2018, these plots were investigated by the authors to find damaged and undamaged trees. The area of each sample plot was 1000 m2 and in the shape of the circle with 17.84 m radius. These plots were investigated to record harmed trees which were uprooted or stem broken. Sample plots are clustered into susceptible (with harmed trees) and unsusceptible (without harmed trees) plots. We recorded the forest stand attributes, as well as tree attributes, which influence the likelihood of trees to be damaged in windstorms. Therefore, we investigate the damaged and resistant trees in the plots within 1000 m2 area. The stand variables were recorded in the plot area such as the mean of the trees’ height in the plot. Some plots (306 plots) were determined where the damaged trees were observed and some others (294 plots) were determined where the target tree in the middle of the plot was undisturbed. In a literature review, we found that stand and tree characteristics influence wind-susceptibility of trees (such as tree diameter and height, spread crown area, rooting system, soil type, stand density, topography, etc.1,3,19,20,21). Therefore, 15 variables in 600 sample plots were recorded that are divided into two categories: 1. Forest stand variables: Plot Slope (PS) (%), Soil Depth (SD) in plot area (cm), trees Mean Diameter at the Breast Height (MDBH) at plot (cm), trees Mean Height (MH) in plot (m), trees Density (De) in plot (Number of trees), trees Diversity (Di) in plot (Number of tree species), Number of Thicker trees in diameter (than the target tree) (NTh), and Number of Taller trees (than the target tree) (NTa).
2.Tree variables (bigger than marketable size): Tree Area (TA) (occupied area by the tree) (m2), Tree Diameter at the Breast Height (TDBH) (cm), Tree Height (TH) (m), Tree Crown Diameter (TCD) (m), Mean Distance from Neighbor trees (MeDN) (m), Minimum Distance from Neighbor trees (MiDN) (m), and Maximum Distance from Neighbor trees (MaDN) (m). Tree heights and some more data were recorded in permanent sample plots before the windstorm. Therefore, we used the recorded data at the stage of creating plots, for damaged trees. In fact, 10 to 20 trees are recorded in each plot and using the recorded data of the trees (species, diameter, distance to the center of the plot, etc.) it is possible to identify target trees (damaged or undamaged) in subsequent monitoring. There are some other factors that influence wind-susceptibility of trees such as forest edge, tree diversity, and land form. In this research, we were looking for the impact of forest plan activities on tree failure; therefore, we neutralized forest edge effects by selecting sample plots inside the forest stands which are far from the forest edges. In land form variables, land slope was considered in stand variables, but altitude and geographical aspect of the hill, as well as tree diversity, were omitted because of limited variation in the samples.
Tree Failure Model (TFM) was developed by recording 15 variables of the trees and forest stands in 600 selected sample plots. In fact, we designed three TFMs with three modeling techniques to achieve the most accurate one based on model accuracy assessment. The damaged trees in the plots were identified by two features: (1) The tree was uprooted by wind forces along the windstorm. (2) The tree was uprooted or stem broken. Leaning trees (under windstorm force) were also counted as uprooted trees. The damaged tree was chosen as the target tree in susceptible plots (plots with a damaged tree). Also, the central tree was selected as the target tree in the wind-unsusceptible plots (plots without damaged tree). Indeed, the output of TFM will be in two classes of damaged trees (1) and stable trees (0). Hence, the response or output of the model will be a discrete class {0,1}. The accuracy of the model is assessed by confusion matrices which detect the number of accurate and false classifications of sample trees.
The new mathematical modeling approaches and machine learning techniques are needed to cover limitation in data collection and forest inventories. Indeed, ANNs are over 50 years old, but just not often applied yet. History of ANN development represents this fact that learning algorithms and structure of neural networks are developed every year. Therefore, we developed artificial intelligence techniques in natural phenomena modeling11,17 namely MLP, RBFNN, and SVM.
Machine learning techniques rely on a specific concept that is “a set of weak learners develop a single strong learner” (by Freund and Schapire22, Breiman23 and Breiman et al.24). As it is known, a weak learner is a classifier correlating slightly with the real (target) classification; while a strong learner is well correlated with real (target) classification. Machine learning algorithms are trying to combine weak classification rules in a one strong classification rule. Based on this approach, we used 15 variables (even if we believe that these variables are not related to tree susceptibility in the wind) and tested some algorithms and variable weights to make weak learners or rules and combining them into one strong rule in the structure of three machine learning techniques.
Multi-layer perceptron (MLP) neural network
ANNs use different methods, such as feed-forward, backward, recurrent and other, to teach the network for output prediction. MLP is a multi-layer form of Feed-forward neural networks without any cycle or loop. In Feed-forward neural networks, the information analysis is performed in one direction from the input layer, through the hidden layer to the output layer47. In this learning method, the errors of the network propagate from the output layer to inputs to revise the weights of input variables. MLP is a multi-layer Artificial Neural Network (ANN) model with self-learning mechanism which uses samples for classification. Indeed, MLP has been using some interconnected processing elements that are called PEs (Processing Elements). MLP learns by using samples and transfer functions which are applied between neurons and hidden layers in a computer program17. In the training process, each PE receives signals periodically from other PEs and sends the new signal to other processors. Considering inputs, MLP adjusts the weights of neurons continuously, and the learning process is completed.
We used some activation functions (such as logarithmic sigmoid, hyperbolic tangent, and linear transfer functions) which determine the relation between inputs and outputs and these functions were tested to achieve the best performance of MLP. Back Propagation (BP) method propagates the error of outputs to the input layer where the first random weights have been assigned. The weights of the network inputs will be justified until the best performance of the network is reached; and after that, the learning process will be completed7,11. Errors between Ynet (MLP output) and Y (real class of tree failure) are decreased by BP when the weight of neurons or Processing Elements (PEs) (w) and input variables (x) come to the best performance, and the output of jth PE on the kth layer (PEkj) will be achieved by Eq. (1):

$$net_{j}^{k} = mathop sum limits_{i = 0}^{n} w_{ji} x_{ji}$$
(1)

Transfer functions are used in the structure of network, and neuron output value is determined by (Eq. 2).

$$Y_{net} = smallint net_{j}$$
(2)

Finally, weights of t samples will be adjusted by delta rule which has been summarized in Eq. (3).

$$w_{ji}^{t} = w_{ji}^{t – 1} + Delta w_{ji}^{t}$$
(3)

By using the ANN function in MATLAB R2013b, 360 uniformly distributed random samples (60% of 600 samples) were defined as training data set. 120 evenly distributed random samples (20% of 600 samples) were defined as validation data set, and 120 samples (20% of 600 samples) were determined as test data set. All data were normalized to the interval of 0 to 1 using the Min–Max technique by mapminmax function in MATLAB R2013b (Refer to Demuth and Beale25 for MATLAB codes for MLP neural network development and related preprocessing algorithms).
Radial basis function neural network (RBFNN)
Radial basis function neural network is architecturally similar to the MLP with different activation function in the hidden layer. RBFNNs have been used in function approximation and classification in researches of the last decade13,26,27,28. RBFNN uses samples in two data sets of training and test. The radial function is applied in each neuron of the hidden layer; and the number of neurons depends on input matrix of variables. Considering two classes of trees failure (0 and 1) in this research, we have two output layers in the structure of RBFNN. Gaussian function is the most frequently used function in the hidden layers of RBFNN13,27. The Gaussian function can find the center of circular classifiers successfully. The Gaussian function regulates the centre of mentioned circular classifiers by Eq. (4).

$$R_{j} left( x right) = expleft( {frac{{||x – a_{j} ||^{2} }}{{2sigma^{2} }}} right)$$
(4)

In Eq. (4), input variables are structured in the matrix “x”, radial basis function has been defined as Rj(x), centre of RBF function is presented as aj, and we have a positive real number as “ϭ”. The outputs of network will be calculated by an output function Eq. (5).

$$y_{k} = mathop sum limits_{j = 1}^{m} w_{jk} R_{j} left( x right) + b_{j}$$
(5)

In Eq. (5), the number of calculation nodes in the structure of hidden layers (j), the number of neurons (m), the weights of neurons (wik), and a bias value (bj) have been used to calculate output (yk).
Neuron weights (wjk) are updated continuously to decrease output errors until network training process comes to end. Network performance is calculated when the number of neurons and the weights of neuron or layers are fixed13. (Refer to Demuth and Beale25 for MATLAB codes for RBF neural network development and related preprocessing algorithms).
Support vector machine (SVM)
SVM is one of the machine learning techniques that requires quite a lot of data for training, but this method also provides more accurate results than other methods when the volume of training data is limited29,30. Therefore, SVM has been used for modeling in this paper to deal with this issue with the collected data along forest inventory.
As a classifier technique, SVM aims to determine the largest margin in decision boundaries that could separate classes of decision31. SVM is looking for the largest margin in the boundaries of classification when the uncertainties in the decision are expected27. This method of prediction minimizes the probability of over-fitting in classes limits of tree failure.
We have two datasets of training and test in the structure of SVM. The values of target are structured in a n-dimensional matrix so it is possible to find the most accurate boundaries and margins. Equation (6) is the SVM model and equation parameters define: y(x) = SVM output, α_i = a multiplier, K = kernel function, and b = threshold parameter.

$$yleft( x right) = mathop sum limits_{i = 1}^{n} alpha_{i} Kleft( {x_{i} ,x_{j} } right) + b$$
(6)

Then we defined Gaussian Radial Basis Function (RBF) in Eq. (7), in the context of non-linear SVM. As we know, RBF is the most popular function in the context of SVM with remarkable ability to control generalization of SVM classifier.

$$Kleft( {x_{i} ,x_{j} } right) = {text{exp}}left( { – gamma| x_{i} – x_{j}|^{2} } right)$$
(7)

The parameters of Eq. (7) are: xi and xj = samples and γ = kernel parameter.
Finally, primal problem in Eq. (8) should be minimized to achieve the most accurate SVM for tree failure prediction.

$$frac{1}{2}|w|^{2} + Cmathop sum limits_{i = 1}^{n} xi_{i}$$
(8)

In Eq. (8), the parameters are: 1/2||w||2 = the margin, Σξi = training errors and C = the tuning parameter.
SVM uses samples in two data sets of training and test. The classes of the target will be summarized in a n-dimensional matrix to determine the nearest classification boundaries and margins. (Refer to Demuth and Beale25 for MATLAB codes for SVM neural network development and related preprocessing algorithms).
Model selection
MLP, RBFNN, and SVM models were run on the training dataset with 15 tree variables as inputs and tree failure classes in 600 selected trees as output. To evaluate prediction accuracy of the MLP, RBFNN, and SVM models, we used the confusion matrix to determine the percentage of accuracy in target tree classification. Also, the number of trees with accurate and failed classification will be detected11.
Sensitivity analysis
Sensitivity analysis was designed to prioritize the most accurate model variables with respect to the significance of variables in output. Sensitivity analysis defines the usefulness of variables in model predictions. In sensitivity analysis, we changed each variable in the range of standard deviation with 50 steps while the other variables were fixed at the value of the average. Then, the standard deviation of outputs for each variable changes was measured as model sensitivity for that variable. Variables with high value in the outputs standard deviation are the most important variables with more influence on model outputs. The trend of model output changes with changing the most significant variables, in the range of standard deviation (50 steps) was illustrated in some figures to find out the way that model outputs are changing with variable changes (negatively or positively) (Refer to Kalantary et al.27 and Jahani et al.13.
Environmental decision support system (EDSS) tool
Finally a user friendly GUI (Graphical User Interface) tool was designed as an EDSS for susceptible tree identification in windstorms. It is applicable for forest managers who are looking for hazardous trees to plan for tree protection and increase the forest stands resistant against windstorms. ANN models use a huge matrix of weights; so model execution should be in the mathematical software (in this research MATLAB R2013b). Users, who are not familiar with the software, need a simple tool to run the model on new samples and get the results of prediction. To design EDSS tool, we developed a GUI extension in MATLAB R2013b software. With this tool, users enter the values of trees and stands variables (based on forest inventory data in other target forests) and the susceptible trees will be identified only by pushing a button. The model will be run on the data and the model outputs for each tree will be appeared in a table (0 or 1). More