A Computational Model for Determining Tiger Dispersal and Related Patterns in a Landscape Complex

Abstract

Species dispersal from one territorial zone to another is a complex process. The reasons for species dispersal are determined by both natural and human factors. The purpose of this study is to develop a cost surface for a hypothetical landscape that accounts for various species dispersion features. With tigers (Panthera tigris tigris) as the focal species, a computational model for a landscape has been proposed to predict the dispersion patterns of the species’ individuals from one habitat patch to another. Knowing how tigers disperse is very crucial because it improves the likelihood of successful conservation. The likelihood is raised because it strengthens conservation efforts in the targeted regions identified by the proposed model and encourages landscape continuity for tiger dispersal. Initially, four major factors influencing tiger dispersal are explored. Following that, grids are overlaid over the tiger-carrying landscape map. Further, game theory assigns a score to each grid in the landscape matrix based on the landscape features in the focal landscape. Specific predefined ratings are also utilized for scenarios that are very complex and may change depending on variables, such as the interaction of the dispersing tiger with co-predators. The two scores mentioned above are combined to create a cost matrix that is shown across a landscape complex to estimate the impact of each landscape component on tiger dispersal. This approach helps wildlife managers develop conservation plans by recognizing important characteristics in the landscape. The results of the model described in this work might be beneficial for a wide range of wildlife management activities, such as corridor management, smart patrols, and so on. A cost surface over any focal landscape may serve as a basis for policy and purpose design based on current landscape conditions.

1. Introduction

Individuals of many species disperse from one habitat patch to another for various reasons, including ecological factors and human disturbances [1]. For a few species, dispersion outside of their native area is a regular phenomenon and an essential part of their lifecycle [2]. Different landscape characteristics in every focal landscape complex might inhibit or facilitate such dispersals. To study these dispersals, the possibility of dispersion and dispersal patterns of individuals of distinct species, it is critical to understand the interaction of the species with the underlying landscape features.

The dispersion of species in the wild occurs naturally. To avoid inbreeding, control food chain pressure, and maintain other ecologically significant features within the focal landscape, species disperse from their home range to another [3]. Therefore, a vital aspect of nature that it is necessary to maintain equilibrium among various phenomena and, consequently, to maintain the ecological balance in species dispersal [4]. This might take place within a single Protected Area (PA) or across several PAs. Since both dispersals are essentially the same, they have a shared origin. Any focal landscape may experience a variety of types of cooperation, defections, support, and multilayer conflicts, all of which can facilitate or obstruct species dispersal.

Landscape complexes have a variety of dynamic biotic and abiotic traits. These traits come together to form a group of elements that interact with the dispersing species and provide it with support on either a favorable or negative scale. Therefore, a species’ individual dispersion is an emergent phenomenon resulting from the interaction with the landscape complex. Additionally, each parameter interacts with different species in different ways, and each species receives a distinct level of support or inhibition. Hence, it may be claimed that a species’ movement and mobility patterns within a landscape are unique to that species [5]. For instance, the mobility of an elephant (Elephas maximus) might not be supported by the presence of a large chital (Axis axis) population in any landscape grid, however the dispersion of a tiger (Panthera tigris tigris) might. The discussion above explains how each species interacts with landscape factors in a unique style, leading to species-specific dispersal patterns in any focal landscape.

Finding and analyzing the tiger’s dispersal patterns in an environment that has various essential components of any landscape is the aim of this study. The tiger is the focal species. Such a model would need to understand why an individual disperses outside of their native range, which would be a vital objective (following the life event models of the tiger). To accommodate the demands and wants of a dispersing tiger, the knowledge learned about the reason for migration may be employed [6]. To understand more about the dispersing tiger’s movement behavior, these demands might potentially be reproduced.

One method to achieve this objective is to initially divide the landscape into grids of equal size. Therefore, each grid functions as an element of the landscape’s matrix. The interactions in each grid are then simulated to produce a cost surface that is placed over the landscape matrix, resulting in scores for each grid that indicate whether it encourages or restricts tigers’ passage across it.

This paper’s major goal is to present a fundamental computational framework for better understanding and forecasting tiger dispersal patterns in any landscape. Understanding these patterns can provide sufficient knowledge on how tigers disperse in different types of landscapes. Knowing when, how, and where the tiger will disperse can give many wildlife stakeholders baseline information to design and prepare conservation plans accordingly. An effective strategy may be very helpful in reducing different illegal activities such as poaching, hunting, etc., as well as human–animal conflict in the dispersion landscape, which would result in better species conservation. The claims made in this study are supported by cognitive definitions of a dispersing tiger’s needs and the presence or absence of landscape quality in every grid of the landscape matrix [7]. As a result, every encounter is influenced by the main landscape structure.

In this paper, the difficulty of understanding tiger dispersal patterns in a landscape is treated as a cost allocation problem. The reason why tigers leave their native habitat is then incorporated into the job via dispersion weights. A cognitive evaluation of tiger requirements based on dispersion causes determines the dispersion weights [8]. It provides the dispersion coefficient for each landscape characteristic, demonstrating how much each attribute impacts the grid’s cost distribution. Additionally, we model the interaction of each attribute using a two-person prisoner’s dilemma game, and the payoffs are merged with the dispersion coefficients to provide a cost to each grid [9]. One of the most important and variable features of the environment that affects tiger dispersion is the presence or absence of co-predators in the grids [10]. Only a few hardbound scores are provided, and even the presence of co-predators is classified based on relative strengths to produce a secondary cost element over the landscape. The original matrix and secondary cost elements are combined to provide the final cost matrix for the entire landscape complex.

In the last few decades, several ideas and techniques for creating wildlife corridors have surfaced. The two well-known and widely accepted methods for creating wildlife corridors are based on either the circuit theory [11] or the principles of the Minimum Spanning Tree [12]. The ideas both support and persuade the question of: “What could be the best path which would support the movement of species in a given landscape?” Additionally, they recommend using a thorough topographic dataset and studying animal habitats to help design the dispersion corridors. They work based on the presence/absence of focal parameters in any landscape grid. Further, it is not necessary for animals to move only along the corridors that have been created. Animals may travel over the terrain through routes that fundamentally do not capture the properties of the most ideal corridors according to the planning principles of the applicable theories, subject to availability and fulfilment of ecological demands [13]. Field studies show that dispersing animals leave the corridors, indicating that the two suggested options for corridor design outlined above do not account for all the corridors that are open for animal dispersion. The solutions are also unable to explain or respond to questions concerning the behavior of species in and around the corridors, which consider the resident territorial populations in the landscape as well as the satellite tiger population in the area. The approach described in this paper collects the priority of landscape attributes present or absent in each grid for the cost calculation. As a result, a more practical and precise method of producing cost surfaces is developed. The suggested model additionally considers co-predators, which is something that is missing from the contributions of earlier research. Further, the current model suggests a local movement and direction to be considered for dispersion rather than scanning the entire graph, which may not be the minimum but accurately captures the deviation of species from their target route and then defines the key routes.

The following arguments do not consider any real-world information gathered by a GIS procedure and a typical field investigation. The findings might serve as a model for conservationists and wildlife managers to utilize when making judgments about tiger dispersal patterns since they focus on the presence or absence of attributes in different grids in the complex and the ease of mobility.

The foundation for the work’s materials and methods is laid out in the succeeding section, and the hypothetical landscape that was used to construct and evaluate the mathematical model presented in this study is further explained. Finally, the study’s methodology is detailed, and the remainder of the paper is devoted to the study’s outcomes, analysis, and conclusion.

2. Matrices, Dispersal Weights, and Game Theory

The current work offers a model for a realistic cost allocation for dispersing tigers in a complex terrain using a few areas of mathematics. The fundamental concepts of various subjects are discussed in this section to make the work self-contained.

Matrix: A matrix is a collection of rows and columns that each have the same number of entries. The element arrangement of a matrix is formally represented as follows:

$$A={\left[\begin{array}{ccc}& \cdots & \\ ⋮& \ddots & ⋮\\ & \cdots & \end{array}\right]}_{m\times n}$$

where the elements of the matrix $A_{m\times n}$ are denoted as: $a_{ij}| i ϵ \left\{1, 2, 3, \dots , m\right\} \& j ϵ \left\{1, 2, 3, \dots , n\right\}$, and the order of the matrix is $m\times n$, which signifies that there are m rows and n columns in the matrix [14]. The landscape is structured as a matrix with grids as its elements.

Dispersal Weights: The term “dispersal weight” refers to a set theoretic technique for ordering the components of any given set based on their probability and needs [15], as proposed in this work. For a given set: $A=\left\{a_1, a_2, a_3, \dots ,a_n\right\}$, and a given set of parameters:$B=\left\{b_1, b_2, b_3\right\}$, for deciding the importance of each element in A, the dispersal weight, M, is given as:

$M=rank\left(a_i\right)| a_iϵ A$, where:

$$rank\left(a_i\right)=a_{i_{\left(b_1\odot b_2\odot b_3\right)}}| \odot \Rightarrow operartion between elements of B.$$

(1)

The importance of dispersal weights has been addressed since they will be used to rate landscape features based on the reason for tiger dispersion.

Game Theory: Game theory has been utilized to simulate the interaction [16] between landscape characteristics and dispersing tigers in this study. A game is defined as a three-tuple $G=\left(P, \theta , \prod \right)$, where $P=\left\{P_1, P_2, P_3, \dots , P_n\right\}$ denotes the number of players, $\theta =\left\{{\theta }_1, {\theta }_2, {\theta }_3, \dots , {\theta }_m\right\}$ denotes the strategy set for each player, and ∏ denotes the associated payoff for each player, such that: ${\prod }_{P_1 X P_2 X\dots X P_n}={\theta }_{P_1} X {\theta }_{P_2} X\dots .X {\theta }_{P_n}$, where ${\theta }_i, i=\left\{1, 2, 3,\dots , n\right\}$ denotes the strategy chosen by player $P_i$ from the strategy set θ for a move. Thus, when one player plays a certain strategy against the other, the payoff is the score they receive.

There are many different types of games that may be used to mimic interactions. To represent the binary interactions between the tigers and the landscape characteristics in this work, a two-person prisoner’s dilemma game has been used. The game is represented as:

$$G=\left(\left\{P_1, P_2\right\},\left\{C, D\right\},\left\{\left(R, R\right), \left(S, T\right), \left(T, S\right), \left(P, P\right)\right\}\right)$$

(2)

where $\left\{P_1, P_2\right\}$ present two players of the game. Next, $\left\{C, D\right\}$ represent the game’s strategy set, in which each player can either cooperate (C) or defect (D). In a strategic form, the payoff matrix expressed in the form of a set in the above representation is expressed as:

		P2
		C	D
P1	C	$\left[\begin{array}{cc}\left(R, R\right)& \left(S, T\right)\\ \left(T, S\right)& \left(P, P\right)\end{array}\right]$
	D

where, R represents the reward for cooperation and has a numeric value of 3, S represents the sucker’s payoff and has a numeric value of 0, T represents the reward for defect temptation and has a numeric value of 5, and P represents the punishment for mutual defection and has a numeric value of 1 [16,17]. As a result, the reward matrix may alternatively be numerically represented as:

		P2
		C	D
P1	C	$\left[\begin{array}{cc}\left(3, 3\right)& \left(0, 5\right)\\ \left(5, 0\right)& \left(1, 1\right)\end{array}\right]$
	D

The ideas in this work are based on the binary interaction between tigers and each grid’s landscape characteristics. The two-person prisoner’s dilemma game was utilized to record these exchanges [18].

3. Hypothetical Landscape for the Study

The hypothetical landscape that was used in this work for modeling purposes is shown in Figure 1. The presence of humans, animals of prey, non-forested terrain, and water bodies are all crucial landscape aspects to consider. Only a few crucial aspects are looked at with the aim of presenting the model and the related mathematical framework. There are many more biotic and abiotic elements that will be present in the landscape and all these parameters must be considered while working on the tiger dispersal pattern.

The forest region mentioned here includes dense, moderately dense, open, and meadow-like woodlands. The presence of people symbolizes the land used for farming, animal grazing, and village settlements. All preferred species as well as injured species that the tigers could devour are included in the prey base. The non-forested terrain includes wasteland, which is devoid of vegetation. The final assessed water base parameters cover all sources of water, from naturally flowing rivers to department-built waterholes [19]. The landscape matrix is divided into important pixels using a grid for evaluation, and afterwards, observation of the landscape features. The model is created to take into consideration the presence or absence of dominating tigers over dispersing tigers, and each pixel of the landscape matrix is considered as a tiger habitat and territory in the hypothetical environment. Consequently, each grid’s collection of parameters is shown as:

$$G=\left\{WB, FA, HP, PB, NF\right\}$$

(3)

where, WB represents the water base, FA represents the forested area, HP represents a human presence, PB represents the presence of a prey base, and NF represents the non-forested land.

4. Methodology

To demonstrate the model suggested in this work, a portion of the landscape matrix containing all the characteristics presented in the Section 3 was studied with the border indicated in Figure 2. The research area was located using the landscape map in a way that ensures it includes all the key study landscape attributes that would be used in the proposed model. The hypothetical map was created from India’s Terrai Arc Landscape utilizing GIS (Geographical Information System) and remote sensing. Further, the area was chosen that is most suitable for presenting the suggested concept after analyzing the landscape and overlaying grids on the map.

To better comprehend tiger dispersal patterns, the work aims to create a cost matrix that can be dispersed across the landscape. It should be noted that the cost matrix would depend on the source and sink aspects of the grids in the focal landscape. When the proposed work discusses the source, it refers to the grids from which a member of a species starts to disperse, whilst the other elements serve as sinks. For instance, the sink grids may be expressed as follows if F3 is the source grid in Figure 2:

$$S=\left\{a_{ij }\right| i ϵ \left\{A, B, C,\dots , J\right\}, j ϵ \left\{1, 2, 3, \dots , 9\right\}, i \ne F and j \ne 3$$

(4)

The preceding explanation clearly indicates that the costs of dispersion for every element of S must be assessed. All the discussed criteria are required during these evaluations, and one of the most important aspects is the presence or absence of co-predators. The existence of co-predators in the region and surroundings is a crucial factor in the tiger dispersion [20]. Figure 3 shows an assumption for the landscape section selected, with 1 and red indicating the presence of stronger co-predators or individuals, −1 and green indicating the presence of weaker individuals, and 0 with white indicating the absence of any individual in the table.

Initially, the cause for an individual’s dispersion is an essential factor in determining their dispersal pattern. Four critical life events from the tiger lifecycle that influence the tiger dispersal pattern were examined for the sake of modeling. These occurrences are extremely beneficial because they allow to better grasp the physical and cognitive requirements of the dispersing individual [21]. While modeling the dispersal situation and understanding the dispersal patterns, it also alters the costs associated with each grid. These events, the reasons for dispersion, have been encoded in a specific manner, described in

Table 1. Reasons for dispersion.

Sl No.	Reason for Dispersion	Code
1	Dispersion for dominance	M1
2	Dispersion away from home	M2
3	Dispersion for food	M3
4	Dispersion for breeding	M4

, and are quite valuable for modeling.

Considering the ramifications of the preceding information, the cost of each grid was computed utilizing the landscape complex characteristics contained in the grid, the cause for dispersion, and the presence/absence of co-predators. In this work, the cost was determined by three factors, given below as:

$$C_G=\left({{\displaystyle \sum }}_{i=A,\hspace{1em}k=1}^{i=J,\hspace{1em}k=9}\alpha X {\prod }_{T,\hspace{1em}{G}_{ij}(M_{k)}}+{(p | 0 | q)}_{M_k}\right) \begin{array}{c}k=4\\ k=1\end{array}$$

(5)

where α indicates the dispersion coefficient based on the cause for tigers’ dispersion. ${\prod }_{T, G_{ij}(M_{k)}}$ represents the payoff received by modeling a two-person prisoner’s dilemma game between the dispersing tiger and each parameter of set G present in the grid $G_{ij}$, considering the reason for dispersion $M_k$, and ${(p | 0 | q)}_{M_k}$ represents the score received due to the presence, absence, as well as the dominance of co-predators in the grid.

For a more in-depth knowledge of the cost evaluations discussed above, the entire landscape may be seen as a network, with each grid acting as a vertex and the connections between the grid’s eight neighborhoods acting as edges. Preferential movement in the proposed research work determines the beneficial links for tiger dispersion. The parameters of the grid or the components of G depending on the cause for dispersion using the dispersion weights are ranked over the network, as shown in

Table 2. Ranking of parameters based on dispersion weights.

Code	WB	FA	HP	PB	NF
M1	3	1	5	2	4
M2	2	3	5	1	4
M3	2	3	5	1	4
M4	2	1	5	3	4

.

This is used to calculate the dispersion coefficient, α. The membership value or the dispersion coefficient has been obtained based on the rank of the parameters according to their needs, as:

$$\alpha =\frac{n\left(G\right)-rank+1}{n\left(G\right)}$$

(6)

The range of α lies between 0 and 1. Earlier studies of the recent past have been utilized to obtain the values of α, based on various reasons for dispersion. The values of α obtained based on the application of dispersion weights are shown in

Table 3. Value of α obtained using Table 2.

Code	WB	FA	HP	PB	NF
M1	0.6	1	0.2	0.8	0.4
M2	0.8	0.6	0.2	1	0.4
M3	0.8	0.6	0.2	1	0.4
M4	0.8	1	0.2	0.6	0.4

.

After determining the degree of influence that each element may have on the grid’s cost, the interactions in the landscape were simulated using game theory [22]. The interaction of dispersing tigers with the landscape factors is a key focus of this work. As a result, the problem in this work is represented using the dispersing individual as one of the players in a two-person prisoner’s dilemma game, with the landscape characteristics as the other players [12]. Therefore, the game’s payoffs are obtained as:

$${{\displaystyle \prod }}_{Tiger,\hspace{1em}D}\left(Strategy\left(Tiger\right), Strategy\left(D\right)\right), D ϵ G$$

(7)

Each of the factors in set G either encourages or hinders tiger mobility in the landscape complex. Table 3 illustrates the contribution of each parameter to any grid’s cost, as well as the degree of support for migration of an individual through the grid.

As mentioned above, the presence or absence of co-predators is one of the most significant factors in determining tiger dispersion, and this work aims to quantify the impact of this on the cost of a grid since interactions with co-predators can take many forms and applying game theory to describe the interaction of a dispersing tiger with co-predators may be problematic. Further, while these interactions may yield a benefit, they may also have negative consequences, such as injuries, weakening, and other conflict-related losses, all of which can limit an individual’s mobility. With this in focus, this study assigned a high inhibitory discrete value of −10 to interactions with greater predators and a low supporting score of +3 to interactions with weaker predators. The score has been set at 0 for regions with no co-predators.

The suggested methodology has been used to conduct a thorough investigation of landscape characteristics for the computation of grid costs over a landscape complex to better understand the tiger dispersions [23]. The cost allocation was performed using the part of the hypothetical landscape depicted in Figure 2 and the example with F3 as a source. The figures below (Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9) illustrate the presence and absence of parameters in the landscape matrix grids. In each figure, 0 indicates the absence of the parameter, whereas 1 indicates its presence.

One of the tiger dispersal scenarios which is dispersal away from home (M2) has been taken in order to illustrate the approach covered above. According to

Table 4. Payoff of elements of G contributing to the grid costs.

Factor	Strategy of Factor	Strategy of Tiger	Associated Score for Grid	Remark [24]
WB	Cooperate	Cooperate	3	Water is a supportive element for any species
FA	Cooperate	Cooperate	3	Forest cover supports the presence and survival of wild species
HP	Defect	Defect	−5	Any human presence hinders the flow of species and is usually neglected by species for movement
PB	Cooperate	Defect	5	Prey base provides food elements to the moving tigers
NF	Defect	Defect	1	No effect other than restricting the movement of individuals

, the dispersion coefficients for the focal event were set, and Figure 9 shows them.

The costs of each grid were further determined using Equation (5), payoffs from Table 4, and the distinct payoffs for the presence/absence of co-predators. Using grid E7 as an example, the score was computed as:

$$C_{E7}=0.8\ast 3+0.6\ast 3+0.2\ast \left(-5\right)+0\ast 5+0\ast 1+1\ast \left(-10\right)=-6.8$$

Similarly, using a matrix simulation over all the grids, the score for each grid was obtained and shown in Figure 10 over the map. In order to keep the model simple and descriptive, the model assumed that a tiger disperses for “dispersion away from home” from the grid F3.

Figure 11 shows the network for dispersion throughout the whole landscape for the dispersing tiger after the scores of each grid have been calculated and taken into account, along with the tiger’s dispersion from grid F3. The network was created utilizing the idea of eight neighborhoods for each grid, whereby when a tiger enters a grid, the model looks at all eight grids and determines which one is most appropriate for the subsequent degree of dispersion.

The complete methodology was used over the hypothetical environment described above to propose a computational framework for figuring out the tiger dispersion network and patterns. If performed with the use of satellite images and GIS, the same process can be highly beneficial. When working with GIS tools such as ArcGIS or Qgis, the landscape images and their respective .shp files can be utilized by placing well-defined symmetric grids over them. Additionally, the tools’ “Identity” function can be used to categorize the grids’ priorities. Finally, using geoprocessing and the defined equation shown in Equation (5), it is possible to deliver the whole cost surface throughout the landscape.

5. Results and Discussion

The scores were generated by modeling each interaction between a dispersing tiger and a landscape parameter after acquiring the presence and absence details of the parameters in the landscape matrix for all four distinct causes of migration [25], as explained in Table 1. The dispersion weight was calculated using the causes of dispersion, and the value of the dispersion coefficient reflects this, as explained in Table 3. In addition to the aforementioned factors, the costs of co-predator presence were considered. The final cost surface for all the dispersion causes investigated in this study was computed and presented in the form of a matrix in Figure 12, Figure 13, Figure 14 and Figure 15.

The proposed work offers a fundamental mathematical framework for calculating the costs of a collection of landscape components that may help or hinder tigers’ dispersion from one location to another. The overall problem of the study was to offer a computational model to extract the cost for landscape grids, modeling the cognitive knowledge and behavior of tigers, and using it to learn about tigers’ dispersion patterns. A significant result of this work is an in-depth investigation of the factors and how the tigers can use these factors for their dispersal. The study also revealed important grids where tigers’ dispersion may be tracked and observed as they leave their native region. The suggested approach provides a framework for creating a cost matrix across a landscape complex using game theory, assuming tigers and landscape parameters interact deterministically. However, the relationship may change depending on the topography and surrounding factors. As a result, the model’s use of only maps for game theoretic modeling would be one of its limitations. If the work is combined with field research carried out in diverse landscapes, this might be enhanced. This can be highly beneficial for wildlife stakeholders in terms of conservation and landscape design.

The work’s main findings are provided in the form of a matrix, which is represented by a series of figures: Figure 12, Figure 13, Figure 14 and Figure 15, which reveal several insights related to tiger dispersion. Finding the cost surface first uses the reason for the tiger’s departure from its native area, which aids in the identification of the dispersing tiger’s primary needs, and therefore the dispersal pattern. It also highlights the most important grids in the terrain where the tigers can disperse and settle, allowing more attention to the connecting pathways [26].

The results demonstrate that there is a cost associated with each grid. The following shows how the acquired costs in this work were linked to the tiger movement:

$$Cost of grid \propto Support for tiger movement$$

(8)

As a result, the higher the cost, the more likely the tiger is to disperse through the grid.

The cost and the tiger dispersion pattern owing to the expenses were examined after obtaining information on the tiger dispersion patterns utilizing the costs connected with the landscape complex [27]. Figure 16 depicts the study and highlights several significant findings. First, it demonstrates that when tigers disperse out of their home area or for food, the costs are identical, and therefore the dispersion patterns are similar. Then, with minor modifications, it shows a link between the cost and the dispersion patterns of tigers dispersing for dominance or breeding. Furthermore, it was observed that tigers dispersing for dominance and breeding have more mobility choices than tigers travelling for food or leaving their home zone. It also informs that tigers moving for food and outside of their native range are both inexperienced and younger than the other dispersing tigers, or they are elderly and defeated.

An examination of the dispersion costs over all grids is shown in the comparative analysis of costs received for each of the four causes of tiger migration. It can be seen from Figure 16′s visualization of the cost data that were acquired that all migration-related causes generally followed a similar trajectory, with minor variances. The analysis on a map and a similarity in the dispersion trajectory for various causes of movement are shown in a cumulative network map in Figure 17.

Species dispersal is a crucial aspect to comprehend for understanding about a variety of conservation concepts [28]. Wildlife corridor design, habitat suitability index, and other essential aspects are some of the key conservation concepts associated with species dispersal [29]. The creation of a cost surface across the landscape complex aids not only in comprehending dispersal but also in determining dispersal patterns, which may then be used for conservation reasons [30]. Based on the preceding discussion, a cost surface over a landscape matrix aids in the development of suitable conservation models. The proposed model aims to quantify the support and vulnerability for tigers as they disperse through a landscape using an appropriate conservation model. To what extent a habitat or landscape is suitable for tiger survival and dispersal may be observed by using the critical factors provided in the computational technique. Using these critical factors would increase the accuracy of conservation strategies and provide a better model for the conservation of the target species.

Another insight provided by the suggested approach in this study is the ability to extract the sensitivity of a grid for tiger dispersal across it. It is clear which grids aid tiger dispersal and which grids obstruct it. As a result, the costs and vulnerability of a grid are related as follows:

$$cost of a grid \propto \frac{1}{vulnerability of the grid}$$

(9)

Understanding a grid’s vulnerability is critical because it depicts grids that may require human intervention to facilitate tiger dispersion and hence protect the species [31]. As a result, related vulnerabilities may be viewed as a guiding concept for developing ideal conservation measures.

Numerous analogies and comments made above imply the requirement of constructing the cost surface throughout a landscape matrix. All the conversations point to the fact that finding a cost matrix and projecting it onto a surface helps to understand how different species disperse across a complex environment, which in turn helps with conservation using different models.

6. Conclusions

The current study sought to obtain a cost surface over the landscape complex, which displayed the landscape complex as a matrix, and to detect the tiger dispersal pattern as well as their underlying scope of existence in a grid using an iterative computational approach.

In this work, a cost surface over the landscape matrix was created using dispersion weights and game theory, and it can be used to examine actual tiger dispersion in any complex environment. The first cost matrix was produced by modeling a game involving landscape-level properties and tigers and integrating it with dispersal coefficients. The interactions of co-predators were also shown in a second cost matrix, which was combined with the first cost matrix to produce the final cost matrix for the landscape. One of the major factors that was not considered in the methodologies for designing corridors, such as the circuit theory or the game-graph theory, was the existence of predators in the surrounding landscapes, which has been addressed in the proposed model. To make it more accurate and exact for the wildlife stakeholders involved in conservation planning, the suggested model in this work also covered the next-to-immediate grid where tigers can go when dispersing.

The suggested model’s cost surface design is primarily focused on linear static interactions, which overlooks several crucial non-linear aspects, such as the amount of co-predation, the degree of cooperation or defection, and so on [32]. To provide a basic computational basis for extracting a cost surface in the tiger’s focus landscape complex, the task was purposefully kept simple. A simplifying presumption in the study was the lack of several contacts with distinct co-predators in a single grid. Firstly, the priority in this work was to focus on cost matrix generation for dispersion patterns, thus improving the quality of interactions rather than the quantity of interactions, and secondly, the work further focused on learning about dispersion through a grid rather than understanding complexities within a grid. These two reasons justify this lack of consideration of multiple interactions. These simplifications could not always match the cost surface scenario in the real world. With the tiger as the focal species, it may be anticipated that the proposed effort may lead to the publishing of a computational template for a cost surface design, which may be significantly improved by including field and GIS data from realistic concerns.

The cost surface identified in the focal landscape complex by dispersion weights and the application of game theory has been mentioned. The cost surface serves only as a skeleton design, as seen by the payoffs of the two-person prisoner’s dilemma game. It is stressed that the results produced in this study require fine-tuning through appropriate validation with actual field data to be relevant for wildlife policy concerns. A secondary sort of restriction emerged from the lack of knowledge of the reasons for the tigers’ departure from their natural habitat. The dispersion of the species can be caused by a variety of factors, including a combination of multiple factors [33]. In this study, only one reason for developing a unique cost surface was examined. As a result, while the findings here may be utilized to produce cost surfaces, they do not demonstrate how well these cost surfaces truly help with problem detection.

Most of this paper focused on computational algorithms and concepts that can be used to generate a cost surface over any landscape complex to better understand the dispersion patterns and use them for conservation purposes. It provides a basic computational foundation that, when combined with accurate field data and GIS modeling, may be extremely beneficial to wildlife conservationists and managers [34].