Ecosystem modelling based on membrane computing is emerging as a powerful way to study the dynamics of (real) ecological populations. These models, providing distributed parallel devices, have shown a great potential to imitate the rich features observed in the behaviour of species and their interactions and key elements to understand and model ecosystems. Compared with differential equations, membrane computing models, also known as P systems, can model more complex biological phenomena due to their modularity and their ability to enclose the evolution of different environments and simulate, in parallel, different interrelated processes. In this paper, a comprehensive survey of membrane computing models for ecosystems is given, taking a giant panda ecosystem as an example to assess the model performance. This work aims at modelling a number of species using P systems with different membrane structure types to predict the number of individuals depending on parameters such as reproductive rate, mortality rate, and involving processes as rescue or release. Firstly, the computing models are introduced conceptually, describing the main elements constituting the syntax of these systems and explaining the semantics of the rules involved. Next, various modelled species (including endangered animals, plants, and bacteria) are summarized, and some computer tools are presented. Then, a discussion follows on the use of P systems for ecosystem modelling. Finally, a case study on giant pandas in Chengdu Base is analysed, concluding that the study in this field by using PDP systems can provide a valuable tool to deepen into the knowledge about the evolution of the population. This could ultimately help in the decision-making processes of the managers of the ecosystem to increase the species diversity and modify the adaptability. Besides, the impacts of natural disasters on the population dynamics of the species should also be considered. The analysis performed throughout the paper has taken into consideration this fact in order to increase the reliability of the prospects making use of the models designed.
Membrane computing is a fast-growing branch of natural computing [
On the one hand, theoretical studies focus on how to design membrane computing models according to the compartmentalized structure and the functioning of biological membranes within living cells and how to evaluate their computational power and computational complexity [
On the other hand, applied research of membrane computing models aims to effectively apply the introduced computational models to handle several practical problems, from basic ones to the modelling of complex systems. For automatic design of membrane computing models (ADMCM), regarded as an automatic computation device, the models can adaptively achieve basic arithmetic operations [
The applications summarized above plus some others show that membrane computing models are useful tools to solve many practical problems of very different nature. It seems clear that each type of computationally hard problem addressed by membrane computing models somehow implies an extension of application fields, providing theoretical and practical foundations, opening paths that can be worth exploring, and widening the application space.
Regarding the contributions of membrane computing to model complex systems, relevant achievements have been made along the last decade, with a special attention to the study of real ecosystems (focusing on endangered or invasive species, among others) and population dynamics in general [
As briefly mentioned, apart from their natural mortality, most species have suffered the effects of environmental disasters. As certain studies point out, some types of such natural disasters have caused or may potentially cause the risk of species biodiversity collapse, or even some species extinction in certain regions [
In order to accurately assess the impacts of these factors, several mathematical models are used to analyse the effect of these elements on population dynamics, e.g., differential equations [
This work focuses on membrane computing (MC) models of species in certain ecosystems, thus involving mostly two main fields: membrane computing and population dynamics. Concerning the former one, MC has among its strengths the availability of rigorous and complete, strongly founded theoretical-practical developments; in addition, it provides parallel distributed devices in a framework with flexible evolution rules. With respect to the latter one, the population dynamics of species obviously involves several biological processes, including some common ones (such as feeding, reproduction, and mortality), and some more specific of certain studies, such as rescue, release, and biochemical reactions of bacteria; besides, the dynamics of the species could also be affected by the potential impacts of natural disasters on the populations under study.
Based on the characteristics of membrane systems and the features of endangered species, the evolutionary behaviour of such species can be expressed by the rules of membrane systems. Hence, along this paper, we recapitulate ecosystem models using different types of P systems. Firstly, we analyse between the elements related with the species and their interactions in the ecosystem and those related with the definition of P systems. So far, there are several references to study the applications of P systems on different real ecosystems. The common characteristics can be summarized as follows: (a) each individual is represented by an object in the P system; (b) different behaviours or processes affecting the individuals of the species are abstracted as the rules in the P systems; and (c) a certain living environment in the ecosystem is abstracted as a membrane structure.
Regarding the dynamics of these systems, at every moment, all individuals will evolve synchronously. As these species inhabit different geographical regions but are subject to the same processes (with the values of certain parameters possibly changing), this scenario can be represented by using multienvironment P systems, where communication of individuals is possible among different environments. For some species, such as plants and bacteria, the evolutionary processes are also modelled according to their characteristics and possibly distinguishing environments with different parameters.
Through the analysis above, we have depicted some of the most relevant facts taken into account when modelling ecosystems based on P systems in order to accurately predict data about the biological evolution of the species, aiming to capture in these models (i.e., to mimic) the relevant elements of the real biological phenomena under study. The rest of this paper is arranged as follows. Section
As outlined in Section
When membrane computing is used to create a representation of an ecosystem, incorporating their main parameters, individuals, processes, etc., involved in their dynamics, this is considered a computational model because it is a model of the ecosystem that is based on a computational paradigm (in this case, membrane computing), whose computation follows the exact rules of the formal model, not requiring any approximate method to be computed. These models of ecosystems are based on membrane computing, so they are usually called membrane computing-based models. Such models are represented by computational devices called membrane systems (commonly referred to as P systems) (commonly referred to as P systems).
As computational devices, membrane systems or P systems are abstracted from the structure and functioning of living cells. There are three main classes of P systems: (1) cell-like P systems, inspired from living cells; (2) tissue-like P systems, inspired from the interactions of cells in tissues; and (3) SN P systems (spiking neural P systems), inspired from the communication of electrical pulses (also known as spikes) in biological neural networks.
Concerning the population dynamics of ecosystems, both cell-like and tissue-like P systems have been useful to inspire the appearance of a new class of P system, originally called the multienvironment P system. Regarding the membrane structures employed in the models built with these devices, they define a structure combining the hierarchical structure of cell-like P systems with an upper layer of the so-called environments, each one containing a single cell-like system and introducing the possibility of communication among environments, similar to that in tissue-like P systems. This structure, as we can observe, is richer than the two previous models, thanks to the combination of the two constituent parts: the internal hierarchical structure present in cell-like P systems (which is not present in tissue-like P systems, where only cells without the internal structure are present); the existence of different regions with cells inside and allowing communication among environments as a graph (which is not possible in cell-like systems).
Of course, with this new class given by the multienvironment P systems, we can also model ecosystems with a single environment involved, defining such environment as the only node in the graph, with cell-like P systems inside, and no other nodes to communicate with through edges of the graph. In contrast, there are more interesting problems that require additional environments. In such cases, a more complex graph must be present to allow the movement of certain elements among environments. In these scenarios, such communication among environments will play a crucial role. In addition, each environment will contain its own hierarchical structure given by the cell-like P system it holds.
With respect to the dynamics of the systems involved in these computational models, mostly two main paths have been followed when dealing with multienvironment systems: a stochastic approach followed by the so-called multicompartmental systems (there are zero or several cell-like P systems inside each environment, which are able to communicate with entire P systems from one environment to another), with rules subject to chemical laws and kinetic constants; a probabilistic approach (there is one and only one cell-like P system in each environment and only single object communicates among environments), with rules subject with probabilities, whose values are typically based on evidence; for further details, refer to [
As just mentioned, PDP systems are a variant of P systems introducing probability mechanisms into membrane systems. The framework constituted by PDP systems was conceived for multiple environments, and therefore belongs to the class of multienvironment P systems, but can obviously support the particular case of having the number of environments which equals to 1 and consequently not having communication among environments. Now, while the framework is uniform, from a practical point of view, it is easy to distinguish systems depending on the number of environments
A portion of classified PDP systems used for modelling ecosystems. (a) A single-environment PDP system with two membranes. (b) A multienvironment PDP system with four environments with the same P system skeleton placed inside each environment (their internal structure being omitted). The system shows population activity of the four environments
(see [
In order to model real-life ecosystems, the rules are abstracted from the behaviour of the species considered, food distributions, natural disasters, bacterium reactions, etc. From the point of view of the certainty of the application of the rules, two kinds of operational rules might be somehow distinguished. The first type would be rules without explicit probability written; this is equivalent to a probability of 1; that is, these rules will be executed whenever selected, which will happen whenever they are applicable, and no rules are competing for the same objects involved (if more than one rule is competing, they would be chosen nondeterministically). The other type of rules, in this sense, would be the rules with explicit probability lower than 1; that is, rules which are once selected will be executed depending on their probability.
Let us consider an example taking Figure
The pattern transformation of the system above would be as follows: let us suppose an object
The system halts when reaching a given condition, typically a number of iterations or cycles of the evolution of the system, because, usually, when modelling complex systems, there is no beginning or end (different from P systems generating numbers, computing functions, or solving computationally hard problems); instead, in this case, the result of the computation is indeed the observation of the system itself, including whichever elements (individuals and other possible variables involved) subject to study.
(see [ Π
Taking Figure
When studying real-world ecosystems, the first type (single environment) can be appropriate to study the population dynamics of species in a region (it might cover more regions with an enriched structure in
In the following, the main uses of PDP systems to model ecosystems are analysed. Thus, a synthesis of several papers published since 2013 illustrates that different types of P systems have been used for predicting population dynamics of ecosystems. Well-known membrane systems can be used for modelling ecosystems in order to assess the projected number of individuals of certain species and their distribution (in terms of ages and locations). So far, a number of endangered species (listed in the literature in Section Step 1: obtain biological data of the species studied. In the present study, some pedigree data are available. The information includes the number of female (male) individuals, age, and birthday or death date. Depending on the biology of the species (usually animals), we need to further know other information which is not recorded in datasets, typically related with processes of interest, for example, their living habits or feeding needs. Step 2: define a conceptual model. According to the evolutionary behaviour of the species, i.e., feeding, reproduction, mortality, and so on, a preliminary general model (conceptual model) is abstracted from these basic processes, and then each module of this model is given a certain priority and sequencing. Step 3: define the computational model. Starting from the conceptual model, the computational model is built based on a mathematical framework, in our case, PDP systems. Natural evolutionary behaviours from the conceptual model are symbolized, representing the underlying processes with the elements of the computational model. The necessary mapping for this model involves (a) designing the membrane structure of the skeleton P systems (cell-like structure) to place inside the environments, including the initial multisets representing individual objects (e.g., an animal Step 4: choose simulation software. The previous model designed might be analysed with manual traces to validate against real data and later use to formulate hypothesis and check the behaviour of the system under potential scenarios of interest. However, the manual analysis of big complex systems is not only tedious or error-prone but also impractical and directly intractable in certain case studies. Thus, we need simulation tools, where we can debug the models, experimentally validate them, and finally use them for intensive virtual experiments under different scenarios of major interest for the ecosystems under study. In the case of PDP systems and similar types of membrane systems, the most widely used software has been the framework provided by P-Lingua and MeCoSim. For the introduction about this software, refer to Section Step 5: output predicted datasets. Taken the statistical dataset of a certain year as the input, along with all the parameters related with the biology of the species and the conditions of the ecosystem, the system predicts a set of experimental results by using the MeCoSim environment and then running the model loaded for a certain number of cycles (usually years) to get the output.
The protocol briefly described above provides an organized generic sequence of steps to design a model based on the PDP system and use it in a practical way to get new insights from the study of the phenomena under study. This not only provides a theoretical but also practical framework for the use of size-based indicators to monitor the ecosystem changes of species. From a conservation and management viewpoint, a key advantage followed with these models based on PDP systems and the tools available (where many potential scenarios can be analysed by simply changing the input data) is that predictions can be obtained according to the evolutionary behaviour of species rather than relying solely on historical baselines that may not be relevant under the current or future environmental conditions. The applications of models in the context studied can also include the analysis of how several parameters, including growth, reproduction, and mortality ratios, or climatic factors, among others, affect predicted changes in the number of species.
Concerns about endangered species arise because most of these known species have smaller range, lower reproduction rate, and higher extinction rate, thus causing the sharp decline of population size or extinction. After some disaster or difficult situation, even if the situation gets better later, endangered species are often not considered to be free of threat because the total population might recover but some populations might be scarce even in the undisturbed fragments, thus potentially causing that such populations may not remain after destruction. The scenarios to consider might be very complex to assess in order to incorporate many parameters and processes affecting the species. In this context, it is worth searching for new types of assessing approaches aiming to capture crucial aspects summarizing the change law of the population dynamics. Particularly, based on the fact that P systems can incorporate and quantify several biological behaviours of species (including reproduction, mortality, and the direct and indirect interactions over migration from one place to another one, among others), such devices are applied to model the population dynamics of complex ecosystems.
The use of P systems in ecosystem modelling concerns mainly the prediction of population size of numerous endangered species using P system devices such that a prospect of the species population in the coming years can be obtained based on the known processes and parameters and the absence of data about such years. In most cases, multienvironment P systems have been designed and simulated. Numerous systems have been studied, with different processes and factors involved. In every ecosystem analysed, the elements to consider had distinct features based on input parameters such as (1) membrane structures to capture physical and abstract compartments and (2) rules about the natural biological behaviour of the species under study, related processes, human intervention, and so on. In Table
Summary of studies that have used a new frontier approach, termed PDP systems with different constraints, to assess the number of endangered species under conditions of different types.
Case study | Region/condition | Comments |
---|---|---|
Colomer et al. [ | Region: the cliff-nesting and territorial mountains in the Catalan Pyrenees (Northeastern Spain) | (2, 1) with two electrical charges (0 or +), where the skin region is used to fix reproduction and mortality and the inner one to fix feeding; five wild and domestic ungulates are included as carrion (prey) species. |
Cardona et al. [ | Region: Catalan Pyrenees (NE) | The structure of this system is the same as that of [ |
Cardona et al. [ | Region: Catalan Pyrenees (NE) | (2, 1) with two charges. This system considers not-nomadic species (also called invasion alien species—see part (b) in Section |
Colomer et al. [ | Region: Catalan Pyrenees (NE) | (11, 4, 1) with three electrical charges (−, 0, +). The model mainly considers four influencing factors: introduced disease such as pestivirus infection, climate change (refer to part (a) in Section |
Colomer et al. [ | Region: the cliff-nesting and territorial mountains in the Catalan Pyrenees (Northeast, Spain). | The computational model of the probabilistic P system is the same as that of [ |
Cardona et al. [ | Region: Catalan Pyrenees (NE Spain)/a fluvial reservoir (Riba-roja-Ebro river, NE Spain) | For the scavengers, the structure is the same as [ |
Colomer et al. [ | Region: Catalan Pyrenees (Spain)/Pyrenean and pre-Pyrenean mountains | (2, 2) with the environment change module, where any of species will move to another area when the capacity reaches a threshold. The model studied: (a) 13 species, including three avian scavengers (three types of vultures) as predator species plus six wild ungulates and four domestic ungulates as prey species; (b) the interactions between species; (c) the communication between two areas; and (d) load capacity regulation. |
Colomer et al. [ | Region: (sub) Alpine (NE Spain) | (5, 5) with climatic variability (part (a) in Section |
Colomer et al | Region: Catalan Pyrenees (NE) | (11, 2) with three electrical charges. This model mainly considers the impacts of environment factors such as weather, orography, and soil conditions on carnivore size. |
Margalida et al. [ | Region: Catalan Pyrenees (NE) | The model only considers wild ungulates due to the limitation of domestic carcasses. Undoubtedly, this causes an impact on the biomass. The model of the (2, 2) structure verified that when considering only wild ungulates, the ecosystem cannot offer enough food for predators. |
Margalida and Colomer [ | Regions: 10 municipalities in Catalonia, Northern Spain | Taking 10 areas and 4 avian scavengers as the research object, the model considers the impact of climate variations, such as seasons (summer and winter) (part (a) in Section |
Colomer et al. [ | Region: reservoir of Ribarroja | (40, 17), where the first 20 membranes are used for 20 weeks of reproductive cycle, 16 for the weeks of the second reproductive cycle, and the last two membranes are used to handle regulation and mortality. |
Huang et al. [ | Two regions: Chengdu Research Base of Giant Panda Breeding (GPBB)/China Conservation and Research Centre for Giant Panda (CCRCGP) (Wolong) | (2, 1), where two membranes are used to evolve and store object information; the evolution process of the species: RMF + rescue module, where RMF is also modified as RFM, FMR, or other forms, showing the robustness of the system independently on the order of the modules. |
Tian et al. [ | Two regions: GPBB/CCRCGP | The membrane structure is the same as in [ |
Bernardini and Gheorghe [ | Region: marine | (9, 1), where multisets of objects are used to model bags or soups of chemicals, whereas rules are used to model generic biochemical processes. |
Romero-Campero and Pérez-Jiménez [ | Region: marine | ( |
Valencia-Cabrera et al. [ | Condition: single-environment | The first membrane computing model applied to reconstruct the behaviour of logic networks of species with PDP systems. |
Valencia-Cabrera et al. [ | Case study: | Based on [ |
In the following section, we will mainly introduce the modelling process of each species studied following the basic sequence summarized in the table mentioned. We will mostly focus on three types of animals (bearded vulture, zebra mussel, and Pyrenean chamois) and two additional not-animal species (
Bearded vulture,
Bearded vulture is a cliff-nesting and territorial large scavenger. This species is the only vertebrate that feeds almost exclusively on bone remains of herbivores living in the three habitats mentioned, i.e., animals such as red deer, fallow deer, roe deer, and sheep. The remains of these animals were predicted to be the major limiting factor for the survival of avian scavengers during winter and summer [
Taking into consideration all the evolutionary characteristics and the core parameters affecting the changes in the population size of bearded vulture, different types of P systems were used to model ecosystems related to bearded vulture. In the initial phase, a bearded vulture model was presented by a single-environment P system, whereas, also, different rule selection methods started to be explored. Thus, in [
According to the analysis for bearded vultures in a region, the reproduction of the vultures in a small area can easily lead to the loss of genetic diversity of these vultures; this phenomenon may happen not only during the founding event but also during subsequent generations when the population remains small and the exchange of individuals with other populations is minimal. In order to modify the breeding rate by increasing genetic diversity and enhance the survival rate of individuals, there should exist different communications among bearded vultures living in different regions. Based on this idea, Colomer et al. [
Zebra mussel,
Zebra mussel has become a dangerous threat by feeding competition and alternation of river sediments to native mussels. As these native mussels are threatened or endangered, current control strategies in Spain water bodies are therefore limited to avoid spreading of zebra mussel by regulating boating and fishing activities. For these reasons, different biochemical and histological biomarkers have been undertaken to study the impacts on the population dynamics of zebra mussel, thus aiming to control the dispersal of the species over others. In general, traditional approaches applied logistic regression [
The most relevant advantage derived from modelling zebra mussel using P systems is that they make it possible not only to mimic the evolutionary features of the population as a whole, exploring the birth or mortality trend of such population, but also add the traceability (at the level of animals instead of populations) of each adult or larvae individual during the evolution of the system. In [
The simulation results obtained showed that PDP models provide very useful tools to model complex, partially desynchronized, processes that work in a parallel way. According to the analysis above, P system-based models could predict better results when handling characteristics such as the ones present in this species (with respect to the previous approaches), thus increasing the confidence in the effectiveness of the methodology proposed.
Pyrenean chamois,
In order to mimic the evolutionary behaviour of this species and estimate the effects of introducing pestivirus affecting the species, Colomer et al. [
In this P system, the model designed considered the impacts of diseases caused by border disease virus (BDV, dangerous pestivirus) on the population dynamics of chamois under study, given that the evolution of this species was highly influenced by an infection of BDV [
According to the simulation results obtained with the model designed, belonging to ecological data of 22 years, some differences were observed with respect to the real data available to validate the model. It was concluded after a deeper study that these differences between the values obtained with the model and the statistical data could be further reduced by introducing more nature conditions into P systems. The modular, flexible, and extensible nature of membrane systems made it possible to introduce new elements without major changes in the existing model. Differently from other modelling techniques, the modularity of P system enables the reusability of existing structures and rules in the construction of increasingly complex models where new processes are incorporated iteratively.
Due to the fact that monitoring data including weather change varies continuously and due to the existing relations among different natural conditions (e.g., climate change can increase or decrease the spread of diseases and invasions of alien species may also bring new diseases), it is likely that, for assessing population dynamics, we should focus on multi-index fusion, not just single-index study. A few potential examples can enlighten this thought.
Giant pandas,
Facing the survival status of giant pandas, approaches on assessing population size are built. As P systems can incorporate and quantify several behaviours of species (i.e., reproduction, feeding, mortality, etc.), along with direct or indirect species interactions implying communication, P systems are being used to model giant pandas. In [
In this section, we survey ecosystem modelling for other biological systems including the quorum-sensing regulatory networks of the bacterium
Quorum sensing is a cell density-dependent gene regulation system that can manage the expression of specific sets of genes. Certain pathogenic bacteria use quorum sensing to regulate genes encoding extracellular virulence factors [
In [
Gene regulatory networks are useful models based on versatile frameworks for biologists to understand the interactions among genes in living organisms. In order to better reproduce the behaviour and the dynamics of gene networks, a PDP system was provided to accurately simulate the behaviour of different types of gene networks of species. Thus, in [
Subsequently, Valencia-Cabrera et al. [
P system simulators have become important computational tools in the processes of model debugging, validation, and later virtual experimentation, among other purposes. In this section, we introduce some simulation software products to design models for ecosystems by means of P systems.
The primitive simulators were mostly ad hoc simulation tools devoted to very specific problems or pedagogical aids in the understanding of computations based on the first variants of P systems. However, very relevant achievements were made with these tools, in the first decade of membrane computing, as extensively explored in [
With the development of simulators, in recent years, different software applications have been applied to the simulation and validation of biological systems. Here, we will introduce several developed software tools in the following sections.
The simulator called MetaPlab (MP for short), designed by Verona University, is used for modelling biological phenomena related to metabolism. It is a computational framework for metabolic P systems. This framework consists of the following four layers: (i) MP graph, which takes MP systems as inputs and visualizes them; (ii) MP store data structure, applied to store all the elements of MP in a suitable Java object form; (iii) data processing, plugin-based module, dealing with biological data; and (iv) MP vistas, coping mainly with the graphical representation of MP structures and dynamics. For more details, refer to the website [
In [
The simulation environment MeCoSim [
In summary, all software analysed mainly focus on different types of ecological systems: MetaPlab is used for modelling the internal mechanisms of biologic systems by means of metabolic P systems, and BioSimWare is used for modelling the multicompartmental complex biological systems. While they achieved great results when applied to different systems, to the best of our knowledge, it is out of the scope of these products to provide the requirements for data verification, model checking, model optimization, and mostly the definition of custom interfaces for the particular end-user applications for ecologists or managers to perform virtual experiments based on validated models. Therefore, due to the need of providing not only a research result by us as model designers but also a final tool for the experts in the giant panda ecosystem not familiar with P systems, MeCoSim has been used to simulate the evolutionary behaviour of many species in nature and has been chosen by this team. Thus, in this work, we will predict giant panda individuals in the coming years by means of MeCoSim
This section analyses a particular case study where the methodology and tools explained in the previous sections are applied. Specifically, the species of interest is giant panda, and the following sections will describe in further detail the purpose, process, and conclusions derived from our study.
Biological data concern mainly on populations (with distributions of age and gender), input parameters (birth rate, mortality rate, etc.), and rules governing the biology of the species, in this case, giant pandas and its evolutionary behaviours. These elements are indeed most of the crucial parts taken into account when modelling ecosystems making use of P systems (more specifically, PDP systems). In this section, we describe the study of the related data about giant pandas in the context of the specific ecosystem considered. Giant pandas studied are from Chengdu Research Base of Giant Panda Breeding (GPBB, for short). Giant panda population of GPBB consists of individuals currently living in GPBB, those in Chengdu Zoological Garden, and those who were born in GPBB but are living outside of GPBB. The reference basis for our research is giant panda pedigree data compiled by the Chinese Association of Zoological Gardens, including data belonging to 13 years (from 2005 to 2017). Adequate processing of these data sets could lead to the extraction of relevant statistical data referred to the number of female and male giant pandas per year, including the age of each individual, being these data the basis and driving force, along with the deep study of the processes involved in the biological evolution of the species, to model the ecosystem.
Since we only study giant pandas in a region, based on the features of giant pandas, we choose as our modelling framework a single-environment population dynamics P system (PDP system, for short), as introduced in Section
The main goal of this stage, in our case study, is the design of a novel population dynamics P system-based model for captive giant pandas in the regions described at the beginning of this section. The processes of interest in the evolution of the ecosystem include the biological aspects related with their life cycle and other possible phenomena happening in the environment; these processes should be simulated by computers according to the model designed and the input data about giant panda populations and related parameters. PDP prediction focuses on the changes in the female or male population size and distribution of ages. In the following, design of the conceptual model is described, starting with the definition of the modules composing the computational model.
In order to define the modules, we must first describe the life cycle of giant panda, the classification of age groups, and types of food required. In this simplified case study, the whole evolution behaviour of giant panda considered consists of four processes: reproduction, mortality, feeding, and rescue. Thus, the ecosystem model to design should also contain modules for these four processes involved.
In this model, according to the specialists’ understanding of giant panda life habits, age groups are classified into six ranges; a detailed introduction is given in Table
Age structure of captive giant pandas in 0–33 years.
Infancy | Subadulthood | Adulthood | Middle-aged | Early old stage | Old stage | |
---|---|---|---|---|---|---|
Age (female) | [0, 1] | [2, 4] | [5, 8] | [9, 17] | [18, 27] | [28, 334] |
Ratio (%) | 20.75 | 17.92 | 21.69 | 26.41 | 11.32 | 1.89 |
Age (male) | [0, 1] | [2, 4] | [5, 6] | [7, 17] | [18, 27] | [28, 33] |
Ratio (%) | 17.98 | 21.34 | 15.73 | 41.57 | 2.247 | 1.123 |
The whole setup (an entire year) of this conceptual model mainly consists of the four models depicted in Figure
A conceptual model graph.
In the following, the description of the four modules is given: reproduction module, mortality module, feeding module, and rescue module.
Before designing this model, which we have just presented, it was necessary to obtain data and qualitative information about different processes and behavioural facts related with the giant panda life cycle. The model had to consider natural factors such as reproduction habits, mortality rates, specific evolutionary behaviour, and conduct patterns, determined according to the actual situation observed. Concerning the rescue module, the data about rescued individuals per age and gender were collected from the past experience, and the causes for these rescues were analysed with the experts in charge of managing the ecosystem. Some decisions were made concerning the estimation of rescued individuals per year, and some increase in the comparative age of these individuals when incorporated into captive life was applied to simulate aging produced by the past wild life in such rescued individuals depending on the amount of years spent in wild conditions.
The main goals of the research conducted on the population of giant pandas in GPBB were to assess the evolution in the population size along the years under certain given conditions and initial populations by using a model based on P systems. The target model involved a number of processes and parameters related with the biology of the species and the ecosystem that should be translated into the concepts belonging to the formal model used: P systems (that is, elements such as environments, membranes, objects, evolution rules, and so on). Besides, the proper semantic constraints and considerations inherent to P systems had to be taken into account, along with the accuracy of these conditions (like the application of certain probabilities associated with the rules) in mimicking the natural processes involved. For PDP systems, once the P system skeleton to be placed inside the environment was defined, we mainly focused on designing the evolutionary rules to capture the processes taking place in our subject ecosystem.
Due to the fact that only one species was the subject of our study and no movement among regions was considered as part of the initial design, no complex environment interactions were required. Therefore, a single environment was enough for this case study. Inside such environment, the P system skeleton was designed with two membranes: the external membrane, denoted as a skin membrane (directly contained inside the single environment) and labelled as 1; the inner membrane (used to perform most of the evolution operations), labelled as 2. Then, inside these two membranes, all processes occur, sequencing the proper operations of three of the modules and simultaneously performing the actions related with the other one: the rescue. In every module, all the individuals subject to the rules of the module evolve in parallel. A trace of a simulation of the model along a cycle (a year in this case) is illustrated in Figure
Evolution patterns of a simulation cycle.
While PDP systems are defined by a more complex structure, given the fact that a single-environment system is defined, in our case, the definition of the PDP system In the individuals in the population, with indexes Initially, each giant panda individual is abstracted as an object Symbol Symbols Symbols The rules in With respect to the initial multisets,
In this system, the rewriting rules (including all the modules) consist of rules for initialization, reproduction, rescue, mortality, feeding, food removal, and update. The rule set
Initialization rules: food supply:
Reproduction rules: Panda individuals in the pre-reproductive age:
Female individuals in the reproductive period who actually reproduce:
Female individuals in the reproductive period who are not reproducing:
Male panda individuals:
Aged panda individuals (postreproductive):
Neonatal individuals (gender determination: female or male):
Rescue rules: Number of giant pandas rescued from the wild field:
Sex for rescued giant pandas:
Age for rescued giant pandas:
Mortality rules: Survival individuals of infancy giant pandas:
Mortality individuals of infancy giant pandas:
Survival individuals of young giant pandas:
Mortality individuals of young giant pandas:
Survival individuals of adult giant pandas:
Mortality individuals of adult giant pandas:
Survival individuals of middle-age giant pandas:
Mortality individuals of middle-age giant pandas:
Survival individuals of middle-aged and old giant pandas:
Mortality individuals of middle-aged and old giant pandas:
Survival individuals of old giant pandas:
Mortality individuals of old giant pandas:
Longevity giant pandas:
Feeding rules: giant pandas in different periods need to acquire different quantities of food; therefore, we divide feeding rules into three periods such as infancy, young, and other periods. Feeding rules for infancy giant pandas:
Feeding rules for young giant pandas:
Feeding rules for giant pandas during other periods:
Update rules: Food removal rules:
Cycle update rules:
Regarding the parameters related with fertility, symbol
With respect to feeding parameters,
Concerning the rescue module, symbols
The values of all these constants have been obtained experimentally after cleaning the data and extracting information through statistical measures from the raw data. However, we must be cautious about the scope of the study and the later applicability to other scenarios, given the variability observed and the relatively reduced size of the samples, in terms of the number of years and specificity of the population. For each probabilistic parameter, a significantly large fluctuation was observed in big values, whereas in small ones, there was no obvious change observed in size. In both cases, it became impossible to obtain truly reliable estimates that can be extrapolated for scenarios apart from the one considered or if significantly different conditions or population distributions appear. That being said, some parameters included in the model show the severe effects derived from the natural stochasticity present in the ecosystem. More specifically, there are very fluctuating factors, such as the number of giant pandas rescued in a year, which can influence the evolution of the population and ultimately depends, among other things, on the presence of natural disasters. For sure, these parameters considered have considerable significance in population and conservation biology [
Step 1: obtain the data set. Data sets about captive giant pandas come mainly from GPBB. Step 2: initialization: designing a successful membrane system can require plenty of parameters such as mortality, reproduction rate, and rescue rate. In order to provide a proper setup for the model design, these parameters should be initialized first. Step 3: design of a basic conceptual model: some behavioural packages such as mortality module are abstracted from the observed daily behaviour of the species. According to its evolutionary cycle, certain sequencing is performed in order for the system to evolve successfully. The model described by the whole picture including different building blocks is called a conceptual model. Step 4: design of a computational model: it consists in applying a formal framework through a mathematical model capturing the details of the conceptual model from the previous given step. More specifically, our model must be computational so that it can be directly computed by an abstract machine, not approximated. Step 5: output: simulate and obtain a predicted number of giant pandas.
In summary, for our given example—a giant panda population prediction method based on membrane systems—, the detailed introduction of this method is as follows: we first need to count the basic information of giant pandas in the researched region (i.e., counts, age, sex, and so on); then, we design a conceptual model with the execution sequence according to the fragmented habits (reproduction, feeding, death, and rescue) of all researched pandas; next, we can also design a computational model containing the elements set by the formal model, including the proper structure, alphabets, initial multisets, and a set of rules abstracted from the evolutionary habits of the species according to the conceptual model given and the detailed observation and study from the expert on the problem domain; and finally, we will obtain a series of computational results by running simulation software, performing plenty of virtual experiments, and processing the data obtained. The theoretical analysis indicates that, in the absence of real data as a reference, this method can effectively help in analysing potential variation trends in the population size and distribution (in age and gender) so that the evolution of the population of giant pandas can be projected under many possible scenarios given different plausible conditions.
This section is devoted to the detailed description of the experiments conducted on the model designed. Along this work, the framework provided by P-Lingua and MeCoSim [
As introduced at the beginning of this paper, PDP systems scale individual-level processes up to ecosystem structure and dynamics. Here, we present in three steps how pedigree data about giant panda can be used to inform the model, where population size of giant pandas in each year is shown in Figure
Population size of endangered giant pandas published in the last 13 years, where all the used data are shown through three histograms. (a) Ecological data: the total number of real giant pandas in each year. (b) Female data: the number of female individuals in a selected year. (c) Male data: the number of male individuals in a selected year. (That is,
First, the individual pedigree data of captive giant pandas that can be used to parameterize the model include food consumption; number of rescued individuals; gender and age; and division of individuals in age groups ranging from offspring and subadults to elderly. Once parameterized, the PDP model can be used to simulate the ecosystem under certain scenarios, aiming to predict the number of individuals along the years. This process requires setting of certain biological parameters. Thus, first, we need to calculate the number of births observed and the mortality of the individuals, among others. These data are used to calculate the fixed size-specific survival, reproductive, and mortality rates (see Figure
The statistical survival rate, reproduction rate, and mortality rate of endangered giant pandas from GPBB for 13 years from 2005 to 2017, given three group trajectories reflecting the dominant cause of changes in population size: natural factors; human behaviour; or enigmatic factors. The purpose of three graphs is to offer the basis reference for setting parameters in the process of running PDP systems such that the data in Table
Naturally, reproductive and mortality rates definitely influence the degree of change (increasing or decreasing) on the population size and distribution, in and out of the studied species. As each individual goes through each module of the model changing its status depending on the application of probabilistic rules, at each time step, the number of individuals varies, and this evolution is subject to natural variability among repetitions of the experiment. The predicted changes in the population size through time are uncertain numerically, but by performing a number of experiments, they are controlled within a given confidence interval. The numerical density of species is summed across all individuals at different age groups to get the final results (but of course, also the details per age and gender remain available for possible later studies). These summarized population sizes are outputted at each time step along with predicted changes. The variation in the population size can be described by fitting, at each time step, a straight line (see Figure
Prediction data changes and statistical data changes based on different initial years taken as input data. There is a significant and rough difference in the average per-year prediction data and statistical data between the size-rise and the size-decline phases across the 5 years analysed. Each pair of values corresponds to the predicted or statistic result of the same year. (a) Taking 2005 as an input, a PDP system is used to predict five-year population size from 2006 to 2010, respectively; (b) taking 2008 as an input, prediction years from 2009 to 2013; (c) taking 2011 as an input, prediction years from 2012 to 2016; (d) taking 2014 as an input, prediction years from 2015 to 2019; (e) taking 2017 as an input, prediction years from 2018 to 2022; (f) this graph describes the comparison of the deviation ratio of five groups of datasets (also, see Figure
Values of the ecological parameters used in this model for giant pandas (GP for short)
Species | |||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
GP (F) | 1 | 1 | 4 | 8 | 17 | 27 | 34 | 0.09 | 0.001 | 0.007 | 0.008 | 0.1 | 0.15 | 6 | 20 | 0.191 | 0.098 | A | A | A | 0 | 0 | 182 | 2920 | 2920 | 292 | 11680 | 10950 | 1276 |
GP (M) | 2 | 1 | 4 | 6 | 17 | 27 | 36 | 0.05 | 0.001 | 0.005 | 0.0058 | 0.034 | 0.091 | 5 | 20 | 0.191 | 0.098 | A | A | A | 0 | 0 | 182 | 2920 | 2920 | 292 | 11680 | 10950 | 1276 |
How the difference occurs in the process of prediction by PDP models (dotted line to solid line). The changes of five-year time interval (2006–2010) deviation rates (2005 as the input); the changes of five-year (2009–2013) deviation rates (2008 as the input); the changes of five-year (2012–2016) deviation rates (2011 as the input); the changes of five-year (2015–2017) deviation rates (2014 as the input); the deviation trajectory generated by the prediction errors. Overlapping prediction parts, i.e., 2009–2010 {input 2005 (5.61% and 0.99%), 2008 (10.11% and 9.9%)}, 2012–2013 {input 2008 (14.41% and 6.98%), 2011 (10.11% and 9.48%)}, and 2015–2016{input 2011 (17.19% and 6.98%), 2014 (4.46% and 2.69%)}, indicate the input data of different years can predict different results for the same year. In this graph, “No value” means no deviation rate due to the lack of statistical data in reality.
In Figure
In this article, we provided an overview of membrane computing models for complex ecosystems and a case study on a complex giant panda ecosystem. Membrane computing models used for modelling ecosystems are very promising, yielding truly distributed and parallel implementations. Distribution is mainly manifested in that the living space of each species is closed, and parallelism is mainly manifested in the simultaneous evolution of different species in different regions at the same time, which are in line with the development trend of ecosystems [
Various P system models have been used to model a large number of species. The differences between these P systems are mainly reflected in the structures and rules of the systems. For the four species most intensively studied, the differences are mainly reflected in the types of species and the types of environment in which species live; in terms of types of rules present in the systems, the distinction gets mainly reflected in the evolutionary behaviours of species and the types of natural disasters they suffer. Most of the ecosystems, described in more detail within the overview, were referred to a variety of models simulated within the framework provided by P-Lingua and MeCoSim. The experimental results show that P systems can approximately predict the trend of population size by mimicking the evolution state of species. As a case study, a single-environment PDP system is used to model giant pandas. It can be seen from the experiment results that the deviation rates in many years between predicted data and statistical data are controlled within 10% expect for those in several years. As P systems can be used to try to predict the number of species in the next few decades based on the current evolutionary behaviours of species, the datasets obtained through the virtual experiments based on the PDP system models provided can assist the decision makers with further prospects enriching the information available in order to make more informed decisions in the future.
Finally, as a future research direction, we may consider the following points: (a) designing a multienvironment P system to model captive or wild giant pandas in different regions, significantly increasing the complexity of the model with respect to the previous model presented in this work. (b) Including potential impacts due to natural or not so natural factors (e.g., climate change influence, introduction of invasive species, and habit destruction produced by environmental disasters such as earthquakes); these elements might be considered in the designed models, possibly having a great influence on the number of individuals of the species, especially on wild species, given a certain setup of conditions for different parameters involved and given a certain population inside each area, including the detailed information or estimation of the distribution of gender and age.
The data used in this paper come from Chengdu Research Base of Giant Panda Breeding. They can be made available upon request to the corresponding author.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
The research structure was conceived and designed by Y. D. and G. Z.; D. Q. provided the experimental data; L. V. and M. J. wrote the program and designed the experiment method; Y. D. and H. R. wrote the paper and analysed the experimental data; and G. Z. made revisions to the final manuscript. The final manuscript was read and corrected by all authors.
This work was partially supported by the National Natural Science Foundation of China (Grant nos. 61672437, 61972324, and 61702428), New Generation Artificial Intelligence Science and Technology Major Project of Sichuan Province (Grant no. 2018GZDZX0043), and Artificial Intelligence Key Laboratory of Sichuan Province (Grant no. 2019RYJ06). The authors also acknowledge the support of the research project TIN2017-89842-P (MABICAP), cofinanced by Ministerio de Economía, Industria y Competitividad (MINECO) of Spain, through the Agencia Estatal de Investigación (AEI), and by Fondo Europeo de Desarrollo Regional (FEDER) of the European Union.