Introduction

The significance of ocean-based economic operations has increased on a worldwide scale. The ocean economy plays an essential role in economic growth and climate action through mining, fishing, tourism, marine aquaculture, transportation, and logistical activities. It assists 31 million workers globally and contributes US$ 1.5 trillion annually, equal to Russia’s GDP (Nham and Ha, 2023). Oceans now face several threats, from natural forces like climate change to manufactured activity like pollution and overfishing. Economic operations that are dependent on the ecological services that marine and coastal habitats offer may find their viability threatened by these risks. Offering services such as fish availability, enforcing regulations such as safeguarding the shoreline, offering cultural services like leisure, and offering support services like biodiversity preservation and genetic resource preservation are necessary for all commercial operations involving the seas (de Groot et al. 2002; Lillebø et al. 2017).

In the global context of promoting sustainable development, strategies must be found to reduce the adverse environmental impacts of human production and consumption activities on marine and coastal ecosystems. The concept of the “blue economy” has gained international attention as a tool for governments to stimulate the economy and support communities to protect natural resources and marine habitats (Morgan et al. 2022). The general definition of a “blue economy” is “the sustainable use of marine resources for economic growth, improved livelihoods, employment, and health of marine ecosystems” (Bank et al. 2017). The blue economy, often referred to as a sustainable BE or sustainable ocean economy, is associated with economically viable ocean business activities in the ocean, encouraging societal integration and maintaining strong coastal and marine ecosystems. In other words, it benefits society and the economy in the present and future while protecting the environmental state of the oceans. Developing and implementing innovative approaches to new, less disruptive ocean economy projects is essential for sustainable practices (Jackman and Moore, 2021; Keen et al. 2018).

Developing and implementing innovative approaches to new, less disruptive ocean economy projects is essential for sustainable practices. The condition of ecosystems that sustain other species as well as humans is declining at a faster rate than in the past, according to the chair of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES). Globally, we are undermining the fundamental foundations of our economies, our means of survival, our food security, our health, and our standard of living (Brondízio et al. 2019). In addition, the Living Planet Index (LPI), which evaluates biodiversity, indicates a 68% reduction between 1970 and 2016, according to the World Wide Fund for Nature (WWF) “with our global natural capital stock down by almost 40% since the early 1990s” (Baldwin et al. 2020). A country’s ecological footprint impact analysis is one way to determine the impact of human activities on ecosystem survival. The role of economic activity, driven by the country’s financial development, can be decisive in the deterioration of the health of the Earth’s ecosystems (Akhtar et al. 2022; Ashraf et al. 2022).

The quantity of water area and biologically productive land needed to generate the products and services consumed by an individual or a community and absorb their waste is known as the ecological footprint (EF). It illustrates how human activity affects the environment and its sustainability (Hochman and Zilberman, 2021). According to the Global Footprint study, most economies have an ecological deficit and risk losing their ecosystems (Doytch, 2020). The rising need for output has severely impacted the atmosphere’s capacity to restore the sustainability of ecosystems.

The approach to quantifying the effect of human activities on ecosystem viability is to look at how different countries’ ecological footprints are affected. The role that economic activity plays, which is fueled by national economies, may be crucial to the declining health of the planet’s ecosystems (Li et al. 2022). The ecological footprint of the blue economy needs to be taken into account for sustainable economic growth. The ecological footprint of human activities can provide insight into the environmental effects of the blue economy. For instance, a nation’s blue economy will suffer if it has a high level of pollution or an ecological footprint deficit (Q. Wang et al. 2024). In another example, according to Schrank (2005), the local economies of Newfoundland and Labrador were badly impacted by the collapse of the cod fishery in the 1990s as a result of overfishing of Atlantic cod. The region had a considerable economic downturn and a long-term fishing prohibition as a result of the unsustainable fishing methods that left an ecological footprint that reduced the cod population. An ecological footprint is a collection of biologically active places that can continually release trash or produce resources (Langnel and Amegavi, 2020; Li Wang et al. 2022). However, to achieve economic progress, energy is a prerequisite. Carbon emissions are reduced when energy is used less (Li et al. 2022). But as the nation grows, increased economic activity causes energy consumption to rise with industrialization (Akhtar et al. 2024; Balland et al. 2022; Xu et al. 2022).

Innovations in technology contribute to decreased energy use, increased energy efficiency, less carbon emissions, and improved ecological conditions in the country (Tong et al. 2021; Q. Wang, Hu et al. 2024). Clean energy from renewable resources is emerging, and trade liberalization is being facilitated by the continued globalization process, the growth of service industries, and the expansion of metropolitan areas have brought about substantial structural transformations in energy, commerce, economics, and society (Li et al. 2021; Q. Wang et al. 2023). A number of areas, including company transformation and government governance, are where the digital economy may be able to support low-carbon emissions (Q. Wang, Sun et al. 2024). The progress of the financial industry helps new businesses by offering loans, funding, and venture capital. This helps creative organizations prosper in the digital economy and encourages the use of new technology and creative business models (Q. Wang, Hu et al. 2024). Because the economies are mostly built on non-renewable consumption, which exacerbates environmental degradation and ecological footprint, this directly impacts the environment (Khan et al. 2020; Muhammad et al. 2023; Wu et al. 2022).

Ecological footprint may be used to evaluate an individual’s or group’s ecological surplus or deficit by comparison with biocapacity (BC), which is the planet’s or region’s possible productive area. Several variables, including population growth, lifestyle choices, resource efficiency, production techniques, and consumption and waste management patterns, can affect it.

Table 1 shows the difference in biocapacity and the ecological footprint of G20 countries in 2022. Argentina, Australia, Brazil. Canada and Russia have a positive value. However, the ecological footprint of all other G20 countries shows an ecological footprint deficit in various trends, which is concerning for the trajectory of sustainable environmental quality. When looking for the necessary conditions for sustainability, the link between an area’s ecological footprint and biocapacity can be used as a guide (Lin et al. 2018). This enables us to create a new global map where countries are categorized as having an ecological footprint surplus or deficit.

Table 1 Difference in biocapacity and ecological footprint for G20 countries.
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An ecological deficit occurs when the ecological footprint is greater than the biocapacity due to the inability of the domestic supply to meet the demands of the nation for resources. These nations frequently rely on other nations, who have plenty of natural resources relative to their own needs (Niccolucci et al. 2012). Conversely, the ecological footprint surplus countries have an abundance of natural resources (Marti and Puertas, 2020). These facts support the claim that natural resources abound in Argentina, Australia, Brazil, Canada, and Russia.

Specifically, the G20 countries, which account for over 84% of the world economy and 65% of its population, are the main drivers of global development and growth. These are beneficial, but the G20 block is responsible for more than 75% of the global ecological footprint. The G20 block’s strength and influence hold it primarily responsible for the majority of the environmental issues the globe is presently confronting, despite the diversity and different paths for growth among its members. Among all the other issues, fast urbanization, unrestrained commerce, increasing energy use to boost economic production, and highly unmaintainable resource usage have resulted in three primary challenges: climate change, significant air pollution, and biodiversity loss (Codal et al. 2021; Geng et al. 2023; Kaplinsky and Kraemer-Mbula, 2022).

However, research hasn’t been done on how ecological footprint affects the BE. It is unknown how ecological footprint and blue economy relate and how these elements may impact the BE. These are making complex network relationships, which are difficult to understand with the most common methodological approaches. Furthermore, the traditional methodological techniques are unable to accurately evaluate the intricate relationships between the variables (HongXing et al. 2022; Memon et al. 2022; Naveed et al. 2024). However, a microscopic-based computational approach is needed to optimistically expose the actual hidden factors of the BE. Therefore, the current study presented a structural learning-based Bayesian neural network (BNN) with PC algorithm by employing score-based and constraint-based methodologies to examine the dynamic impacts of ecological footprint, GHG, POT, and GDP on BE in G20 nations and probabilistic relationships of the random variables of the Bayes network topology. In fact, this artificial intelligence (AI)-based approach can estimate the joint probabilistic distribution and conditional dependency of random variables of Bayes network topology, which differentiates from the inferences of conventional approaches of the previous studies that enhance the significance level of the present study. Another advantage is that the present AI-based approach can provide a graphical representation of the joint probabilistic distribution of random variables in network topology with mesh query, which robustly the analysis part of the study and also differentiates from previous study analysis inferences. Moreover, the BNN can easily tackle a big dataset more efficiently and accurately than most common approaches (Alhussam et al. 2021; HongXing et al. 2023). However, it should be noted that this study also uses OLS, FE, and GMM approaches as robustness estimation tests to assess the dynamic effects of ecological footprint, GHG, POT, and GDP on BE in G20 nations.

Our study will make several marginal contributions. Firstly, considering the pressing need for BE in matters like ecological degradation and climate change, greenhouse gas emissions, population growth, and economic growth, BE needs more significant consideration. The effect path of ecological footprint on BE globally will be thoroughly investigated in this research, and the challenges posed by the existing state of affairs will also be covered. Secondly, our investigation will center on the causal connection between ecological footprint and BE. The empirical findings will show that ecological footprint has a positive or negative effect on BE. Consequently, an ecological footprint will either help or impede BE’s growth at different times. Third, this study will offer policy implications by analyzing the evolutionary paths of many countries influencing BE through ecological footprint.

There are five sections in this study. The section “Literature review and hypothesis development” offers a discussion of previous studies and hypothesis development. The variable selection and empirical models are justified in the section “Data, selection of variables and empirical methodology”. After examining the data in the section “Results and discussion” and section “Conclusion and policy implications” ends with conclusions and some policy recommendations.

Literature review and hypothesis development

One important field of research that tackles the harmony between economic growth and environmental sustainability is the relationship between ecological footprint and the BE. The “blue economy” idea strongly emphasizes using ocean resources sustainably to support employment creation, better livelihoods, and economic expansion while safeguarding the well-being of marine ecosystems. An overview of the studies conducted on the connection between the ecological footprint and the blue economy is provided below:

The three interconnected industries agriculture, forestry, and fisheries (AFF), use natural resources to create food, fiber, fuel, and other products (Chen et al. 2023). In forestry, trees, and forests are managed for various uses; in agriculture, crops, and cattle are raised on land; and in fishing, aquatic species that are either wild or domesticated are collected from bodies of water. AFF may boost GDP by giving billions of people access to food and nutrition, creating jobs and income, boosting trade balance and foreign exchange profits through exports, improving rural development and the fight against poverty, encouraging technological innovation and adoption, safeguarding traditional knowledge and cultural heritage; developing shock and catastrophe resistance and maintaining ecosystem services including water control, carbon sequestration, and biodiversity preservation (Barrett, 2021). However, if AFF is not carried out sustainably and fairly, it can impede inclusive growth (IG) (Muraca and Neuber, 2018). Degradation of the environment, including soil erosion, deforestation, desertification, greenhouse gas emissions, pollution, biodiversity loss, and water shortages, can be caused by AFF (Meckling and Allan, 2020). They can also cause societal issues like marginalization, exploitation, inequality, land conflicts, and human rights abuses (Sovacool et al. 2020).

An analysis of the relationship between the BE, deciding variables, and marine condition was conducted by S. Wang et al. (2021) using the Tapio decoupling model. The results showed the growth patterns and intrinsic connection of the maritime natural environment with the dynamic shifts of the BE. While China’s coastal provinces and cities now have better marine ecological efficiency, the country’s southern and northern areas still have comparatively poor marine ecological efficiency. In addition, the link between BE and ecological footprint showed a downward trend in 11 coastal zones, suggesting that investment in marine resources played a crucial role in the expansion of BE and exerted pressure on the marine environment.

A vital integrated strategy for attaining a sustainable BE is integrated ocean management (IOM). IOM is an all-encompassing strategy that integrates and builds upon current departmental governance initiatives. It is built on an ecosystem and knowledge. It strives to coordinate maritime uses to maximize the BE while preserving marine ecosystems’ resilience and sustainability. Phelan et al. (2020) research examines how South Sulawesi Province, Indonesia’s coastal area, may make use of ecotourism that is rooted in the community to encourage the responsible use of marine resources. This research offers coastal communities with limited resources a way to get started in the blue economy. Communities most require multilateral help in three critical areas: market entry, reception abilities, and trash management.

Using Qingdao as an example, a coupled coordination model and an extensive indicator system were used to statistically analysis how the connection between development and urbanization of the natural environment changed between 2000 and 2008. The most significant contributions to environmental systems and urbanization came from these two statuses. Urbanization and the natural environment are coupled, and this coupling connection was greatly impacted by the economic subsystem of urbanization and reaction (Fu et al. 2020).

For the offshore supply chain, Kong et al. (2023) created a carbon reduction model based on system dynamics. A detailed analysis was conducted on the interaction between enterprises, the economy, the environment, energy, and policy, using Shanghai Port as an example. The potential for reducing emissions from coastal power was great, but emission trading systems had little effect on reducing emissions and may even increase carbon dioxide emissions. The most effective option for decreasing the offshore supply chains CO2 emissions, regardless of the emission reduction methods implemented. Therefore, the most efficient way to cut carbon dioxide emissions under permissible conditions was to use various resources fully. In a study by Hossain et al. (2024) using PCSE and GMM, it was found that GHG emissions and economic growth had a positive impact on BE for 25 selected countries for the period 2002–2019.

Clapp et al. (2018) investigated how the BE sectors’ characteristics will be affected by climate change. The impact of GHG emissions, marine life resources, maritime transportation, and port operations on the rise of per capita income has also been the subject of several economic studies (Bădîrcea et al. 2021; Luhtala et al. 2021). Indications that ocean acidification is still happening, as well as its negative consequences on marine creatures and the food chains that support them, were shown by Catherine, McMullen (2009). These effects eventually cause significant disturbances within whole ecosystems. Because of the increase in atmospheric CO2 concentrations over the past century, the pH of the whole surface ocean has lowered, which prevents BE development.

Alharthi and Hanif (2020) employed the feasible generalized least squares method to analyze panel data from South Asian Association for Regional Cooperation (SAARC) states covering the years 1995–2018. According to the research findings, elements of the BE have a notable impact on the economic growth of SAARC member states, which in turn helps to attain SDG 14. According to several studies, the BE has an effect on economic growth over the long run (Bădîrcea et al. 2021; Opritescu et al. 2020). Furthermore, Peng et al. (2020) found a connection between the growth of the fishing sector and ocean pollution using an environmental Kuznets curve. A panel threshold regression technique was employed by Song et al. (2020) to investigate whether threshold effects exist on marine economic growth. The results demonstrated a nonlinear, U-shaped link between the expansion of the marine economy in coastal China and financial development.

As two fundamental BE factors, tourism and fisheries have benefited Asia-Pacific nations’ sustainable ocean governance and management strategies. Consequently, this has enhanced these nations’ economic growth (Bhattacharya and Dash, 2021). The majority of coastal residents depend on fishing and other sectors for their living, which means they either directly or indirectly contribute to the nation’s economic development. Many East African nations have extensive coastlines that border the Indian Ocean, which presents prospects for economic growth within the framework of the BE concept. A surge in commerce, entrepreneurship, company expansion, and employment rates are all facilitated by a variety of maritime resources and serve to expand the economy (Mohanty and Dash, 2020). Nevertheless, since none of these studies have looked at how ecological footprint affects the BE, there is a clear gap in the body of knowledge.

This study’s main goal is to encourage coordinated development between the ecological footprint and the blue economy by combining research with the high-quality enhancement of marine fisheries. Thus, the following will be the research hypothesis of the study:

H1: Ecological footprint negatively affects the blue economy in G20 countries.

Three holes in the current body of research are identified by the literature review. (1) The majority of academics study the sustainable blue economy and the effects of urbanization on BE, with most research concentrating on the IOM, ecotourism, and offshore supply chains. (2) Existing studies have been carried out coupled coordination model, Tapio decoupling model, PCSE, GMM, and feasible generalized least squares, but the econometric model does not account for the ecological footprint element. (3) The majority of research concentrates on a single nation or area, ignoring heterogeneity and the dearth of studies that compare other populations.

This study adds to the past literature in several noteworthy ways, even if the breadth of the earlier material is comparable to that of the current work. First of all, this article creatively combines all significant structural components into a single analytical framework, taking into account the impacts of an ecological footprint on the blue economy, in contrast to the current literature that often picks specific aspects in a targeted way for investigation. The findings are more rigorous since all of the affecting factors were taken into account. Second, it is evident from the body of current literature that taking the heterogeneity of the study object into account for structural elements is crucial. Nonetheless, the majority of studies are focused on a single nation or economic entity, and there aren’t many assessments of heterogeneity for many study subjects. The creation of policies connected to the blue economy at the income group and global levels is balanced in part by this consideration of heterogeneity. Lastly, this study employs BNN, OLS, FE, and GMM as its approach, combining four sets of econometric techniques based on various data types.

Data, selection of variables, and empirical methodology

Data and selection of variables

The study investigates the effects of ecological footprint, greenhouse gas emissions, population growth, and economic growth on the BE. Blue economy’s data was collected from the Food and Agriculture Organization databaseFootnote 1 (FAO), ecological footprint data was collected from Global Footprint NetworkFootnote 2 (GFN), GHG emissions data was collected from Our World in DataFootnote 3 (OWD), data for population growth, and economic growth was collected from the World Development IndicatorFootnote 4 (WDI). These all-data sources are reliable and valid. Based on data availability for all selected variables, a panel dataset covering the years 2000–2021 was gathered from G20 countries. Due to the unavailability of ecological footprint data, we excluded the European Union from our panel sample estimations. The chosen variables are explained in the context of this study in Table 2.

Table 2 List of the variables.
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In the twenty-first century, the interaction between economic activity, environmental considerations, and sustainable development has become an important field of study (Adebayo et al. 2023). This study looks at the effects of ecological footprint, GHG emissions, population growth, economic growth, and how these factors interact with one another to support BE, and the responsible use of ocean resources to raise living standards, advance economic growth, and strengthen marine ecosystems.

Blue economy

The study’s variables align with previous empirical literature. The dependent variable that has been chosen is BE. However, the total production of fisheries and marine aquaculture (Tones) was used as a proxy for BE in certain earlier research (Hossain et al. 2024; Sun et al. 2024).

Ecological footprint

The independent variable that has been chosen is ecological footprint. The ecological footprint is stated in units of GHA per person. We observed from the literature review that the two main factors influencing ecological footprint are economic growth and population growth. For example, according to Pata (2018), deterioration of the environment is positively impacted by population growth, however Wei and Zhang (2017) found mixed results.

GHG emissions

It is imperative to recognize that oceans are on the verge of reaching a crisis point in a number of ways. This theoretical framework is based on a knowledge of environmental sustainability, with a focus on GHG emissions. GHG emissions include CO2, methane, and nitrous oxide from all sources, including land-use change. When energy-intensive machinery that consumes coal and oil is used in overfishing or in the exploitation of other blue economic resources, greenhouse gases are released into the environment (Mulazzani et al. 2016). Additionally, Konar and Ding (2020) claimed that worldwide benefits might result from investments made within the BE framework in ocean-related initiatives. However, in terms of blue economy activities, more shipping, GHG emissions, pollution, trash creation, ocean ecological disturbance, and coastal tourism would result in a higher ecological footprint.

Population growth

In line with research by Dong et al. (2018), who noted the impact of population growth, which is defined as the total population size, is used as a control variable in this study.

Economic growth

The GDP per capita (constant 2015 US dollars) is employed as a stand-in for economic growth in the study. The importance of marine resources in fostering economic development and progress has been the subject of several scholarly studies (González-Val and Pueyo, 2019). In accordance with Solow's (1956) neoclassical growth theory, production per worker attracts more capital investment and yields high returns on capital in less developed countries. There is evidence to support this notion from certain academics who have meticulously suggested that there is a significant lag in the relationship between marine resources and economic growth (K. Ahmed et al. 2016; Zhang and Chen, 2022). Additionally, countries must appropriately align with the Paris Agreement and SDGs 14 and 13, which address the conservation and sustainable use of seas, oceans, and marine resources to advance economic growth, within the framework of the BE.

Econometric model

Equation (1) describes the fundamental econometric model and the research functions:

$${{BE}}=f\left[{{\rm{EF}}}+{ {GHG}}+{ {POT}}+{{GDP}}\right]$$
(1)

We transform raw data into a logarithmic form in order to prevent heteroscedasticity in the processed data findings. Log-linear data often produces more trustworthy and practical insights than linear data. The functions’ log-linear form is shown below in Eq. (2):

$${ln}{{{BE}}}_{{it}}={\beta }_{0}{+\beta }_{1}{{ln}{{EF}}}_{{it}}+{\beta }_{2}{ln}{{ {GHG}}}_{{it}}+{\beta }_{3}{ln}{{{POT}}}_{{it}}+{\beta }_{4}{ln}{{GDP}}_{{it}}+{\varepsilon }_{{it}}$$
(2)

Structural learning-based Bayesian neural network

A BNN approach based on structural learning is used for the random variables in this study. It is a method for investigating the random variable’s probability distribution and conditional dependency. The score and constraint-based algorithms are used in the structural learning-based BNN technique for both kinds of analysis (Al Moussa et al. 2015).

Margaritis (2003) states that the information on the conditional independence of random variables that indicates whether specific arcs is provided by the theorem and the constraint-based method. Let suppose, we have the W, X, Y, and Z are random variables in the directed acyclic graph (DAG) that is presented in Fig. 1.

Fig. 1
figure 1

Genetic directed acyclic graph structure.

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In Fig. 1, the structure variable nodes W, X, Y, and Z in the N structure of the D data represent random variable nodes. In the initial DAG example, Z acts as the parent node for the X and Y variable nodes, with X and Y serving as child nodes of the Z variable node. In the second DAG example, the X and Y variables are parent nodes for the W variable, and W, in return functions as a child node of the X and Y variables. For DAG’s execution scenario of conditional dependence on random variables of Bayes network topology, it is presented as P(X, Y|Z). This notation illustrates the likelihood of the X and Y variable nodes. The following scores can be supported for structure learning-based Bayesian neural network executions.

Score-based learning approach

Let P(B) be the earlier B network probability distribution derived from the D dataset. According to Cooper and Herskovits (1992), Neil et al. (2001), and Shulin and Kuo-Chu (2002), the prior probability of the B network may be obtained using Eq. (3):

$${\rm{P}}\left({\rm{B}}|{\rm{D}}\right)=\frac{{\rm{P}}\left(B,\,{\rm{D}}\right)}{{\sum }_{{B}^{{\prime} }}{\rm{P}}\left({B}^{{\prime} },{\rm{D}}\right)\,}=\frac{{\rm{P}}\left(B\right)\,{\rm{P}}\left(D|{\rm{B}}\right)}{{\sum }_{{B}^{{\prime} }}{\rm{P}}\left({B}^{{\prime} }\right){\rm{P}}\left(D|{B}^{{\prime} }\right)}$$
(3)

Robinson (1977) demonstrates that it is easy to determine an ideal structure given that class N-P. The K2 searching algorithm and the evolutionary algorithm are two methods that may be employed to determine the optimal network structure (Perry, 2003). The following scores support the score-based learning approach of BNN:

  1. i.

    Scores from Bayesian Dirichlet

    Eqs. (4) and (5) use the D dataset, B network, and \(\theta\) vector parameters to provide the Dirichlet score.

    $${\rm{BD}}:{{S}}_{{{D}}}\left(B\right)=\log \left(P\left(B\right).{\int }^{P}\left({D}\,\left|\,{B},{\theta }\right.\right)\cdot {P}({\rm{\theta }}\,\left|\,{B}\right.){\rm{d}}{\theta }\right)$$
    (4)
    $$\begin{array}{l}{\rm {BD}}(B,D)=\,\log (P(B))+\mathop{\sum }\limits_{{\rm{i}}=1}^{{n}}\mathop{\sum }\limits_{{j}=1}^{{qi}}\left(\log \left(\frac{\varGamma ({N}_{{ij}}^{{\prime} })}{\varGamma ({N}_{ij}+{N}_{{ij}}^{{\prime} })}\right)\right.\\\qquad\qquad\qquad\qquad\qquad\,+\,\left.\mathop{\sum }\limits_{{k}}^{{{r}}_{{i}}}\log \left(\frac{\varGamma ({N}_{ijk}+{N}_{ijk}^{{\prime} })}{\varGamma ({N}_{ijk}^{{\prime} })}\right)\right)\end{array}$$
    (5)

    In the D dataset, the \({N}_{{ijk}}\) represents the total number of observations where the random variable \({X}_{i}\) takes \(j{{\rm{th}}}\) value and its parents take \(k{{\rm{th}}}\) value. For the provided network B, it is assumed that the former vector parameter distribution \(\theta\) is a Dirichlet with hyperparameters as \(\alpha ={\alpha }_{{ijk}}={N}_{{ijk}}\).

  2. ii.

    Information theory scores

All of the variable nodes in the Bayes network topology have either an active or inactive primary value Cheng et al. (2002). Arcs represent the noisy information channels that link each value. The study used the most recent information theory to evaluate the following scores:

  1. a.

    Entropy scores

    In the Bayes network architecture, entropy measures the amount of lost information about random variables. However, entropy is permanently lost if complete random variables are treated deterministically. Bouckaert (2004) and Bozoklu et al. (2020) explained the current entropy measure H (D, B) for the B network and the D dataset that can be visualized in Eq. (6).

    $$H\left(B,{\rm{D}}\right)=-{\rm{N}}\mathop{\sum }\limits_{i}^{{\rm{n}}}\,\mathop{\sum }\limits_{j}^{{{\rm{q}}}_{i}}\,\mathop{\sum }\limits_{k}^{{ri}}\,\frac{{N}_{{ijk}}}{N}{\mathrm{log}}\frac{{N}_{{ijk}}}{{N}_{{ij}}}$$
    (6)

    The notation\({N}_{{ijk}}\) in Eq. (6) represents in the D dataset the total count of observations. Whenever the parents of the \({X}_{i}\) Variable receive their \(j{{\rm{th}}}\) value, and the\({X}_{i}\) variable takes its \(k{{\rm{th}}}\) value.

  2. b.

    Mutual information score

    To obtain the edge score between the \({X}_{i}\) and \({X}_{j}\) random variables are shown in Eq. (7) as follows (Chow and Liu, 1968). For this significant methodological purpose, we incorporate the PC algorithm for mutual information scores of \(I({X}_{i},{X}_{j})\):

    $$\,{\rm{I}}\left({X}_{i}\,{X}_{j}\right)=\mathop{\sum }\limits_{{X}_{i}{X}_{j}}^{{n}}{\rm{P}}\left({X}_{i}{,{\rm{X}}}_{j}\right)\log \frac{{\rm{P}}\left({X}_{i},{X}_{j}\right)}{{\rm{P}}\left({X}_{i}\right){\rm{P}}\left({X}_{j}\right)}$$
    (7)

The number of edges inside the random variables is the numerator (n) of summing in a Bayes network structure. The optimal Bayes network topology that raises the variable probability distribution of the data is found by using the PC algorithm.

Constraint-based learning approach

The conditional dependence between the random variables is carried out using the constraint-based learning technique with the PC algorithm. Nonetheless, as shown in Eq. (8), the current study uses the constraint-based learning methodology to investigate the conditional dependence of random variables (Natori et al. 2015; Spirtes et al. 2000).

$${X}^{2}=\mathop{\sum }\limits_{n}^{{r}_{Y}}\mathop{\sum }\limits_{k}^{{r}_{X}}\frac{{\left({P}_{{nk}}-{D}_{{nk}}\right)}^{2}}{{D}_{{nk}}}$$
(8)

The expected and desired frequencies are represented by the \({P}_{{nk}}\) and \({D}_{{nk}}\) in that context. Using a partial pearson correlation (PPC) method, the conditional independence test is frequently used to assess the connection between random variables for continuous variables. Equation (9) provides the statistical measures for the PPC (Tsagris, 2019).

$${{P}}_{{{pearson}}}=\left.\,\frac{1}{2}\,\right|\left.\log \frac{1\,+\,{r}_{\left.X,\,Y\right|Z}\,}{1\,-\,{r}_{\left.X,\,Y\right|Z}}\right|\sqrt{n-\left|Z\right|-3}$$
(9)

In the above equation, the \(n\) denotes the size of the sample dataset, \(\left|{Z}\right|\) represents the number of conditioning variables in the\(\,{X}\) dataset and \({r}_{\left.X,{Y}\right|{Z}}\) exhibits the PPC between X and Y variables by conditioning Z.

Results and discussion

Diagnostic and descriptive statistics

The descriptive statistics for every variable in the G20 countries are compiled in Table 3. A sample size of 418 observations is used in the current study. The results of G20 countries show that the average blue economy over the study period is 10.8489, the minimum value of 2.2083 is of Argentina, and China has the maximum value, which is 17.4699, which shows that China is efficiently benefiting from the blue economy as compared to other G20 countries. The average ecological footprint is 1.3980; the minimum value of –0.2944 is of India, and the USA has the maximum value, which is 2.3912, which shows that the USA's ecological footprint is highest in G20 countries. The average GHG emissions, population growth, and GDP are 20.7949, 18.4499, and 27.7602, respectively. Table 3 also displays the findings of a variance inflation factor (VIF), which was used to ascertain if any explanatory factors were multicollinear. Because the data are well inside the permitted range, VIF < 10, which confirms no multicollinearity among the variables, the data support the absence of multicollinearity (Damodar, 2003).

Table 3 Descriptive statistics in G2O countries.
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Evaluation of BNN-based predictions

Using graphical and score-based techniques, the probability distribution between random variables is displayed by the Bayesian network using a structurally based PC algorithm. The BNN offers a more thorough explanation of the relationship between each variable.

The network structure of the Bayesian neural network based on structural learning is depicted in Fig. 2, which offers the following details: (1) The network topology represents the probabilistic association between ecological footprint and BE; (2) The network topology represents the probabilistic-based association among BE and control variables (GHG, POT, and GDP); (3) The network topology also represents the conditional dependency that is presented among random variables nodes of this Bayes network.

Fig. 2
figure 2

The architecture of Structural learning-based BNN.

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The degree of correlation between the variable nodes in the Bayes structure is shown in Table 4. As evidenced by –0.0002, ecological footprint exhibits a negative, weak association with BE. Moreover, control variables such as GHG, POT, and GDP are linked to BE, with coefficients of 0.0362, 0.0313, and 0.1115, respectively. GHG, POT, and GDP are positively associated with BE. The study’s findings indicate that GHG, POT, and GDP are linked to increased BE. GDP has a relatively stronger relationship with BE. Although the ecological footprint has a direct relationship with BE, but BE is also conditionally dependent on ecological footprint, given the percentage effect of GHG and POT, which is indicated by the edges of the Bayes network topology and score of Table 4.

Table 4 The degree of correlation between the variable nodes in the Bayes structure.
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It is important to emphasize that the mesh query shows the probability distribution of the combined random variable inside the Bayesian network structure. Additionally, the intensity of the combined probability distribution of the independent and control variables is graphically represented by the color bar in graphs A–D. Although the joint probability distributions between ecological footprint and blue economy are shown in graphs A in Fig. 3, the majority of data prefer intermediate values, which are denoted by the hues white, yellow, and red. According to Graph A, BE is negatively impacted by ecological footprint, but BE is positively impacted by GHG, POT, and GDP. But when ecological footprint and BE values are abnormally high or low, data diverge dramatically, causing black to spread over the graphs. When combined with control variables, this study’s results look at how ecological footprint impacts the blue economy for the first time in the literature (see Fig. 4).

Fig. 3
figure 3

Joint probability distribution of BE, EF, GHG, POT, and GDP with Mesh Query.

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Fig. 4
figure 4

Summary of results.

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This work has extensive ramifications overall. In the section “Evaluation of BNN-based prediction”, the BNN is used to compute the research outcomes of this article with respect to theoretical aspects. Panel data analysis using the model is appropriate for examining the nonlinear effects of ecological footprints in G20 nations. It can offer theoretical backing for researching the impact of a nation’s or economy’s ecological footprint. After variable transformation, the model may be used as a guide to investigate the nonlinear connection of additional indicators. Practically speaking, this research highlights the significance of the ecological footprint, and the blue economy offers recommendations that are ideal for addressing these issues as well as GHG emissions, population growth, and economic growth.

Robustness estimation

The robustness and efficacy of the results of the BNN-based model were further assessed using the OLS, fixed effects, and two-step generalized method of moments to validate the robustness and effectiveness of the findings of the BNN-based findings. In addition to unobserved individual components, endogeneity, and heteroskedasticity are potential causes for worry since they may result in the inefficiency of the model coefficients. Thus, the GMM for endogeneity and the robust standard errors for heteroskedasticity were carried out.

Table 5 presents the statistically adverse effects of an ecological footprint on the blue economies of G20 nations. The results indicate that for every extra year of ecological footprint decreases blue economy (β = –0.3373, p > 0.10), (β = –0.9418, p > 0.10), and (β = –0.5851, p < 0.10) under the OLS, FE, and GMM, respectively. These outcomes show that an increase in ecological footprint decreases the blue economy of G20 countries. The findings demonstrate an ecological footprint is important to advancing the blue economy by increasing food security and livelihood options in G20 countries. Comparably, GHG emissions influence the BE positively. The BE will rise with a modest 1% increase in GHG emissions (β = 1.7723, p < 0.01), (β = 2.8603, p < 0.10), and (β = 1.6717, p < 0.05) under the OLS, FE, and GMM, respectively. Furthermore, the results indicate that population growth influences the BE. The BE will rise with a modest 1% increase in population growth (β = 2.2763, p < 0.01), (β = 6.4829, p < 0.10), and (β = –2.6019, p > 0.10) under the OLS, FE, and GMM, respectively. Comparably, economic growth positively influences the BE; according to the OLS, FE, and GMM, respectively, 1% increase in economic growth, there has been an estimated rise of BE around (β = 0.8864, p < 0.01), (β = –0.2755, p > 0.10), and (β = 0.4961, p < 0.01). Although there is not much research on the topic, introducing new technologies like ships, boats, and mining equipment may cause CO2 emissions to rise during the BE’s early stages. Ecological footprint causes a decrease in the blue economy; therefore, countries should formulate policies to decrease the ecological footprint, and the hypothesis of the study is supported by the findings. On the other hand, the literature on this association is scarce.

Table 5 Robustness analysis.
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Robustness estimation of different income group

According to their degree of economic development, the World Bank classifies all nations into four income categories: nations with low income, lower middle income, higher middle income, and high income (Li et al. 2021). Further, the G20 countries are subdivided into high-income countries and middle-income countries, as shown in Table 6. OLS, FE, and GMM outcomes of two income categories are shown in Table 7.

Table 6 Two groups of G20 countries on the basis of their income.
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Table 7 Robustness analysis of two-income groups G20 countries.
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Table 7 shows the nonlinear relationship between ecological footprint and the blue economy in the two income groups. The blue economy is positively impacted by the ecological footprint in the high-income group but negatively impacted in the middle-income group. High-income group countries are financially strong, due to which they can manage ecological footprints in a better way, while in the middle-income group, there are included populated countries of the world like China and India, and it is not possible for them to manage ecological footprints. Both income groups’ GDP and GHG have a positive effect on BE, whereas POT has a positive effect on BE in the high-income group and a negative influence on BE in the middle-income group.

Discussion

Nowadays, nearly all of the economies of nations that border the ocean rely heavily on the blue economy for their GDP. According to a recent estimate by the OECDFootnote 5, oceans can provide around 3% of the global value added. The world’s population is mostly dependent on ocean economies for both food and living. Beyond only their economic benefits, oceans also have major positive environmental consequences. The aforementioned points reinforce the Blue Economy’s strategic significance on a national and worldwide level in several countries. In light of this, a “Blue Economy” needs to be viewed as a long-term plan that enhances human well-being, promotes social justice, and protects the environment by leveraging industries and activities associated with the ocean. The United Nations has created a comprehensive strategic framework with the 2030 Agenda and Sustainable Development Goals (SDGs), but it needs to be customized to meet the particular needs of every maritime nation. In this regard, the G20 countries can assume a leadership role.

Shahzad et al. (2017) report that there is evidence linking rising trade activity to rising CO2 emissions. In order to efficiently utilize ocean resources during the BE’s first phase, more commercial activities and a larger marine vessel deployment are required. Although these increased activities support economic growth, they also have the unfavorable externality of raising CO2 emissions. Consequently, it is crucial to make sure that the logistics of marine trade do not entail the shipping of hazardous substances. Such materials can leak and have disastrous effects on marine ecosystems, especially when it comes to ruining fisheries. Before leaving their numerous hubs, the ships must be tightly sealed.

Few studies have examined the relationship between CO2 emissions and BE growth, possibly because there has been more attention focused on how environmental changes affect seas (Bădîrcea et al. 2021). Consequently, we concentrate on the effects of ecological footprint on BE in our assessment of the literature. Research from Bangladesh on BE and climate change indicates that extreme weather events linked to climate change increase ocean temperatures and acidity, putting coral reefs at risk (Sarker et al. 2018). Aquaculture’s potential to improve sustainability in the BE was investigated by N. Ahmed and Thompson (2019). Levin et al. (2019), in a similar vein, highlighted the significance of the deep ocean and the necessity for widespread worldwide scientific observation of its conditions. They also emphasized important social and scientific issues that, in the long term, call for certain observational standards.

The research studies presented in this study have important policy implications for G20 countries. First, it is imperative for policymakers to actively advocate for a sustainable blue economy that can enhance production and profitability while ensuring the preservation of environmental quality and social fairness. Achieving this goal requires the implementation of efficient rules, incentives, and monitoring systems to mitigate overfishing, pollution, and disputes among stakeholders. Second, it is crucial for policymakers to actively encourage economic diversification in order to reduce dependence on the agriculture, forestry, and fishing industries. These sectors not only provide inadequate value but also incur substantial environmental liabilities. Thirdly, policymakers should give priority to the reduction of the ecological footprint, as this action may quite successfully mitigate environmental degradation and the negative consequences of climate change that present a significant risk to an equitable blue economy. The attainment of this objective requires the adoption of green growth techniques that improve resource efficiency and environmental conservation by combining technological advancements with changes in behavior. In addition, it is critical that governments promote the use of renewable energy sources in order to minimize the use of fossil fuels and mitigate the emission of greenhouse gases, both of which can have negative environmental repercussions.

Obstacles facing the blue global economy

A conceptual framework for evaluating sustainable markets and development forms the foundation of most BE management research. Given that sustainable development and blue growth in the marine ecosystem are intimately related, the blue economy is growing and will require collaborative efforts. The idea of the blue economy’s expansion for sustainable development has led to a rise in interdisciplinary study, particularly on the key issues surrounding it. The several fields of the blue economy are fraught with difficulties. The food and nutrition sectors greatly benefit from the fishing and aquaculture industries; nevertheless, some aquaculture practices exacerbate environmental problems already present, such as the loss of habitat, the release of pollutants, escapes, and disease, and the overuse of fishmeal and oil in diets (Coppa et al. 2021). The problem of CO2 emissions brought on by the direct and indirect usage of fossil fuels in industrial systems needs further attention, as does the conversion of areas with significant carbon sequestration, including forest zones, mangroves, and sea grass, to aquaculture production (FAO, 2018). From an environmental standpoint, the primary pressure on the shipping industry is to avoid contaminating the seas and coasts. Numerous factors, including bulk oil, liquefied gases, and chemicals; anti-fouling devices; packaged and bulk hazardous materials; sewage; trash; and bio-fouling engine exhaust, might be the source of this (which includes carbon dioxide, nitrous oxides, and sulfur) (Choudhary et al. 2021).

Since tidal and wave energy technologies are still in their infancy and lack maturity, there is a dearth of knowledge on the greenhouse gas emissions or life cycle evaluations of these maritime energy technologies, which creates doubts over their commercial deployment (Amponsah et al. 2014; Naseem et al. 2023). Additional unknown hazards to noise pollution from development are habitat loss for different species, obstacles to bird, sea turtle, and whale migration, altered seabed due to oil spills and sedimentation, and altered water movement in estuaries.

A significant factor in greenhouse gas emissions and subsequent climate change is coastal tourism. Development and construction have destroyed mangroves, dune complexes, and coastal wet areas, reducing biodiversity, lowering carbon sequestration, and releasing pollutants into the land and sea. The environmental components of the blue global economy must be balanced to prevent long-term harm to livelihood due to repercussions like substantial ecosystem devastation. These industrial and economic factors are crucial to the long-term growth of energy outputs from all economic kinds, including brown, green, and blue economies. From an industrial and environmental standpoint, integrating energy sources from green and blue economic zones may create solid and sustainable prospects (Choudhary et al. 2021).

Possibilities for an integrated blue economy

Using ecological support, imitating the biological environment, and increasing productivity across all economic sectors, the blue economy adheres to the circular economy paradigm and guarantees zero waste (Venkata Mohan et al. 2020). The growth and use of the BE, however, crosses the borders between land and marine ecosystems, necessitating a review of the economic ties between the marine and terrestrial environments. According to a thorough literature review, connecting the BE regarding the SDG of the UN becomes even more complicated when there can be a contradiction between the sustainability of the socio-environment and industrial goals. Reaching the 17 SDGs calls for a multi-stakeholder consensus among governments and nations to alter global economic strategy. The main emphasis of this study is the identification of significant blue economy development drivers such as ecological footprint, greenhouse gas emissions, population growth, and economic growth that may pave the way for integrated SDG paths.

Conclusion and policy implications

This study looked at factors that affect the BE, concentrating on the ecological footprint, greenhouse gas emissions, population growth, and economic growth, examined through a BNN-based multivariate regression model, leveraging advanced artificial intelligence computing methods. We also applied the OLS, FE, and GMM approaches to capture the dynamic changing effect of ecological footprint. The context of the G20 countries was used to perform this study. The critical metrics utilized in this examination were derived from data collected from 2000 to 2021. The findings show that the ecological footprint negatively affects the BE. Furthermore, GHG emissions, population growth, and economic development positively affect the BE. As a result, hypothesis H1 is supported.

Policy recommendations

Five recommendations for developmental policies are based on the study’s findings to increase the G20 countries’ BE’s sustainability.

  1. (1)

    Establish a green, blue economy: Our objective is to mitigate the adverse effects of conventional marine businesses on ecology by offering monetary and financial incentives to promote maritime technology innovation and new energy. Since marine commerce and transportation have an impact on the BE’s capacity to contribute to global economic growth, countries must develop other strategies. One potential replacement would be to power trading ships using renewable resources. Furthermore, there ought to be a stronger focus on the use of renewable resources for terrestrial ecosystems as well as marine ecosystems, especially those that are close to seas, oceans, or other bodies of water.

  2. (2)

    Government regulations: Governments have to think about creating a single regulatory body to manage all issues related to marine ecology, including environmental and industrial issues. It is anticipated that this action would lessen the problems with coordination and governance. It is advised to form a cooperative group that recognizes local economic and environmental objectives by sharing national databases that are pertinent to areas that are aquatic. This will make it much easier for countries to think about cooperative operating prospects in the marine sector, such as exchanging cutting-edge technology and talent development, deep-sea mining, marine transit, and sea-based trade.

  3. (3)

    Strengthen the marine administration: Create a collaborative management mechanism that spans regional sea areas, maximizes marine spatial planning, tightly regulates coastline development, and guarantees marine ecosystems’ security.

  4. (4)

    Preservation and restoration of resources: Create protected zones, prohibit or limit excessive exploitation of marine resources, and support initiatives to restore and allow marine ecosystems to regenerate naturally.

  5. (5)

    Increase engagement and public knowledge in environmental preservation: Activate the passion and inventiveness of all societal segments for involvement, create a multi-party network to protect the maritime environment, and step-up public awareness and education about marine protection. Furthermore, in light of the disparities in regional development, the execution of policies must be customized to local circumstances, prioritizing and allocating resources more heavily to places with vulnerable marine ecosystems or lower levels of marine development.

The study suggests that the first step in resolving the conflicts between blue economic expansion and natural environment conservation is encouraging international collaboration and exchange. Since the water knows no borders, international cooperation is needed to maintain the marine ecosystem. In addition to fostering scientific research innovation, we can fortify international collaboration, exchange best practices for preserving the marine environment, and work together to advance the growth of the BE. Encourage and assist organizations and businesses to carry out innovative scientific research in the areas of ecological environment protection and BE. In order to uphold the legislation, this involves creating cutting-edge technology for environmental preservation and the effective use of marine resources. Enforce substantial legal penalties for actions that harm the maritime environment, improve pertinent rules and guidelines in favor of conserving marine resources and safeguarding the maritime environment, and encourage green consumption. Enterprises may progress toward green development by increasing public knowledge of protecting the environment and promoting the purchasing of products and services with low environmental effects. Lastly, construct a long-term mechanism. To guarantee that policy implementation is a long-term assurance rather than a band-aid fix, a permanent, effective management structure, and technical assistance are required, particularly in fields like resource management and pollution prevention.

Limitations of the study

This study has three primary areas of constraint: data sampling, BE-influencing variables, and BNN. Regarding data sampling, the G20 countries were chosen for this study, and depending on the resources of the nations bordering other seas, the BE’s position may change. The second limitation has to do with elements that influence the BE. Several aspects might impact the BE when talking about aquaculture and marine environments. The only four criteria considered in this study were the ecological footprint, greenhouse gas emissions, population growth, and economic growth. In the BE, adding more variables might have different outcomes; future research can be done considering other factors. Third, although the structural learning-based Bayesian neural network gives very interesting and wide-ranging information with score-based and constraint-based approaches. However, the Chow-Liu, TAN, search & score, clustering, and hierarchical algorithms are not supported by the structural learning-based model of BNN, especially on the panel dataset of ecological footprints and blue economy. Only the PC algorithm supported the structural learning-based model of BNN for blue economy estimation in G20 countries. However, this study recommends a time series network of BNN, which may be supported by other well-known algorithms for optimal blue economy estimation. Future research, however, may think about using deep neural networks (DNNs) to examine the effects unique to certain quantiles.

The fact that this study was limited to examining the combined output of marine aquaculture and fisheries is another way the BE was examined. Mineral resources and other ocean resources are included in the BE, nonetheless. Future research may leverage these resources to represent the BE if the exact quantity is known.