Model | GEMS-Taiwan

DryLab Model Overview

CLICK HERE

DryLab Model Description

Biosafety Model

Introduction

Background

To ensure that our product doesn’t cause unintended consequences to the coral holobiont or the larger ocean ecosystem, our team utilized quorum sensing and a MazEF toxin-antitoxin mechanism to safely kill off our Genetically Modified Organisms (GMO) if they were to disperse into the environment. We developed a biosafety model to explore population dynamics and interactions, predicting outcomes when bacteria remain within or escape from the coral application site.

Research Question

What are the dynamics between our engineered bacteria, the toxin, the quorum-sensing molecules (AHL), the number of bound AHL receptors in each bacteria, and the antitoxin?
Does the biosafety system hold an unstable equilibrium?

Mathematical model

Equations

Our model aims to simulate the major events after our GMO gets employed into the ocean. These events include: the growth and decay rate of our AHL quorum sensing molecules, MazF toxins, Sar11 bacteria, AHL binding receptors, and our MazE antitoxins.

\begin{cases} \frac{dS}{dt} = k_SS(1-\frac{S}{S_c}) - dSM \\ \ \\ \frac{dM}{dt} = Sk_M(1-\frac{r}{r_c}) - kMa \\ \ \\ \frac{dA}{dt} = v_AS - d_AA \\ \ \\ \frac{dr}{dt} = k_rA(1 - \frac{r}{r_c}) \\ \ \\ \frac{da}{dt} = Sk_a - kMa \end{cases}

We modeled the interactions between five variables: SAR11 (biofilm-producing bacteria, S), MazF (bacteria-regulating toxin, M), AHL (acyl-homoserine lactone signaling molecule, A), receptor (bound receptor count per SAR11 cell, r), antitoxin (MazF neutralizing molecule (MazE), a).

The rate of change of SAR11 is modeled by equation 1, where we assume that the bacteria is regulated by a logistic growth with k_S representing the multiplication rate of the bacteria and d representing the death rate of SAR11, which is also regulated by the toxins that are present and the SAR11 that is currently present.

The rate of change of MazF concentration is represented by equation 2. MazF’s growth is represented by exponential growth with a decreasing growth rate which is all proportional to S, along with a death rate proportional to the concentration of MazF and MazE. The death rate of MazF follows first-order kinetics with a rate constant of k.

AHL production rate is proportional to SAR11 with a rate constant of v_A, and degradation of AHL follows first-order kinetics with a rate constant of d_A.

The rate of receptor binding per SAR11 cell is modeled by exponential growth, with a decreasing growth rate that is proportional to the concentration of AHL.

MazE’s growth is represented by a linear growth with a rate constant k_a, in proportion to S, along with a similar death rate proportional to the concentration of MazF and MazE. The death rate of MazE follows first-order kinetics with a rate constant of k.

Parameters

Name	Meaning	Value	Unit	Source
K_S	SAR11 growth constant	0.97	K^-1	You et al., 2004
S_c	SAR11 carrying capacity	1.24	CFU ml^-1	You et al., 2004
d	SAR11 death rate from toxin	4e-3	nM^-1h^-1	You et al., 2004
K_M	Max per capita toxin production	5	h^-1	You et al., 2004
r_c	SPer capita receptor quantity	40	h^-1	YJin et al., 2002
k	Rate constant of toxin-antitoxin reaction	0.122	nM^-1s^-1	Nikolic et al., 2018
v_A	AHL production rate constant	4.8e-7	nM ml h^-1	You et al., 2004
d_A	AHL degradation rate constant	0.639	h^-1	You et al., 2004
k_r	Receptor binding rate constant	0.42	s^-1	Chesla et al., 1998
k_a	Per capita constitutive antitoxin production	0.4	nmol s^-1	https://parts.igem.org/Part:BBa_J23113

For the parameters of kr and k, we were unable to find relevant data on these reaction constants; therefore, we settle for similar parameters from the literature. However, we have designed a method to measure k in the future, which would allow us to calculate the value of kr mathematically.

Using a green fluorescent protein (GFP), we can conduct a fluorometric assay for the quantity of MazF within bacteria (Wang & Hergenrother, 2007). By measuring both the fluorescence and the bacterial population through crystal violet staining, we are able to find the quantities of toxin and antitoxin produced, which then allows us to find the reaction rate between the two proteins. Using this rate and the quantities of both substances, we would be able to determine the reaction rate constant.

Discussion

In the following, we will explore the relationships between our five variables under two opposing scenarios.

The first scenario describes a situation where the starting population of SAR11 is low, indicating a situation in which the bacteria is not located at the intended delivery site on the coral.

The second scenario depicts a high starting population of SAR11, which would occur under the circumstances of the bacteria being attached to the coral, as the biofilm formation on the coral would give the bacteria a suitable environment for growth without dispersion caused by ocean currents. The following graphs were scaled from hours to minutes to highlight the curve trends.

SAR11-AHL-Receptors

The relationship shown here is the relation between the population of SAR11 and its effect on changes in quorum sensing.

Scenario 1 is expressed in Figure 1. In this case, we can see that the AHL concentration will decrease as it is constitutively produced at a constant level by each individual bacteria. This lower concentration would then cause a slowdown in the binding of AHL to the receptors. Therefore, we see a halt in the growth rate of bound receptors per bacterium.

Figure 2 shows scenario 2. In this case, the population of bacteria would be allowed to grow to its carrying capacity. This higher SAR11 population would allow for more rapid production. This would result in the bound receptors approaching the total receptor capacity.

Fig 1. Low bacterial count S-A-r specific relationship

Fig 2. High bacterial count S-A-r specific relationship

Toxin-Antitoxin-Receptors

Figures 3 and 4 show the effect that the bound receptor trend shown previously will have in scenarios 1 and 2, respectively.

While the quantity of bound receptors in each bacteria is low, figure 3 shows that the amount of toxin will surge. This will result in the rapid annihilation of the existing antitoxin. Therefore, we see a decreased antitoxin concentration and an increased toxin concentration in the graph.

When the bound receptor count is high in Figure 4, toxin production will be lowered as toxin production is repressed in plasmids with bound quorum sensing receptors. This allows for constitutive antitoxin production to outpace toxin production, which would lead to the neutralization of the majority of the toxin. Thus, there is a reduction in toxin concentration.

Fig 3. Low bacterial count M-a-r specific relationship

Fig 4. High bacterial count M-a-r specific relationship

SAR11-Antitoxin-Toxin

Figures 5 and 6 connect the toxin and antitoxin levels described previously to their effect on the SAR11 population.

In Figure 5, where the toxin level surpasses the antitoxin, the death rate will increase due to the heightened levels of toxin. The increased death rate causes the SAR11 population to fall.

In Figure 6, the population initially experiences a short dip as a result of the toxin not yet being neutralized. However, since the toxin production is low enough to later be neutralized by the antitoxin, there will be a lower death rate for SAR11, and the population will rebound. This allows the SAR11 to continue growing to its carrying capacity.

Fig 5. Low bacterial count S-M-a specific relationship

Fig 6. High bacterial count S-M-a specific relationship

Combined View

Fig 7. Low bacterial count all variable relationship

Fig 8. High bacterial count all variable relationship

Stability Analysis

In our biosafety mechanism, we design our toxin-antitoxin system to act dynamically in different SAR11 populations, which theoretically leads to unstable equilibriums. In the following section, we aim to perform a stability analysis to validate this argument.

First, we set the system of differential equations to zero and find the equilibrium points. The unique equilibrium (S,M,A,r,a) = (0,0,0,rc,0), defined as E0. Then, we attempt to linearize the system around this equilibrium point by finding the Jacobian matrix at E0, resulting in the matrix J(E0).

\begin{align*} J = \begin{bmatrix} k_S - 2\frac{k_S}{S_c}S - dM & -dS & 0 & 0 & 0 \\ \ \\ k_M - \frac{k_M}{r_c} & -ka & 0 & -\frac{k_M}{r_c}r & 0 \\ \ \\v_A & 0 & -d_A & 0 & 0 \\ \ \\0 & 0 & k_r & -\frac{k_r}{r_c} & 0 \\ \ \\k_a & -ka & 0 & 0 & -kM \\ \end{bmatrix} \end{align*}

\begin{align*} J(E_0) = \begin{bmatrix} 0 & 0 & 0 & 0 & 0 \\ \ \\ 0 & 0 & 0 & -k_M & 0 \\ \ \\v_A & 0 & -d_A & 0 & 0 \\ \ \\0 & 0 & k_r & -\frac{k_r}{r_c} & 0 \\ \ \\k_a & 0 & 0 & 0 & 0 \\ \end{bmatrix} \end{align*}

Then, we calculate the characteristic polynomial of J(E0) by finding |J(E0) - tI|, the determinant of J(E0),

\begin{align*} |J(E_0) - tI| &=\begin{vmatrix} -t & 0 & 0 & 0 & 0 \\ \ \\ 0 & -t & 0 & -k_M & 0 \\ \ \\v_A & 0 & -d_A-t & 0 & 0 \\ \ \\0 & 0 & k_r & -\frac{k_r}{r_c}-t & 0 \\ \ \\k_a & 0 & 0 & 0 & -t \\ \end{vmatrix} \\ \ \\ &= (-t)(-t)(-d_A-t)(-t)(-\frac{k_r}{r_c}-t) \\ \ \\ &= -t^5 - \frac{d_Ar_c+k_r}{r_c}t^4 - \frac{d_Ak_r}{r_c}t^3 \end{align*}

Referring to the Routh-Hurwitz Criterion from Introduction to Linear Control Systems (BAVAFA-TOOSI, 2017), we see there are zero coefficients for the quadratic term. Thus, by the criteria, the solutions to the characteristic polynomial do not all lie on the left complex plane, meaning there will be eigenvalues with non-negative real parts, eventually proving the instability of the system.

Assumption

The dynamics of the biosafety system are described by the model's six essential assumptions.

Cell density is determined by logistic growth kinetics, which includes a per capita growth rate (k_S) and a carrying capacity (S_c). The death rate of bacteria (d) is determined solely by intracellular toxin concentration (M) and discounts environmental and natural causes of death.
The rate of cell death (d) in a cell is directly proportional to the intracellular concentration of toxin (M).
The production of toxin (k_M) is directly proportional to the number of unbounded AHL receptors.
The AHL synthesis rate (v_A) is proportional to cell density (S).
Toxin and AHL degradation are determined using first-order kinetics and rate constants (k and d_A).
AHL to receptor binding and toxin-antitoxin annihilation are determined using second-order kinetics and rate constants (k_r and k).

These assumptions serve as the foundation for this mathematical model used to study system behavior and regulatory dynamics under ideal circumstances.

Limitations

There are several factors that we did not consider in our model that may affect the behavior of our mechanism. The first of these is that we modeled the bacterial population in a closed system with a constant volume. However, this mechanism is to be implemented in real-world ocean conditions, in which currents will affect the bacterial concentration and may cause its decrease through the dispersion of bacteria. Likewise, ocean environments may also differ in temperature, pH, salinity, and other factors that may affect the growth rate and survival of bacteria.

Conclusion

Through our biosafety mechanism, we aim to control the spread of our engineered bacteria. When the bacteria is located in the intended delivery area, we would like to limit the effect of our biosafety mechanism, allowing it to grow unrestricted by the mechanism. However, when the bacteria escape from the coral, we attempt to quickly eliminate the population. By running our mathematical model through simulations in Matlab, we are able to visualize the desired dynamics between the engineered bacteria, toxin, and antitoxin. Our biosafety model portrays an unstable equilibrium, which is the natural result of the desired functionality of our system. Our stability analysis seconds this instability, ensuring the elimination of escaped bacteria through the toxin.

References

BAVAFA-TOOSI, Y. (2017). Introduction to Linear Control Systems. Academic Press.

Chesla, S. E., Selvaraj, P., & Zhu, C. (1998). Measuring two-dimensional receptor-ligand binding kinetics by micropipette. Biophysical journal, 75(3), 1553-1572. https://doi.org/10.1016/s0006-3495(98)74074-3

Jin, Y., Yu, J., & Yu, Y. G. (2002). Identification of hNopp140 as a binding partner for doxorubicin with a phage display cloning method. Chemistry & biology, 9(2), 157-162. https://doi.org/10.1016/s1074-5521(02)00096-0

Nikolic, N., Bergmiller, T., Vandervelde, A., Albanese, T. G., Gelens, L., & Moll, I. (2018). Autoregulation of mazEF expression underlies growth heterogeneity in bacterial populations. Nucleic acids research, 46(6), 2918-2931. https://doi.org/10.1093/nar/gky079

Wang, N. R., & Hergenrother, P. J. (2007). A continuous fluorometric assay for the assessment of MazF ribonuclease activity. Analytical biochemistry, 371(2), 173-183. https://doi.org/10.1016/j.ab.2007.07.017

You, L., Cox Iii, R. S., Weiss, R., & Arnold, F. H. (2004). Programmed population control by cell–cell communication and regulated killing. Nature, 428(6985), 868-871. https://doi.org/10.1038/nature02491

LCA Model

Introduction

Latent Class Analysis (LCA) is frequently employed in statistical analysis for analyzing individual choices in the context of discrete choice experiments. LCA is used to identify such clusters according to the observed variables’ characteristics. In this study, we perform an LCA on results gathered from our survey regarding the willingness to pay (WTP) for coral conservation. We aim to explore the impact of respondents' socioeconomic variables on their willingness to pay, seeking insights for more effective coral conservation promotion.

Survey Design

Surveys have been designed to investigate public WTP in different scenarios (Imamura et al., 2020). Our team first conducted a pre-test survey before the outpour of the official survey.

As the following table shows, we gave the respondents 3 different hypothetical conservation scenarios, towards which one would be willing to contribute monetarily: extended conservation scenario 1, extended conservation scenario 2, and normal conservation scenario; these scenarios had 70%, 50%, and 10% maintenance effectiveness, respectively. We gathered the respondents’ WTP through a free response question that directly asked them to state their WTP for each conservation scenario.

Fig 1. Pre-Test Survey

From our pre-test results, several modifications were made to our official survey. We simplified the desired responses of WTP into three discrete choices: 0, 400, and 600 NTD, based on clusters observed and the removal of outliers. Due to the high emergence in the pre-test, we included two additional choices for respondents who have no interest in paying, which are: "Coral sightings should be free" and "I think this issue shouldn't be prioritized.”

Method

Participants and Procedure

The data for LCA were collected from the official survey, with a total of 460 samples of Taiwanese people’s WTP for coral conservation. We believe 8 factors affect each respondents willingness to pay:age, education level, household size, monthly income, frequency of visiting beaches or marine parks, frequency of participating in ocean charities, whether they have houses near the oceans, and whether they have seen coral reefs before (Imamura et al., 2020). For the discrete choices in the questions, we convert them from categorical data into numerical data (1 to 5). In our survey, three groups are classified by different levels of WTP. The first group includes 54.1% of respondents who are paying NTD 600 to reach an extended conservation scenario 1; the second group includes 22.2% of respondents who are paying NTD 400 to acquire an extended conservation scenario 2; and the third group includes 23.7% of respondents who are paying NTD 0 to maintain a normal conservation scenario.

Latent Class Analysis

LCA was employed to identify latent classes among the 8 variables and WTP. We utilize Jamovi, a free software used for statistical analyses, to fit our data into different numbers of classes. To choose the model with the best fit, we observe the changes in Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values, which are estimators of prediction errors for a given set of data. A lower AIC or BIC value indicates that the specific classification system is a more suitable fit for the data. With a suitable number of classes, we can then explore the underlying factors that are potentially influencing one’s WTP.

Empirical Results Analysis

Table 1 showcases the frequency of each socio-economic characteristic from the total sample under the three “willingness to pay choices” respectively.

We see that Willingness To Pay is negatively correlated with the INCOME factor. This can be derived from Table 1, in which 133 (53.7%) of the 248 respondents who are willing to pay 600 NTD are students with no income. Comparing these 133 student respondents to the total 217 student respondents, 61.3% of the students who filled out the survey chose the 600 NTD conservation plan over the 0 and 400 NTD plans. Moreover, 45.5% of the individuals who make 40,000 - 60,000 NTD a month are only willing to pay 400 NTD for coral conservation, while 58% of individuals who earn minimum wages of 25,000 NTD a month are willing to pay the maximum 600 NTD. Also, the CHARITY factor also plays a big role in one’s willingness to pay, as out of the 7 respondents who frequently donate to ocean-related charities, 6 (85.7%) of them are willing to pay 600 NTD for coral conservation.

Table 1. Frequency of socio-economic factors for each WTP amount

Table 2 displays the fit indices, AIC and BIC, for each class size respectively. Our team created four separate models, each had a different number of latent classes ranging from two to five. The three-class model is considered the best-fit model, for it having the lowest average of the two fit indices statistics (7303.5) out of all the models.

Table 2. Fit indices from latent class analysis

Fig 2. Latent class solution of willingness to pay.

Slicing up the 3 latent classes, we dig into the quantitative distribution of the composition of each class, which is critically shown in Figure 2 above. Very quickly we see that there are factors showing little differences in relation to WTP: CORAL, HOUSEHOLD, OCEAN, VISITS. We also see that Class 2 has the highest willingness to pay, followed by class 1 and class 3 (by a considerable margin), respectively.

Between AGE and EDUCATION, a set of roughly parallel lines can be observed from Figure 2, indicating the occurrence of the Salsa effect. This suggests that a monotonic sample may have been coerced into the classes, and the identified classes may just be representative of severity scales of both AGE and EDUCATION.

In the following, Table 3 serves as reference to the quantitative results from all 8 variables, Table 4 shows the numerical averages of each character from all 3 classes. When examining the influence of age on WTP, it is evident that Class 2, primarily composed of respondents aged 30-49 (3.37), demonstrates the highest WTP. Conversely, Class 1, consisting mainly of teenagers (18 and below) with a WTP of 1.33, represents the lowest WTP group. Class 3, with an average age of 2.97, suggests a prevalence of respondents aged 50 or above. These findings imply that older individuals and teenagers are most willing to support coral conservation, while middle-aged individuals are less inclined or entirely unwilling to do so.

Table 3. Quantitative translations of survey responses

Table 4. Numerical composition of each class in Fig 1.

Correlation Matrix and T-Test

A correlation matrix is employed to provide numerical relevance between all 8 factors and WTP. The correlation matrix utilizes the Pearson-r value, which ranges from -1 to 1, and the closer the number is to 1 or -1, the stronger the correlation is between the two variables.

Table 5. Correlation Matrix Data

There is a strong, positive relationship between AGE and INCOME (0.663)
There is a moderate, positive relationship between AGE and EDUCATION (0.389)
There is a moderate, positive relationship between CHARITY and WTP (0.204)
There is a weak, positive relationship between EDUCATION and WTP (0.051)
There is a weak, positive relationship between INCOME and WTP (0.073)
There is a weak, negative relationship between AGE and WTP (-0.071)

Furthermore, a T-Test is performed to verify the relationship between the four significant factors (AGE, EDUCATION, INCOME, CHARITY) and WTP. The T-Test tells us whether or not we can completely reject the null hypothesis. The null hypothesis states there is no relationship (or an insignificant relationship) between two variables. Our team looked into the p-value we acquired from the T-Test, rejecting the null hypothesis when the p-value is less than 0.05.

Significant Factor	p-value
AGE	0.82
EDUCATION	0.257
INCOME	< 0.001
CHARITY	< 0.001

Table 6. Significant factors and its respective p-value

The t-test statistics shows that:

Can reject the null hypothesis

INCOME versus WTP(<0.001)
CHARITY versus WTP (<0.001)

Can’t reject the null hypothesis

AGE versus WTP (0.82)
EDUCATION versus WTP (0.257)

We conclude that the INCOME and CHARITY factor’s effect on one’s WTP is significant, thus, it is valid that our latent classes separate respondents based on these two factors. EDUCATION, though not as significant as INCOME and CHARITY, still shows signs of having some effects on WTP. However, AGE has a relatively high p-value, suggesting its weak correlation with WTP.

Conclusion

Through latent class analysis, we discovered that the three main socio-economic characteristics that influence an individual’s willingness to pay for coral conservation are AGE, EDUCATION, and INCOME. Those who are the oldest in age, are the best educated, and have the highest income (Class 1), are the most likely to pay to support conservation plans or programs. Following close as the second most willing to pay group is made up of young teenagers with no income (Class 2). Class 3 is the least likely to pay, which is composed of middle-aged individuals, mostly under or overgraduate that make around 40k to 60k a month. Furthermore, through the CHARITY factor, our team is able to draw the conclusion that young teenagers (Class 1) are highly engaged in ocean conservation and are willing to support these programs despite being students and having no income at all.

We understand potential biases in the survey results are inevitable. Range bias that may inaccurately reflect respondent’s true WTP as they are limited to the given choices, and mental accounting bias which can lead to respondents overestimating their true WTP, are all possible. Our sample size of around 500 people limits the availability to generalize our results to the total population.

Correlations between the variables also gave us positive ideas when looking into coral conservation in the future. Strengthening marine ecological conservation education at all education levels will not only help expand the spread of conservation knowledge, but also increase chances for one to participate in related charities. Government can also consider lowering ticket prices for marine parks. This shifts the purpose of marine parks from profiting off visitors to allowing people to form emotional connections with corals and bring greater benefits to the entire marine ecosystem.

Beyond this research, we believe every iGEM team will come across some form of experimental data, and would love to gain insights from the hidden patterns within.

Latent Class Analysis Tutorial:
https://video.igem.org/w/3USAB1CH7bKbUKcANdLY2h

Reference

Grafeld, S., Oleson, K., Barnes, M., Peng, M., Chan, C., & Weijerman, M. (2016). Divers' willingness to pay for improved coral reef conditions in Guam: An untapped source of funding for management and conservation?. Ecological Economics, 128, 202-213. https://doi.org/10.1016/j.ecolecon.2016.05.005

Imamura, K., Takano, K. T., Kumagai, N. H., Yoshida, Y., Yamano, H., Fujii, M., ... & Managi, S. (2020). Valuation of coral reefs in Japan: Willingness to pay for conservation and the effect of information. Ecosystem Services, 46, 101166. https://doi.org/10.1016/j.sapharm.2016.11.011.

Schreiber, J. B. (2017). Latent Class Analysis: An example for reporting results. Research in Social & Administrative Pharmacy, 13(6), 1196–1201. https://doi.org/10.1016/s1074-5521(02)00096-0

Seenprachawong, U. (2003). Economic valuation of coral reefs at Phi Phi Islands, Thailand. International Journal of Global Environmental Issues, 3(1), 104-114. https://doi.org/10.1504/ijgenvi.2003.002413

Tseng, W. W. C., Hsu, S. H., & Chen, C. C. (2015). Estimating the willingness to pay to protect coral reefs from potential damage caused by climate change—The evidence from Taiwan. Marine pollution bulletin, 101(2), 556-565. https://doi.org/10.1016/j.marpolbul.2015.10.058

Economic Model

Overview

Coral reefs, essential for ecological balance and economic stability, are threatened by human-induced pressures. This research starts by addressing the existing gap in comprehensively valuing their direct, indirect, and non-use contributions. We assess their economic benefits from fisheries and tourism, as well as indirect services like coastal protection and water treatment. Our findings highlight the significant value of coral reefs, suggesting a need to reevaluate conservation funding strategies. A holistic resource allocation approach that considers all coral reef values is essential for optimal environmental outcomes.

We aim to answer three economic research questions:

What values do corals hold?
What would the total monetary value of corals in Taiwan be?
How should we allocate the conservation fund to reach maximal environmental benefits from corals?

Q1: What values do corals hold?

Among all ecological services, coral reefs lead in total monetary value (De Groot R. et al., 2012).

Fig 1. Range and the average of the total monetary value of the bundle of ecosystem services per biome (in Int. dollar/ha/yr 2007). The total number of values per biome is given between brackets; the average of the value range is shown as a star (De Groot R., et al., 2012).

Coral reefs represent the ocean's most diverse ecosystem, with unparalleled biological productivity. They offer an extensive array of benefits and services, such as supporting fisheries, promoting marine tourism, safeguarding coastal areas, and contributing to medicinal research. Without coral reefs, the coasts of Taiwan could be endangered as waves and storms become larger, eroding the coasts, and jobs that rely on the existence of coral reefs could be lost.

Coral reefs offer more than just scenic views; they provide a range of economic benefits. Their direct use values, the benefits provided by an ecosystem that is directly linked to the economy, come from resources like fisheries and tourism attractions. They also offer less obvious advantages for research and education. Beyond direct benefits, reefs play an important role in coastal protection, an example of an indirect use value, helping to maintain water quality and reduce erosion. Even more, they hold non-use values: We value their existence even if we don't directly use them because they preserve biodiversity, offer future research potential, and fulfill an ethical duty to protect vulnerable ecosystems. As we consider using probiotics to help these reefs, we believe it's crucial to understand the various benefits corals bring.

Fig 2. Total Economic Value map

Direct Use Values

A crucial foundation for fisheries, their complex structures create essential spawning, nursery, and feeding grounds for a diverse range of marine species. This intricate habitat ensures the productivity of local fisheries, which in turn supports global seafood chains. With these thriving ecosystems, communities find sustenance, and economies thrive. Parallelly, the allure of these underwater wonders greatly bolsters Tourism. As divers, snorkelers, and marine enthusiasts are drawn to the spectacle of vibrant reefs, they fuel local economies, providing jobs and bolstering industries from hospitality to transport. The direct correlation between a healthy reef and a flourishing tourism industry cannot be overstated. Additionally, the reefs play a supporting role in Aquaculture, fostering an environment conducive to the breeding and growth of myriad marine species. This symbiosis enhances seafood production, underscoring the tangible interconnected benefits of coral conservation.

Indirect Ecological Services

Beyond direct economic benefits, reefs render indispensable ecological services. As natural fortifications, they offer invaluable Coastal Protection. Their robust structures diminish the erosive power of waves, defending shorelines and making them havens for coastal settlements. Additionally, through their intrinsic capacity for Water Treatment, reefs act as sieves, trapping sediment and pollutants. This function ensures clearer waters, benefiting both marine ecosystems and human activities. Furthermore, reefs are catalysts for Biomass Production, nurturing intricate food webs that sustain a plethora of marine organisms. By championing reef conservation, we highlight the pivotal role these ecosystems play in the broader health and balance of marine environments.

Non-use Values

However, the value of reefs transcends utility. Many harbor an intrinsic appreciation for these marine wonders, recognizing their significance even without direct benefits. This sentiment often translates into a societal Willingness to Pay for their protection and conservation, which is an essential study we have studied in our Willingness to Pay statistical model. Emphasizing this perspective brings to light the deeper appreciation and ethical responsibility we hold, ensuring that coral reefs are cherished for the present and future generations.

Q2: What would the total monetary value of corals in Taiwan be?

The assessment of the total economic value of natural resources poses a significant obstacle: how to assign a monetary value to the goods and services offered by coral reefs, which are usually not subject to market transactions. With the structure outlined in Q1, in this section, we attempt to put a number on the total economic value of Taiwan’s coral reefs. Utilizing the works of Cesar in Hawaii's evaluation (P. v. Beukering and H. Cesar, 2004) as a guideline, our selection focused on 4 values: recreational, fisheries, coastal protection, and biodiversity (Fig. 3).

Fig 3. Subdivision of total economic value of coral reefs

Coastal protection

With an average of 3.7 typhoons and damages surmounting NTD 12.8 billion (398 USD million) per year (Kuo, 2022; Wu & Kuo, 1999), the role of coral in protecting coastal ecosystems is vital. To calculate the economic value of the coastal protection of coral reefs, we determined the net benefit of coastal protection in Southeast Asia through the earlier work of Cesar (2003), which is 0.0567 USD million per reef area (square kilometer). To determine the total area of Taiwanese coral reefs, we derived it by multiplying the proportion of Taiwanese coral reef area with the global coral reef area (500 km^2 out of 700,000 km^2) (Data acquired from interview with Professor Tang) by the estimated global coral reef area of 259,647 km^2 (GCRMN, 2021), resulting in a calculated area of 185 km^2. Multiplying our result with the net benefit of coastal protection provides insight into the monetary value of coastal protection, which is 10.48 USD million provided for Taiwan, and the consequences if they were to bleach and die.

Fisheries

By referencing the previous work of Cesar, we estimate the impact of coral reefs on the economic value of fisheries in Southeast Asia (2003), adding up to a potential net benefit of 0.0256 USD million per km square. We then calculated the net value in Taiwan, which was 4.72 USD million.

Recreational value

Recreational benefits refer to individuals' benefits from engaging in recreational activities associated with coral reefs, such as snorkeling, scuba diving, and marine park visits. We calculated the potential net gain of coral reefs in Southeast Asia with Cesar’s value to be 0.0547 million US dollars per square kilometer. Subsequently, we determined that the net benefit within Taiwan amounts to 10.06 USD million.

Biodiversity Value

To capture the biodiversity value of coral reefs, we created a three-dimensional Excel graph consisting of people from different age ranges and income levels based on our empirical results in our willingness-to-pay(WTP) survey (Link to LCA page). We examined the WTP value for each age range and income level and generalized our data to the entire Taiwanese population to understand Taiwan’s average willingness to pay, obtaining the distribution of the average WTP in Taiwan in Figure 4. Then, we divided the value by the total coral reef area in Taiwan to get the biodiversity value of coral reefs in Taiwan, which is approximately 0.91 US$ million.

Fig 4. Distribution of average WTP in Taiwan

Total Economic Value

Summing all four constituent values, the total economic value of Taiwanese coral reefs is 26.17 US$ million.

Q3: How should we allocate the conservation fund to reach maximal environmental benefits from corals?

Introduction

In 2022, the Taiwanese government's environmental conservation expenditures were allocated 7.7 USD$million for marine conservation (Taiwan Legislative Yuan, 2023). However, when allocating conservation funds for coral reef protection, a key question emerges: Should we focus on critically damaged areas or spread funds across various reefs? Traditional methods often neglect the intertwined nature of environmental benefits, such as the cumulative impact observed when biodiversity in a reef improves after surpassing a conservation threshold. We argue that a more effective strategy would embrace the unique characteristics of each reef, emphasizing comprehensive planning and recognizing the interplay between different reef-related resources. The goal should be holistic environmental enhancement, not just reef area conservation.

Conservation Benefit Maximization

Fig 5. Environmental Benefits of Resource Conservation (Wu & Boggess, 1999)

Imagine two reefs competing for conservation funds. Fig 5 plots the total environmental benefit against conservation expenditure, assuming a logistic growth to a maximal capacity. We observe a surge and a plateau in the growth rate of B before and after a certain inflection point, we call that our environmental threshold.

Fig 6. Marginal Benefit (MB) Graph (Wu & Boggess, 1999)

Fig 6 is the derivative of Fig 5, where a spike in marginal benefit can be observed. Post-climax, these marginal benefits decline sharply, suggesting that every additional investment unit after the threshold yields a lesser environmental return. In our graph, M_bar represents the funds are allocated, M_0 represents the inflection point in Fig 5, where the growth of gain in MB is maximized, and M_m represents the maximum amount of MB that can be gained. We argue that when funds are allocated evenly, maximal marginal benefits will not be reached for each coral site. The following discussion explores the different fund allocation cases and coral quality differences.

We discuss how funds should be allocated to two different regions of coral reefs with equal quality, meaning that Fig 6 for both regions would be identical. Under this assumption, we discuss three funding scenarios, each with different levels of funds available. The three scenarios discussed in this section are when M_bar < M_0 (low budget), M_0 < M_bar < 2M_m (average budget), and 2M_m < M_bar (high budget).

Fig 7. Fund allocation between two identical reefs with a low budget (< M0) (Wu & Boggess, 1999)

We utilize the framework of the allocation graphs from Wu & Boggess (1999), where the Y-axis represents the marginal benefit and the total program budget is equal to the separation between the two vertical axes (whole X-axis), and each point on the horizontal axis represents an allocation.

When M_bar < M0 (low budget), all funds should be allocated to one region to gain the maximal MB. If funds are allocated equally to both regions, the MB gained are only those in the middle, red-shaded region. However, when funds are allocated to just one region, the marginal benefits from equal allocation are preserved, and an extra portion of MB, the blue-shaded portion, is also gained.

Fig 8. Fund allocation between two identical reefs with an average budget (M0 < < 2Mm) (Wu & Boggess, 1999)

When M_0 < M_bar < 2M_m (average budget), or when the allocated funds are enough to fulfill one MB graph but not both, funds should first be allocated to one region only until M0 for one region is reached, then the remaining funds will be allocated to the second region. This maximizes the MB and adds an additional blue-shaded part of the MB on top of the always-reached red-shaded part. Thus, achieving a higher cumulative benefit than an equal allocation.

Fig 9. Fund allocation between two identical reefs with a high budget (2Mm < ) (Wu & Boggess, 1999)

When 2Mm < M_bar (high budget), the MB peaks of the two regions no longer overlap, thus by moving the funds allocated away from the midpoint, representing equal allocation, MB would be lost from one region while the other region retains what was already gained. This meant that there would be a net loss of MB if the funds allocated were not equally distributed. Therefore, an equal allocation split is desired when ample funds are available.

However, the previous scenarios are idealistic since real reefs will have differing qualities. Thus, a more realistic discussion is required. We assume that the reef with less quality will have a greater potential MB, meaning that its peak will be higher than the MB peak of the higher-quality reef (Fig 10).

Fig 10. Fund allocation between two reefs with different levels of MB (Wu & Boggess, 1999)

If A1 (representing the benefit from the low-quality coral reef) is larger than A2, then the additional benefit from the low-quality reef surpasses that of the high-quality reef. In such cases, funds should first go to the low-quality reef, as its marginal benefit (MB) exceeds that of the high-quality one. If, however, A2 is larger, funds should prioritize the high-quality reef for greater MB.

In the case of Taiwan, where conservation funds are at 7.7 million USD, we believe Taiwan would match Fig 8 (average budget), with funds being enough to provide maximum MB for one coral reef but not enough for two or more coral reefs. Thus, conservation efforts must be focused and not spread across many regions.

Taiwan-specific evaluation

In Taiwan, there are 7 coral hotspots, as shown in Fig 11: the Northeast Coast, East Coast, Green Island, Lanyu, Kenting, Xiao Liu Qiu, and Penghu (starting from the top and going clockwise). Based on a 12-year report health report on Taiwan coral reefs (台灣珊瑚礁體檢12年成果報告) done by the Taiwan Environmental Information Association, the coral reefs are categorized into three different qualities, represented by the three different colors used to draw the graphs shown in Fig 12 (Green>Yellow>Red).

Fig 11. Taiwan’s coral hotspots and their quality

With different qualities, the Marginal Benefit (MB) graphs would also look different: green representing the highest quality, having the greatest growth rate and highest MB maximum; red representing the lowest quality, having the slowest growth rate and the lowest MB maximum.

Fig 12. MB graphs corresponding to three different situations of Taiwan’s coral sites

Our ideal allocation model prioritizes funding based on coral quality and potential environmental benefits. Below, we analyze the factors attributed to determining optimal conservation expenditures under five different levels of funding, and the results are visualized in Fig 13.

Fig 13. The ideal fund allocation order in Taiwan

To start, we allocate resources to maximize the Marginal Benefit (MB) for the green region known as Lanyu. Our fundamental belief is that directing substantial funds to reefs of superior quality should take precedence over any distribution to other areas.

Subsequently, we choose Kenting out of the three yellow regions. Kenting is located at the southernmost tip of Taiwan, which boasts exceptionally heat-resilient reefs and serves as a benchmark to determine the impacts of temperature on other coral regions.

Afterward, we allocate resources to the Penghu region over Green Island. Penghu's corals have demonstrated remarkable resilience after surviving a mass bleaching event, highlighting their intrinsic strength. Moreover, the proximity of Lanyu and Green Island leads us to believe that any improvement in the condition of Lanyu would also indirectly benefit Green Island.

Between Green Island (yellow) and the Northeast Coast (red), we believe that the Northeast Coast is a better recipient of conservation funds. Despite being labeled as red, signifying high endangerment, revitalizing these corals could potentially be pivotal to transforming Taiwan’s marine ecosystems. With projected cooler temperatures in the northern regions, this area could emerge as Taiwan's primary coral sanctuary.

Once the maximum MB of the Northeast Coast is reached, we choose Green Island over the East Coast due to its better health condition and resilience from mass bleaching events, despite the East Coast holding prominent value in coastal protection.

Currently in Taiwan, the inefficacy of the allocation is evident, as shown in Fig 14. Based on a logistical function (as shown in Fig 15), optimal benefits are achieved when allocations reach the function's inflection point—a currently unmet threshold. Our proposed model offers the promise of enhancing overall benefits compared to the existing methodology.

Fig 14. Current coral preservation fund allocation (Left)

Fig 15. Our ideal coral preservation fund allocation (Right)

Conclusion

Coral reefs in Taiwan are fundamental economic pillars, providing direct support to vital sectors, offering indispensable ecological services, and embodying societal acknowledgment of their criticality through non-use values. Economically, these reefs, with a valuation of 26.17 US$ million, rank among the top tiers of ecosystem services, underscoring the pressing need for dedicated conservation measures. Meanwhile, strategic allocations of conservation funds would preserve the multi-faceted benefits that corals provide.

In light of the invaluable importance of Taiwan's coral reefs and the mounting challenges they face, both the Ocean Affairs Council (OAC) and the Environmental Protection Administration (EPA) could play pivotal roles. The OAC, responsible for maritime policies, can spearhead coral reef conservation and restoration initiatives. Meanwhile, the EPA should enact stringent greenhouse gas emission guidelines and regulations specifically designed for the marine environment. Our three discussions aim to offer deeper marine conservation insights for policymakers. Effective policy changes today can yield significant long-term benefits, safeguarding coral ecosystems for future generations.

Reference

Burke, L., Spadling M., & Selig, L. (2002). Reefs at risk in Southeast Asia.

Cesar, H.S.J.S.J., & Beukering, P. (2004). Economic Valuation of the Coral Reefs of Hawai'i. Pacific Science, 58(2), 231-242. doi:10.1353/psc.2004.0014.

Cesar, H., Burke, L., & Pet-Soede, L. (2003). The economics of worldwide coral reef degradation

Compilation, A. G. (2008). Economic values of coral reefs, mangroves, and seagrasses. Center for applied biodiversity science. Conservation International, Arlington, VA, USA. http://www.seaturtle.org/PDF/ConservationInternational_2008
_Economicvaluesofcoralreefsmangroves.pdf.

De Groot, R., Brander, L., Van Der Ploeg, S., Costanza, R., Bernard, F., Braat, L., ... & Van Beukering, P. (2012). Global estimates of the value of ecosystems and their services in monetary units. Ecosystem services, 1(1), 50-61. https://doi.org/10.1016/j.ecoser.2012.07.005.

TKuo, Y. L., Liu, Y. M., Chu, H. J., & Lee, H. C. (2022). Are the Rich less Prone to Flooding? A Case Study on Flooding in the Southern Taiwan during Typhoon Morakot and Typhoon Fanapi. Natural Hazards and Earth System Sciences Discussions, 1-19. https://doi.org/10.5194/nhess-2022-38.

Magalhães Filho, L., Roebeling, P., Bastos, M. I., Rodrigues, W., & Ometto, G. (2021). A global meta-analysis for estimating local ecosystem service value functions. Environments, 8(8), 76. https://doi.org/10.3390/environments8080076

Moberg, F., & Folke, C. (1999). Ecological goods and services of coral reef ecosystems. Ecological economics, 29(2), 215-233. https://doi.org/10.1016/S0921-8009(99)00009-9

Souter, D., Planes, S., Wicquart, J., Logan, M., Obura, D., & Staub, F. (Eds.). (2021). Status of coral reefs of the world: 2020 report. Global Coral Reef Monitoring Network (GCRMN) and International Coral Reef Initiative (ICRI). https://doi.org/10.59387/WOTJ9184

Wu, C., & Kuo, Y. (1999). Typhoons affecting Taiwan: Current understanding and future challenges.Bulletin of the American Meteorological Society, 80(1), 67-80. https://doi.org/10.1175/1520-0477(1999)080%3C0067:TATCUA%3E2.0.CO;2

Wu, J., & Boggess, W. G. (1999). The optimal allocation of conservation funds. Journal of Environmental Economics and management, 38(3), 302-321., https://doi.org/10.1006/jeem.1999.1091

墾丁國家公園資源經濟效益評估-兼論資源保育之哲學觀與資源價值之內涵. 國家公園學報, 11, 2001, 1: 1-29. http://ntur.lib.ntu.edu.tw/handle/246246/178164

台灣珊瑚礁體檢12年成果報告(2009~2020). 環境資訊中心. (2022, June 7). https://e-info.org.tw/node/234252