Oyster Salinity-Based Habitat Monitoring in Bandon Bay, Surat Thani, Thailand: a Coupled Eco-Hydrological Model Approach

ESEARCH ARTICLE R ScienceAsia 46 (2020): 93–101 doi: 10.2306/scienceasia1513-1874.2020.010 Oyster salinity-based habitat monitoring in Bandon Bay, Surat Thani, Thailand: A coupled eco-hydrological model approach a a,b, b,c Kalanyu Sunthawanic , Kornkanok Bunwong ∗, Wichuta Sae-jie a Department of Mathematics, Faculty of Science, Mahidol University, Ratchathewi, Bangkok 10400 Thailand b Centre of Excellence in Mathematics, CHE, Bangkok 10400 Thailand c Department of Applied Mathematics and Informatics, Faculty of Science and Industrial Technology, Prince of Songkla University, Surat Thani Campus, Surat Thani 84000 Thailand ∗Corresponding author, e-mail: [email protected] Received 16 Jul 2019 Accepted 23 Jan 2020 ABSTRACT: Bandon Bay in Surat Thani Province, Thailand, is one of the most productive aquaculture for oysters. In order to monitor a suitable area for oyster culture related to salinity, a coupled ecological and hydrodynamical model was constructed to describe the interaction between biological and physical processes in estuarine and coastal environments. The oyster food web is modified from the classical NPZ model in which the region of attraction, the existence of equilibrium points, their asymptotic stability conditions, and the non-existence of closed orbit were analyzed. The Princeton Ocean Model with monthly mean surface wind and river discharge was employed for ocean circulation. Finally, numerical simulation has revealed the interrelation between oyster population and their salinity- based habitat, with an output that quantify the consequences for oyster density, leading to suitable oyster culture areas possibly located around the mouths of Tha Chana canal and Thatong canal. KEYWORDS: coupled model, ecological model, hydrodynamic model, oyster, salinity MSC2010: 00A71 34A34 34C60 65M06 INTRODUCTION around the river mouth. The average concentration of each nutrient was approximately 0.06 mg l in a Bandon Bay is an estuary of Tapi and Phumduang / dry season and 0.10 mg l in a wet season. Nutrients rivers, located between latitude 9°10 –9°40 N and / 0 0 are from agriculture fields and shrimp aquaculture longitude 99°20 –99°60 E, covering an estimated 0 0 flowing along the discharge. Consequently, Bandon area of 1070 km2 in Surat Thani Province, Thailand, Bay has become one of the most productive habitat with the total coastline of about 80 km long 1 . [ ] of Thailand for bivalve spawning, breeding, nursery, The abundance of the estuary mainly comes from and shelter. 20 subordinate rivers and channels containing nu- Oysters are suspension-feeding bivalves impor- trients and organic matters. Thai Royal Irrigation tant on both ecological level and economical level. Department reported that Tapi-Phumduang river They naturally inhabit in estuary and brackish water watershed is the biggest source of freshwater, releas- area. Suspended phytoplankton will be trapped and ing monthly discharge around 2 108 m3 in a dry filtered along with the water flow by oyster’s gill. season and more than 10 108 m×3 in a wet season. C. belcheri (white scar oyster) is the main species, These cause a huge load of× phytoplankton support- cultured in this bay 5 . Recently, the occurrence ing the ecosystem and aquaculture, especially the [ ] of heavy rain and flood crisis has caused a low bivalve species such as oyster, cockle, and mussel. salinity spread over the bay. In March 2011, there Phytoplankton is a subset of algae whose growth was a discharge of more than 3000 m3 s, 10 times can be monitored via chlorophyll-a level, usually / more than the average annual amount, flowed into varies from around 2–10 mg m3 2,3 . In addition, / [ ] the bay. A flood crisis may occur in November, Chumkiew et al 4 investigated the concentration [ ] the transition timing between the wet and the dry of nutrients such as NH4 N, NO2, NO3, and PO4 − www.scienceasia.org 94 ScienceAsia 46 (2020) seasons, resulting in as much as 500 million baht deficit in oyster’s value, as higher oyster’s mortality and lower filtration rate may have arisen from lower salinity. + Oysters are in fact osmoconformer; therefore, 21 unbalanced osmotic pressures between inside and 2 outside body’s fluid could be the cause of oyster’s 1+ death. Oysters can tolerate variation in salinity but 2 cannot expose to very low salinity or freshwater for 1+ + 11 a long period of time. Previous field research has 2 2 suggested relation between oyster’s mortality and salinity 7,8 , and Ehrich et al 6 has introduced [ ] [ ] 0 0 an interrelation between oyster’s filtration rate and River Discharge salinity as a hyperbolic tangent function, generally displayed as an S-shape curve. Suitable salinity Fig. 1 A schematic diagram of oyster dynamics. for oysters was recorded in the range of 15–20 psu depending on culture sites and bivalve species. This paper is organized as follows. We first Table 1 Parameters and their ecological meanings. consider an ecological model of nutrient, phyto- Parameter Ecological meaning plankton, and oyster populations. Then a hydrodynamic model based on Princeton Ocean Model D Water flux input and wash out rate will be applied to the observed data to illustrate N0 Concentration of nutrient input P Concentration of phytoplankton input the water current and salinity variation in Bandon 0 a Maximum specific ingestive rate of phyto- Bay. We finally couple the ecological model and 1 plankton they hydrodynamic model to monitor the effect of a2 Half-saturation constant of phytoplankton salinity on oyster population. b1 Maximum specific ingestive rate of oyster b2 Half-saturation constant of oyster ECOLOGICAL MODEL k1 ¶ 1 Conversion factors from nutrient to phytoplankton In this section, we will propose a system of ordi- k2 ¶ 1 Conversion factors from phytoplankton to nary differential equations describing the nutrient- oyster phytoplankton-oyster interactions within the homo- d Oyster’s death rate geneous domain. For convenience, let N(t), P(t), All parameters are non-negative. and B(t) denote the nutrient concentration, the phytoplankton population, and the oyster population at time t, respectively. system of ordinary differential equations: Model formulation dN a1NP = D(N0 N) , The nutrient-phytoplankton-oyster interactions can dt − − a2 + N be illustrated in Fig. 1. The model is based on dP a1NP b1 PB = D(P0 P) + k1 , (1) the following assumptions. River discharge flowing dt − a2 + N − b2 + P into coastal region brings inputs of nutrient and dB b1 PB phytoplankton while outflowing bay water carries = k2 dB, dt b2 + P − out nutrients and phytoplankton [9]. Nutrients are taken up by phytoplankton while phytoplankton are where N(0), P(0), B(0) > 0. The definitions of the grazed upon by oysters, where both of the rates parameters are summarized in Table 1. The equa- are limited and can be described by the Holling tions are non-dimensionalized while the meaning of type II functional response. The growths of phy- parameters are preserved. toplankton and oyster depend on the presence of nutrient and phytoplankton, respectively. Moreover, Theoretical results the layers are thoroughly mixed at all times. Thus Throughout this paper, R+ is the set of nonnegative the dynamic of the nutrient-phytoplankton-oyster real number, n is the Euclidean n-space, and 3 is R R+ interactions can be represented by the following the nonnegative octant. The validity of system (1) is www.scienceasia.org ScienceAsia 46 (2020) 95 asserted by its uniform boundedness which will be equilibrium point E2(N2∗, P2∗, B2∗) exists, where proved in the following lemma. d b2 3 P2∗ = , Lemma 1 Suppose Ω : N, P, B 0 N P k2 b1 d = ( ) R+ ¶ + + B M where M : DfN P /η2 andj 0 < η − a1 P2 ¶ = ( 0 + 0) ¶ N a ∗ ∆ min D,gd . Then all solutions of system (1) starting 0 2 D + p N2∗ = N0 + − − − , in f3 areg uniformly bounded and Ω is the region of 2 R+ k D attraction. 2 B2∗ = [k1(N0 N2∗) + (P0 P2∗)], d − − Proof: Let N t , P t , B t be a solution of sys- a P a N P ( ( ) ( ) ( )) with ∆ : N a 1 2∗ 2 4 1 0 2∗ . tem (1) starting in 3 and define W t : N t = ( 0 + 2 + D ) D R+ ( ) = ( ) + − P(t) + B(t) and 0 < η ¶ min D, d . Therefore, Proof: All equilibrium points E(N ∗, P∗, B∗) of sys- f g tem (1) could be obtained by setting (1) to zero, dW a1NP D N0 N D P0 P a N P dt = ( ) a N + ( ) 1 ∗ ∗ − − 2 + − D(N0 N ∗) = 0, a2 N a1NP b1 PB b1 PB − − + ∗ k1 k2 dB a N P b P B + a N b P + b P 1 ∗ ∗ 1 ∗ ∗ 2 + − 2 + 2 + − D(P0 P∗) + k1 = 0, (2) − a2 + N − b2 + P = DN0 + DP0 DN DP dB ∗ ∗ b P B a−NP − − b PB k 1 ∗ ∗ dB 0. 1 k 1 1 k 1 2 b P ∗ = ( 1) ( 2) 2 + ∗ − − − a2 + N − − b2 + P Solving the third equation of (2), we obtain ¶ DN0 + DP0 ηW, − b P B 0 or k 1 ∗ d 0. where 0 < η ¶ min D, d and k1 ¶ 1, k2 ¶ 1. Then ∗ = 2 b P = dW f g 2 + ∗ − dt + ηW ¶ DN0 + DP0. Applying the differential inequality, we obtain For the case B∗ = 0, System (2) reduces to the following two dimensional nonlinear system ηt (1 e ) ηt 0 W t D N P − W 0 e . a1N P ¶ ( ) ¶ ( 0 + 0) − + ( ) − D N N ∗ ∗ 0, η ( 0 ∗) a N = − − 2 + ∗ (3) a N P Consequently, D P P k 1 ∗ ∗ 0. ( 0 ∗) + 1 a N = − 2 + ∗ lim sup W(t) ¶ M, t Solving system (3), we obtain the oyster-free equi- !1 librium point E1(N1∗, P1∗, 0), where where M := D(N0 + P0)/η.

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