The population-dynamic model incorporates three components: a three-dimensional coupled physical–biological model that provides temperature, food, and currents to influence growth and movement of A. aurita; a Lagrangian particle-tracking model that simulates movement and determines positions of A. aurita; and an energy balance model that regulates the growth of medusa ( Figure 1 ).

Data for model validation are from laboratory experiments and field surveys. Aurelia aurita ephyrae were incubated at 18°C with food concentration of 0.1 mg C L⁻¹ and without food in the laboratory to get the respiration and growth processes. The feeding rate of A. aurita medusae with bell diameter of 2 cm at different food concentrations was obtained by incubation experiments. Ephyrae and medusae in the experiments were sampled from the Jiaozhou Bay. Details on laboratory experiments can be found in Wang (2015). Bell diameters from May to September in 2011 were obtained by surveys conducted in the Jiaozhou Bay. Ephyrae and young medusae were selected and identified under a dissecting microscope immediately after towing and measured with a vernier caliper. For detailed descriptions, refer to Wang and Sun (2015).

The multiple linear regression method is utilized to quantify the relationship of interannual variations of A. aurita biomass with controlling factors. It is a statistical technique that uses several explanatory variables to predict the outcome of a response variable. When analyzing the links of A. aurita abundance and individual weight with temperature, one-variable linear regression is used for abundance against temperature duration suitable for strobilation, and a quadratic equation is established between the individual weight and temperature duration suitable for A. aurita growth.

Simulated respiration, growth, and feeding rate are calibrated with laboratory experiments ( Figures 3A–C ). DW of A. aurita ephyrae indicates an exponential decreasing trend against incubation time under respiration, with a determination coefficient of 0.86 between the simulation and laboratory experiment results. With temperature at 18°C and food concentration at 0.1 mg C L⁻¹, DW of ephyrae rises monotonically with a determination coefficient of 0.98. The feeding rate of A. aurita medusa increases monotonically against food concentration with a determination coefficient of 0.99.

Simulated bell diameter during A. aurita growth period is compared with field observations in the Jiaozhou Bay in the Yellow Sea ( Figure 3D ). The simulated variation of the bell diameter is similar to that of the observations. The bell diameter is overall <10 mm in early and mid-May, suggesting that the ephyrae is released shortly. It increases markedly through the end of May to July, with the maximum bell diameter of about 175 mm in mid-July. After the peak time, the bell diameter begins to decrease. The comparison suggests that the model well reproduces the individual growth of A. aurita.

Temperature, zooplankton, and currents influence strobilation, growth, movement, and further population dynamics of A. aurita. Figures 4 – 6 shows monthly distributions of temperature, zooplankton, and currents during April–September in 2011 to present their seasonal variations. Temperature in the upper layer (3.5 m) shows significantly seasonal fluctuations ( Figure 4 ). In April, it is cold in most of the Bohai Sea and northern Yellow Seas with temperature of about 7°C, but relatively warm in the southern part of the Yellow Sea and coastal areas with temperature even >10°C. Considering the temperature of 10°C–16°C for strobilation, ephyrae start to be released in April. In May, temperature increases markedly with most areas >12°C but <16°C and is suitable for strobilation. Temperature continues to rise with values between 16°C and 24°C in June and July and over 24°C in August, but deceases slightly in September.

Zooplankton indicates prominent spatiotemporal variations, with high concentrations in coastal areas and during June–August ( Figure 5 ). In April, the zooplankton concentration is about 0.06 mg C L⁻¹ in the Bohai Sea and shallower areas of the Yellow Sea and over 0.12 mg C L⁻¹ in the vicinity of the coast. It increases in May, June, and July and maintains a high level with concentrations over 0.12 mg C L⁻¹. The zooplankton concentration decreases in August with values over 0.06 mg C L⁻¹ in most areas but decreases drastically in September. During April–September, strong currents occur near temperature fronts (indicated by positions with surface-bottom temperature difference of 0.2°C, Zhang et al., 2020), especially through July–September ( Figure 6 ). In the Bohai Sea, a basin-scale anticyclonic gyre is present in the central area. Overall, the currents flow southward in the west part of the Yellow Sea and northward in the east part.

Seasonal variations of A. aurita population abundance are presented in Figure 7 . In April, ephyrae begin to appear in some coastal areas with low abundance. In May, the abundance becomes prominently high but still near the coast. The jellyfish is apparently dispersed during June to September that suggests the impact of currents on jellyfish distribution. The abundance presents notable spatial differences, with relatively high values more than 1,000 ind km⁻² in coastal areas and the middle Bohai Sea. The bell diameter is small in April and May, increases drastically in June and July, and reaches its maximum around 18 cm in July, but then decreases in August and September ( Supplementary Figure S1 ). The biomass, affected by the abundance and the individual size, indicates a similar variation with the bell diameter ( Supplementary Figure S2 ). The spatial distribution of the bell diameter indicates the characteristic with relatively larger size in the more northern region and smaller size in the more southern region.

Figure 8A shows the time series of A. aurita total biomass, magnitude (total amount), food concentration, and temperature during jellyfish growth period in the BYSs. In early April, the magnitude began to increase due to ephyrae release through strobilization, with the average temperature over 10°C. The magnitude increases rapidly with the rising temperature in May. In early June, it becomes stable as the temperature reached approximately 16°C, and the strobilization is almost done in this year. Due to the low magnitude and the short period of growth, the total biomass was relatively small in April and May. The biomass increases rapidly in June as a result of the rapid growth medusa. In July, the biomass continued to increase and peaked in mid-July. After then, it gradually decreases that associates with the too high temperature and decreasing food concentrations.

Seasonal and spatial distributions of A. aurita abundance in 2012–2017 show similar patterns with that in 2011, which reflects the principle seasonal cycle of the marine system of the BYSs ( Supplementary Figures S3–S8 ). However, quantitative differences exist during these years. Figure 9A indicates variations of yearly peak biomass, the magnitude, and the averaged food concentration during the growth period through 2011–2017. There are notable differences in the peak biomass and the abundance, with the least biomass and abundance in 2013 and the highest biomass in 2017 and the greatest abundance in 2014.

The variations in total biomass and magnitude are not completely consistent. Relatively higher magnitude corresponds to higher biomass during 2012–2015, while this is not case in other years. It is also noted that the variation in the magnitude is <20%, while it is more than 100% for the biomass. This means that both the magnitude and the jellyfish size are important for the biomass variations. The magnitude is controlled by ephyrae release through strobilization that is related to temperature, and the jellyfish size is the result of individual growth that is affected by the food supply and temperature. Factors influencing interannual variations will be discussed in the following section.

This study develops a population-dynamic model to investigate seasonal and interannual variations of the A. aurita population in the BYSs. The model is able to reproduce metabolic processes and individual growth of jellyfish by quantitative comparison with laboratory experiments and field observations and is thus used to research population dynamics. Compared with previous modeling studies, such as the life-cycle model without movement of jellyfish (Henschke et al., 2018; Xie et al., 2021) and simulation of jellyfish movement without considering the individual growth (Moon et al., 2010; Wei et al., 2015; Wu et al., 2017), the model in this study considers both the bioenergetics and the effect of currents on movement of jellyfish A. aurita. It is also noted that the environment factors (such as temperature and zooplankton) at the jellyfish’s position determine its growth. Thus, the model attempts to simulate jellyfish dynamics in the actual ecosystem.

Nevertheless, due to the complexity of the life strategies and habitat of A. aurita and difficulties of adequate field observations, there exist shortcomings in this model. Polyps tend to settle on hard substrate in coastal shallow areas (Toyokawa et al., 2011; Lucas et al., 2012). However, the actual distribution and abundance of polyps in the BYSs is unknown. Therefore, the substrate is assumed to be evenly distributed in waters shallower than 10 m for ephyrae release through strobilation in the model. Vertical mitigation of A. aurita could exist, which is associated with temperature and/or zooplankton distribution, but it differs geographically (Barz and Hirche, 2005; Kogovsek et al., 2012). No vertical mitigation is considered in the current model. Hence, further understanding of these aspects in the BYSs would help improve the model performance.

The ephyrae of A. aurita began to appear in April, and the abundance rises rapidly in May. The biomass increased rapidly in June and peaked in July but decreased markedly in August, which is consistent with the previous general understanding of the abundance and biomass of A. aurita population in the Northern Hemisphere (Möller, 1980; Olesen et al., 1994; Bonnet et al., 2012). In coastal areas of BYSs, ephyrae are observed as early in April, and medusa is observed in June, July, and August (Wang B. et al., 2012; Wang and Sun, 2015; Xue et al., 2021). These observations are consistent with the results of simulations. Spatially, these relatively high abundance and biomass in three bays of the Bohai Sea are in agreement with field observations (Zuo et al., 2016; Wang et al., 2020). In addition, the simulated spatial distribution in these years also indicates aggregation near Hongyanhe Power Plant at the east coast of the Liaodong Bay where jellyfish including A. aurita clogged the cooling water intakes repeatedly in summer (Sun et al., 2019; Zhang et al., 2019).

In order to explore the key influencing factors on the individual growth of A. aurita, the relationship between the average individual dry weight (IW) and food concentration and temperature is statistically analyzed ( Figure 8B ). It is indicated that the relatively higher IW corresponds to a certain range of food concentration and temperature ( Figure 5A ). Overall, when the temperature was >16°C, the IW began to increase significantly. The IW is kept in relatively high levels with temperatures between 16°C and 26°C and food concentration >0.06 mg C L⁻¹. By integration of IW along food concentration, Figure 8C shows the variation of the biomass with temperature. The biomass is quite low with slow increasing rate when temperature is lower than 16°C, increases almost linearly during 16°C–24°C with peak at 24°C, and begins to decrease drastically as temperature continues to rise. When the temperature reaches 28°C, the biomass just remains <5% of the peak.

It is suggested that 16°C–24°C is a suitable temperature range for individual growth of A. aurita in the BYSs, characterized by a nearly linear growth rate against temperature. Longer duration of this range would promote individual growth and therefore higher biomass of A. aurita population. Specifically in the BYSs, the duration is 51, 50, and 45 days for the Bohai Sea, the North Yellow Sea, and the South Yellow Sea ( Table 3 ). The corresponding bell diameter is 11.5, 10.7, and 10.2 cm, respectively, suggesting the effect of duration for growth on the individual size. The characteristic of relatively larger size in the more northern region and smaller size in the more southern region is in agreement with observations (Wang et al., 2020).

To further analyze influencing factors on interannual variations in the biomass, a statistical relationship is established between the biomass and the abundance, effective accumulated temperature (EAT), and the food concentration. The EAT here is defined as the sum of mean temperature subtracting 16°C at jellyfish positions during the growth period from the start time of 16°C to time of the biomass peak. The food concentration is also averaged during this period. First, normalize these four variables through dividing the anomalies by the mean values through years of 2011–2017. Then, get the relationship by the multiple regression method. The regression equation is given as

where pW denotes the normalized biomass; pT, pF, and pN are normalized EAT, food concentration, and the abundance, with the determination coefficient R² over 0.9 ( Figure 9 ).

The contributions of pT, pF, and pN to interannual variations of pW are quantified in Table 4 , indicating their different roles in different years. The biomass shows the lowest in 2013, with the normalized value of −33.4% in which pT, pF, and pN account for 2.3%, −14.8%, and −20.9%, respectively. Therefore, the relatively less magnitude, dependent on strobilization of ephyrae, is mainly responsible for the lowest biomass in 2013, followed by the food concentration. The highest biomass in 2017 corresponds to a normalized value of 34%, with pT, pF, and pN accounting for 15.6%, 10.4%, and 8.0% respectively, suggesting the consistent contribution of the EAT, food concentration, and the abundance. Sensitivity experiments further confirm the combined effects of these factors on interannual variations ( Supplementary Figure S9 ).

If only considering the effect of temperature, another statistical method is introduced. As the biomass is the product of the magnitude and the averaged IW, the magnitude and the averaged IW at the timing of the biomass peak can be singly regressed against temperature-related variables, respectively. The abundance is mainly determined by strobilization of ephyrae. Hence, the abundance is linearly regressed against the duration of the temperature for strobilization (10°C–16°C) ( Figure 10A ). The equation is given as

where N is the magnitude, and x_b is the duration of 10°C–16°C, with the determination coefficient R² of 0.98. Therefore, the biomass can be represented by temperature and food concentrations that are variables in the marine environment. Analysis in Section 3.2 reveals a suitable temperature range for growth of A. aurita. The averaged IW is regressed against the duration of EAT ( Figure 10B ). The equation is given as

where w is the averaged IW, and x _s is the duration of EAT, with the determination coefficient R² of 0.79.

The effect of temperature variations on A. aurita dynamics has been assessed in some coastal regions under the background of climate warming, with the conclusion of climate warming benefiting A. aurita (Holst, 2012; Ruiz Segura et al., 2012). The simplified relationships can reflect the linkage between temperature and jellyfish magnitude and biomass in some ways, despite the complexity of the marine ecosystem. They would contribute to further understanding the impact of temperature on the population dynamics in the warming BYSs (Lu et al., 2021).