Effects of Bee Density and Hive Distribution on Pollination Efficiency for Greenhouse Strawberries: A Simulation Study

Abstract

The cultivated strawberry Fragaria × ananassa Duch. is widely planted in greenhouses around the world. Its production heavily depends on pollination services. Bee pollination can significantly improve fruit quality and save considerable labor requirements. In this paper, we used a simulation model to study the effects of bee density and hive distribution on pollination efficiency for greenhouse strawberries. Simulation experiments allowed us to obtain the pollination efficiency under different conditions and track every bee, flower, pollen and fruit in detail without great planting cost. In particular, we found that fruit quality cannot be significantly improved once bee density is higher than one bee/plant due to a saturation effect. Distributing bee hives and strawberry interplanting spatially can improve fruit quality. In addition, the simulation results suggested that a continuous bee pollination process can significantly reduce the influence of stigma receptivity. This effect and the even distribution of pollen are the top two reasons explaining how bee pollination outperforms artificial pollination.

1. Introduction

Strawberry is one of the various, low-growing perennial plants of the genus Fragaria in the rose family. The most common strawberries grown commercially are cultivars of the garden strawberry Fragaria × ananassa Duch., which has been the most widely distributed fruit crop in the world. It is grown in every country with a temperate or subtropical climate and even in many tropical countries in highland areas, where the climate is mild. Strawberry fruits are highly prized for their universal appeal to the human senses of sight, smell and taste [1].

Strawberries can be self-, wind- or bee-pollinated. Honey bees (Apis mellifera) are recognized as the main pollinator of the strawberry crop [2]. If there are no honey bees, the combined action of gravity and wind assures the basis of the pollination because the stamens can scatter pollen onto many of the pistils as they open [3]. However, these flowers may not be completely self-fertilizing in this way, which may result in a low fruit-setting rate and malformed fruits. Pollination by bees not only increases crop yield but also improves aspects of fruit quality [4]. Recent research suggests that when strawberry plants in greenhouses were isolated from honeybees, fruit set was 50–59% lower compared to the case where bees were present, which can achieve, on average, 80% of fruit set when bees were present [2,5,6].

Understanding the bee pollination process is relevant for improving strawberry yield and quality [6,7,8]. However, many factors, such as bee foraging behavior, planting pattern and the spatial complexity of the greenhouse environment interacting over time and space, are major obstacles to understanding bee pollination dynamics. For example, bees are attracted by the appearance of inflorescence during foraging, so the foraging patterns might differ in various landscapes [9]. This suggests that the planting pattern in a greenhouse could affect bee foraging distance and direction and consequently result in the dynamics of pollination efficiency. This interaction in space is difficult to understand quantitively without the help of simulation models because bee behavior and plant floral display obvious spatial heterogeneities and vary across individuals [10]. Previous strawberry models focused on strawberry growth processes [11], including modeling the water balance for irrigation [12], statistical yield forecasting via weather conditions [13] and prediction of phenological stages based on regressions [14]. To our knowledge, there is no systematic, holistic study of bee pollination on the strawberry due to the cost. Moreover, there is still no universal explanation for the advantage of bee pollination over artificial pollination.

Hence, we modeled strawberry plants and honey bee foraging behavior for the first time and analyzed the simulation results of fruit production quantitatively. Modeling strawberry pollination allows us to track the total flowers, pollen and fruits and reveals hidden relationships between variant organisms to better understand the pollination service in greenhouse strawberries. According to the results, we proposed some reasonable planting suggestions for strawberry growers. The main contributions of this paper are as follows: (1) We propose a firmly validated simulation model that incorporates much of what is known and hypothesized about the pollination and growth ecology of strawberry agroecosystem; (2) We analyzed the optimal bee density based on the simulation results; (3) The effects of hive distribution, bed spacing and strawberry interplanting in a greenhouse on pollination efficiency were analyzed; 4) For the first time, the quantitative effects of stigma viability on strawberry fruit quality were analyzed, which revealed the top reasons explaining how bee cross-pollination outperforms artificial pollination.

2. Materials and Methods

2.1. Strawberry

The cultivated strawberry Fragaria × ananassa Duch. is widely planted in greenhouses around the world [6]. Therefore, we selected the species because of its extensive history of study [4,15,16,17,18] and economic importance. In this paper, we studied the popular species Red Face. For other species, the simulation software codes include a variety of adjustable parameters on strawberry growth that users can modify to adapt to different species.

2.1.1. Greenhouse

The most popular strawberry cultivation system in China is a solar-powered plastic greenhouse, and this type of cultivation system uses only solar energy for crop production. The greenhouse not only prevents damage caused by adverse climatic conditions but also provides a suitable environment for strawberry cultivation and protects the crop from insects and pests [19]. The microclimate in greenhouses is significantly more suitable than that in an open environment [19].

Strawberry fruit production in China generally takes place from November to April, starting with the planting of bare root transplants in November. There is a close relationship between solar light and the inside temperature in a greenhouse. All the greenhouses were controlled at a fixed temperature and relative humidity condition [20]. Low temperatures will increase the possibility of damaged fruits and changes in fruit size, and high temperatures reduce the plant’s photosynthetic rate [21]. Among the environmental conditions, temperature is one of the most important factors [22] that affect fruit and seed set at different stages of the reproductive development process. The general temperature ranges [19,23] in two weather conditions and four months are shown in Table S1.

Standard greenhouses are usually 80 m long and 8 m wide in China. Strawberry plants were planted on raised beds with a plastic film cover on the soil (plastic mulching). The distance between two strawberry beds is usually about 0.4 m, and the single bed width is about 0.6 m. There are two rows of strawberry plants per bed, about 0.24 m apart. The distance between two strawberry plants is about 0.2 m. As a result, there are 12 rows in the greenhouse and 390 strawberry plants in each row. This standard greenhouse includes 390 × 12 × 2 = 9360 strawberry plants. Beehives are generally arranged on the east side of the greenhouse where the temperature is high, according to practical planting experience. The simplified greenhouse diagram is shown in Figure S1.

2.1.2. Inflorescence and Flower

Strawberry flower clusters occur on a series of double branches with a flower in the fork of each branch [9]. Generally, strawberry plants have one primary inflorescence, two secondary inflorescences and up to four tertiary inflorescences. The existence of competition within inflorescences was demonstrated by obtaining heavier secondary berries after removing the primary [17]. Therefore, only fruits in primary and secondary inflorescences were used to estimate yield, as they are the only fruits usually considered marketable [17]. In order to improve the yield and quality of strawberry fruits, it is usually necessary to cut off some low-level inflorescences in production, i.e., flower thinning. In the simulation, each strawberry plant retains one primary inflorescence and two secondary inflorescences, as showed in

Table 1. Flower information of strawberry in the simulation.

Inflorescence	Number per Plant	Number of Flowers per Inflorescence	Number of Pistils (Ovules) per Flower	GDD for Blooming *
Primary	1	6	350	N(586, 70)
Secondary	2	3	260	N(946, 70)

*: The Growth Degree Day for strawberry plants is assumed to follow normal distribution N(µ,σ²). Note that µ represents the mean value and σ² represents the variance.

.

Strawberry fruit weight and achene number showed a consistent decrease from primary inflorescences to secondary ones. The primary flowers bear about 350 stigmata (ovules), the secondary ones about 260, and the tertiary ones only about 180 [24]. The pistils are arranged in a regular spiral on the stem end of the receptacle. The pistil base, commonly called the seed, contains one ovary. One ovary contains one ovule, and each achene can be considered a single seed that is actually an individual fruit [3].

The strawberry flowers bloom in sequential order, starting with primary inflorescences, followed by secondary inflorescences and finally up to tertiary inflorescences [24]. The primary ones bloom earlier, and the secondary ones bloom later with a time gap of around 20 days [4,25,26,27,28], usually resulting in two harvest peaks in continuous harvests. The average weight of berries produced decreased at each harvest, which is a common experience for strawberry growers [29,30,31,32,33,34]. A flower contains around 25 stamens (anthers) and a large number of strawberry pollen grains [3]. Generally, each anther contains about 18,000 normal pollen grains, and a flower contains about 18,000 × 25 = 450,000 pollen grains.

2.1.3. Strawberry Fruit Weight

Achenes, resulting from fertilized ovules, are large and surrounded by well-developed fleshy tissue, whereas the achenes resulting from unfertilized ovules are less voluminous and closer together. The weight of a berry is proportional to the number of fertilized ovules (achenes), and the number of stigmata per flower determines its potential weight [35]. The primary berry is the largest, and each subsequent berry gets smaller. A secondary berry is about 80 percent of the primary [3]. Therefore, all pistils of the flower must be pollinated for maximum berry size.

It is assumed the fruit is evenly developed and there is a fitted linear equation between fruit weight and total achene number [26,33], which is derived from the observed data:

$$Y=0.05\times X+2.0$$

(1)

where Y is the weight of the strawberry fruit (g), and X is the number of achenes per strawberry fruit [24]. Adjustments have been made to the equation according to the contemporary strawberry empirical data that we collected. It should be noted that the fitted equations for variant strawberry species are not the same.

2.1.4. Malformed Fruit

Fruit malformation is a phenomenon commonly observed in commercial strawberry species with a negative impact on the economic benefit of crop production [23]. Fruit shape, when not damaged by diseases, frost or mechanical action [36], depends on the percentage of fertilized ovules [17]. Malformed fruits have significantly fewer achenes than well-formed fruits, and unfertilized achenes lead to malformation. Successful fertilization and adequate numbers of achenes are necessary for a marketable shape and size of strawberry fruits [37]. The environment in a greenhouse is generally suitable for strawberry growth, so only the influence of pollination is considered in the simulation, while other environmental factors are ignored.

An average of 11 honey bee pollinator visits per flower are required to attain normal berries (fertilization rate, 87%) [38]. Achenes containing fertilized ovules can release a hormone that stimulates the growth of the receptacle. When an achene does not contain a fertilized seed, it remains small, and the receptacle in its area fails to grow [34]. Only fruits with a high percentage (more than 87%) of fertilized achenes will develop normally without major malformations that reduce overall yield and marketability [15]. Fruits are deformed in parts in which achenes are not fertilized. Malformed fruits are common during strawberry production, with an average rate of about 3%–10% [2,32].

Generally, artificial pollination results in a high malformed fruit rate, poor fruit shape and, consequently, low economic benefit in strawberry planting [19]. Bee pollination can reduce malformed fruit rates [2]. However, there is no universal explanation for bee pollination’s advantage over artificial pollination previously.

2.1.5. GDD

Thermal time models are widely used in vegetation phenology, and they are based on the accumulation of growing degree days (GDDs) or heat units. The GDD methodology consists of defining a constant base temperature and then calculating the sum of those temperatures that exceed the base temperature $T_{base}$ in the temperature time series. The parameters for the strawberry development GDD model are based on reference [22,33]. In this simulation, the daily cumulative GDD formula is simplified as:

$$GDD=(T_{max}+T_{min})/2-T_{base}$$

(2)

where $T_{max}$ is the daily maximum temperature, and $T_{min}$ is the daily minimum temperature. In this model, it is assumed that the simulation starts from January 1st for simplicity, and then strawberry plants enter the blooming period in early February and enter the peak of fruit maturity in early March. Based on the reference [31,39], the GDD requirement follows the Gaussian normal distribution.

The blooming time in different inflorescences is also different. Normally, the blooming time of primary flowers is earlier than that of secondary flowers, with an average interval of about 20–30 days. It is assumed that the required accumulated GDD distribution for primary flowers follows N(586, 70), and the distribution for secondary flowers follows N(946, 70). Therefore, there are two harvest peaks, i.e., first harvest and second harvest, due to the blooming time gap [39]. The accumulated GDD requirement for ripeness follows N(284, 30) with $T_{base}$ of 3 °C. The ripening of strawberry fruits is characterized by red coloring and softening. As the temperature when secondary flowers bloom is higher than primary flowers, the time secondary fruit ripens is shorter. The average time for the development of a single fruit in first harvest is about 30 days, while that in second harvest is about 24 days (

Table 2. Accumulated GDD requirements information.

Harvest	Inflorescence Rank	GDD for Ripeness	Time for Ripeness
First	primary	N(284, 30)	About 30 days
Second	secondary	N(284, 30)	About 24 days

). The timing schedule for two harvests and two blooming peak periods are shown in Figure S2.

2.2. Honey Bee

Currently, 80% of strawberry greenhouses use the Apis mellifera, which is highly commercialized for pollination [2,22,40,41,42]. The number of bees is commonly determined by growers based on the greenhouse area and the strawberry planting density. Generally, there are about 4000–8000 bees in one colony [7] in strawberry planting in China, but the hive-leaving rate (number of bees leaving the nest for foraging/total bee number in the hive) is low [43]. In the bee colony, worker bees can be divided into bees doing internal service and bees doing external service according to age. Generally, only about 40% of the worker bees actually forage outside in the greenhouse every day [44], and this proportion is influenced by population structure and food factors.

2.2.1. Bee Activity

Many studies suggest that weather conditions affect the foraging behavior of honey bees, of which temperature is the most important [29,45]. The suitable temperature range for bees to forage is 15–25 °C, and bees will stop foraging when the temperature is below 14 °C or above 30 °C [2]. Affected by the low temperature and weak light, bees are basically inactive on cloudy days and only occasionally active around noon when the temperature is high [21]. Bee foraging activity is set to a period from 8:00 to 17:00 every day [38,46]. In the morning and evening, bees are basically inactive; bees are active from 11:00 to 14:00 [46]. Due to the position of the sun overhead, bees are less active at noon than at 13:00. The activity of bees is mainly affected by the temperature in the greenhouse and can be described by the proportion of bees leaving the nest for foraging at this time period [14,15,31], as shown in

Table 3. The proportion of bees leaving the nest on different hours.

Time	Proportion of Bees Leaving Nest (Sunny)	Proportion of Bees Leaving Nest (Cloudy)	Time	Proportion of Bees Leaving Nest (Sunny)	Proportion of Bees Leaving Nest (Cloudy)
8:00	0	0	9:00	0	0
10:00	1.13%	0	11:00	2.03%	0
12:00	2.70%	0.25%	13:00	3.15%	0.50%
14:00	2.60%	0.25%	15:00	1.20%	0
16:00	0	0	17:00	0	0

. For simplicity, it is assumed that the hive releases bees on the hour scale in the simulation.

During foraging, bees are capable of controlling their flight speed [47] while searching flowers to achieve a tradeoff between searching efficiency and accuracy [48]. In the simulation, a bee can complete one activity every minute, including searching for nearby flowers, visiting flowers and returning to the hive [49]. The process is scheduled by phenology and physiological conditions in the greenhouse.

2.2.2. Bee–Plant Interaction

The flower-visiting pattern of honey bees is centralized and adopts the principle of proximity with continuity and repetition in flower visiting. Normally, bees can visit several flowers in succession on the same inflorescence. After visiting all flowers in one inflorescence, bees will fly to nearby inflorescences nearby to continue visiting. Bees move infrequently among inflorescences, with an average distance of 1.1 m. According to the references [21,43], the average number of flowers visited by bees per minute is 2.5–3.8, the average interval between visits is about 10 s and the residence time of a single flower is about 10 s.

Flower pollination must be successful after 11 honeybee visits [24], and the number of deposited pollen grains for a honeybee per visit is set to 30 [32]. The pollen removal ratio is about 20% [32], so the number of pollen grains removed per visit is about 9000.

It is usually agreed that pollen availability might be a factor in determining which flower to visit. However, as for strawberry flowers, reference [21] suggests bees are not selective in strawberry flowers, and the probability of visiting flowers of different ages is basically equal.

2.3. Strawberry Pollination

Pollination processes mostly happen during the first 4 days after the flowers bloom [16]. In the model, the blooming period of strawberries is set to 5 days. The suitable temperature for pollen germination is 20–30 °C, which is similar to the greenhouse temperature. The proportion of dehisced anthers increased with increasing temperature and peaked at noon, coinciding with the peak pollen-collecting activity of bees [29]. After the deposited pollen successfully falls on the stigma through honeybee activity, the ovule fertilization process comprises two stages: receiving stage and accepting stage.

2.3.1. Receiving Stage

In the receiving stage, the probability of receiving pollen grains of a stigma positively correlates with pollen viability and stigma receptivity [29]. The viability of the pollen deposited by bees onto stigmas is an important component of individual pollination effectiveness [20]. Stigma receptivity is mainly determined by flower age, and the viability hits its peak within three days of blooming and sharply declines in 5 days [50]. Value R ranged 0–1 can be used to quantify the stigma viability, as follows:

$$R=e^{-0.01\times ag{e}^{3.6}}$$

(3)

R represents the stigma viability and age represents the flower age. On the other hand, not all pollen grains carried by bees have high viability. Related research shows the average proportion of pollen with high viability is about 50–70% [36,50], while the mixed saliva of bees when collecting pollen may reduce the viability [20], which results in a 30% proportion of active pollen carried by bees [43]. Therefore, the pollen-receiving rate in this stage can be described as Equation (4). $P_{\mathrm{receive}}$ represents the pollen-receiving rate and age represents the flower age.

$$P_{\mathrm{receive}}=0.3\times e^{-0.01\times ag{e}^{3.6}}$$

(4)

2.3.2. Accepting Stage

In the accepting stage, the pollination process is mainly influenced by strawberry self-compatibility (acceptance rate = mean compatible pollen grains/mean received pollen grains). Hence, even if a pollen grain has high viability and the stigma has high receptivity, it may not necessarily lead to pollen tube growth. These flowers that were pollinated with both foreign and native pollen grains by pollinators can develop large fruits of high quality [19]. There is no correlation between pollen viability and pollen self-compatibility [9].

However, in the actual traditional greenhouse planting, strawberry species are always propagated vegetatively, either by runners or micropropagation. As a result, all strawberry plants are cloned, and each plant within one cultivar is genetically identical to other individual plants. In greenhouses, only one cultivar is usually grown, resulting in genetically identical plants in one greenhouse compartment. Comparing the number of strawberry bee fruit seeds and fruit weight under different pollination patterns, the self-compatibility probability was fixed at 80% in this simulation [18,19,31].

2.4. Modeling

2.4.1. Modeling Logic

We modeled strawberry pollination by identifying the significant entities and interaction processes of entities, and then we scheduled these agents based on empirical data. The simulation model consists of two types of significant entities: (1) regular entities, e.g., greenhouse, strawberry plants, inflorescence and flowers and honey bees in the real-world production system; and (2) virtual entities, e.g., the environment, system scheduling and weather, that provide a spatial and temporal reference for the interactions among regular entities [49].

The entities are modeled as agents interacting with each other in a virtual greenhouse (Figure 1). The greenhouse is composed of 9360 strawberry plants. One primary and two secondary inflorescences with flowers are distributed within one plant. A fixed number of flowers is reserved by flower thinning according to the inflorescence rank. Bees are spatially initialized in the hive site that is arranged on the east side of the greenhouse. Bee foraging is modeled as searching and flower visiting from one flower to another. The pollination interacting process between flowers and bees is defined as pollen exchange with a receiving stage and a accepting stage.

The simulation covers 120 days from January to April. Then, all agents are scheduled according to strawberry phenology on a daily basis for strawberry development or on a minute basis for bee foraging. One simulation step is one execution in which a bee can accomplish its activity according to time and weather conditions. When the first flower blooms according to the GDD requirement, bees begin to forage from the hive. We assume that a bee can accomplish one activity in 1 min on average based on bee interaction behavior [21,43]. We set a period of 9 h for one simulated day considering bee foraging from 8:00 to 17:00. Therefore, one day contains 9×60 = 540 cycles in simulation. Pollination ecology data were used to parameterize the model. The simulation model incorporates much of what is known and hypothesized about the pollination ecology of a strawberry agroecosystem.

2.4.2. Modeling Software

The open-source simulation model has been implemented in the GAMA modeling platform [51]. The software is friendly to use and includes many adjustable parameters of strawberry phenology and bee foraging activity to adapt to variant cultivars. The graphical user interface of the software and the simulated continuous strawberry growth process is shown in Figure S3.

2.4.3. Modeling Validation

The simulation results largely agreed with the existing literature [4,15,19,32,43] and the growing experience of the growers, which showed the validity of the model. The simulated average yield, average fruit weight and healthy fruit setting rate were basically consistent with the actual planting, which showed the validity of the model, as shown in Figure 2 and Figure 3. The data of fruit set rate in actual planting in Figure 2B were collected by growers who cooperated with us.

More model validation are in the Supplementary Materials section. These experiment results suggested our model was firmly validated, which was considered to be critical to make precise assessments and suggestions for strawberry bee-pollination efficiency in a greenhouse.

3. Simulation Experiments

For the first time, we closely analyzed the responses of fruit quality to different bee densities based on the firmly validated simulation model.

3.1. Experiment I: Bee Density and Fruit Quality

Bee density in a greenhouse showed a strong positive correlation with fruit quality [15]. However, there is no universal conclusion about the relationship between the number of strawberries and the number of bees in greenhouse planting. For example, McGregor recommended 12–25 colonies of honeybees per hectare of strawberries for optimum fruit production [16], while Williams recommended 2.5 and Scott-Dupree 1.2 colonies of honeybees per hectare [5].

Therefore, we conducted experiments to study the impact of bee density on strawberry quality in a greenhouse. A series of simulation experiments with different bee-density values (bee number from 2000 to 12,000) was conducted with the same other factors. Based on the results, the influence of bee density can be estimated quantitatively, and the optimal ratio can be selected, which may provide reasonable suggestions for growers in practical strawberry planting in a greenhouse.

3.2. Experiment II: Cause of Bee Pollination Advantages

It is known that bee pollination has a significant advantage over artificial pollination. Based on the growing experience and previous studies on bee pollination, we believed that the advantage might be caused by three factors: pollen receiving rate, pollen acceptance rate and pollen distribution on the stigma. As for pollen distribution, some researchers believed honey bee pollination could achieve uniform pollination of a great number of stigmata, thereby producing well-shaped and commercially high-quality fruits [17]. For example, Wietzke believed the distribution of pollen grains across the receptive stigmas seems to be important for fruit development [6]. However, they did not have sufficient evidence to support this hypothesis.

Here, we conducted experiments to study the impact of the accepting stage and the receiving stage in bee pollination and artificial pollination. By adjusting the simulation parameters of the two stages, the influence can be quantitatively analyzed. Although the pollen distribution is too complex to be simulated, the fruit quality improvement of bee pollination over artificial pollination is well known [11], and we can estimate the impact of pollen distribution indirectly by excluding the improvement caused by the accepting stage and the receiving stage.

Firstly, the accepting stage was considered. Since all the strawberry plants in a greenhouse are genetically identical, artificial pollination and bee pollination can be both regarded as self-pollination. Therefore, self-compatibility cannot be the cause of bee pollination’s advantage over artificial pollination. In the simulation, the self-compatibility probability was fixed at 80%.

Secondly, the receiving stage was considered. Some research revealed that bees could lower the survival of the pollen they carry [20], and the pollen clinging to the body of honeybee foragers had lower viability than that in the flowers. Therefore, bee pollination’s advantage cannot be caused by the pollen’s viability factor. Similarly, reference [19] shows that pollen viability has little effect on the number of undeveloped fruits. Bee pollination can occur on flowers of different ages uniformly [21], while stigma viability is different at different flower ages. We found artificial pollination by growers in practical strawberry plating is usually conducted randomly during the early blooming stage (day 1–2), middle blooming stage (day 2–3) and later blooming stage (day 3–4). Compared with stochastic bee pollination, the time of artificial pollination (i.e., the stigma viability) may be the factor affecting the fruit quality.

As for bee pollination, we conducted experiments to test the effect of stigma receptivity at different flowering stages on fruit quality quantitatively. Through the results, we analyzed the influence of stigma viability on bee pollination. Then, the impact of the receiving stage on strawberry quality can be quantified. It is known that bee pollination can increase fruit weight by about 30% compared with artificial pollination [2,5,6]. Consequently, we can indirectly estimate the impact of the pollen distribution factor by excluding the improvement caused by the receiving stage.

3.3. Experiment III: Greenhouse Planting Pattern and Bee Hive Location

Normally, the bee hive is placed on the east side of a greenhouse in which the temperature is high. This placement mode may lead to uneven pollination distribution due to the difference in the distance between the strawberry and the bee hive. We proposed a hypothesis that fruit quality can be improved if bees are spatially distributed not only in one hive in a greenhouse due to bee foraging behavior. To test the hypothesis, we proposed two experiments: (1) Placing bees in one hive in a greenhouse (see Figure S21); (2) Placing bees in two hives in different positions.

It is known that the distance between two beds in a greenhouse is important in strawberry planting. Generally, the value is set to around 0.4 m. The distance may influence the flight path of bees during foraging and pollination efficiency. Due to the irrigation demand and limitation of the greenhouse area, the distance between beds was set to 0.35 m, 0.40 m and 0.45 m separately in the simulation experiments.

In the traditional actual planting, all strawberry plants are genetically identical in a greenhouse since the pollination efficiency may be impacted by the self-compatibility factor. Therefore, we proposed a hypothesis that planting two cultivars of strawberries in a greenhouse (interplanting) is conducive to the respective pollination efficiencies if we assume that the two cultivars are the same in phenology except for the genes. To test the hypothesis, we proposed simulation experiments. For simplicity, we assumed that different cultivars were planted in the interval beds (see Figure S22).

4. Results

In this section, each experiment runs 10 times for SPSS analysis (n = 10). In the simulation, one day contains 540 cycles, and one run contains 540 × 120 = 64,800 cycles.

4.1. Experiment I

Firstly, we simulated a greenhouse which is 80 m long and 8 m wide. Through 10 simulation experiments, the effects of bee density on average strawberry healthy fruit setting rate, average berry weight, average malformed fruit rate and average yield were studied, as shown in Figure 4 (more detailed simulation results are shown in Table S2).

Figure 4 showed that the quality of strawberry fruit correlated positively with bee density. High-quality strawberry fruit means a high healthy fruit setting rate, low malformed fruit rate and high berry weight. However, when the number of bees reached about 9000 (bee density was about 1.00 bee/plant), this improvement was not significant, which showed a saturation effect on bee pollination efficiency.

Secondly, in order to further verify the conclusion, we simulated a small greenhouse that was 60 m long and 8 m wide. In this condition, there were 280 strawberry plants in each row, so the small greenhouse contained 6720 plants. Through 10 simulation experiments, similar results were shown in Figure S4 and Table S3, in which the improvement in fruit quality was not significant as the bee density reached about 1.00 bee/plant.

4.2. Experiment II

To study the receiving stage, we conducted experiments to simulate the bee pollination and artificial pollination processes in different flower ages. SPSS 26.0.0 was used to analyze the results. As for artificial pollination, the average proportion of received pollen with high viability is about 0.99, 0.93, and 0.73 in the early blooming stage, middle blooming stage and later blooming stage, respectively (see Method part). The results are shown in

Table 4. Impacts of stigma receptivity in bee pollination simulation.

Stigma Receptivity	Average Berry Weight (g)	Malformed Fruit Rate (%)	Pollination Pattern
$R=e^{-0.01\times ag{e}^{3.6}}$	15.72 ± 0.23 a	4.10 ± 0.83 a	Bee pollination
0.99	15.91 ± 0.12 b	2.28 ± 0.73 b	Early stage
0.93	15.88 ± 0.10 b	3.52 ± 0.90 c	Middle stage
0.73	15.68 ± 0.12 a	4.23 ± 0.89 a	Later stage

Means ± standard error (n = 10) within each column followed by the same letter are not significantly different (p > 0.05).

. The data presented show that there were significant differences in the fruit quality with different stigma receptivity values (p < 0.05). It suggested that the earlier the pollination process is in the blooming period, the better the fruit quality can be. However, this improvement is not significant quantitively, and the average fruit weight in the early blooming stage is less than 5% higher than the that in later blooming stage.

As for artificial pollination, we conducted experiments to test the effect of stigma receptivity on strawberry fruit quality. The results suggested that stigma receptivity and fruit quality basically showed a linear relationship (see

Table 5. Impacts of stigma receptivity in artificial pollination simulation.

Stigma Receptivity	Average Berry Weight (g)	Malformed Fruit Rate (%)	Pollination Pattern
0.99	14.81	14.12%	Early stage
0.93	14.65	15.32%	Middle stage
0.73	14.25	16.78%	Later stage

). The results revealed that the fruit quality under bee pollination was significantly better than under artificial pollination with the same stigma receptivity condition, which showed the bee pollination advantage over artificial pollination.

4.3. Experiment III

Firstly, the relationship between strawberry plant coordinates in a greenhouse and fruit quality was studied. The results based on SPSS 26.0.0 are shown in Figure 5 (more detailed results in Figures S5 and S6). The red line in the figure is a fitting line for all strawberry plants in the greenhouse. The data presented show that the fruit weight distribution east–west is not uniform with a significant difference (p < 0.05). As expected, fruit weight distribution north–south was basically uniform without significant difference (p > 0.05).

Secondly, the impact of hive location on fruit quality was studied. The greenhouse in the simulation is 80 m long and 8 m wide. We placed all bees in one hive and then placed the hive in different locations in a greenhouse. The four sides and center were tested. We tested two scenarios in which bee numbers are 8000 and 4000, respectively. The results are shown in

Table 6. Impacts of diverse hive locations with only one hive (bee number is 8000).

Location of Hive	Average Berry Weight (g)	Malformed Fruit Rate (%)
Middle of east side	15.72 ± 0.23 a	4.10 ± 0.83 a
Middle of west side	15.78 ± 0.20 a	3.57 ± 1.01 a
Greenhouse center	15.73 ± 0.18 a	3.83 ± 0.79 a
Middle of south side	15.70 ± 0.14 a	4.79 ± 1.34 a
Middle of north side	15.68 ± 0.12 a	4.31 ± 0.98 a

Means ± standard error (n = 10) within each column followed by the same letter are not significantly different (p > 0.05).

and Table S4, respectively. The data presented show that there was no significant difference (p > 0.05) in fruit quality in the two scenarios. The results suggested that the hive location has little effect on fruit quality overall, with only one hive in the greenhouse, when the effect of position on temperature and light were not taken into consideration (detailed information in Supplementary Material).

Thirdly, we placed bees in two hives to test their pollination efficiency. As discussed above, when the bee number reached around 8000, the improvement of fruit quality from bee foraging behavior was not significant due to a saturation effect. As a result, the bee number was set to 4000 in the simulation. There were 2000 bees in one hive on the east side and 2000 bees in another hive on the west side in a greenhouse. The results are shown in

Table 7. Location impacts of two hives (bee number is 4000).

Location of Hive	Average Berry Weight (g)	Malformed Fruit Rate (%)
Only east side	11.76 ± 0.41 a	46.53% ± 2.64 a
West side + east side	12.38 ± 0.29 b	43.42% ± 2.01 b

Means ± standard error (n = 10) within each column followed by the same letter are not significantly different (p > 0.05).

. The low fruit quality was a result of a low number of bees. The data presented show that there was a significant difference in fruit quality in the fruit with different hive locations (p < 0.05). The spatially distributing bee hives can improve fruit weight by about 5% and reduce malformed fruit rate by about 3%.

We conducted three experiments to test the distance between beds’ impact on fruit quality. The distance influenced the bee’s flight path when foraging and pollination efficiency. The simulation results (see

Table 8. Impacts of the distance between beds.

Distance between Beds	Average Berry Weight (g)	Malformed Fruit Rate (%)
0.35 m	15.81 ± 0.28 a	3.40 ± 0.76 a
0.40 m	15.72 ± 0.23 a	4.10 ± 0.83 a
0.45 m	15.70 ± 0.26 a	4.19 ± 0.85 b

Means ± standard error (n = 10) within each column followed by the same letter are not significantly different (p > 0.05).

) showed there was no significant difference in berry weights (p > 0.05) and a significant difference in malformed fruit rates (p < 0.05) with different hive locations. It suggested that bed spacing may have little effect on strawberry fruit weight and minor effects on malformed fruit rate, and the best distance between beds is 0.35. We think that this was because a short distance between beds can reduce the impact of the foraging distance constraint of flowers nearby that a bee can find.

Lastly, we conducted two experiments to study the pollination efficiencies in the two patterns. In the simulation, the bee number was also set to 4000 for comparison, as we talked about before, and the low fruit quality was a result of the low number of bees. For simplicity, different cultivars were planted in the interval beds in the second pattern. The simulation results (see

Table 9. Interplanting impacts on the pollination efficiencies (bee number is 4000).

Planting Pattern	Average Berry Weight (g)	Malformed Fruit Rate (%)
All beds with one cultivar	11.76 ± 0.41 a	46.53% ± 2.64 a
Different cultivars planted in the interval beds	12.91 ± 0.59 b	43.42% ± 2.91 b

Means ± standard error (n = 10) within each column followed by the same letter are not significantly different (p > 0.05).

) showed the second planting pattern was more conducive to pollination in the simulation environment. There was a significant difference in fruit quality (p < 0.05) in different patterns. We think that this was because this interplanting pattern can effectively reduce the constraints of the self-compatibility factor, which is conducive to both cultivars.

5. Discussion

An inadequate number of bees in the greenhouse has significant adverse effects on fruit quality. As a result, sufficient bee density is a must for strawberry planting. The data presented show that when the bee density was higher than 1.00 bee/plant, the fruit quality was not significantly improved. In addition, we found similar conclusions in some references to support our conclusion [52]. We suggested that it is a saturation effect on bee pollination efficiency. In practical greenhouse planting, strawberry pollination may be affected by mechanical actions, diseases and other factors, making it necessary for growers to ensure the bees significantly outnumber the strawberry plants (bee density is more than 1.00 bee/plant) in a greenhouse.

Stigma receptivity is an important factor in the pollination process. The continuous bee pollination process can significantly reduce the influence of stigma receptivity, while the discontinuous artificial pollination process is limited by this factor. The results showed that stigma receptivity influences the fruit quality in both bee pollination and artificial pollination, while the influence is more significant in artificial pollination. We suggested that strawberry growers should conduct artificial pollination in time after blooming if they do not use bee pollination.

Therefore, we believed the continuous bee pollination process can significantly reduce the influence of stigma receptivity, which is the cause of the bee pollination advantage over artificial pollination. The quantitative analysis showed the fruit-weight-improvement rate by this effect is lower than in practical planting (about 30%) [2,22]. It revealed this effect is a cause but not the unique cause of bee pollination’s advantage over artificial pollination. Based on the above discussion, we believed that bees help distribute pollen grains to all strawberry pistils, promoting well-shaped fruits, which is an important cause of bee pollination’s advantage over artificial pollination in strawberry planting. We proved this by observing the artificial pollination process of growers and the distribution of strawberry achenes under two pollination conditions (see Supplementary part 11). This conclusion is consistent with the proposed hypothesis by Wietzke [6]. In addition, the even pollen distribution can effectively reduce the malformed fruit rate. Therefore, in bee pollination, not only the pollen transport but the even pollen distribution caused by bees is important. To conclude, through this evidence, we suggested that evenly distributing pollen in pistils during bee pollination and reducing pollen compatibility and stigma receptivity through the continuous bee pollination process are two of the top reasons explaining how bee cross-pollination outperforms artificial pollination.

Fruit weight distribution was non-uniform on east–west but basically uniform on north–south, as expected. By tracking the tracks of bees, we analyzed that the phenomenon was due to the foraging distance constraint of flowers nearby that a bee can find [21] because the distance influenced the bee’s flight path when foraging. We found that spatially distributing bee hives can significantly improve fruit quality, which suggested a novel effective method that growers should use when placing the bee hive. Strawberry growers can place bees in multiple hives instead of one hive and then place these hives in different locations in a greenhouse. In this way, the influence of bee foraging distance constraints can be reduced. In addition, we found that planting two cultivars of strawberries in a greenhouse was conducive to pollination efficiency when only considering the impacts of bee dynamics in the simulation if we assumed that the two cultivars were the same in phenology except for the genes. We think that this was because this interplanting pattern can effectively reduce the constraints of the self-compatibility factor, which may provide reasonable suggestions for growers.

Despite the firm validation, this simulation model still has some limitations. There are some tiny differences between the real strawberry and the model strawberry subject, which are limitations of the simulation. In addition, as the shape of strawberry fruits is observed with the naked eye subjectively and fruit malformation can be caused by diverse factors, there may be discrepancies in the malformed fruit rate between simulation and empirical data [2,19,23]. In addition, the influence of sunlight and humidity on bee foraging behaviors was ignored in the simulation. More attention shall be paid to these limitations in further studies.

6. Conclusions

In conclusion, we used the simulation method to study the effects of bee density and hive distribution on pollination efficiency for greenhouse strawberries. The simulation model, which allows us to track every bee, flower, pollen and fruit in detail without great planting cost, incorporates much of what is known and hypothesized about the pollination ecology of the strawberry agroecosystem. In particular, we found that fruit quality cannot be further improved when bee density is higher than 1 bee/plant due to a saturation effect, and spatially distributing bee hives can significantly improve fruit quality. In addition, the simulation results suggested that the continuous bee pollination process can significantly reduce the influence of stigma receptivity. Based on the experiment results, we provided some reasonable suggestions for growers about reducing the bed distance and planting two cultivars in a greenhouse. The general simulation approach that we used has the potential for translation to other crop pollination systems.