A
LTERNATIVE
FOOD
FOR
NATURAL
ENEMIES
DOES
NOT
ALWAYS
LEAD
TO
BETTER
BIOLOGICAL
PEST
CONTROL
F
REQUENCYANDQUANTITYOFSUPPLYINGALTERNATIVEFOODAFFECTSTHEDYNAMICSOFPESTANDPREDATOR Hanneke de LangeResearch internship carried out by Annabel Landman & Hanneke de Lange
Supervised by Arne Janssen, Institute of biodiversity and ecosystem dynamics (IBED), University of Amsterdam
A
BSTRACT
Biological pest control uses natural enemies to reduce pest densities. Initially mainly specialist predators were used, feeding mainly on a specific pest species only. However, nowadays generalist predators, feeding on various food sources, are used more often. These generalist predators enable the use of alternative food for the predator as a tool to maintain and increase predator densities. According to a theory about indirect interactions between prey species that share a predator, supplying alternative food will result in decreases of pest densities in the long term because of increased predator densities (so-called apparent competition). However, the same theory predicts positive effects on pest densities when supplying alternative food results in satiation or switching of the predator, in the short term, this will result in an increase in pest density (apparent mutualism). Little is known about what quantity and frequency of supplying alternative food results in a sufficient decrease of pest densities and crop damage. A high pulse quantity or a high frequency of feeding can cause satiation or switching of the predator, resulting in reduced predation on the pest (apparent mutualism). Yet, supplying alternative food at a low frequency or low quantity may not result in high predator densities to sufficiently decrease crop damage. To investigate this, a stage-structured predator-prey model with food pulses was used to simulate the effects of different quantities and frequencies on pest densities. Model simulations show that a higher initial predator density combined with short intervals and medium to high pulse quantities is favourable for reducing crop damage. In contrast, short intervals with high quantities of alternative food result in higher pest densities with a lower initial predator density. Hence, this research shows that the optimal frequency and quantity of supplying alternative food depends on the initial densities, which should be considered when using this strategy of crop protection.
Key-words: Apparent competition – Apparent mutualism – Predator prey model – Resource pulses – Alternative food – Food quantity – Time distribution – Natural enemies – Generalist predator
T
ABLE
OF
C
ONTENT
Abstract... 1 Table of Content... 2 Introduction... 3 Methods... 5 Predator-prey-pollen model...5 Model simulations...7 Results... 8Predator-prey-pollen model, time series...8
Predator-prey dynamics...9 Predator-prey-pollen dynamics...10 Discussion... 13 Obtained perspectives...13 Future research...13 Acknowledgements... 15 References... 16
I
NTRODUCTION
The control of pest species in agriculture is of great importance to maintain a profitable yield. Chemical pesticides are most often used in pest control; pesticides kill the pest species or reduce their development. Pesticides however, contain hazardous chemicals that have negative effects on human health and the environment (Crall et al., 2018; Yamamuro et al., 2019). In contrast, biological pest control uses natural enemies of pest species to reduce pest densities. Biological pest control has no negative effects on the health of farm-workers, no toxic effects on plants (van Lenteren et al., 2018), and little negative effects on the environment (Yamamuro et al., 2019). There is some concern about non-target effects of the introduced predator on the environment, therefore van Lenteren et al. (2003) designed a risk assessment method for this problem.
Theoretical population biology has always played a role in biological control (Murdoch et al. 1985). For example, Holt introduced the concept of apparent competition in 1977, showing that, in theory, the addition of an extra, alternative prey species to a predator-prey system resulted in a decrease in the equilibrium density of the resident species. Although this theory was not specifically aimed at biological control, it has been important for this area of applied research (Englisch-Loeb, Karban & Hougen-Eitzman, 1933 ; Karban, Hougen-Eitzman & Engilsh-Loeb, 1994). The theory focuses on adding an alternative prey, which provides the predator with extra food. This decreases the mortality- and reproduction rate of the pest species, which in return increases predation of the pest species by the predator (Messelink, van Maanen, van Steenpaal & Janssen, 2008).
The interaction between the pest population and the alternative prey is characterized by two effects: apparent mutualism and apparent competition. Both are indirect interactions caused by the connection of both prey species through a shared predator (Nomikou, Sabelis, & Janssen, 2010). Apparent mutualism is a positive interaction between the two prey species, which means that if the population density of one prey increases, the population density of the other prey will increase too. This can be due to satiation of the predator or switching of the predator between two prey species (Abrams & Matsuda, 1996). Apparent competition portrays a negative interaction between the two prey species; an increase in the density of one prey will cause a decrease in the density of the other prey. If the food availability of the predator increases, the density of the predator can rise, which in turn will cause a decrease in the density of both prey species (Abrams & Matsuda, 1996). These mechanisms are found to occur on different time scales: apparent mutualism occurs in the short-term and apparent competition in the long-term (Nomikou et al., 2010). Abrams et al. (1998) show that apparent mutualism can occur in a system with major differences in the cycles of a two-prey system.
Since the introduction of the theory of apparent competition by Holt (1977), much research regarding this topic in biocontrol has been published. Van Rijn, van Houten, & Sabelis (2002) tested alternative food for a predatory mite species, but the food could also be eaten by the pest species, this was not considered in the theory of apparent competition so far (Holt & Lawton, 1993). Although it is possible that the pest species would benefit from the alternative food, the research showed that additional food increased the predator densities and decreased prey densities, as with apparent competition. Sato, El-Sabaawi, Campbell, Ohta, & Richardson (2016) carried out a field experiment with pulsed resource subsidies to examine the influence of the food pulses on the ecosystem. They concluded that the response of the consumer population depended on the timing of the resource subsidies. This indicates the importance of further research about timing of supplementing predator populations with food.
The use of additional food in biological pest control induced the use of generalist predators instead of specialist predators, because they feed on various food sources (Janssen & Sabelis, 2015), which can result in lower pest densities due to apparent competition-like dynamics. In a system with specialist predators, which feed on one
type of food source, the predator can only survive if the specific pest populations are present, hence, specialist predators can only be introduced into a crop when pest density is sufficient to ensure predator persistence (Janssen & Sabelis, 2015). In contrast, the use of generalist predators in combination with alternative food created the possibility of increasing generalist predator populations, even when there is less or no prey present because they can survive on other food types for some time (Janssen & Sabelis, 2015).
Research that investigates the frequency and quantity of pulses of food for predators is scarce, even though this can be of great importance for the success of reducing the pest population. Especially in a food web that exists for a short period of time, as in crop growth in greenhouses (Nomikou et al., 2010). Supplying food too often or too much can make the predator switch from prey to the alternative food, resulting in apparent mutualism; an increase in the population density of the prey (van Maanen et al., 2012). There is little knowledge about the optimum frequency and quantity of supplying alternative food to predators in semi-closed systems with limited natural influx of
alternative food, like in greenhouses. Nonetheless, it is important to know how to maximally reduce the damage caused by pests. The addition of alternative food is thought to decrease fluctuations of pest densities and to lower the maximum densities (van Rijn et al., 2002; Nomikou et al., 2010; Holt, 1977). The frequency of applying alternative food is important in this process, because a low frequency can result in higher peaks in the pest population (Janssen & Sabelis, 2015). However, high frequencies do not necessarily result in better pest control but quite the opposite, it can also result in apparent mutualism in case of satiation of the predator (Messelink et al., 2008).
Besides the frequency of adding alternative food to a semi-closed system, the quantity of food that is added also needs to be carefully investigated. The quantity of food for the predator can influence densities of both the predator and the pest species. This in turn has its effect on the interaction between predator and prey species. Quantities that are too high can cause the predator population to become satiated (Messelink et al., 2008) or causing it to switch towards the more abundant prey; the pollen (Abrams & Matsuda, 1996). In contrast, too low quantities cannot support the predator population in times of low prey densities. Holt (2008) tested the distribution of
alternative food with multiple short pulses or one long pulse, keeping the total amount of food over time constant. It could be even more interesting to research higher or lower amounts of food per time unit with different frequencies of feeding. According to Nomikou et al. (2010) and van Rijn et al. (2002) the quality of pollen remains good for at least one week, but then decreases in quality as a consequence of natural decay. Nomikou et al. (2010) used 25-30 mg pollen, which was confirmed to be a suitable quantity to sustain a population of predators. No other research has confirmed this quantity.
It is interesting to research the effect of different quantities of food with different frequencies of
provisioning on the population dynamics, as no other research has combined changes of both variables. Therefore the research question of this research is: What quantity and frequency of alternative food will decrease crop damage
caused by pest species sufficiently? Answering this might lead to new insights that are useful for society and industry.
Theoretical research about alternative food is important because it can provide sufficient information for field studies about biological control. Further research can contribute to the decreasing use of chemicals, and therefore result in less of the negative effect of pesticides. Besides, research about the frequency and quantity of food can be used as indicators for natural disturbances and their influence on ecosystems.
In this study, theoretical research will be carried out through modelling of a predator-prey system with alternative food, comparable to the systems studied by van Rijn et al. (2002) and Nomikou et al. (2010).
M
ETHODS
P
REDATOR-
PREY-
POLLENMODELTo research the optimal frequency and quantity of pollen, differential equations were used to model a predator-pest system with pulsed alternative food. This system was modelled after a stage-structured predator-prey interaction in greenhouses (closed system), studied by van Rijn et al. (2002) and was adapted to fit the aim of this research. Van Rijn et al. (2002) researched the influence of alternative food, which could be eaten by predators and herbivores (the pest population), on prey densities and plant damage. The alternative food used in the research of van Rijn et al. (2002) was plant pollen (A) which was produced by the host plant.
The consumption of pollen(A) by predators(P) is influenced by the number of prey(N) in the system and vice versa, this results in a type II (saturating) functional response for the consumption of pollen (cc, equation 1) (van Rijn et al., 2002). This functional response is influenced by multiple parameters. First, fa is the maximum rate of pollen consumption by predators (P). Also, the pollen (A) was assumed to differ in quality as food from that of the prey (N1) (Φ). In the model of van Rijn et al. (2002) pollen were preyed at a higher rate, even though the prey was present (k).
nf is the prey and pollen density at which predation rate is half its maximum (eq. 1.).
cc=
Φ∗f
❑
aN
1+
n
f+
Φ∗A +k∗A∗N
1(1)
The research of van Rijn et al. (2002) assumed a constant rate of production of pollen by the plant, a rate of natural decay (b) and consumption by prey and predators. In this research, the pollen was artificially added to the system in pulses (pp). Furthermore, I assumed that the prey species did not feed on pollen, because this is a rather specific peculiarity of the system investigated by van Rijn et al. (2002). The amount of pollen consumption is influenced by cc (eq. 1) and by the amount of feeding juvenile (P2) – and adult predators (P3), where juvenile predators (P2) have a lower consumption rate (j) than adult predators (P3, equation 2).
d A
dt
=
pp−b∗A−cc∗A∗
(
j∗P
2+
P
3)
(2)
The reproduction of adult prey and thus population growth of the system of prey, was assumed to depend on the density of all three life stage(h, equation 3), controlled by the carrying capacity of the system for prey (C, eq. 3) and the maximum rate of reproduction r (eq. 3).
h=r∗max
(
0,1−
N
1+
N
2+
N
3C
)
(3)
The prey(N1) is predated by the predator (P) following the saturated functional response mm (equation 4), where fn is the maximum predation rate, nf is the prey and pollen density at which predation rate is half its maximum,
Φ is the difference in quality as food from that of the pollen (A) and predation of prey by the predator declines with
increasing amounts of pollen (A)(k).
mm=f
n/
(
N
1+
n
f+
Φ∗A+k∗A∗N
1)
(4)
The prey population consisted of three life stages, a vulnerable (N1, equation 5) and an invulnerable (N2, equation 6) juvenile phase and an invulnerable reproductive phase (N3, equation 7). Van Rijn et al. (2002) assumed unlimited growth of prey with the expectation that this would never occur because the pest would eventually be controlled by the predators. However, this assumption was not in line with the goals of this research, where different pollen supplement regimes could cause prey to escape from control. All three life stages feed on the plant and become food limited at high population densities (eq. 3).
Predation of the invulnerable prey (N1) by the feeding juvenile predator (P2) is lower than by the adult predator (P3). The vulnerability of the larvae of the prey declines with age. Where rate d1 defines the development of vulnerable juveniles (N1) to invulnerable juveniles (N2). Correspondingly invulnerable juveniles (N2) develop with rate
d2 to the adult (reproductive) phase (N3). Reproduction of N3 was limited by the maximum reproduction rate v (eq. 7).
d N
1dt
=
N
3∗
h−mm∗N
1∗
(
j∗P
2+
P
3)
−
d
1∗
N
1(5)
d N
2dt
=
d
1∗
N
1−
d
2∗
N
2(6)
d N
3dt
=
d
2∗
N
2−
v∗N
3(7)
The reproduction of the adult predator (P3) is directly affected by the densities of prey (N1) and pollen (A) through a Michaelis-Menten function (van Rijn et al., 2002)(equation 8). With g being the maximum reproduction rate of the predator, ng the prey density at which the net reproduction is half of its maximum, Φ the food value for the predator of pollen relative to prey and m the maintenance costs, i.e. the food needed for predator survival (eq. 8).
0, g∗(
N
1+
Φ∗A
N
1+
Φ∗A+n
g−
m)
w=max
¿
(8)
The mortality of adult predators is an inversed Michaelis-Menten equation and is said to increase with decreasing food densities (equation 9)(van Rijn et al., 2002). The maximum mortality rate (µ0) is at really low densities of prey and pollen and the minimum mortality rate (µ) at high densities of prey and pollen, with Nµ being the density of prey at which mortality is half its maximum. The other parameter Φ is as above.
l=min
(
μ
0,
μ∗N
1+
Φ∗A+N
μN
1+
Φ∗A
)
(9)
Like the prey, the predator population was divided into three life stages; non-feeding (P1, equation 10)- and feeding (P2, equation 11) juveniles and feeding adults (P3, equation 12) that can reproduce. Both adult predators and feeding juvenile predators predated on prey and pollen; however, juvenile predators were assumed to consume only a fraction of what the adults consume (j, eq 2 & 5). Development from non-feeding juvenile to feeding juvenile is defined by rate e1. Correspondingly development from feeding juvenile predators into feeding adult predators is defined by rate e2 (eq. 12).
d P
1dt
=
w∗P
3−
e
1∗
P
1(10)
d P
2dt
=
e
1∗
P
1−
e
2∗
P
2(11)
d P
3dt
=
e
2∗
P
2−
l∗P
3(12)
Parameter Description Value Units
Pollen
b
Rate of natural decay 0.21*0.8 Pollengrains/day
pp
Quantity of pulsed food varying Pollen grains/plant/Prey and pollen
Φ
Food value of pollen relative to prey 0.34 Prey/104Pollen grains
k
Interaction between prey and pollen 0.04 Plant/104Pollen
n
f Prey and pollen density at which predation is half its maximum1.5 Prey/plant
f
a Maximum rate of pollen consumption by predators 0.085 Pollengrains/adult/day
j
Consumption rate of juvenile predators relative to adult predators0.25 Pollen grains/adult /day
Prey
d
1 Developmental rate of the vulnerable prey larvae to invulnerable prey larvae1/3 Per day
r
Maximum rate of production 2.0 Offspring /adult/dayC
Carrying capacity 105.82f
n Maximum rate of prey predation 4.0 Per dayd
2 Developmental rate of invulnerable prey larvae toinvulnerable adult larvae
1/15 Per day
v
Decline of adult net reproduction rate 0.11Predato
r
e
1Developmental rate of non feeding to feeding juvenile predator
1/3 Per day
g
Maximum rate of net production 1.875 Offspring /adult/dayn
g Prey density at which net reproduction is half of its maximum1.0 Prey/plant
m
Maintenance costs of the predator 0.2 Ratioe
2 Developmental rate of feeding juvenile to the feeding adult predator1/5 Per day
N
μ Prey density at which adult mortality is half its maximum0.08 Per day
μ
0 Maximum adult mortality 0.2 Per dayμ
Minimum adult mortality 0.0625 Prey/plantTable 1. Parameter explanation and parameter values used in the pollen-prey-predator model (van Rijn., 2002; p.c. Janssen, 2020) In the model the initial densities for the predator and prey are: N1 = 0.168, N2 = 0.39, N3 = 0.042, P1 = 0, P2 = 0 and P3 = 0.1 or 5 (individuals per
plant)(van Rijn., 2002; p.c. Janssen, 2020)
M
ODEL SIMULATIONSThe model was implemented and simulated using R (R Core Team 2019) and R studio with the package deSolve. After implementation of the model in R, the dynamics were run with increasing pulse quantity and increasing interval lengths of the pulse with a given step size from a starting point to a limit point. It is important to look at the patterns over short periods (so-called transient dynamics) since production cycles in greenhouse systems are too short for populations to reach an equilibrium (van Rijn et al. 2002). Therefore the influence of changing parameter values on transient dynamics, summarized as average and maximum densities, is shown below.
To evaluate the level of control of the pest, threshold values were used, above which plant damage would result in economic damage. The damage threshold value for the prey density was assumed as 30 larvae per plant (van Rijn, 2002; p.c. van Rijn, 2020). Maximum densities were used to decide which values of pulse quantity and pulse time did not provide adequate pest control. The mean values were used as a measure for average crop damage caused by the prey. Together, the two measures of pest densities were used to decide which quantity and which
interval resulted in the lowest prey densities and thus lowest crop damage. The quantity was increased with steps of 0.10*104 from 0 to 3.4*104 pollen grains per plant and each quantity was tested with an increasing interval from 1 to
31 days.
R
ESULTS
P
REDATOR-
PREY-
POLLEN MODEL,
TIMESERIESFigure 1 shows an example of the densities of pollen, prey and predators through time (100 days). Pollen densities (Figure 1A) follow the pulses of pollen, applied every 31 days. This low pulse quantity and a long interval result in a peak in vulnerable juvenile prey densities between 15-30 days (Figure 1B) and a lagging peak of (feeding) predator densities 10-20 days after the peak of the prey (Figure 1C). The increase of predator densities follows shortly after the food pulses. However the biggest peak follows shortly after the peak of the vulnerable prey (30-40 days). The peak in predator densities results in a decrease of the vulnerable prey until day 30, causing decreases in the invulnerable juvenile and invulnerable adult prey later on. After the second food pulse and the peak of the prey, a small second peak of the predator is visible (juvenile and adult)(Figure 1C). The third food pulse induced a small increase of the predator around 100 days, the effect of the food pulse is also visible around 90 days in the prey graph (Figure 1B), where a slight increase can be seen. Food pulses in a system with prey and predator can result in short periods of satiation of the predator and consequently, a small increase in prey densities (apparent mutualism).
Figure 1: Pollen, prey and predator densities through time (x-axis, in days). The y-axis shows the densities per plant. A shows the pollen
added in pulses of 0.1*104 pollen grains per plant with an interval of 31 days, B shows the densities of the three different prey stages, C
shows the densities of the three different predator stages, and D shows the pollen density and total prey- and total predator densities in individuals per plant.
Another single simulation was done with a higher pulse quantity (1.5*104 pollen grains per plant) and the same
interval as above (31 days). Because of the higher availability of pollen, the predator density increased faster during the first 30 days and consequently, more prey were attacked, reducing the peak densities of the prey (cf. Figure 1). Because of this lower peak in pest density, the predator density did not increase as much as in figure 1C. The third pulse resulted in satiation of the predator, with a small temporary rise of the prey density around the 65-day mark as a consequence. Moreover, the high prey- and pollen densities resulted in a second peak of the predator population. The last food pulse also resulted in satiation of the predator and thus apparent mutualism, i.e. a slight increase in prey densities, followed by a rise in predator densities. Hence, these peaks are mainly driven by the food pulses. A pulse quantity of 1.5*104 pollen grains per plant results in lower prey densities than a pulse of 0.1*104 pollen grains
per plant. However a bigger pulse does induce more fluctuations in the dynamics of both prey and predator.
Figure 2: Pollen, prey and predator densities through time (x-axis in days). The y-axis shows the densities per plant. A shows the pollen
added in pulses of 1.5*104 pollen grains per plant with an interval of 31 days, B shows the densities of the three different prey stages, C
those of the three different predator stages, and D shows the pollen density and total prey- and total predator densities in individuals per plant.
P
REDATOR-
PREYDYNAMICSSubsequently, multiple simulations of this predator-prey model were run with increasing quantities and different intervals of pollen supply. Each run was summarized using the mean and maximum densities of prey and predators, so in figures 3, 4 and 5, every point of a line is in reality one run of a 100 days. In a system without prey and with pollen (Figure 3), short interval pulses induce high mean densities of the predator, whereas a longer interval reduces population densities. A low quantity results in low population densities and a high quantity in high
population densities, whereas the shortest interval has the highest density. An initial predator density of 0.1 individuals per plant (Figure 3A), results in increases in density with an interval between 1 and 16 days and a pulse quantity between 0.2*104
and 3.4*104
increases in density for all tested intervals and a pulse quantity between 0.1*104 and 3.4*104 pollen grains per plant.
The average predator densities are lower with increasing interval and quantity in a system with an initial predator population of 0.1 individuals per plant (Figure 3B) than with an initial predator population of 5 individuals (Figure 3A). These simulations without prey can be useful to compare the different effects of the predator-prey-and-pollen system.
Figure 3: Mean population density of the predator in a system without prey and with pollen. The initial values are 0.1 individuals per plant
(A) and 5 individuals per plant (B). On the x-axis the pulse quantity from 0 to 3.4*104 pollen / plant and on the y-axis the mean density of
the predator population. The lines in different colours show the effect of a different interval size.
P
REDATOR-
PREY-
POLLEN DYNAMICSSubsequently, the model was run with prey, pollen, and an initial predator population of 0.1 individuals per plant (Figure 3). The maximum densities of prey larvae rises above the threshold value of 30 with a pulse smaller than 0.8*104 pollen grains per plant for all interval sizes (Figure 4A). A pulse between 0.8*104- and 3.4*104 pollen grains
induced a decrease in maximum densities for all intervals between 4 and 31, but resulted in an increase in maximum prey larva densities with an interval of 1 day. This is caused by satiation of the predator because of high amounts of pollen, resulting in a decrease of predation on the pest (apparent mutualism). Hence, all intervals resulted in control of the pest below the threshold density as long as the pulse quantity is bigger than 0.8*104 pollen grains per plant.
However, at the threshold value of 30 individuals per plant, farmers will decide to spray chemicals against the pest. Therefore, it is better to keep the maximum pest density further below this threshold value. A pulse quantity of 1.3*104
pollen per plant with a corresponding interval between 4 and 31 days reduces maximum densities further below the threshold value.
The mean prey larvae densities were between 4 and 14 individuals per plant with every pollen quantity and interval size (Figure 4B). An interval of 1 day resulted in the lowest mean prey larvae densities with small pollen quantities (0.1*104
and 1.2*104
pollen grains per plant), but quantities higher than 1.2 pollen grains and an interval between 4-31 days resulted in higher average prey larvae densities with the shortest interval (Figure 4B).
The mean total prey density shows the same pattern as the mean prey larvae densities (Figure 4C). The mean prey densities are related to the amount of crop damage. An interval of 1 day results in decreasing prey densities with quantities between 0 and 1.3*104 pollen grains per plant and results in an increase in mean prey
densities with quantities between 1.3*104 and 3.4*104. This increase in densities with increasing pulse quantity
coincides with an increase in predator densities with an increase in the quantity of pollen with an interval of 1 (Figure 4D), but apparently also results in satiation of the predators, resulting in a net increase of the pest densities. In contrast, an increase in pollen quantity from 0.1*104 to 3.4*104 with an interval between 4 and 31 result in a
The mean predator densities (Figure 4D) shows a sharp increase, with increasing pulse quantity and a small interval of 1 day. With interval sizes between 4 and 31, an increase in the densities of pollen also increases the predator densities, until 110 individuals.
To summarize, in a system with an initial predator density of 0.1 individuals per plant, intervals between 4 and 31 days tend to result in decreased densities of prey larvae and total prey with increasing pulse quantities, and pulse quantities above 0.8*104 are able to keep the maximum prey larvae densities below the threshold value of 30
individuals per plant.
Figure 4: Population densities of prey, prey larvae and predators (y-axes) with pulse quantities from 0 to 3.4*104 pollen grains / plant
(x-axes) and different interval lengths (colour-coded curves) and an initial predator density of 0.1. The x-axis shows the pulse quantity per pulse. Each line is the result of simulations with a different interval (1 pulse every day to one pulse every 31 days) and an increasing pulse quantity. The curves show the average and maximum numbers of prey and predators per plant (y-axes). The maximum prey larvae density (A) shows whether the pest density would reach the threshold value (30 larvae). The mean prey density (C) are a stand-in measure of the total amount of crop damage caused by the prey. The mean predator density indicates the total number of predator in the system (D).
Furthermore, simulations were run with an initial predator density of 5 individuals per plant because a larger predator population is less likely to satiate with increases in alternative food (Figure 5). Here, small interval sizes result in the lowest prey densities, which is in contrast with figure 4, where large interval sizes resulted in the lowest prey densities.
For all pollen quantities, the maximum prey larvae densities were far below the threshold value (Figure 5A). Intervals between 1 and 19 resulted in maximum reduction of the prey larvae densities, where a short interval and low pulse quantities result in the largest decrease, and larger quantities of alternative food are needed with longer intervals to result in the same decrease.
With every quantity and interval size, the mean prey larvae densities were below 2.0 individuals per plant (Figure 5B). The mean prey larvae densities showed the same pattern as the max prey larvae densities, a short interval resulted in low mean density and a longer interval between 4 and 16 days results in lower intervals with higher quantities. The lowest prey value is 0.25 individuals per plant and can be achieved with intervals between 1 and 13 days with high pulse quantities (above 3.0*104 pollen grains). With intervals between 16 and 31, mean
densities do not reach the minimum of 0.25 individuals obtained with shorter intervals, indicating a smaller effect of pulse quantity with big interval sizes.
With every quantity and interval size, the mean prey density was below 2.8 individuals per plant (Figure 5C). The smallest intervals (1-7 days) reduced prey densities to the lowest value of 0.3 individuals with pulse quantities between 1*104 and 2.5*104 pollen grains, whereas longer intervals (10 to 16 days) induce the lowest value with pulse
quantities between 3*104
and 3.4*104
pollen grains. As with the mean prey larvae, mean prey densities do not reach the minimum of 0.3 individuals with intervals between 16 and 31 days, indicating a smaller effect of the pulse quantity with long intervals.
An interval of 1 day causes the mean predator density to increase sharply above 200 individuals per plant (Figure 5D) and stay below 100 individuals per plant with an interval size between 4 and 31 days. Moreover, the longest interval induces the lowest predator density. The increase in mean predator densities is smaller with increasing interval and quantity in a system with an initial predator density of 5 individuals (Figure 5D) compared to an initial predator density of 0.1 individuals (Figure 4D). Furthermore, with every quantity and interval, the mean prey and mean prey larvae densities were below 3.0 individuals per plant (Figure 5C & 5B), whereas in a system with an initial predator population of 0.1 individuals, the mean prey and mean prey larvae densities reached up to 20 individuals (Figure 4C & 4B). This indicates that a bigger initial predator population is better capable of reducing the prey densities than a small initial predator population.
Figure 5: Population densities of prey, prey larvae and predators (y-axes) with pulse quantities from 0 to 3.4 *104 pollen grains / plant
(x-axes) and different interval lengths (colour-coded curves) and an initial predator density of 5. The x-axis shows the pulse quantity from 0 to per pulse. Each line is the result of simulations with a different interval (1 pulse every day to one pulse every 31 days) and an increasing pulse quantity. The curves show the average and maximum numbers of prey and predators per plant (y-axes). The maximum prey larvae density (A) shows whether the pest density would reach the threshold value (30 larvae). The mean prey density (C) are a stand-in measure
of the total amount of crop damage caused by the prey. The mean predator density indicates the total number of predator in the system (D).
D
ISCUSSION
O
BTAINEDPERSPECTIVESBiological control has always been supported by theoretical population biology (Murdoch et al., 1985), this research argues the importance of theoretical research prior to performing practical research. The results promote the importance of adding alternative food in a correct way, with system specific quantity and interval sizes.
This research focused on what interval and quantity of alternative food sufficiently decreases crop damage caused by pest species. Model simulations with an initial density of 0.1 adult predators per plant, result in the lowest pest densities with higher pulse quantities and longer intervals. With medium to high pulse quantities the pest densities decreased below the threshold value (30 individuals per plant). The lowest mean and maximum densities were found with higher pulse quantities and longer intervals (Figure 4). In contrast, short intervals, combined with high pulse quantities, resulted in the lowest pest densities with an initial predator density of 5 adult predators per plant. (Figure 5). These results show that the supply of alternative food to a predator population has to be tuned to predator densities and likely also to pest densities. Although not suppressing pest densities as much as with high initial predator densities, the low initial predator density did succeed in decreasing the pest density well below the threshold value and could be used in preventing crop damage. The introduction of higher predator densities has been found to sufficiently decrease crop damage with high pulse quantity and short intervals.
An important note is that in figure 5, the system with high initial predator densities, the curves of longer intervals fluctuate. This can be due to the interference between the fluctuations inherent to the transient dynamics of the predator-prey system, the pulsed alternative food supply and the fixed length of the simulation, cutting off the dynamics at a random phase of the fluctuation. Increasing simulation length can reduce these fluctuations, however the length of the simulation is best to align with the duration of crop growth.
One of the risks of supplying additional food to a predator population is the chance of occurrence of apparent mutualism, where the pest benefits from the addition of alternative food supply. As can be seen in the results, apparent mutualism was found, when pollen pulses resulted in satiation of the predator population, enabling the pest density to increase. Moreover, apparent mutualism occurred in almost every time simulation (Figure 1 and 2), more pronounced after the first few pulses and less so after pulses later on. Apparent competition also occurred during the time simulations (Figure 1 and 2), especially after 50 days. The overall effects of supplying alternative food on pest densities were more often negative (i.e. apparent competition and better control) than positive, causing a decrease in pest densities (Figure 4B, 4C, 5B & 5C). If done carefully, provision of alternative food can result in apparent competition and reduce crop damage. However, the results of figure 4 and 5 show that the effect of alternative food depends greatly on the initial predator densities, and they will probably also depend on pest densities. As a consequence adding food to the system in a random way will not inevitably lead to a reduction of crop damage.
An important assumption in this research was that the predator had no preference for the pest or the alternative food. Even with high pest densities, the predator still fed on pollen and vice versa. This assumption probably has a large effect on the population dynamics of both pest and predator. When the predator would have a preference for pollen, addition will result in switching of the predator from feeding on the pest to feeding on pollen, which enables the pest population to grow, causing apparent mutualism. In this case, a lower quantity of food pulses can prevent the pest from increasing too much. In contrast, if the predator would have a preference for the pest, the predator will mainly feed on it, even if pollen is added, causing a decrease in pest density (apparent competition). The pollen in this latter case is then especially important to maintain predator populations when pest densities are low. When testing the optimal quantity for a specific predator-prey system, this assumption has to be adapted to the preference of the predator used in that research.
F
UTURERESEARCHThis model is based on a system where the predator has no food preference, with a cropping season of 100 days and a specific life cycle of both predator and pest. Before the results obtained from this model can be used for specific cases of pest and predator species, it has to be adapted to the characteristics of that pest, predator and crop to test the best strategy. For example, the total length of the simulation is equal to the growing season, in which the pest can invade. The length of the life cycle of the predator and pest can also be included when testing for different interval lengths in between food pulses. If the life cycles are short, food pulses will be added with a shorter interval and longer life cycles can be successful with a longer interval. Lastly, the food preference of the specific predator has to be taken into account as explained above.
This research has simulated a predator-prey-pollen system where only the predator feeds on the pest. The findings of this research argue that the supplementation of alternative food does often, but not necessarily always result in better pest control. It is important to know which combination of interval and quantity of a resource pulse results in a positive interaction between the pest and the alternative food (apparent mutualism) to prevent an increase in pest densities. Van Rijn et al. (2002) found that, in case of the Western flower thrips (Frankliniella occidentalis), which also feeds on pollen (Sirkin, Kravar-Garde, Reynolds, Jones & De Courcy Williams, 2006; van Rijn et al., 2002), concentrating the distribution of pollen grains over the plant benefits the predator and detriments the
pest. Furthermore, Leman & Messelink (2015) tested the nutritional quality of different types of food sources to find out which foods supported the predator population more than the pest population. Nutritional quality and whether or not the pest species feeds on the alternative food has to be taken into account when researching the optimal quantity and -interval size for such systems.
Something that has not been tested in this research is to introduce the predator and alternative food in the system before pest invasion, so that the predator population can first reach an average density based on the
alternative food. Furthermore, the optimal density of the predator can be determined to maximally reduce the risk of pest invasions. This research considered two different initial predator densities. Future research could investigate what size of the predator population is best in restraining an invasion of pest and which quantity and interval of food pulses is best in maintaining an adequate predator density for control. Furthermore, it is interesting to investigate how large an average pest invasion is, to use a realistic pest value at introduction.
In future field research, it could be important to take the non-target effects of the use of generalist
predators into account (van Lenteren et al., 2003). The risk of generalist predators is their wide host range, which can result in invasion of generalist predators into the environment around the greenhouses, where its presence is not wanted and can negatively affect the local ecosystem (van Lenteren et al., 2003). However, there is little risk of permanent establishment of most of the predator species used in Northern European greenhouses, because most predators used can not survive outside greenhouses in winter.
Lastly, labour- and purchase costs can be included in the decision-making process. Addition of food in a greenhouse system can be labour intensive, if the alternative food is dispersed by hand and with a high frequency, for example. Therefore it could be better to include dispersion of food through the watering system or the aeration in pulses (van Rijn et al., 2002), only there has of yet been little research about the influence of different methods of dispersion. Furthermore a high frequency and high quantity of alternative food can be expensive in purchase costs, these costs could be compared with the reduction of crop damage in comparison to lower frequency and quantities.
To conclude, this research shows that addition of alternative food does not always result in the reduction of crop damage. Therefore more research is needed before introducing alternative food in a specific crop for the natural enemy of a pest species. The success of the supplementation of alternative food depends on the size of the predator population, the food preference of the predator and the size of the pest population, in combination with the quantity of the food and the interval between feeding.
A
CKNOWLEDGEMENTS
First of all I would like to thank Annabel Landman, we worked on the model together. I would like to thank her for the mental support in times of the COVID19 pandemic and the endless conversations about the research. I would also like to thank Arne Janssen, my supervisor, for the skype meetings as well as the clear and supporting feedback and the interesting insights in the research sector. I want to thank Paul van Rijn too, for letting us (me and Annabel) use his stage-structured predator-prey model, which we adapted to the aim of this research. I also want to thank Jelte, for the mental support and for feedbacking my writing. Furthermore thanks to my
roommates, Tessa and Fleur, for making me coffee and food and for supporting each others working spirit. I also want to thank my parents for being my talking point in times of need and thanks to my brother for the support all the way from China.
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