Assessing the spatial relationships between the predatory hoverfly
and aphid pests in complementary habitats: an Individual-Based
Modeling Approach.
By
Marc Robert
University of Amsterdam
Supervisor: Paul van Rijn
Date: 24-7-2020
Abstract
Aphids are small insects, but can form major pests for many agricultural plants. Their high abundance is (partly) caused by the low abundance of natural enemies. In this study, the focus will be on biological control of aphids by the predatory hoverfly (Diptera: Syrphidae: Syrphinae). The larvae of this species predate aphids, while the adults depend
on flowers for survival and reproduction. Aphid colonies and floral resources are often spatially separated in agricultural systems, which can be problematic for hoverflies. Using an Individual-Based Modelling approach (IBM), this study aims to explore the interactions between the environment and the abundance and spatial distribution of predatory hoverflies and aphids. It was found that hoverflies can profit from aphid honeydew consumption, as it
increased hoverfly survival and reproduction. Next, comparing population dynamics with different habitat configurations showed that there is an optimal distance (where hoverfly survival and reproduction is highest) between flower margins in the crop field (152 meters). Here, virtually no aphids were present close to the flower margin, and significant suppression was present up until 50 meters from the margins. This illustrates that a careful,
well-thought design of flower margins can improve the biological control of aphid pests.
Key words:
Natural pest control; Functional agrobiodiversity; Complementary habitats; Field margins; Floral resources; Predatory hoverflies; Individual-based modeling; Aphididae.
INTRODUCTION
The Aphididae, the largest family of aphids, includes some major pests of many agricultural plants which can cause major food and financial losses (Powell & Pickett, 2003). One of the reasons why they have become such a big problem is because the abundance of natural enemies in agricultural landscapes is significantly lower than in natural landscapes (Martin et al., 2015). This low abundance is associated with a low functional agrobiodiversity (FAB), increasing this can improve natural pest control (Pfiffner et al., 2013). Another reason why aphids are a big problem in Dutch agriculture is the commonness of monocultures. They provide aphids, which have a highly specialized parasitic lifestyle (Kennedy & Stroyan, 1959), with a high resource abundance which contributes to their population growth. Extensive sampling in the Netherlands by Van Rijn (2008) showed that in potato and wheat fields the main pests were aphids (mainly Macrosiphum avenae, Metopolophium dirhodum, Rhopalosiphum padi in wheat; Aphis nasturtii and Macrosiphum euphorbiae in potato). In addition, it was found that in these arable crops the most important natural enemies of aphids were predatory hoverflies, ladybeetles, parasitoid wasps and lacewings. Using natural enemies to combat aphid pests could be very effective because predation is the biggest natural cause of mortality in pests (Cornell et al., 1995).
To combat aphid pests, insecticides were often used. However, several problems arise from these insecticides. Large scale application of insecticides causes a severe environmental load (Van Marrewijk & Dieleman, 1980) and can lead to increased toxin concentrations in groundwater (Tilman et al., 2002). Next, insecticides are not only dangerous to aphids, but also to beneficial insects such as their natural enemies (Theiling & Croft, 1988) and can therefore decrease biodiversity. They can also impact the well-being of humans, since they may cause food safety risks (Tilman et al., 2002). Finally, a big problem with insecticides is that in the long-term they are not always effective: pests often come back after the treatment. This causes more and more application of insecticides to be necessary (Hafez, 1961), which in turn increases all earlier described detrimental effects. Therefore, to make Dutch agriculture more sustainable, the use of natural enemies of a pest as a form of natural pest control should be studied and implemented if proven to be effective.
In this study, the focus will be on predatory hoverflies, in particular Episyrphus balteatus. This species was chosen because it is one of the most abundant hoverfly species around agricultural fields in the Netherlands (Creemers, 2009) and because it is a commercially available biocontrol agent (Ingels & De Clercq, 2011) and therefore well-studied. This species predates aphids during the larval life stage. During this stage, the larvae are unable to move over long distances, which is why adult females choose to lay their eggs close to patches with aphid colonies (Almohamad et al., 2008). In contrast, adults do not predate aphids but are highly dependent on flowers. Van Rijn et al. (2013) showed that pollen from flowers are essential for egg maturation of hoverflies, and Hogg (2011) showed that the presence of flowers significantly increased egg production. Moreover, as the primary food source for adults, nectar is important for adult survival (Van Rijn et al., 2013). Adults thus depend on two spatially separated resources: flowers for survival and reproduction, and aphid populations to lay eggs. As this study also showed that the adult female hoverfly only has limited storage capacity, she should regularly switch between searching for oviposition sites and foraging for her own energy needs. In agroecosystems, this dependence on two resources can be problematic for hoverflies, because oviposition sites are within the crop field where aphids colonies live on crops, while floral resources are scarce and often only present at the margins of crop fields. This spatial separation of resources forces hoverflies to travel between the two habitats. The bigger the distance they need to travel, the more time and energy they waste that otherwise could have been spent on reproduction or survival. It is therefore interesting to study how the configuration of floral resources (e.g. the distance from crop fields to floral resources, the size of flower strips) in agriculture can influence the suppression of aphid pests by predatory hoverflies. This strategy complies with the concept of the Integrated Pest Management (IPM) (Simberloff & Rejmánek, 2011), which was designed to decrease the use of insecticides in crops by monitoring and assessing the danger of pest populations. In the IPM, there are three categories of control tactics: manipulation of the host plant, manipulation of the pest organism, and manipulation of the environment. The use of predatory hoverflies to suppress aphid populations, is part of the second category tactics. While using flower strips to support hoverfly populations is part of the third category tactics.
Almarza Díaz & Van Rijn (n.d.) used an individual-based modeling approach in a large field of aphid infested crops with a flower strip in the middle to study the dispersal patterns of female hoverflies and the resulting distribution of eggs, hoverfly larvae and aphids. The model was made in Netlogo and was called ‘ForFlies’. This model will be used as a basis and it will be analyzed and further extended where necessary. Some improvements of the model could be the incorporation of
honeydew, which is an important food source and oviposition stimulus for hoverflies (Budenberg & Powel, 1992;
Almohamad et al., 2009); the influence of the resource density on the foraging behavior of hoverflies (Tenhumberg, 2006); or the development of larvae into adults. These lacking parts of the model will be incorporated, along with other parts of the model that will be critically evaluated. The model will show what factors affect the abundance and distributions of predatory hoverflies and aphids. For example, the importance of flower strips will be analyzed by running the model for
different flower strip sizes and distances to the field. Testing this will yield valuable information for agriculture on how to use flower strips and predatory hoverflies to combat aphid pests. This theoretical study will hence extend our knowledge on biological pest control of aphids by answering the questions:
1. How can our current knowledge be modeled and which uncertainties are there?
2. What are the spatial relationships between predatory hoverflies, aphids, and the environment?
3. How, and to what extent can natural pest control by hoverflies be effective under different environmental conditions?
To answer these questions, the model will be analyzed on its current state and discussed in detail (§2.1-§2.5). Next, foraging decisions made by hoverflies will be analyzed and optimized (§2.6 & §3.1-3.3). Subsequently, the spatial relationship between hoverflies, aphids, and the environment will be analyzed by comparing the model output under different environmental conditions (§2.6 & §3.5). This will indicate to what extent hoverflies can be an effective measure against aphid pests in the short- and long-term (§3.5 & §3.6). Finally, a sensitivity analysis (§2.6 & §3.7), along with an assessment of the impact of the newly added sub-model of honeydew (§2.6 & §3.4) will be carried out to assess the model functioning, and find where uncertainties (e.g. about parameter values) may be.
It is expected that model extensions such as the incorporation of a varying energy threshold (§2.6) and the addition of honeydew (§2.6) will increase hoverfly reproduction and survival, and subsequently aphid suppression. For the former because a varying threshold will enable hoverflies to adapt their behavior to what is optimal for them at any particular moment. For the latter because with honeydew incorporated they will be provided with an additional food source. This will likely grand them additional survival, which would be similar to the findings in Van Rijn et al. (2013). Moreover, with increased food availability the hoverflies may have more time and energy available to lay eggs, leading to a higher abundance of predatory larvae which could in turn help combat aphids. Finally, the importance of the maximum distance of flower strips to the crop field may decrease. Without honeydew, hoverflies solely depend on the flower strips for their food, which causes the number of hoverflies to decrease further from the flower margin. But with honeydew being available wherever there are aphids, hoverflies may be able to survive further from the flower margins. Finally, since hoverflies depend on floral resources for both reproduction and survival, it is expected that aphid suppression will be most effective when the distance between flower margins is smallest, so that hoverflies need to travel as little as possible.
2. METHODS
The aims of this study were primarily to increase our understanding of the interplay between aphids, hoverflies, and their environment, and how this can contribute to natural pest control. It was therefore explorative in its nature. The research was conducted by creating a model of the agroecosystem. These models can be useful to increase our knowledge and to predict the dynamics of the agroecosystem. However, the predictions of a model are only useful if the model has been built carefully. An inaccurate model could yield incorrect predictions, which can have major consequences if the conclusions from the model are implied in management strategies. Therefore models must be always critically analyzed. By evaluating the potential effects and accuracy of assumptions, reassessing them and possibly incorporating more detail, the predictions of models can be narrowed down to give more certainty about the future (Wiens et al., 2009).
2.1 IBM model ‘Forflies’
The model ‘ForFlies’ made by Almarza & Van Rijn (n.d.) was used as the foundation of this study. The model was made using the ‘Individual-Based Modelling’ approach (IBM). IBM refers to models that treat individuals as unique, discrete units that have at least one property that changes during the simulation period (e.g. age, weight, social rank, reproductive value) (Grimm, 1999). Because of this feature, IBM models are often preferred over state variable approaches because these only describe population means, characteristics of individuals are therefore not considered in state variable approaches, which can bring deficiencies to the model (Grimm, 1999). In this study, the IBM
approach is preferred because it allows the individuals to behave differently: individuals that reside closer to the field margin with flowers can behave differently from individuals in the center of the field. Additionally, in a state variable approach model it would be impossible to model some part of the individuals in the flower strip and some in the crop field, which is necessary in this study. Consequently, the IBM model can generate spatial distributions that can be useful to analyze which would not be generated by models that treat all individuals in the population the same way. The original ForFlies model was lacking in a few aspects: e.g. honeydew was not incorporated; the energy threshold value was constant and did not vary with resource density; the consumption and presence of pollen was not incorporated; larvae did not develop into pupae and subsequently adults. These lacking parts, along with smaller details that were inaccurate or missing were added in this study to make the model a better representation of the agroecosystem.
The ForFlies model contains many variables and parameters. For the sake of simplicity, any variables and parameters that are discussed later in this article will not be defined or explained separately, instead, they can all be found in tables 1 and 2 with accompanying explanations and sources.
Table 1: Variables used in ForFlies. Note: these are only the variables that were used to explain the most important procedures of this model.
Variable Agent Type
(length)
Meaning Initial value and source
R0eggs - Integer The mean number of (female) eggs laid
(eggs/adult)
0
R0pupae - Integer The mean number of (female) pupae offspring
(pupae/adult)
0 Fresheggs Patch Integer Number of freshly laid eggs in the current
timestep.
0 Peggs Patch Array (4) A list of 4 items. Items move one place further
every day and thus reflect the number of eggs in each day-class. They hatch into larvae after 4 days.
0
Plarvae Patch Array (25) The number of larvae of n days old. 0 Pweight Patch Array (25) The weight of larvae of n days old. 0 Wt Patch Integer The total larval biomass in the entire patch. 0 Newpupae Patch Integer The number of larvae in the patch that have
reached their maximum weight and are ready to become pupae.
0
class
Energy Hoverfl
y
Integer Internal energy level of an individual. 1 ±0.44 [mg/insect]
Pollen Hoverfl
y
Integer The number of pollen grains from which the nutrients are stored in a hoverfly.
2000 [grains/insect]
MemoryF Hoverfl
y
Integer List of the F-ratios of the last 15 visited flower patches.
10 [flowers/hoverfly] F-ratio Patch Integer Amount of food (nectar) in a patch relative to
the local number of hoverflies.
- [flowers/hoverfly]
MemoryP Hoverfl
y
Integer List of the P-ratios of the last 15 visited patches.
10
[preybiomass/predatorbiomass]
P-ratio Patch Integer The amount of aphid relative to the amount of predators, both in terms of weights.
- [preybiomass/predatorbiomass]
Load Hoverfl
y
Integer Amount of eggs that a hoverfly can lay during the rest of its life.
Normaldistribution with μ = 800, ρ = 200 (Vanhaelen, 2002, Laubertie et al., 2012) Eggs Hoverfl y
Integer Amount of available eggs for the current day. Pollen / 50 [eggs/adult] Flowers Patch Integer The number of flowers in the patch. 20 ± 8 [flowers/patch] Nectarflowers Patch Integer Number of flowers containing nectar in the
patch.
20 ± 8 [flowers/patch] Pol_patch Patch Integer The number of pollen grains per patch. 1000 * flowers
FV Hoverfl
y
Integer Flower visitation rate. 0 [number/time step]
EA Hoverfl
y
Integer Eating reward: how much energy a hoverfly gained from eating nectar.
0 [mg/time step] Aphids Patch Integer The number of aphids in the patch. Exponential distribution
with mean =15 [Aphids/patch] Honeydew Patch Integer Amount of honeydew [mg] in the patch. 0 [mg/patch]
S% Hoverfl
y
Integer Percentage of maximum energy where the threshold lies.
Optimized in the Tenhumberg test (see methods & results). Pol_threshold Hoverfl
y
Integer Threshold pollen value at which hoverfly starts/stops looking for pollen.
Optimized (see methods & results).
pcolor Patch Boolean The color of the patch. Can be either green (crop patches) or red (flower patches)
Red/green.
Table 2: parameters used in ForFlies. Note: these are only the parameters that were used to explain the most important procedures of this model.
Parameter Procedure Meaning Value and source
Mean_flowers Set-up-patches Mean number of flowers per patch. 20 [flowers/patch] Sd_flowers Set-up-patches Standard deviation of the mean
number of flowers per patch.
8 [flowers/patch]
Nectar_p Set-up-patches
& time
The amount of nectar available per flower
0.1 [mg/flower] Pol_flower Set-up-patches The number of pollen grains per
flower.
1000 [number/flower] Pollen_max Set-up-hoverflies Maximum number of pollen grains
stored per hoverfly.
5000 [grains/insect]
A Eat Flower exploration rate. 0.5 [surface/time step]
Th Eat Flower handling time. 0.1 [time steps]
predatory larvae on aphids al., 1997)
H Time Half saturation aphid density 300 [Aphid/patch] (estimate of
1/(a*Th))
ma Time Maintenance costs of larvae. 0.05 [Energy/day]
weight_hatch Time The weight of larvae when they hatch from the egg.
0.063 [mg] (Branquard et al., 1997)
Weight_max Time The maximum weight of larvae. 28 [mg] (Hart et al., 1997)
r Time Maximum rate of population
increase of aphids.
0.23 [proportion/day] (Davis et al., 2006)
K_aphids Time Carrying capacity of aphids. 1200 [aphids/patch] (Ro & Long, 1999)
Honeydew_production Time Honeydew production per aphid. 0.025 [mg/aphid]
Decay_honey Time The proportion of honeydew that
decays per day.
0.15 [mg/day]
b Time Scale parameter gamma
distribution.
Optimized
c Time Shape parameter gamma
distribution.
1.3
Gamma_c Time Factorial of shape parameter. 0.897
Multi Time Multiplication factor. Optimized
Pol_costs Lay The nutrient requirements of laying
one egg.
50 [pollen grains/egg] Ovi_costs Lay The energy costs of laying one egg. 0.003 [mg/egg]
2.2 The environment
The landscape in the model (see figure 3a) represents two crop fields which are separated in the middle by a 4.5-meter wide flower strip (in habitat configuration ‘a’, see methods). It comprises 140,580 cells (1065 cells in the x-direction and 132 cells in the y-x-direction). Each cell represents a patch of 0.57 m2
(0.75 * 0.75 m). The fields are therefore 397 x 99 meters each. The world wraps vertically, which means that the vertical grid border is permeable and any hoverflies that cross this boundary will appear on the opposite side. The crop patches contain nearly three potato plants per patch (6 plants/m2) and are seeded with aphids. The number of aphids is drawn from an
exponential distribution with a mean of 15 aphids per patch. Flower strip patches contain flowers providing nectar as food to the hoverflies. The number of flowers per patch is calculated from a normal distribution (mean_flowers = 20, sd_flowers = 8) and every flower contains 0.1 milligrams of nectar, this amount is replenished each night. The total number of hoverflies (called turtles in NETLOGO) at the beginning of the simulation was set to 1600.
2.3 Model setup
In NetLogo, the commands in a code are carried out by agents. In ForFlies, the only agents are patches and turtles, the turtles represent the hoverflies. The patches are set up in a procedure called SET-UP-PATCHES. Here, the patches are given their initial values as described above, along with some other details which can be found in the model in the Data Repository (see Appendix C). The turtles are initially defined in the procedure SET-UP-HOVERFLIES. This
procedure gives them initial values for their starting position, energy levels, memoryF/P, egg load, and other details (see the full model in the Data Repository). Hoverflies can die in three ways: when their energy level is below 0; due to a daily natural mortality risk; and when their load is below 0, the load is the number of eggs it can lay in the rest of its life, when this is below 0 the hoverfly has no reproductive value for the population anymore, and therefore dies.
2.4 Hoverfly dynamics and behavior Strategy choice
Since hoverflies depend on two different habitats, one where they can feed on floral resources for their own survival and reproduction and one where they can lay eggs to hatch into predatory larvae, they need to decide when to perform which behavior. In the original ForFlies model, the decision between these two behaviors depended solely on their internal energy level. In this study, however, the pollen level of each individual was also incorporated. This addition was made because it makes ForFlies more realistic, as hoverflies need both resources for their reproduction. But the addition was also necessary after the addition of honeydew as an additional energy source. The addition of honeydew could potentially make it unnecessary for hoverflies in the model to visit flower strips, while in reality, they would still need to visit flower strips (all be it at a lower rate) to feed on pollen. In ForFlies, the energy and pollen levels of each individual are modeled as an internal state (energy and pollen). When these drop below a certain threshold value, an individual chooses to search for floral resources; when it rises above the threshold it chooses to search for oviposition sites (Takasu and Lewis 1993, Weisser et al. 1994, Sirot and Bernstein 1996, Lewis et al. 1998). After choosing for either foraging for food or searching oviposition sites, they need to make choices on how to find the resources (see figure 1).
Figure 1: Simplified diagram of the modeling of hoverfly choice behavior. Here, E stands for the internal energy level state of an individual; Pollen stands for the internal pollen level state of an individual; pol-threshold stands for the pollen threshold level; S stands for the threshold energy level value; P stands for the oviposition site quality; P-memory stands for the mean oviposition site quality of the previous 15 visited patches; F stands for the food patch quality; F-memory stands for the mean food patch quality of the previous 15 visited patches; H stands for the honeydew availability in the patch.
When the pollen level of a hoverfly is below the pollen threshold, it starts searching for flower patches and starts consuming pollen within the first flower patch it encounters at a constant rate. It is thus assumed that the abundance of pollen within a flower patch is not a limiting factor, but the time allocation is. Additionally, when the pollen level is above the threshold and the energy level is below the energy threshold, the hoverfly also starts searching for flower patches. In contrast to the pollen searching behavior, hoverflies assess the quality of every flower patch they
encounter. They compare the quality of each patch with the 15 previously encountered flower patches. Their memory is represented by a variable called memoryF. It contains the F-ratio of the 15 previously visited patches for every single hoverfly. The F-ratio is a measure of food availability for every patch and is calculated using a reporter as shown in code block 1. When the F-ratio of the patch they encounter is higher than the mean of memoryF they stay in the patch and start feeding (see patch exploitation and reproduction).
Code block 1: calculation of the F-ratio. ‘Count turtles-here’ gives the number of hoverflies present in the current patch.
If a hoverfly initially chooses to search for oviposition sites with the procedure OVIPOSITION, it searches in the crop field for patches with high aphid densities as prey for their larvae. The hoverfly will assess the quality of a patch to lay eggs in it. It assesses the quality by comparing the P-ratio of the patch with the P-ratio of the 15 previously visited patches (memoryP), code block 2 shows how the P-ratio is calculated. If the P-ratio in the current patch is higher than the hoverflies memoryP than it chooses to stay in the patch and lay an egg. In addition, the P-ratio also has to be higher than 20, this is the minimum ratio that is required for larvae to pupate.
Code block 2: calculation of the P-ratio. The parameters a_weight and egg_weight represent the mean weight of an aphid and a predator egg (respectively) in mg and Wt represents the weight of all predator larvae in the patch.
In addition to the original model, the crop patches also contain honeydew. Honeydew is a sugar-rich liquid that is secreted by various phloem sap-feeding insects, it consists mainly of the residue of phloem sap after digestion and assimilation in the insect gut. It is secreted via the anus onto plant surfaces (Douglas, 2009). Honeydew can be an important energy source for adult hoverflies both in the presence and absence of floral resources (Pinheiro et al., 2015, Van Rijn et al., 2013). In the model, it is assumed that hoverflies only consume honeydew when their internal energy levels are not saturated and when the honeydew concentrations in the patch are high.
Movement between patches
While searching for a resource (either floral food or aphid prey), hoverflies are assumed to perform Lévy-flight. This strategy has been observed in similar insects and turns out to be efficient (Reynolds & Rhodes, 2009). It means that at each movement step the direction is selected randomly and the step size is selected randomly from a power-law distribution (Gupta & Campana, 2002). There are some additions made to the basic Lévy-flight model: the maximum step size is limited to what is possible within one time-step (truncated Lévy-flight); when searching for floral
resources, closer to the flower strip the direction becomes skewed toward the flower strip, assuming the use of visual or olfactory cues; and all patches encountered during a time step are evaluated resource patches, assuming the use of olfactory cues (kairomones) from (plants with) aphid colonies or visual cues from flowers (Almohamad, 2008).
to-report F
report (nectarflowers / (1 + count turtles-here)) end
to-report P
let a_weight 0.2 let egg_weight 0.1
report aphids * a_weight / ( (1 + sum (peggs)) * egg_weight + Wt) end
Patch exploitation and reproduction
When a patch is selected in the FORAGING procedure, the hoverflies proceed to the procedure EAT (code block 3). The visitation rate per hoverfly (FV) is modeled as a Holling Type II functional response as shown in equation 1. The consumption rate per hoverfly (EA) is calculated using the visitation rate and is subtracted from the amount of nectar in the patch and added to the energy level of the hoverfly. A hoverfly will keep foraging within the patch until its internal energy level reached its maximum (1.47 mg) (equation 2). In this equation, a stands for the exploration rate, Th stands for the flower handling time, B stands for the number of nectar containing flowers, nectarp stands for the amount of nectar produced per flower, and E_max stands for the maximum energy storage capacity of an individual hoverfly.
f ( B)=
aB
1+T
haB
[1]E
A=
max
[
nectar
p∗
f ( B) , E
max−
E
]
[2]Code block 3: modeling of the eating procedure.
During the OVIPOSITION procedure, hoverflies will eat honeydew if the amount of honeydew in the patch is higher than some threshold (250 mg) and if their energy level is not saturated yet. If the hoverfly does not choose to consume honeydew, it proceeds to lay an egg in the patch. One fresh egg is added to the patch, at the cost of some energy and egg load of the hoverfly (code block 4).
Code block 4: LAY procedure where one egg is laid at the expense of eggs, load and energy.
The number of eggs that a hoverfly can lay on a day is updated daily and is a function of the pollen level: every egg costs 50 pollen grains, the number of eggs is hence equal to the pollen level divided by 50, but never more than 40.
2.4 Patch dynamics
In NETLOGO only agentsets can carry out procedures, in ForFlies the only agentsets are patches and hoverflies (called turtles by default in Netlogo). Therefore, patches were set up to contain other variables such as the number of eggs (peggs), the number and weight of larvae (plarvae and pweight), the number of pupae (ppupae) and the aphid population (aphids). In the procedure TIME (code block 5), these variables were updated every day. This daily simulation is carried out by letting the procedure run only once every 144 ticks, a tick is one time-step in Netlogo. In ForFlies, one tick represents 5 minutes. Assuming that hoverflies are only active during daytime, one day is thus represented by 144 ticks.
to eat
let FV a * nectarflowers / (1 + Th * a * nectarflowers)
ifelse (nectar_production * FV) > (energy_max - energy) [set EA nectar_production * FV] [set EA energy_max - energy] set nectarflowers nectarflowers - EA
set energy energy + EA end
to lay
set eggs eggs - 1 set load load – 1
set pollen pollen – pol_costs set energy energy - ovi_costs end
Code block 5: continuous simulation within every patch of 1) eggs, 2) larvae, 3) pupae, 4) aphids, 5) sprouting of adults and 6) food resources.
In Code block 5 the number of eggs in the patch (peggs) is updated by adding the number of freshly laid eggs to the first item of the array (1). Subsequently, the development of larvae is modeled by a number of variables (2). The number of larvae per age class (in number of days) is stored in plarvae and is coded by adding the number of eggs that are ready to hatch (number of four-day-old eggs). Pweight contains the weight of larvae in every age class. The first item of this list is the hatching weight of larvae, the weight of older larvae is calculated with the help of an anonymous reporter (i) and the map function (Netlogo Dictionary, n.d.), this enables the model to perform equation 3 on every item in the pweight list.
w
t+1=
w
te
g( At)(1− wt w∞ ) [3]g ( A )=(σf
A
A+H
)−
m
The total larval biomass (Wt) in the patch is finally calculated by taking the sum of the product of every item of
plarvae and pweight according to equation 4.
W=
∑
a=0 25
n (a) w (a)
[4]Where a is the age of the larvae, n is the number and w the weight of the larvae in each age class. In code block 5, for every item of pweight, it is verified if the value of that item (the weight of larvae of this age) approaches its maximum weight. If that is the case, the number of larvae of that age (corresponding item number in plarvae) is added to newpupae. Next, the items corresponding with the larvae that developed into pupae of plarvae and pweight are set
To time
1 set peggs but-last peggs set peggs fput fresheggs peggs set fresheggs 0
2 set plarvae but-last plarvae
set plarvae fput item 3 peggs plarvae set pweight but-last pweight
set pweight fput weight_hatch pweight set g sigma * f_p * ((aphids / (aphids + H)) - ma)
set pweight map [i -> (i * e ^ (g * (1 - (i / weight_max))))] pweight set Wt sum (map * plarvae pweight)
3 set newpupae (map [[a d] -> ifelse-value (a > 0.95 * weight_max) [d] [0]] pweight plarvae) set ppupae but-last ppupae
set ppupae fput sum (newpupae * 0.5) ppupae set plarvae (map - plarvae newpupae)
set padults last ppupae * 0.6
4 set aphids aphids * e ^( r * ( 1 - (aphids / K_aphids))) - Wt * f_p * (aphids / (aphids + H)) if aphids < 0 [set aphids 0]
5 if padults > 0 [
sprout-hoverflies ]
6 set nectarflowers flowers
set honeydew honeydew + honey_production * aphids - decay_honey * honeydew end
back to 0. Finally, newpupae is added to the first item of ppupae and the last item of ppupae (pupae that reached adult age) is added to padults. Once a day, if there are adults ready to emerge (padults > 0), the procedure SPROUT-HOVERFLIES is called (5). Rojo et al. (1996) showed that the mortality of larvae and adults of Episyrphus Balteatus is on average 28% and 21% respectively. Simulations showed that larval survival was initially too high (around 50%), therefore, an additional mortality rate of 50% was added (set ppupae fput sum (newpupae * 0.5) ppupae) to
approach Rojo’s findings. For pupal mortality, an additional mortality rate of 40% was added after simulations showed that the number of adults emerging in the second generation was extremely high (>10.000) and also exceeded the memory available for Netlogo. This additional mortality of pupae could avoid this, and also be more realistic since it has been shown that not all pupae survive. This additional mortality for both larvae and pupae is obviously a simplification of reality, and is therefore a point of improvement (see discussion).
Aphids (4) grow logistically and are consumed by predator larvae with a saturating (Type II) functional response to aphid density according to the Monod equation (second term in equation 5) (Healey, 1980).
A
t +1=
A
te
r (1−At K)−
W
tf
A
tA
t+
H
[5]In Code block 5 the amount of honeydew in a patch is updated daily (6). Aphids produce honeydew with a constant rate per aphid. Some honeydew decays, which can be caused by abiotic and biotic factors such as consumption by other insects or simply by being washed away by rainfall (Lommen et al., 2013). Similarly, flowers (6) refill all of their nectar every day. Note that this code is only executed once every 144 timesteps (1 timestep is equal to 5 minutes and only daytime is simulated), which means that it only regenerates once a day.
2.5 Second generation hoverflies
As explained in 2.4, the TIME procedure calls the procedure SPROUT-HOVERFLIES if enough pupae of a certain age (11 days) are present. The number of larvae of 11 days old are multiplied by 0.5 (to correct for sex, since only female hoverflies are studied here) and a variable signifying a carrying capacity of 2000 hoverflies. The product is added to the current patch and the new hoverflies are given a setup similar to SET-UP-HOVERFLIES. Finally, the number of 11 days old ppupae is set back to zero.
2.6 Model functioning and output analysis Optimization of foraging decisions
a) Resource density and the energy threshold
In the original ForFlies model from Almarza, the threshold (S) value was kept constant at the optimal value that was found through maximizing the total reproduction of the hoverfly population. However, Tenhumberg et al., (2006), showed that this optimal threshold value varies with the resource density (figure 2).
Figure 2: Optimal foraging behavior as a function of food availability and internal energy reserves. The energy reserves indicate the proportion of the maximum amount of energy in a hoverfly. Food searching is the optimal strategy in areas below the curve, while searching for hosts is optimal above the curve (Tenhumberg, 2008).
To test whether this relation between the threshold and the resource density is also present in ForFlies, the model was run for different resource densities with varying threshold values in 10-day simulations. In this test, honeydew was not incorporated (likewise in the sensitivity analysis), because the presence of honeydew could blur the relationship between floral resources and hoverfly survival and reproduction. The resource density was varied by varying flower_mean between 0 and 100. The threshold value was defined as a percentage (S%) of the maximum internal energy level of a hoverfly (1.47 mg). For every resource density, the model was run with varying S%. Subsequently, the S% yielding the highest net reproduction of the hoverflies (R0pupae) could be found. Here, net
reproduction is defined as the average number of daughters (pupae) per adult hoverfly. By comparing the optimal S% for different resource densities it could be found if Tenhumberg’s conclusions apply to this model.
To model the relationship between the threshold value and the resource density, a Gamma-distribution was made (see code block 7). The equations that are used here were derived from Van Rijn et al. (1995).
S=
multi∗1
b∗Γ (c )
y
c-1 e-y, where y =mean(memoryF)
b
[6]
Code block 6: Threshold (S) and resource density relationship.
In this code, the shape parameter (a) is kept constant. The scale parameter (b) and the multiplication factor (multi) were optimized by finding what values yield the highest reproductive output within one generation. This optimization was carried out by running the model with different parameter-settings and recording the output of R0eggs, R0pupae and
adult survival. The parameter setting that yielded the highest R0pupae was used for the rest of this study. R0 is used as
a proximity for fitness, which is assumed to be maximized by natural selection (Kour et al., 2015). b) Pollen threshold
The pollen threshold level where hoverflies decide to start searching for flower patches is unknown, therefore it was set at the optimal value, maximizing net reproduction. This optimal value was found by running the model for different fractions of the maximum pollen storage capacity, and finding what value yielded the highest reproduction. This threshold was used in the rest of the study.
Honeydew impact
To test the impact, the model was simulated with and without honeydew incorporated, and the dynamics of hoverfly and aphid populations were analyzed.
to time
ask turtles [
set food_density mean [memoryF] of self set y_g (food_density) / b
set S multi * (((1 / b * gamma_c) * y_g ^ (c - 1) * exp(-1 * y_g))) ]
Habitat configurations
Since hoverflies depend on flower strips for their survival, increasing the presence of floral resources could be effective to increase suppression of aphid pests (Ramsden et al., 2015, Hogg et al., 2011). This will be tested by making use of different habitat configurations. The initial configuration (a in figure 3) was with two crop fields of roughly 400 x 100 meters, divided by a 4.5-meter wide flower strip. Three more configurations were analyzed: (b) with two additional flower strips that split both crop fields into two; (c) with six flower strips evenly distributed over the width of the field; (d) with flower strip distances that could help with maximum aphids suppression (configuration to be determined later). Since the number of flower plots will increase when more flower strips are added, it may be obvious that pest control will increase just for the reason that there are more resources, and not because of the way the resources are distributed. Therefore, there was corrected for this increase to keep the total number of flower plots equal. This means that in the second configuration (with three flower strips instead of one in the initial
configuration), the strips were made thrice as narrow (1.5 meters wide instead of 4.5 meters wide) as in configuration ‘a’. A similar correction was made for configuration ‘c’. From the findings of these configurations, it was finally assessed to what extent hoverflies are able to suppress aphid populations. If aphid suppression is too little in these configurations, another configuration will be made purposed to find conditions where maximum aphid suppression will be accomplished (configuration ‘d’)
Figure 3: Habitat configurations. (a): one flower strip of 6 patches wide and 132 patches long (792 patches in total); (b): three flower strips of 2 patches wide and 132 patches long (792 patches in total); (c) six flower strips of 1 patch wide and 132 patches long (792 patches in total).
Apart from the adaptions to the distribution of resources, another modification of the model was made between the three configurations. Namely, in model ‘a’ the hoverflies search using Lévy-flight with a direction that is skewed toward the flower strip in the middle. But since floral resources are not only present in the middle of the crop field in configurations ‘b’ and ‘c’, the hoverflies should also search in the direction of other floral resources. Therefore, the target was coded differently in the three models and the differences can be found in code blocks 8, 9 and 10. Note that the ‘target’ is not the real target, but acts as the center of a (circular normal) probability distribution of directions.
Code block 7: target formulation in model configuration ‘a’. It is simply directed toward the flower strip, which has xcor = 532, ycor can be of any value.
Code block 8: the target is updated according to the hoverflies current location. The closest flower margin is chosen as the target.
Code block 9: the target is updated according to the hoverflies current location. The closest flower margin is chosen as the target.
Second generation hoverflies
Paragraph 2.5 described how the second generation of hoverflies was modeled. The functioning of this sub-model was tested to see if a viable, stable hoverfly population can be sustained.
Sensitivity analysis
Finally, a sensitivity analysis (SA) can be used to study how uncertainties in the output of the model can be allocated to different sources of uncertainty in the model, such as parameter values or initial values of variables (Saltelli, 2002). Here, different values for the initial number of hoverflies and aphids were analyzed, as well as different parameter values such as the mean number of flowers per patch (mean_flowers) and the maximum energy storage in an adult hoverfly (E_max). For every varied parameter/variable, the model was run with five threshold values (S), and the data output was stored and analyzed. The simulation was stopped when the development of larvae ended, because the effects of aphid suppression are apparent after one generation.
if xcor <= 267 [set target patch 266 ycor]
if xcor > 267 and xcor <= 399 [set target patch 267 ycor] if xcor > 399 and xcor <= 532 [set target patch 532 ycor] if xcor > 532 and xcor <= 666 [set target patch 533 ycor] if xcor > 666 and xcor <= 798 [set target patch 798 ycor] if xcor >= 799 [set target patch 799 ycor]
if xcor <= 152 [set target patch 152 ycor]
if xcor > 152 and xcor <= 228 [set target patch 152 ycor] if xcor > 228 and xcor <= 304 [set target patch 304 ycor] if xcor > 304 and xcor <= 380 [set target patch 304 ycor] if xcor > 380 and xcor <= 456 [set target patch 456 ycor] if xcor > 456 and xcor <= 532 [set target patch 456 ycor] if xcor > 532 and xcor <= 609 [set target patch 609 ycor] if xcor > 609 and xcor <= 685 [set target patch 609 ycor] if xcor > 685 and xcor <= 761 [set target patch 761 ycor] if xcor > 761 and xcor <= 837 [set target patch 761 ycor] if xcor > 837 and xcor <= 913 [set target patch 913 ycor] if xcor > 913 [set target patch 913 ycor]
3. RESULTS
3.1 Tenhumberg effect test
Testing whether ForFlies has a relationship between the optimal threshold value and resource density yielded the results in figure 4. Underlying data can be found in Appendix A.
0 20 40 60 80 100 120 0 10 20 30 40 50 60 70
Optimal threshold
Flowers_mean (number/patch) S%Figure 4: distribution of the optimal threshold with different resource densities.
These results show that the optimal threshold indeed varies with the resource density. The optimal threshold is highest at 10 flowers per patch, and decreases with either lower or higher resource abundances.
3.2 Pollen threshold optimization
Testing the model for different pollen threshold yielded the data in table 3. Pol_threshold is the fraction of the total pollen storage capacity.
Table 3: optimization of the pollen threshold. Bold numbers are the highest in their category.
Pol_threshol
d (%)
R0
egg(eggs/adul
t)
R0
pupae(pupae/adul
t)
Larvae
surviva
l (%)
90
145
22
15.2
60
144
22
15.3
40
144
22
15.3
30
141
23
16.3
25
139
24
17.3
20
129
27
20.9
17.5
124
25
20.2
15
121
25
20.7
10
110
26
23.6
7.5
99
24
24.2
5
87
23
26.4
2
86
24
27.9
1
77
21
27.3
With increasing pollen threshold, the number of eggs laid per female increases to a maximum of around 145. R0pupae
is affected less severe but has an optimum at a relative threshold of 20%. As a result, larval survival increases with a decrease of R0eggs. Except for the survival at a pollen threshold of 1%, this was lower than survival at a pollen
threshold of 2%, even though the number of eggs was lower.
3.3 Adaptive Energy Threshold function
To find the ideal gamma function for the relationship between the threshold energy level (S) and the resource density, the scale parameter (b) along with the multiplication factor (multi) of the gamma-model were optimized.
Theoretically, an infinite number of permutations could have been tried. But due to a lack of time (partly caused by very slow simulations), only a limited amount of permutations (16) were carried out. The choice of permutations was based on the simulation outputs with constant thresholds, the shape of the function and the change of memoryF in the simulations (fairly similar in all simulations). For example, with b = 0.25 and multi = 0.8, the threshold drops to 0 at memoryF > 2. This strong decline is caused by the low value of the scale parameter. The model could have been run with the same scale parameter with different multiplication factors, but since this would not make any difference when memoryF > 2 (the threshold would still be 0) these permutations were not carried out, since this would very likely not yield high reproduction and still be time-consuming. Furthermore, the highest point of the function could not be higher than the maximum energy storage capacity (1.47 mg) of a hoverfly, therefore the parameters were designed to keep the highest point below 1.47. The results of this optimization can be found in table 4.
Table 4: optimization data of the gamma threshold function. Here, the three highest outputs of R0eggs, R0pupae and hoverfly survival are written in bold.
Scal
e
Multiplication
factor
Function
highest point
(% of E_max)
R0-egg
(eggs/adult)
R0-pup
(pupae/adult)
Larvae
survival (%)
Hoverfly survival
(days)
7.5
23
95.2
104
27
26.0
51
10
20
34.0
125
26
20.8
47
20
20
68.0
119
26
21.8
41
5
15
95.2
123
25
20.3
42
10
30
74.8
130
23
17.7
48
20
50
95.2
125
23
18.4
47
5
10
68.0
108
22
20.4
40
20
60
95.2
123
20
16.3
46
3.5
11
95.2
97
20
20.6
35
15
50
100
81
19
23.5
63
10
5
17.0
85
17
20.0
31
5
5
34.0
90
16
17.8
27
2
5
74.8
65
13
20.0
23
1
3
95.2
59
12
20.3
20
0.5
1.5
88.4
55
12
21.8
19
0.25
0.8
100
50
10
20.0
19
The highest R0pupae was thus found with a scale parameter (b) of 7.5 and a multiplication factor (multi) of 23. The
Figure 5: gamma distribution found through optimization with scale (b) = 7.5 and multiplication (multi) = 23. The x-axis is plotted until memoryF = 30, since the simulation showed that memoryF never exceeded this value.
The highest point of the threshold is in this function at 95.2% of the maximum energy capacity at mean memoryF = 2.5 flowers/hoverfly. This means that at this resource density, the hoverflies will only decide to lay eggs when their energy level is higher than 95.2% of their maximum energy capacity. With lower memoryF, so when food is (very) scarce, the threshold declines rapidly, indicating that hoverflies will lay eggs also at lower energy levels. With higher food densities, however, the threshold declines asymptotically.
3.4 Honeydew impact
The addition of honeydew in the model had a significant impact on the reproduction by the first generation of hoverflies. R0eggs increased from a total of 125 eggs tot 151 eggs, and R0pupae increased from 24 to 42. Larval survival hence also
increased from 19.2% to 27.8%. The hoverflies furthermore spend less time eating nectar, but they did not visit the flower strip less often. The mean energy level of hoverflies increased while the standard deviation decreased. Eggs were laid further from the flower margin, which caused aphid suppression to occur further from the flower margin. As aphid numbers are higher further from the flower margin, mean memoryP increased strongly, especially at the end of the simulation. A summary with graphs of these results can be found in table 5. Here, the processes that were not (significantly) impacted by the incorporation of honeydew (e.g. adult survival, internal pollen level, number of available eggs) are not shown but can be found in the Data Repository (see Appendix C).
Table 5: Comparison of the model with and without honeydew incorporated.
Without honeydew With honeydew
R0eggs 125 151
R0pupae 24 42
Energy
Adult survival
Mean aphid density Eggs Memory P 3.5 Habitat configurations
In the comparison of habitat configurations, honeydew, pollen and the gamma-function for the energy threshold were incorporated. Between the configurations, the total number of flower patches remained equal (792), but they were divided into more and narrower flower strips. The provisioning of floral resources was thus distributed more equally over the crop field, so that hoverflies could allocate them more easily. The most important results, with graphs, can be found in table 6. Reproduction increased significantly. Adult mortality decreased in the beginning of the simulation, however, the last hoverfly of the first generation died at approximately the same day in all configurations. The mean number of aphids was significantly higher in configuration ‘a’ compared to configuration ‘b’ and ‘c’. These three configurations indicated that full aphid suppression only happens at the first 25 meters from the flower strip. Therefore, habitat configuration ‘d’ was also made with the expectation that full aphid suppression should be accomplished over the entire crop field when the maximum distance between flower strips is 27 meters. However, this is not what was found. In fact, aphid suppression was even weaker than in configurations ‘a’, ‘b’, and ‘c’. Also, the reproductive output of the first generation of hoverflies was lower. Only larval survival was improved in configuration ‘d’ compared to ‘a’, ‘b’ and ‘c’.
Table 6:comparison of the most significant differences between habitat configurations a, b, c and d. Note that the x-axis in the last graphs is not labeled correctly: it shows the distance from the middle of the field, combining the left and the right direction.
Habitat configuration a Habitat configuration b Habitat configuration c Habitat configuration d Distanc e betwee n strips (m) - 266 152 27
R0eggs 151 252 252 145 R0pupae 42 78 97 71 Larval survival 27.8% 31.0% 38.5% 49% Adult survival Mean aphid density Eggs Aphid suppres sion 3.6 Second generation
To test how the model predicts the emergence of the second generation hoverflies, the model was run with habitat configuration ‘a’, and with honeydew, pollen and the gamma function for the energy threshold incorporated.
Figure 6: (a) number of hoverflies alive through the simulation, (b) net reproduction rate of pupae and (c) mean larval biomass and number of eggs.
Figure 7a shows how after 39 days the second generation of hoverflies starts to emerge. With an R0pupae of 42 (see table 6),
which is multiplied by 0.5 (to correct for sex) and a variable representing a carrying capacity for adults, the second generation was insignificant. The reproduction of the second generation was per hoverfly also lower than in the first generation (figure 7b). With fewer adults, this therefore led to a significantly lower total reproduction. Note that the simulation stopped at the end of the curve, but unfortunately not intentional. At this point in the simulation, the memory usage of the model becomes so big, that the program crashes. So in fact, it is unknown how the rest of the simulation would have turned out, and if the hoverfly population was going to be stable. However since the growth of larvae was already severely decreasing at this point (see figure 7c), R0pupae will most likely go to 0 within a few days. A third-generation will
3.7 Sensitivity analysis Initial number of hoverflies
Figure 7: sensitivity analysis output for different initial numbers of hoverflies. Here, adult cohort survival is measured as the time in days until the last adult of the initial population died. The aphid suppression distance is defined as the distance where the number of aphids is half the maximum number of aphids at the end of the simulation.
Figure 8 shows the trajectory of the reproductive outputs (R0eggs and R0pupae), adult survival and the aphid suppression
distance with an increasing number of initial hoverflies. With an increasing number of hoverflies, the R0 (the number of eggs/pupae produced per adult) decreases. The survival of larvae also decreased, and adult cohort survival slightly increased. Aphid growth is inhibited further from the flower margin.
Initial number of aphids
Figure 8: sensitivity analysis output for different initial numbers of aphids. Here, larvae survival is the proportion of larvae that developed into adults (R0pupae/R0eggs) and the aphid suppression distance is defined as the distance where the number of aphids is half the maximum number of aphids at the end of the simulation.
With an increasing initial number of aphids, the reproductive output of eggs increases slightly. With increased larval survival, the reproductive output in terms of pupae increased more significantly. And finally, the distance of aphid suppression decreased slightly, as enough aphids could be found closer to the flower strip.
Maximum energy storage
Figure 9: sensitivity analysis output for different energy storage capacities. Here, adult cohort survival is measured as the time in days until the last adult of the initial population died and the aphid suppression distance is defined as the distance where the number of aphids is half the maximum number of aphids at the end of the simulation.
An increase of the maximum storage capacity of hoverflies increased the number of eggs that are laid and eventually also increased the number of pupae that developed, despite that there is no significant difference in R0pupae between
E_max = 0.735 and E_max = 1.47. This stabilization is caused by a decrease in larvae survival. The aphid suppression distance increases with increasing energy storage capacity. Finally, the survival of the adult cohort increases significantly for lower threshold values (S=20 and S=35) but does not change for intermediate or high threshold values.
Mean number of flowers per patch
Figure 10: sensitivity analysis output for different initial numbers of hoverflies. Here, adult cohort survival is measured as the time in days until the last adult of the initial population died. The aphid suppression distance is defined as the distance where the number of aphids is half the maximum number of aphids at the end of the simulation.
The mean number of flowers in flower patches seemed to have the lowest impact on the model. There is no significant effect on R0eggs, on adult survival and on aphid suppression. On the other hand, larval survival (not shown) was affected and
4. DISCUSSION Sensitivity analysis
In the sensitivity analysis, the behavior of the model was analyzed for different initial values of four aspects of the model: the initial number of hoverflies; the initial number of aphids; the number of flowers per patch; and the energy storage capacity of hoverflies.
An increase in the initial number of hoverflies led to a decrease in fecundity (R0eggs,) which is probably caused by increased
competition between adults for suitable oviposition sites. With more adults, there will be more eggs laid in total. This increase in the total number of eggs will increase the competition between individual adults because patches will contain more eggs, forcing adults to reject patches more often because there are already too many eggs. This will in turn decrease the individual measure of reproduction: R0eggs. R0pupae decreased even stronger than R0eggs with an increase in the number of
hoverflies. This is caused by increased competition between larvae, because the total number of eggs (R0eggs multiplied by
the number of hoverflies) increased, the number of larvae per patch also increased. Therefore larval competition increased, which made it harder for larvae to grow to 28 milligrams upon which they pupate. The distance of aphid suppression increased significantly, there are two reasons why: since adults search for oviposition sites in a random direction, an increase of the number of adults increases the chance that some adults reach areas further from the flower margin; and since the total number of eggs and larvae in patches increased, the adult hoverflies were forced to search further from the flower margin for patches with high prey/predator ratios. The survival of the first generation of hoverflies increased slightly (except for threshold S% = 20). Since this increase is very small, it is most likely caused by random chance. The hoverflies have a daily random natural mortality risk, and therefore the number of hoverflies that survive each day is bigger if the number of hoverflies is bigger and the total time until the last hoverfly dies increases. The optimal threshold (S%) increases with the initial number of hoverflies, being 35%, 50%, and 80% consecutively. A reason for this could be that more hoverflies lead to more competition (between adults for high-quality food and oviposition patches and between larvae for prey), which is why it is more efficient to spend time and energy on survival instead of on reproduction. However, the differences in reproductive output for different thresholds are so small that it could also be caused by random chance or other effects. An increase in the initial number of aphids per patch led to an increase of R0eggs, this is most likely caused by an increase of
the quality of oviposition sites: patches with more aphids are more appealing for hoverflies to lay eggs. The increase of
R0pupae was similar to R0eggs, but more significant. This is caused by the increased survival of larvae. With more aphids, there
is a higher food availability for the larvae, which enables more larvae to reach their maximum weight and pupate. The impact of aphid numbers on the threshold is very small: for every aphid level, the threshold at 50% of energy capacity is optimal.
With increasing energy storage capacity, the number of eggs laid by the first hoverfly cohort increased significantly, as expected. The life expectancy of hoverflies increased slightly which gave them more time to lay eggs. But the energetic mortality risk of laying eggs also decreased, i.e. they could lay eggs at lower relative thresholds (S%) because with increased maximum energy capacity the energy threshold also increased. Consequently, the optimal threshold (threshold yielding the highest R0pupae) decreased with increasing energy capacity. The survival of pupae showed unexpected behavior with
increasing energy storage. With increasing storage capacity it first decreased and then increased again. The former was expected, since an increase of eggs will lead to more competition between larvae. But the latter was unexpected. However, it could be explained by the distance from the margin where hoverflies were able to lay eggs. With higher energy levels they were able to lay eggs further into the field. The competition between larvae was lowered because they were distributed over a bigger area, consequently, larval survival increased.
Finally, the sensitivity analysis with varying numbers of suitable flowers showed the most unexpected results. There was no significant effect on R0eggs, adult survival, and on the aphid suppression distance. Only larval survival, and consequently
R0pupae, showed significant variations with the mean number of flowers. It was lowest for intermediate flower means, and
was highest for lower flower means. Unfortunately, none of the findings are what was expected or what should be expected. The exact cause of these unexpected results is unknown. Apparently, larval competition was lowest in the simulation with low floral resources. Even though it was expected that larval competition should be higher with fewer resources for adults, since low resource availability would mean that adults have lower energy levels, disabling them to spread their eggs further from the flower margin. Moreover, an increase in resource abundance should increase the longevity of adult hoverflies because it should provide them with more energy. Furthermore, with more floral resources, it was expected that R0eggs would increase. It should have increased the internal energy levels of hoverflies, enabling them to
lay more eggs (because they need to spend less time looking for food). Additionally, with higher energy levels they should have been able to travel further into the crop field, where the prey/predator ratio is higher, consequently supporting them to lay more eggs and suppress aphid populations further from the flower margin. Ultimately, an increase in resources should always increase, not decrease R0, otherwise the hoverflies do not respond optimally.
Honeydew incorporation
By adding honeydew to ForFlies, the model was made more realistic. After all, studies have shown that honeydew can be an important food source for adult hoverflies. Excluding it from the model will therefore give uncertainties about the reliability of model predictions. As expected, the addition of honeydew improved hoverfly performance, i.e. adults had more energy available which consequently resulted in a higher reproduction (both fecundity and R0-pupae) and a slight improvement of aphid suppression. However, adult survival did not increase. This unexpected result could be partly caused by the daily mortality risk (from other causes then starvation) which was not changed. Another reason could be that the competition between adults for oviposition sites increased (see the increase of memoryP in table 5). This forced the adults to search longer and further from the border for oviposition sites, since this costs a lot of energy it could have increased mortality. However, if the latter is true, this should be visible in the graphs of the energy level, but this is not the case. Perhaps this is not visible because of a small mistake in the modeling or visualization of energy. A final reason, and perhaps the most plausible one, could be that more adults died because they had no more reproductive value for the population: every adult can lay 800 eggs during its lifetime (load), as soon as it has no eggs left, it also dies. These three (potential) reasons for increased mortality could have balanced the expected increase of survival due to higher energy levels.
Habitat configurations
The comparison between habitat configuration a, b and c showed that a more even distribution of floral resources can help in suppressing aphid populations. The mean number of aphids at the end of the simulations decreased from 1670 aphids per patch to 1500 aphids per patch. This number is still high enough to be very damaging for the crop yields. However, it should be noted that this is the mean over the entire field. Aphid suppression decreases severely with increasing distance from the flower margin: complete suppression (no aphids when larvae have developed) only reaches roughly 20 meters from the margin, and already at 80 meters there is no suppression at all. Closer to the flower margins the suppression is significant. It was therefore expected that when even more flower strips are present (and therefore closer together), larval predation will be large enough to completely suppress aphid populations. Since there is full aphid suppression up to 20 meters from the flower margin, it was expected that the flower margins should be separated by approximately this distance. Therefore, the outcomes of habitat configuration ‘d’ were very unexpected. Lowering the distance between flower strips to 27 meters actually had detrimental effects for aphid suppression: R0 decreased, mean aphid density increased and there was no full aphid suppression anywhere on the field. Only larval survival went up, indicating that the larvae were distributed more evenly on the field, which can also be noted in the graph with the mean number of eggs throughout the crop field. Therefore, farthest from the flower margin, the number of aphids was lowest in this configuration compared to the others. But nowhere on the field it was field high enough to suppress aphid growth, which is why aphids were able to approach their carrying capacity everywhere on the field. It thus seems that there is an optimal distance between flower strips, which is not simply the lowest possible distance, which was expected since this would provide hoverflies with the most resources. With the configurations tested here, the optimal distance was 152 meters, because this yielded the highest reproduction and lowest aphid numbers. Note that this analysis was performed with only one set of conditions for the model: only one initial number of hoverflies; one initial number of aphids; only one generation was analyzed. Similarly to the sensitivity analysis, running the different habitat configurations with different initial conditions might yield different results. For example, in reality, the number of hoverflies is not constant but will respond to the conditions created. With better conditions (e.g. more flower strips) more hoverflies will be attracted or will emerge from the field itself. A wider distribution of flower strips may therefore also need a higher number of hoverflies to be effective. It would, therefore, be interesting to perform a sensitivity analysis on all the habitat configurations.
Second generation
The simulation where pupae were sprouted into the second generation of hoverflies showed that the reproduction is too low to sustain a stable population. This would thus mean that natural control by hoverflies will, alone, not be sufficient to suppress aphid populations. However, due to technical difficulties with the model this conclusion is not final. First of all, as discussed in 3.5, the program consistently crashed during long simulation periods, due to a memory overflow. Therefore, the simulation could not be fully analyzed. Second, there may be a modeling mistake with the sprouting of the second
generation of hoverflies. With an R0pupae of 42, there should be enough input for the second generation. But the simulation
showed that the second generation was very small. The exact mistake in the model is currently unknown, but it may be caused by a too high mortality of pupae. In future research, ForFlies could be analyzed to find the causes of this.
