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DM-AM_model.nlogo
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; Author: Tillman Reuter
; Date: 22.07.2024
;##############################################################################################
globals [
initial-number-caves
number-bwps
number-target-patches
cave-mortality
caves-per-bwp
]
breed [bwps bwp] ;Black Woodpecker pair (Dryocopus martius)
breed [hbs hb] ;Western Honey Bee swarm (Apis mellifera)
breed [hives hive] ;Domesticated Honey Bee hive
breed [caves cave] ;Tree cavity produced by Black Woodpecker
breed [dates date] ;helper breed to create date display in upper right
patches-own [forest? target?] ;all variables that end with ? are of data type boolean
bwps-own [target]
hbs-own [pot-homes target parent]
hives-own [free? grade mortality-rate]
caves-own [free? grade mortality-rate age]
;##############################################################################################
;##############################################################################################
;## SETUP ## SETUP ## SETUP ## SETUP ## SETUP ## SETUP ## SETUP ## SETUP ## SETUP ## SETUP ####
;##############################################################################################
;##############################################################################################
to setup ;main setup
clear-all
setup-grid
setup-bwps
setup-hives
setup-caves
setup-date
reset-ticks
end
;##############################################################################################
to setup-grid
ask patches [
set pcolor 48 ;first, make everything non-forest land
set forest? false
]
ask patches with [(pycor <= 15 AND pycor >= -15) AND (pxcor <= 15 AND pxcor >= -15)] [ ;patches inside square a=31, patches are turned to forest
set pcolor 56
set forest? true
]
end
;##############################################################################################
to setup-bwps
set number-bwps round (bwp-density * 9.61) ;computing integer of bwp pairs using forest area
create-bwps number-bwps [ ;woodpeckers are initialized to be located in the forest
set shape "dmam-bwp"
set size 7
set color black
setxy random-float 30 - 15 random-float 30 - 15
]
end
;##############################################################################################
to setup-hives
let target-patches patches with [forest? = false] ;non-forest patches are selected as possible locations for hives
ask n-of number-beekeepers patches with [not forest?] [set target? true] ;of those, x are the homes of the beekeepers
ask patches with [target? = true] [
ask patches in-radius 3 [set target? true] ;in a radius of 300m the beekeepers have their hives
]
ask patches with [target? = true] [
ask patches with [forest? = true] [ ;the patches within 300m can't lie in the forest, and are therefore removed from the possible hive spots
set target? false
]
]
set number-target-patches count patches with [target? = true] ;helper variable to determine, how many of the possible spots are selected to sprout a hive
ask patches with [target? = true] [
if random 100 > (100 * number-hives / number-target-patches) [set target? false] ;stochastic process to determine which of the possible spots sprout hives
]
ask patches with [target? = true] [ ;selected patches sprout 1 hive each
sprout-hives 1 [
set size 3
set free? false
set shape "dmam-hive-occupied"
set grade 30
]
]
end
;##############################################################################################
to setup-caves
set initial-number-caves round (number-bwps * 9.3 - number-bwps ^ 2 * 0.42) ;the initial number of caves are calculated using parameters from a prior fitted
;quadratic linear model
;(data used: Zahner et al, 2017; Abs et al, 1980; Hoffmann, 2005; Müller, 2013)
set cave-mortality (cave-prod-prob / initial-number-caves * number-bwps) ;the cave-mortality is then directly coupled to the cave-prod-prob
;of a pair of Black Woodpeckers and the caves per woodpecker pair
create-caves initial-number-caves [
set shape "dmam-cave-free"
set size 3
setxy (random 30 - 15) ;free caves are placed inside forest with a random age
(random 30 - 15)
set age random-exponential (1 / cave-mortality) ;initial age distribution is set like it would emerge after long time
set grade 35 * grade-misestimation ;because the grade is calculated later in the year, than it is needed,
set free? true ;it is set to the longterm average 35 for the first year
]
end
;##############################################################################################
to setup-date
create-dates 1 [ ;date agent is placed in upper right; because sim starts with beginning of the year
set size 5
set color black
set shape "m-jan" ;first shape is January
setxy 22 23
]
end
;##############################################################################################
;##############################################################################################
;## GO ## GO ## GO ## GO ## GO ## GO ## GO ## GO ## GO ## GO ## GO ## GO ## GO ## GO ## GO ####
;##############################################################################################
;##############################################################################################
to go ;main go
proceed-date
(ifelse
ticks mod 12 = 0 [kill-bees] ;January: bees die of freezing
ticks mod 12 = 3 [produce-caves] ;April: Woodpeckers produce caves
ticks mod 12 = 4 OR ticks mod 12 = 5 [swarm] ;May and June: Honey bees swarm
ticks mod 12 = 9 [weather] ;October: Caves weather
ticks mod 12 = 11 [destroy] ;December: Caves get destroyed during winter storms
[ ])
display-labels
tick
if ticks = 1199 [ask hives [die]] ;to check the main hypothesis (is honey bee pop viable), the hives are removed after 100 years
;If pop is viable, it should hold without being fed with swarms from outside
if count (turtle-set caves with [not free?] hives with [not free?]) = 0 [stop] ;sim stops if no colonies are alive in either caves nor hives
end
;##############################################################################################
to proceed-date ;every tick (month) the symbol in the upper right changes according to the month of the year
ask dates [
(ifelse
ticks mod 12 = 0 [set shape "m-jan"]
ticks mod 12 = 1 [set shape "m-feb"]
ticks mod 12 = 2 [set shape "m-mar"]
ticks mod 12 = 3 [set shape "m-apr"]
ticks mod 12 = 4 [set shape "m-may"]
ticks mod 12 = 5 [set shape "m-jun"]
ticks mod 12 = 6 [set shape "m-jul"]
ticks mod 12 = 7 [set shape "m-aug"]
ticks mod 12 = 8 [set shape "m-sep"]
ticks mod 12 = 9 [set shape "m-oct"]
ticks mod 12 = 10 [set shape "m-nov"]
ticks mod 12 = 11 [set shape "m-dec"]
[ ])
]
end
;##############################################################################################
to kill-bees
ask hives with [not free?] [
set mortality-rate (100 - grade) ;simple estimation is used to determine the mortality-rate
if random 100 < mortality-rate [
set free? true ;hive parameters are changed to unoccupied
set shape "dmam-hive-free"
]
]
ask caves with [not free?] [
set mortality-rate (100 - grade)
if random 100 < mortality-rate [
set free? true
set shape "dmam-cave-free"
]
]
end
;##############################################################################################
to produce-caves
ask bwps [
set target one-of patches with [forest?] ;all woodpeckers move to a random forest patch
face target
move-to target
if random (1 / cave-prod-prob) < 1 [ ;with a specified probability, each pair produces a new empty cave with its base variables
hatch-caves 1 [
set shape "dmam-cave-free"
set size 3
set age 0
set grade 50
set free? true
]
]
]
end
;##############################################################################################
to swarm
let index ticks mod 12 - 3 ;variable that determines if this is the first (May) or second (June) swarm of the year
if index = 1 [
ask hives with [free?] [ ;95% of hives, whose colony died in winter get refilled by beekeepers using a freshly fertilized queen
if random 100 < 95 [
set free? false
set shape "dmam-hive-occupied"
]
]
]
ask (turtle-set caves with [not free?] hives with [not free?]) [ ;all occupied caves and trees have the probability to swarm based on their grade (half for June swarm)
if random 100 < ( grade / index ) [
hatch-hbs 1 [
set shape "dmam-hb"
set size 3
set parent myself ;the colony from which the swarm originates is noted as a variable for later needed returning of the swarm
(ifelse member? myself caves [set color yellow] [set color black]) ;swarms from caves get colored yellow, so their swarm line is drewn in yellow, for hives black
]
]
]
repeat 3 [ ;the following process is repeated 3 times, because swarms compete for new homes, and if two swarms want to
;move into the same home, one can't and has to find itself another still available home
ask hbs [
set pot-homes (turtle-set hives caves) in-radius (max-swarming-distance / 100) ;potential homes are ones, that are inside a circle of the maximum distance
set pot-homes pot-homes with [distance myself > (min-swarming-distance / 100)] ;and outside a circle of minimum distance
set pot-homes pot-homes with [free?] ;pot homes have to still be available
ifelse any? pot-homes [
set target min-one-of pot-homes [abs (distance self - (prf-swarming-distance / 100))] ;the one closest to the preferred swarming distance is selected as target
][
set target nobody
]
]
ask hbs [
draw ;draw swarming lines if draw-swarming-lines is on
if target != nobody [
face target ;swarms face their desired new home and move there
fd distance target
]
pen-up
]
ask hives with [free?] [
let candidates hbs in-radius 0.1 ;all swarms located directly on top of a free home are selected to be candidates to move in
let chosen1 one-of candidates ;one is randomly selected
if any? candidates [
set shape "dmam-hive-occupied"
set free? false
ask chosen1 [die] ;because the swarm is now a colony in the home, the swarm dies
]
]
ask caves with [free?] [
let candidates hbs in-radius 0.1
let chosen1 one-of candidates
if any? candidates [
set shape "dmam-cave-occupied"
set free? false
ask chosen1 [die]
]
]
ask hbs [
draw
face parent ;because in the next iteration of the loop, the selection of potential homes has to be repeated, the swarms
fd distance parent ;are moved back to their parent
pen-up
]
] ;end of the repeat loop
ask hbs [die] ;all swarms, that haven't found a home die
end
;##############################################################################################
to draw
if draw-swarming-lines? [ ;put pen down if switch is on
pen-down
]
end
;##############################################################################################
to weather
ask caves [set age age + 1] ;all caves age by 1 year
ask caves with [age < 11] [set grade 40]
ask caves with [age > 10 AND age < 21] [set grade age * 4] ;nonlinear function, that holds the grade of a cave from age 0 to 10, increases it linearly until 20
ask caves with [age > 20] [set grade 80]
ask caves with [age > 30 AND age < 46] [set grade age * -4 + 200] ;holds it again until 30, and decreases it linearly again until 45
ask caves [set grade grade * grade-misestimation]
end
;##############################################################################################
to destroy
ask caves [
if random (1 / cave-mortality) < 1 [die] ;every year, there is a 2% chance of dying for every cave
]
end
;##############################################################################################
to display-labels ;was used to monitor variables for bugfixing
;ask caves [set label age]
end
;##############################################################################################
@#$#@#$#@
GRAPHICS-WINDOW
208
10
879
682
-1
-1
13.0
1
10
1
1
1
0
0
0
1
-25
25
-25
25
0
0
1
ticks
30.0
BUTTON
30
145
85
178
NIL
setup
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL
1
BUTTON
87
145
142
178
NIL
go
T
1
T
OBSERVER
NIL
NIL
NIL
NIL
1
PLOT
878
83
1271
233
Number of caves and occupied caves
Years since start of simulation
Count
0.0
100.0
0.0
0.0
true
true
"" ""
PENS
"occupied caves" 1.0 0 -1184463 true "" "if ticks mod 12 = 1 [plot count caves with [free? = false]]"
"all caves" 1.0 0 -14454117 true "" "if ticks mod 12 = 1 [plot count caves]"
"hives are removed " 1.0 1 -6759204 true "" "if ticks mod 12 = 0 [ifelse ticks = 1200 [plot initial-number-caves * 1.1] [plot 0]]"
SLIDER
30
385
201
418
number-hives
number-hives
1
60
46.0
1
1
NIL
HORIZONTAL
SLIDER
29
452
201
485
max-swarming-distance
max-swarming-distance
0
2000
1000.0
100
1
m
HORIZONTAL
PLOT
878
232
1271
382
Ratio of caves occupied
Years since start of simulation
Ratio
0.0
100.0
0.0
1.0
true
true
"" ""
PENS
"occupied caves" 1.0 0 -16777216 true "" "if ticks mod 12 = 1 [plot count caves with [free? = false] / count caves]"
"total" 1.0 0 -7500403 true "" "if ticks mod 12 = 1 [plot 1]"
"hives are removed " 1.0 1 -6759204 true "" "if ticks mod 12 = 0 [ifelse ticks = 1200 [plot 1] [plot 0]]"
SLIDER
29
486
201
519
prf-swarming-distance
prf-swarming-distance
0
1200
450.0
50
1
m
HORIZONTAL
SLIDER
29
419
201
452
min-swarming-distance
min-swarming-distance
0
1000
200.0
50
1
m
HORIZONTAL
SLIDER
29
522
200
555
cave-prod-prob
cave-prod-prob
0.1
0.2
0.15
0.05
1
NIL
HORIZONTAL
BUTTON
145
145
200
178
NIL
go
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL
1
SWITCH
954
52
1139
85
draw-swarming-lines?
draw-swarming-lines?
1
1
-1000
SLIDER
29
351
200
384
number-beekeepers
number-beekeepers
3
10
6.0
1
1
NIL
HORIZONTAL
TEXTBOX
1144
14
1273
93
If draw-swarming-lines is activated, every swarm attempt is drawn. Swarm attempts by swarms that originated from hives are drawn in black, those from caves in yellow.
8
0.0
1
TEXTBOX
26
10
198
72
DM-AM model
25
0.0
1
TEXTBOX
30
48
215
148
An Agent-Based Model to investigate the influence of the density of Dryocopus martius\non the viability of a population of Apis mellifera
13
0.0
1
MONITOR
29
301
201
346
Number of caves
count caves
17
1
11
MONITOR
29
554
201
599
NIL
cave-mortality
3
1
11
MONITOR
29
257
201
302
NIL
initial-number-caves
17
1
11
SLIDER
906
425
1078
458
grade-misestimation
grade-misestimation
0.75
1.25
1.0
0.125
1
NIL
HORIZONTAL
MONITOR
954
12
1139
53
Feral HB population density [1/km^2]
count caves with [not free?] / 9.61
2
1
10
MONITOR
878
10
953
83
YEAR
(floor (ticks / 12) + 1)
17
1
18
SLIDER
29
181
201
214
bwp-density
bwp-density
0.104
1.144
0.208
0.104
1
/ km^2
HORIZONTAL
MONITOR
29
214
201
259
NIL
number-bwps
17
1
11
MONITOR
1165
166
1272
211
Years without hives
(floor (ticks / 12) + 1) - 100
0
1
11
TEXTBOX
907
407
1057
425
for sensitivity analysis:
13
0.0
1
@#$#@#$#@
# ODD-Protocol for the DM-AM model
## PURPOSE
The purpose of the DM-AM model is to determine the density of Black Woodpeckers that is necessary to supply enough caves for a population of feral Western Honey Bees to be viable in an average german forest.
## ENTITIES, STATE-VARIABLES, and SCALES
### Entities
- bwps: Pairs of Black Woodpeckers (Dryocopus martius L.)
- hbs: Swarms of Western Honey Bees (Apis mellifera L.)
- hives: Boxes, in which Honey Bee colonies are held domestically by beekeepers
- caves: Tree cavities built by bwps
### State-variables
#### bwps
- target: possible patches to fly to and potentially build next cave
#### hbs
- pot-homes: all unoccupied caves or hives, that are at least the minimum swarming distance and at most the maximum swarming distance away
- target: the 1 potential home, that lies closest to the preferred swarming distance
- parent: the hive or cave, the swarm originates from
#### hives
- free?: determines, if a hive is free or occupied
- grade: quality of the hive from a bee colonies perspective
- mortality-rate: probability of a colony to die
#### caves
same as hives +
- age: time since the cave was produced
### Scales
#### Temporal
- Grain: 1 month
- Extent: until Honey Bees have gone extinct
#### Spatial
- Grain: 1 ha (100 m * 100 m)
- Extent: 26 km^2 (5.1 km * 5.1 km)
## PROCESS OVERVIEW and SCHEDULING
Because processes happen in a yearly cycle, ticks are assigned months. Following this, processes happen only in specific months. The model starts with January (tick 0). Which agent sets are affected by which process is described in Chapter Sub-models.
- **January:** kill-bees
- **April:** produce-caves
- **May:** swarm
- **June:** swarm
- **October:** weather
- **December:** destroy
The simulation stops when the Honey Bee population has gone extinct.
## DESIGN CONCEPTS
### Basic Principles
The DM-AM model features essentially two relationships:
- The relationship of the Woodpecker density on the density of tree cavities
- The relationship of the density of tree cavities on the viability of the feral Honey Bee population.
Both relationships are coupled in this model through A -> B -> C.
The validity of the model depends on the hypothesis, that caves are at the moment the main limiting factor of feral Honey Bee viability. All other limiting factors like food resources and parasitic load (Varroa destructor) have therefore been neglected from the model. Both could later be implemented using a density regulation.
Viability is understood in the way, that the feral Honey Bee colonies can sustain the population on their own, i.e. without the support of the domesticated colonies (which are usually reinstated every year). Therefore, all domesticated bee colonies are removed in the model after 100 years, so the viability of the feral colonies can be monitored. 100 years is chosen, because under all combinations of parameters, the system has reached equilibrium until then.
### Emergence
The results show that, as expected, with more Woodpeckers, more caves emerge, and therefore the Honey Bee population is more viable.
For the model results to be interpreted properly, a follow up population viability analysis (PVA) has to be done. The goal is to find the density of Woodpeckers, for which at least 95% of Honey Bee populations last for at least 100 years after the hives have been removed.
### Sensing
Sensing appears in the form of the swarms finding possible homes around them.
In reality, scouting bees would explore the surrounding and lead the swarm to the best fit based on a democratic process. This is modelled by assuming, the swarm senses all possible homes within the maximum swarming distance (and outside the minimum swarming distance).
### Interaction
Swarms interact only indirectly by competing for possible homes to move into. In denser areas, the competition is higher by logic, because multiple swarms select the same free homes and have the same ones close to their preferred distance.
### Stochasticity
The following processes are include random choices:
#### During initialization
- Where woodpeckers and caves are placed (inside the forest)
- Where beekeepers are located (outside the forest)
- Which of their surrounding cells contain a hive
- The initial ages of caves
#### During simulation run
- Which one out of multiple candidates moves into a free home
- If a cave gets destroyed in December
- If a cave or hive releases a swarm
Except for the ages of initial caves, which are drawn from an exponential distribution, all random processes are drawn from the uniform distribution.
### Observation
- In the upper right corner of the arena and right next to it, there are a month and a year counter, to track when changes are happening. (Those counters are realized via a helper agent-set and and a common monitor respectively)
- Two plots are used to monitor the amount of caves in total and those who are occupied, and the ratio of occupied over all caves. In both, a vertical line is drawn at the moment when the hives are removed
- The shape of hives and caves is determined by their state of occupation (free?) and shows a big Honey Bee on top of it if occupied
- If a switch is activated, lines are drawn, were swarms fly. Swarms originating from hives draw black lines, from caves yellow lines
## INITIALIZATION
#### Patches
The forest is a square of side length 3.1km placed in the center of the arena. All area around the forest (ring of width 1km) is farmland / urban. This is realized using a boolean forest? and the patch color.
#### Parameters
The following parameters are needed for initialization:
- Density of woodpecker pairs: 0.1 - 1.1 / km^2 (Abs et al 1980) (this is the main input parameter)
- Number of beekeepers: 6 (derived from average beekeeper density in Germany (Deutscher Imkerbund, 2024)
- Number of beehives: 46 (derived from average beehive density in Germany (BMEL, 2024)
- Minimum swarming distance: 200 m
- Maximum swarming distance: 1000 m
- Preferred swarming distance: 450 m (all three derived from swarming preferences in Seeley & Morse, 1977 and Kohl & Rutschmann 2018)
- Probability of a woodpecker pair to produce a cave per year: 15 % (Abs et al 1980)
###### Induced parameters
- Out of the density of woodpecker pairs, an absolute number is calculated using the area of the forest.
- The initial number of caves distributed in the forest is induced by the number of woodpeckers using the following quadratic equation. The equation results from a linear model, which was fitted on data by Zahner et al 2017, Abs et al 1980, Hoffmann 2005, and Müller 2013:
> f(x) = -0.42x<sup>2</sup>+9.3x
- To guarantee, that the increment and the decay of caves are balanced out, the cave mortality is induced from the cave production probability per woodpecker pair, and the caves per woodpecker using the following equation:
> cave-mortality = (cave-prod-prob / initial-number-caves * number-bwps)
#### Patterns
- Woodpeckers and caves are placed in the forest
- Beekeepers and therefore the hives are placed in the farmland / urban area
- The hives are distributed as clusters of radius 300m around the beekeepers but strictly outside the forest
#### Distributions
The age distribution of caves follows the exponential distribution which is parameterized using the cave mortality:
`set age random-exponential (1 / cave-mortality)`
## SUBMODELS
#### kill-bees
Honey Bee colonies die of harsh conditions with a probability determined by the grade of their hive or cave by the following equation:
> mortality-rate [%] = 100 - grade
#### produce-caves
All Woodpeckers fly to a random forest patch and with a probability of 15% produce a new empty cave.
#### swarm
In May, the swarm procedure works as follows:
- 95% of hives whose colony has died in the most recent January get restocked with a new colony (common practice in bee-keeping).
- All caves and hives release a swarm with the probability [%] of their grade.
- Now all swarms look for possible free homes in a range of specified distances (described in Initialization). They select the one possible free home that is closest to their preferred swarming distance and fly there. If only one swarm flew to this free home, it can move in. If multiple swarms candidate for this home, one gets chosen randomly to move in. All others return back to their origin for then possible free homes are recalculated and the next most preferred free home is flewn to. This process repeats 3 times. Swarms, that at this point still haven't found a home to move into, die.
In June, the swarm-procedure skips the first step. In the second step, the probability to release a swarm is halved. The rest is the same. This is based on personal experience of Honey Bee swarming behaviour.
#### weather
All caves age by 1 year. Using that age, the grade is calculated following the below shown hump-shaped non-linear relationship (blue).
Hives don't weather and therefore keep a constant grade of 30 (shown in green). The dashed lines show the margin of uncertainty, which is tested using a sensitivity analysis. This uncertainty is a factor (0.75 - 1.25), which scales the grade.
#### destroy
With a probabity of `cave-mortality`, a cave gets destroyed during a winter storm.
## SOURCES
- Hoffmann, M. (2005). Der Schwarzspecht (Dryocopus martius) im Burgwald–Bestandsentwicklung, Brutbaumauswahl und Höhlenanlage. Zeitschrift Für Vogelkunde Und Naturschutz in Hessen. Vogel Und Umwelt, 16, 67–91.
- Kohl, P. L., & Rutschmann, B. (2018). The neglected bee trees: European beech forests as a home for feral honey bee colonies. PeerJ, 6, e4602. https://doi.org/10.7717/peerj.4602
- Müller, J. (2013). Schwarzspecht Dryocopus martius und Mittelspecht Dendrocopos medius als Leitarten für den Waldnaturschutz in der Vorbergzone des Nordschwarzwaldes. https://www.ogbw.de/images/ogbw/files/orn_jh/29/02_MuellerWaldvoegel.pdf
- Seeley, T. D., & Morse, R. A. (1977). Dispersal Behavior of Honey Bee Swarms. Psyche: A Journal of Entomology, 84, 199–209. https://doi.org/10.1155/1977/37918
- Zahner, V., Bauer, R., & Kaphegyi, T. A. M. (2017). Are Black Woodpecker (Dryocopus martius) tree cavities in temperate Beech (Fagus sylvatica) forests an answer to depredation risk? Journal of Ornithology, 158(4), 1073–1079. https://doi.org/10.1007/s10336-017-1467-2
- Bundesanstalt für Landwirtschaft und Ernährung. (1. Mai, 2024). Anzahl der Bienenvölker in Deutschland in den Jahren 2007 bis 2023 (in 1.000) [Graph]. In Statista. Zugriff am 22. Juli 2024, von https://de.statista.com/statistik/daten/studie/487925/umfrage/bienenvoelker-in-deutschland/
- Deutscher Imkerbund. (1. März, 2024). Anzahl der Imker in Deutschland nach Landesverbänden des Imkerbundes im Jahr 2023 [Graph]. In Statista. Zugriff am 22. Juli 2024, von https://de.statista.com/statistik/daten/studie/1085577/umfrage/anzahl-der-imker-in-deutschland-nach-regionen/
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