Batavian Demography and Army Recruitment

; Model name: HouseholdDemographics.nlogo
; Version: 3 (10 July 2015)
; Author: Philip Verhagen (VU University Amsterdam, Faculty of Humanities)

; This model is an appendix to the paper
; Verhagen, P., J. Joyce and M. Groenhuijzen 2015. 'Modelling the dynamics of demography in the Dutch limes zone' in: Proceedings of LAC2014 Conference, Rome, 19-20 September 2014

; list of global variables
; [n-deaths] number of deaths per tick/year (an integer number)
; [f-deaths] number of adult female deaths per year (an integer number)
; [sum-age-at-death] the summed age of all humans who died (an integer number)
; [sum-n-children-at-death] the sum of the number of children per deceased adult female per year (an integer number)
; [n-children-per-female] the number of children per deceased adult female per year (an integer number)
; [n-born] the number of children born per year (an integer number)

globals [n-deaths f-deaths sum-age-at-death sum-n-children-at-death n-children-per-female n-born]

; list of agent-sets
; [humans] are agents representing a single human
; [households] are agents representing a single household, containing a certain number of humans

breed [humans human]
breed [households household]

; attributes for the agent-set 'humans':
; [age] records the age of each human in number of years (an integer number; = number of ticks)
; [gender] records the gender of each human (a string; options are "F" (female) or "M" (male))
; [fertility] records the fertility rate of a female human (a floating point number between 0.0 and 1.0)
; [recruit] records the number of years that a recruited male human has served in the army (an integer number)
; [widowed] records whether the human is widowed (a binary number 0/1)
; [n-children] records the number of children born to a human (an integer number; recorded for females only?)
; [my-household] records the household of the human (a single agent from the agent-set households)
; [my-mother] records the mother of the human (a single agent)
; [my-father] records the father of the human (a single agent)
; [my-spouse] records the spouse of the human (a single agent; can be no-one)

humans-own [age gender fertility recruit widowed n-children my-household my-mother my-father my-spouse]

; attributes for the agent-set 'households':
; [household-members] records the agents who form part of the households (a number of agents from the agent-set humans)

households-own [household-members]

to setup
  
; setup creates a base set of 200 humans, with a 50% chance of them being either male or female
; first, the ages of the humans are determined in the procedure 'to age-determination', and are taken from the life table chosen in the graphical interface
; (see 'to-report mortality' for details on the life tables)

; then, all females over 18 years of age will be coupled to a spouse of the right age bracket (when available) and they will form a household
; humans who are not married will be distributed at random over the households; this is not a realistic assumption, but is only done for quick model initialisation
; for the same reason, there are in this stage no widows and no recruits, and [n-children] equals 0

  ca
  
  create-humans 200
  [

    ; determination of the age of each human is done in the module age-determination

    age-determination

    ; determination of the gender of each human, with a 50% chance of them being either male of female

    ifelse random-float 1 < 0.5
     [ set gender "M" ]
     [ set gender "F" ]

    ; the value of the variables [widowed], [recruit], [n-children] and [my-household] are set to 0

    set widowed 0
    set recruit 0
    set n-children 0
    set my-household 0

  ]
      
  ask humans with [gender = "F" and age > 17]
  
  ; all females over 18 are coupled to a spouse
  
  [
    ; a male is eligible as a husband when he is between 7 and 15 years older than the female
    
    let f-age age
    let husband one-of humans with [gender = "M" and my-spouse = 0 and age - f-age > 6 and age - f-age < 16]
    
    ; if a husband is found, he is coupled to the female, and vice versa
    
    if husband != nobody
    [
      set my-spouse husband

      ask husband [
        set my-spouse myself
      ]

      ; the couple (a temporary agent-set) then will 'hatch' a new household, which only consists of the couple itself
      
      let couple (turtle-set self husband)

      hatch-households 1
      [
        set household-members couple
        ask couple
        [
          set my-household myself
        ]
      ]
    ]
  ]
  
  ask humans with [my-household = 0]
  
  ; those humans who could not be married, are now added to a random household
  
  [ 
    ask one-of households [
      set household-members (turtle-set household-members myself)
      ask myself [
        set my-household myself]
    ]
  ]
   
  ; the global variables are now all initialized to 0 
   
  set n-deaths 0
  set f-deaths 0
  set sum-age-at-death 0
  set sum-n-children-at-death 0
  set n-children-per-female 0
  
  reset-ticks
end 

to go
  
; the model is run in four consecutive steps, executing the procedures 'to dying', 'to reproducing', 'to recruiting' and 'to marrying'
; each tick represents one year
; the order of execution implies that the steps are taken consecutively for the whole agentset of humans, so not for one human at a time
; 1 - it is determined how many new humans will be hatched this year
; 2 - it is determined how many humans will die this year
; 3 - it is determined how many males in age 18-25 will be recruited for military service this year (making them unavailable as spouses)
; 4 - it is determined how many females (unmarried or widowed) will marry this year
  
  reproducing

  dying
  
  recruiting
  
  marrying
  
  tick
  
  if f-deaths > 0 [
   set n-children-per-female sum-n-children-at-death / f-deaths
  ]

  ; the model will stop after 200 ticks/years
  
  if ticks = 201 [
    
    stop
    
  ]

  set n-deaths 0
  set f-deaths 0
  set sum-age-at-death 0
  set sum-n-children-at-death 0
end 

to age-determination

; determine the age of the population
; for each human, an age is attributed according to the following rules:
; the probability of having an age in a 5-year cohort is determined on the basis
; of the life table selected at set up (see 'to-report mortality' for more details)
; the age within the 5-year cohort is then determined at random, so a human
; in the age cohort 25-29 years will have an equal (20%) chance of being either 25, 26, 27, 28 or 29 years old
   
   ask humans
   [
     let a-number random-float 1
     
     if Life_table = "West 3 Female"[

      if a-number < 0.1472
      [ set age 0 ]
      if a-number >= 0.1472 and a-number < 0.2900
      [ set age random 4 + 1 ]
      if a-number >= 0.2900 and a-number < 0.4190
      [ set age random 5 + 5 ]
      if a-number >= 0.4190 and a-number < 0.5319
      [ set age random 5 + 10 ]
      if a-number >= 0.5319 and a-number < 0.6294
      [ set age random 5 + 15 ]
      if a-number >= 0.6294 and a-number < 0.7124
      [ set age random 5 + 20 ]
      if a-number >= 0.7124 and a-number < 0.7821
      [ set age random 5 + 25 ]
      if a-number >= 0.7821 and a-number < 0.8396
      [ set age random 5 + 30 ]
      if a-number >= 0.8396 and a-number < 0.8860
      [ set age random 5 + 35 ]
      if a-number >= 0.8860 and a-number < 0.9226
      [ set age random 5 + 40 ]
      if a-number >= 0.9226 and a-number < 0.9505
      [ set age random 5 + 45 ]
      if a-number >= 0.9505 and a-number < 0.9707
      [ set age random 5 + 50 ]
      if a-number >= 0.9707 and a-number < 0.9843
      [ set age random 5 + 55 ]
      if a-number >= 0.9843 and a-number < 0.9926
      [ set age random 5 + 60 ]
      if a-number >= 0.9926 and a-number < 0.9971
      [ set age random 5 + 65 ]
      if a-number >= 0.9971 and a-number < 0.9991
      [ set age random 5 + 70 ]
      if a-number >= 0.9991 and a-number < 0.9998
      [ set age random 5 + 75 ]
      if a-number >= 0.9998 and a-number < 0.99998
      [ set age random 5 + 80 ]
      if a-number >= 0.99998
      [ set age random 10 + 85 ]
     
     ]
     
     if Life_table = "Pre-industrial Standard"[

      if a-number < 0.1346
      [ set age 0 ]
      if a-number >= 0.1346 and a-number < 0.2661
      [ set age random 4 + 1 ]
      if a-number >= 0.2661 and a-number < 0.3867
      [ set age random 5 + 5 ]
      if a-number >= 0.3867 and a-number < 0.4945
      [ set age random 5 + 10 ]
      if a-number >= 0.3867 and a-number < 0.4945
      [ set age random 5 + 15 ]
      if a-number >= 0.4945 and a-number < 0.5899
      [ set age random 5 + 20 ]
      if a-number >= 0.5899 and a-number < 0.6732
      [ set age random 5 + 25 ]
      if a-number >= 0.6732 and a-number < 0.7452
      [ set age random 5 + 30 ]
      if a-number >= 0.7452 and a-number < 0.8063
      [ set age random 5 + 35 ]
      if a-number >= 0.8063 and a-number < 0.8573
      [ set age random 5 + 40 ]
      if a-number >= 0.8573 and a-number < 0.8988
      [ set age random 5 + 45 ]
      if a-number >= 0.8988 and a-number < 0.9316
      [ set age random 5 + 50 ]
      if a-number >= 0.9316 and a-number < 0.9565
      [ set age random 5 + 55 ]
      if a-number >= 0.9565 and a-number < 0.9744
      [ set age random 5 + 60 ]
      if a-number >= 0.9744 and a-number < 0.9864
      [ set age random 5 + 65 ]
      if a-number >= 0.9864 and a-number < 0.9936
      [ set age random 5 + 70 ]
      if a-number >= 0.9936 and a-number < 0.9991
      [ set age random 5 + 75 ]
      if a-number >= 0.9991 and a-number < 0.9997
      [ set age random 5 + 80 ]
      if a-number >= 0.9997
      [ set age random 10 + 85 ]
     
     ]
       
     if Life_table = "Woods 2007 South 25"[

      if a-number < 0.1547
      [ set age 0 ]
      if a-number >= 0.1547 and a-number < 0.3046
      [ set age random 4 + 1 ]
      if a-number >= 0.3046 and a-number < 0.4389
      [ set age random 5 + 5 ]
      if a-number >= 0.4389 and a-number < 0.5547
      [ set age random 5 + 10 ]
      if a-number >= 0.5547 and a-number < 0.6528
      [ set age random 5 + 15 ]
      if a-number >= 0.6528 and a-number < 0.7345
      [ set age random 5 + 20 ]
      if a-number >= 0.7345 and a-number < 0.8015
      [ set age random 5 + 25 ]
      if a-number >= 0.8015 and a-number < 0.8557
      [ set age random 5 + 30 ]
      if a-number >= 0.8557 and a-number < 0.8987
      [ set age random 5 + 35 ]
      if a-number >= 0.8987 and a-number < 0.9320
      [ set age random 5 + 40 ]
      if a-number >= 0.9320 and a-number < 0.9571
      [ set age random 5 + 45 ]
      if a-number >= 0.9571 and a-number < 0.9750
      [ set age random 5 + 50 ]
      if a-number >= 0.9750 and a-number < 0.9870
      [ set age random 5 + 55 ]
      if a-number >= 0.9870 and a-number < 0.9943
      [ set age random 5 + 60 ]
      if a-number >= 0.9943 and a-number < 0.9979
      [ set age random 5 + 65 ]
      if a-number >= 0.9979 and a-number < 0.9994
      [ set age random 5 + 70 ]
      if a-number >= 0.9994 and a-number < 0.9999
      [ set age random 5 + 75 ]
      if a-number >= 0.9999 and a-number < 0.999996
      [ set age random 5 + 80 ]
      if a-number >= 0.999996
      [ set age random 10 + 85 ]
     
     ]
     
   ]
end 

to reproducing
  
  ; procedure to determine if any females reproduce
  ; this depends on marriage and age; fertility ratios are determined in procedure 'to report fertility-rate'
  
  ; first, set the number of newborns for this year to 0
  
  set n-born 0
  
  fertility-rate ; determine the fertility rate of the female for this year
      
  ; then determine for each married female whether she will give birth
  
  ask humans with [gender = "F" and my-spouse != 0]
  [  
    
    ; the fertility rate is a floating-point number between 0.0 and 1.0 determined in 'to-report fertility-rate', and is based on age and the fertility estimates from Coale and Trussell (1978)
    
    if random-float 1 < fertility
    
    ; for each married female, a random number will determine whether she will become a mother
    
    [

      let mother self
      let father my-spouse
      
      hatch-humans 1 ; the possibility of having twins is not incorporated in this stage, as it is not clear how this relates to the fertility estimates used; see notes in info-section for details
      
      [
        
        ; hatched humans automatically inherit the attributes of their parents, so these should be adapted
        
        set age 0
        set my-spouse 0
        set fertility 0
        set n-children 0
        set my-mother mother
        set my-father father
        if random-float 1 < 0.5 ; the child's gender needs to be determined; since the child is produced by a female human, it will automatically be hatched with gender "F"
        [
          set gender "M"
        ]
              
        ; add the newborn to the household of its parents; the child will automatically be hatched with my-household of the mother
        
        ask my-household [
         set household-members (turtle-set household-members myself)
        ]      
      ]
        
      ; update the count of newborns for this year
      
      set n-born n-born + 1
      
      ; update the count of children of the mother
      
      set n-children n-children + 1
      
      ; update the count of children of the father (this feature is not used in the current version of the model)
      
      ask humans with [my-spouse = myself]
      [
        set n-children n-children + 1
      ]
    ]   
  ]
end 

to dying
  
; procedure to determine which humans will die this year
; the risk of dying is determined on the basis of the model life table selected at setup
; statistics will be collected to determine the number of children left behind per adult female
  
  ask humans 
  [
    
    ; the risk of dying for each human is a floating-point number between 0.0 and 1.0 determined in 'to-report mortality', and is based on age and the life table chosen at setup
    
    let risk-of-dying mortality
    
    ; for each human, a random number will determine whether they will have died
    
    if random-float 1 < risk-of-dying
    [

      set n-deaths n-deaths + 1 ; increase the number of humans who died by 1
      set sum-age-at-death sum-age-at-death + age ; get the sum of ages of humans who died
      
      if gender = "F" and age > 17 [
        set f-deaths f-deaths + 1 ; increase the number of adult females who died by 1
        set sum-n-children-at-death sum-n-children-at-death + n-children ; get the sum of the number of offspring of adult females who died
      ]
      
      ; the spouse, if applicable, will become widowed
      
      ask humans with [my-spouse = myself]
      [
        set my-spouse 0 ; it should be set to 0, otherwise my-spouse will be set to nobody, i.e. the turtle that is about to die, creating problems down the line when selecting married/unmarried turtles
        set widowed 1
      ]
      
      die
    ]
    
    ; for those humans who did not die, increase age by 1 year/tick
    
    set age age + 1
    
  ]
  
  ; it may be that the person who died was the last one of a household; in this case, the household will be deleted
  
  ask households with [count household-members = 0]
  [ 
    die
  ]
end 

to recruiting
  
  ; this procedures determines whether unmarried males between 18 and 25 years old will be recruited for army service
  ; this age is thought to be a realistic reflection of actual recruitment practices of the Roman army
  ; the recruitment rate is set using the slide at setup, and can vary between 0.0 and 0.2 (with steps of 0.01)
  ; recruited males are not available as spouses until they have finished their service term
  ; this may not be a completely realistic assumption, but it is used here to understand the
  ; consequences of removing a certain proportion of males from the reproduction pool
  
  ; recruitment will start after stabilization of the model at ticks = 100
  
  if ticks > 100 [
  
   ask humans with [gender = "M" and age > 17 and age < 26 and my-spouse = 0]
   
   ; for each unmarried male between 18 and 25 years old, a random number will determine whether he will be recruited
   
   [
     if random-float 1 < recruitment
     [
       set recruit 1
     ]
   ]
 
   ; for every year served, the value of [recruit] will be increase by 1
   ; after serving a 25-years term in the army, the male will be added to the reproduction pool, and will be available for marriage again
 
   ask humans with [recruit > 0]
   [
     set recruit recruit + 1
     if recruit > 25
     [
       set recruit 0
     ]
   ]

  ]
end 

to marrying
  
  ; this procedure will try to get unmarried females over 18 married; they will start a new household if necessary
  ; in this model, they will always be married when a suitable unmarried male is present, but many more options could be explored here; see info-section for more details
  
  ask humans with [gender = "F" and age > 17 and my-spouse = 0]
  
  [
    
    ; any unmarried male over 25 is a potential partner; this includes widowers and soldiers returning from their army service
    
    let husband one-of humans with [gender = "M" and age > 25 and my-spouse = 0 and recruit = 0]
   
    ; when a suitable husband is found, determine if a new household should be started
   
    if husband != nobody [
      set my-spouse husband
      set widowed 0
    
      let couple (turtle-set self husband)
     
      ; if the male is widowed, then the female will be added to his household
      ; else the couple will start a new household
      ; in this model, this feature is not used for any particular purpose, but it serves to keep the number of agents as low as possible
   
      ask husband [
        set my-spouse myself        
        ifelse widowed = 0
         [
           hatch-households 1        
           [
            set household-members couple
            ask couple
            [
             set my-household myself
            ]
           ]
         ] 
         [
          ask my-household [
            set household-members (turtle-set household-members self)
          ]
          set widowed 0
         ]
       ]
     ]
   ]
end 

to-report mortality
  
  ; in this procedure, the mortality rate (risk of dying) of each human is determined; it is based on one the three life tables from which the user can choose at setup; these are:
  
  ; Coale and Demeny's (1966) Model West Level 3 Female 
  ; Wood's (2007) South High Mortality with e0=25, and 
  ; and Séguy and Buchet's (2013) Pre-Industrial Standard table
  ; N.B. the first two are adapted versions taken from Hin (2013)!
  
  ; the life tables used here represent mortality rates per 5-year cohort, so mortality will only change when the human has lived for another 5 years (passes into the next cohort)
  ; this could be a little bit more sophisticated (see e.g. Danielisová et al. 2015)
  
  let mortality-5year 0 
  
  if Life_table = "West 3 Female" [
   if age = 0 [set mortality-5year 0.3056]
   if age > 0 and age <= 4 [set mortality-5year 0.2158 / 4]
   if age > 4 and age <= 9 [set mortality-5year 0.0606 / 5]
   if age > 9 and age <= 14 [set mortality-5year 0.0474 / 5]
   if age > 14 and age <= 19 [set mortality-5year 0.0615 / 5]
   if age > 19 and age <= 24 [set mortality-5year 0.0766 / 5]
   if age > 24 and age <= 29 [set mortality-5year 0.0857 / 5]
   if age > 29 and age <= 34 [set mortality-5year 0.0965 / 5]
   if age > 34 and age <= 39 [set mortality-5year 0.1054 / 5]
   if age > 39 and age <= 44 [set mortality-5year 0.1123 / 5]
   if age > 44 and age <= 49 [set mortality-5year 0.1197 / 5]
   if age > 49 and age <= 54 [set mortality-5year 0.1529 / 5]
   if age > 54 and age <= 59 [set mortality-5year 0.1912 / 5]
   if age > 59 and age <= 64 [set mortality-5year 0.2715 / 5]
   if age > 64 and age <= 69 [set mortality-5year 0.3484 / 5]
   if age > 69 and age <= 74 [set mortality-5year 0.4713 / 5]
   if age > 74 and age <= 79 [set mortality-5year 0.6081 / 5]
   if age > 79 and age <= 84 [set mortality-5year 0.7349 / 5]
   if age > 84 and age <= 89 [set mortality-5year 0.8650 / 5]
   if age > 89 and age <= 94 [set mortality-5year 0.9513 / 5]
   if age > 94 [set mortality-5year 1.000 / 5]
  ]
  if Life_table = "Pre-industrial Standard"[
   if age = 0 [set mortality-5year 0.200]
   if age > 0 and age <= 4 [set mortality-5year 0.150 / 4]
   if age > 4 and age <= 9 [set mortality-5year 0.052 / 5]
   if age > 9 and age <= 14 [set mortality-5year 0.029 / 5]
   if age > 14 and age <= 19 [set mortality-5year 0.038 / 5]
   if age > 19 and age <= 24 [set mortality-5year 0.049 / 5]
   if age > 24 and age <= 29 [set mortality-5year 0.054 / 5]
   if age > 29 and age <= 34 [set mortality-5year 0.060 / 5]
   if age > 34 and age <= 39 [set mortality-5year 0.068 / 5]
   if age > 39 and age <= 44 [set mortality-5year 0.079 / 5]
   if age > 44 and age <= 49 [set mortality-5year 0.093 / 5]
   if age > 49 and age <= 54 [set mortality-5year 0.115 / 5]
   if age > 54 and age <= 59 [set mortality-5year 0.152 / 5]
   if age > 59 and age <= 64 [set mortality-5year 0.202 / 5]
   if age > 64 and age <= 69 [set mortality-5year 0.275 / 5]
   if age > 69 and age <= 74 [set mortality-5year 0.381 / 5]
   if age > 74 and age <= 79 [set mortality-5year 0.492 / 5]
   if age > 79 and age <= 84 [set mortality-5year 0.657 / 5]
   if age > 84 [set mortality-5year 1.00 / 3.55]
  ]
  if Life_table = "Woods 2007 South 25"[
   if age = 0 [set mortality-5year 0.2900]
   if age > 0 and age <= 4 [set mortality-5year 0.1900 / 4]
   if age > 4 and age <= 9 [set mortality-5year 0.0546 / 5]
   if age > 9 and age <= 14 [set mortality-5year 0.0429 / 5]
   if age > 14 and age <= 19 [set mortality-5year 0.0707 / 5]
   if age > 19 and age <= 24 [set mortality-5year 0.1065 / 5]
   if age > 24 and age <= 29 [set mortality-5year 0.1234 / 5]
   if age > 29 and age <= 34 [set mortality-5year 0.1301 / 5]
   if age > 34 and age <= 39 [set mortality-5year 0.1366 / 5]
   if age > 39 and age <= 44 [set mortality-5year 0.1392 / 5]
   if age > 44 and age <= 49 [set mortality-5year 0.1490 / 5]
   if age > 49 and age <= 54 [set mortality-5year 0.1655 / 5]
   if age > 54 and age <= 59 [set mortality-5year 0.1857 / 5]
   if age > 59 and age <= 64 [set mortality-5year 0.2613 / 5]
   if age > 64 and age <= 69 [set mortality-5year 0.3853 / 5]
   if age > 69 and age <= 74 [set mortality-5year 0.5288 / 5]
   if age > 74 and age <= 79 [set mortality-5year 0.6403 / 5]
   if age > 79 and age <= 84 [set mortality-5year 0.7431 / 5]
   if age > 84 [set mortality-5year 1.00 / 3.55]
  ]
  
  report mortality-5year
end 

to fertility-rate
  
  ; in this procedure, the fertility rate (probability of reproducing) of each female is determined, based on the figures given in Coale & Trussell (1978)
  ; the figures used here represent fertility rates per 5-year cohort, so fertility will only change when the female has lived for another 5 years (passes into the next cohort)
  
  ; a more realistic approach would take into account the time that has passed since the previous birth
  ; however, this would make the model much slower, since we would then have to use time steps of one month
  
  ; not that fertility will be determined once a female has reached age 15; however, in this model reproduction is not allowed until the female is married
  
  ask humans with [gender = "F"]
  [
     if age < 15
     [
       set fertility 0.000
     ]
     if age > 14 and age <= 19
     [
       set fertility 0.411
     ]
     if age > 19 and age <= 24
     [
       set fertility 0.46
     ]
     if age > 24 and age <= 29
     [
       set fertility 0.431
     ]
     if age > 29 and age <= 34
     [
       set fertility 0.395
     ]
     if age > 34 and age <= 39
     [
       set fertility 0.322
     ]
     if age > 39 and age <= 44
     [
       set fertility 0.167
     ]
     if age > 45 and age <= 49
     [
       set fertility 0.024
     ]
     if age > 49
     [
       set fertility 0.000
     ]
  ]
end