Batavian Demography and Army Recruitment
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; 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
There is only one version of this model, created over 8 years ago by Philip Verhagen.
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