3.2 System of human population: the Human Module
3.2.1 Structure of the household agent
As already outlined above, the structure of the household agent is as follows:
Household Agent=(Household Profile, Internal Rules, Landscape Vision, Decision Module)
In the following, we will describe all of these four components in detail, and introduce the range of variables used within the model of the household agent.
Household Profile
The Household Profile (Hprofile) includes seven sub-types of variables: social identity and livestock (Hsoclive), human resources (Hhuman), land resources (Hland), financial resources (Hincome), environmental variables (Henv), irrigation variables (Hirr), and policy-related at-tributes (Hpolicy):
Hprofile={Hsoclive, Hhuman, Hland, Hincome, Henv, Hirr, Hpolicy}
The social identity and livestock factor (Hsoclive) includes age of the household head (Hage), village code (Hvillage), the number of wives of the household head (Hwives), the number of cattle belonging to the household (Hcattle), the livestock index (Hlivestock), and the group membership (Hgroup):
Hsoclive={Hage, Hvillage, Hwives, Hcattle, Hlivestock, Hgroup}
The agent’s human resources (Hhuman) consist of household size (Hsize), labor availability (Hlabor), the dependency ratio (Hdepend), and Hpool dry and Hpool rainy, which are the labor pool in the dry respectively in the rainy season (in labor days). The dependency ratio is the ratio of labor availability and household size, representing the composition of workers and non-workers in the household:
Hhuman={Hsize, Hlabor, Hdepend, Hpool dry, Hpool rainy}
Household land resources Hland comprise six variables including total area owned by the household (Hholdings), total area owned per capita (Hholdings per cap), cultivated area in the dry season (Hcult dry), cultivated area in the rainy season (Hcult rainy), and land-use composition vectors for each of the two seasons ([H% i dry], i=(1 . . . N)) and ([H% i rainy], i=(1 . . . M)):
Hprofile
Hsoclive Hhuman Hland Hincome Henv Hirr Hpolicy
? ? ? ? ? ? ?
Age Hage
Household Size Hsize
Total Holdings Hholdings
Gross Income per
capita Hgross percap
Distance to Main River Hdist river
Dry-Season Status Hdry dummy
Number of Credits Hnr credits Village
Hvillage Labor
Availability Hlabor
Holdings per capita Hhlds percap
Gross Income Dry
Hgross dry
Distance to Dams Hdist dams
Irrigation Method Hirr method
Credit Status Hcredit Wives
Hwives Dependency
Ratio Hdepend
Cultivated Area Dry
Hcult dry Cash
Income Dry Hcash dry
Distance to Water Sources Hdist water
Neighbors Doing Irrigation Hneigh irr
Years of Irrigation Farming Hyears irr
Motor Pump Hpump Cattle
Hcattle
Labor Pool Dry Hpool dry
Cultivated Area Rainy
Hcult rainy Gross Income
Rainy Hgross rainy Livestock
Hcattle
Labor Pool Rainy
Hpool rainy
% Land-Use Dry hH% lu dryi
Cash Income Rainy Hcash rainy Group ID
Hgroup
% Land-Use Rainy hH% lu rainyi
% Income Land-Use Rainy H% inc rainy
Figure 3.2: Household Profile
Hland={Hholdings, Hholdings per cap, Hcult dry, Hcult rainy, [H% i dry], [H% i rainy]}
where i indexes the dry-season respectively the rainy-season land-use types.
The factor of financial resources of the household (Hincome) comprises total gross income per capita (Hgross per cap), gross and cash income in the dry season (Hgross dry) and (Hcash dry) respectively, gross and cash income in the rainy season (Hgross rainy) and (Hcash rainy) re-spectively, as well as an income composition vector of income from rainy-season cultivation ([H%j], j=(1 . . . M)), with j indexing the rainy-season land-use types:
Hincome={Hgross per cap, Hgross dry, Hcash dry, Hgross rainy, Hcash rainy, [H%j]}
The environmental variables (Henv) include distances from the compound of the household to main river (Hdist river), to dams (Hdist dams), and to water sources in general (Hdist water), which represents the distance to irrigable areas and is calculated as the minimum of Hdist river and Hdist dams:
Henv={Hdist river, Hdist dams, Hdist water}
The state of a household agent regarding irrigation (Hirr) includes five variables: i) a dummy variable variable (Hdry dummy) indicating if the farmer is inherently capable of doing irriga-tion, ii) a second variable reporting the kind of irrigation technology (Hirr method) for those households with (Hdry dummy= 1), ranging from bucket irrigation, pump irrigation to dam irrigation, iii) a variable indicating the percentage of household heads practicing irrigation among the five nearest households, iv) a variable representing the number of years the farmer has practiced irrigation (Hyears irr), and v) a dummy variable (Hpump) indicating whether the household owns a motor pump.
Hirr={Hdry dummy, Hirr method, Hneigh irr, Hyears irr, Hpump}
The variables of Hpolicyinclude two variables: i) the credit status Hcredit, a dummy variable indicating whether the household has obtained credit in the current year, and ii) Hnr credits, the number of credits the household has obtained so far.
Internal Rules
During model run, most of the model variables are subjected to changes over time. Changes in the performance of the household module involve i) modifications of variables of the House-hold Profile of agents, and ii) the creation and deletion of agents. The Internal Rules only comprise simple rules defining the changes of household variables, while the deletion and creation, which involve more complicated mechanisms, are described in the subsequent sec-tion.
It is important to understand the kinds of changes the variables of Household Profile undergo over time. We can categorize these variables into four categories: i) variables that
undergo no change, ii) variables whose changes are due to the effects of household agent activities during simulation (e.g. changes in gross annual income and/or land resources), iii) variables whose changes are defined by natural events, independent of the agent’s actions (e.g. the increase of the age of the agent), and iv) changes that are defined by settings outside the system, e.g. policies. The only Household Profile variables that undergo no changes are village code and distance to main river. All variables that are among the sets of Hland, Hincome and Hirrbelong to the second category and are thus subjected to the internal changes within the system. However, changes of variables within the third and fourth category have to be modeled explicitly, since they are not a result of human-environmental interactions. This task will be accomplished by the procedures of the Internal Rules:
Variables of the third category that undergo natural changes include Hage, Hwives, Hcattle, Hlivestock, Hlabor, and Hdepend.
The rule for the changes in age is simple. The age of the household head Hagewill increase by 1 after each time step, until the upper bound maxageis reached. The rule is as follows:
t+1Hage= ( t
Hage+1 iftHage<maxage
die iftHage=maxage (3.1)
All other variables of this third category are also event-driven phenomena, but they are affected by many causes that are beyond the scope of our study. It is, therefore, reasonable to proximate stochastically the values of these household attributes within uncertainty ranges of the values of the previous time step. For all these variables, the kind of rule follows the same pattern. We will exemplify this pattern by the example of Hcattle:
t+1Hcattle= round(tHcattle−σcattle+random(2·σcattle)) (3.2)
where t+1Hcattleis the number of cattle at time step t+ 1, tHcattle the number of cattle at time step t, andσcattlethe standard deviation for Hcattlecalculated from empirical household data sets. The random command determines a random number within [0,2·σcattle]. Thus,
t+1Hcattle lies within an uncertainty range of [−σcattle, σcattle] around the value of tHcattle.
Below we will give the rules for all other variables of the third category, following the same kind of rule as in the example for cattle. As some of the variables are regarded as integers, they need a round command to ensure integer outcome values.
t+1Hwives= round(tHwives−σwives+random(2·σwives)) (3.3)
t+1Hsize= round(tHsize−σsize+random(2·σsize)) (3.4)
t+1Hlabor=round(tHlabor−σlabor+random(2·σlabor)) (3.5)
t+1Hdepend= round(tHdepend−σdepend+random(2·σdepend)) (3.6)
whereσis the standard deviation of the single variable derived from the empirical data set.
(The annual variation of the livestock index Hlivestock will be determined by the specific biophysical sub-model of livestock dynamics.)
Variables of the fourth category comprise exclusively variables that are set externally, i.e.
policy access variables. Variables that are counted among this set comprise distance to dams Hdist dams, distance to water sources Hdist water, current credit access Hcredit, and number of credits received so far Hnr credits.
Since new dams can be added to the initial settings of the landscape as a policy, the distance to dams for households also has to be changed automatically. For this, a routine checks the distances to the various dams, and finally chooses the minimum. The procedure can be described as follows:
for all dams : set current-dist-dam (distance from house to dam) if (Hdist dams>
current-dist-dam) [ set Hdist damscurrent-dist-dam ]
The distance to water sources distance to water sources is then defined as the minimum of the distance to dams and the distance to the main river:
Hdist water=min(Hdist dams, Hdist river)
The percentage of households obtaining credit is given outside the model as a policy param-eter, whereas the amount of credit is fixed, and the period of credit provision is set to 2 years.
This was the observed pattern within the study area, and cannot be changed within the model,
since possible effects of a different credit pattern cannot be derived from the empirical data set. Within the model, credits are given randomly within the population of household agents, whereas those with a lesser number of credits obtained so far are favored. The variable of Hcreditcan therefore be determined as follows:
tHcredit=
( 1 iftcredit=true
0 if otherwise (3.7)
wheretcredit denotes whether a household was chosen to access credit in time step t.
Changes in the number of credits that households obtained Hnr creditsare calculated accord-ingly:
t+1Hnr credits= ( t
Hnr credits+1 if t+1credit=true
tHnr credits if otherwise (3.8)
The other two components of the household agent structure, Landscape Vision and Decision Module, will be described in later chapters. The Landscape Vision, as an integral part of the multi-level organization of the landscape, will be handled within the description of the patch-landscape module. The Decision Module will be outlined in a separate section of this chapter (section 3.4).
Creation and deletion of agents
Agents who reach their maximum age (see equation 3.1), are deleted. If agents within the same compound id, i.e. living in the same compound, exist, all land belonging to the dead agent is equally distributed among these. If no such agents exist, a new agent is created within this compound who inherits the land;
for all patches with (Powner=dead agent), set Powner=new agent
Apart from land, the new agent inherits the values for all variables, that are house-hold related (e.g. cattle amount, househouse-hold size, ownership of motor pump), while personal variables (e.g. number of wives, age, years of irrigation experience) are assigned values from a random agent with age under 30. Variables concerning the agent’s livelihood strategy (e.g.
group id) are classed among personal variables and thus obtain their values from the random agent.
But agents are not only created as successors for deleted agents, but are also cre-ated in the course of population growth. In each time step, the population of households is recalculated, based on the logistic growth function:
P(t)= CP0ert
C+P0(ert −1) (3.9)
where P(t) is the population size at time step t, P0 the initial population size at time 0 (i.e.
the year 2006), and C and r parameters. In each time step, P(t)−P(t−1)+D(t), new agents are created, where D(t) is the number of agents deleted in time step t without successor.
These agents are allocated randomly to the compounds of the study area, i.e. to patches with Pcompound=1. The locations of these patches had been determined prior to the development of GH-LUDAS (for details see section 3.6). These new agents adopt all their variable values from another random agent under age of 30. To ensure that all new agents obtain land, these agents are given priority within the moving phase of land acquisition (see section 3.4.2), where agents search for new patches. That is, new agents are allowed to search for unused patches before any other agent. If any of these unused patches are not owned by anybody, the ownership of these patches is transferred to the new agent. This is the first mechanism that ensures the ownership of patches. The second mechanism consists of the inheritance system as defined above. In case an agent (without successor) dies, the land is equally distributed among the other compound members, including the formerly new agent.
All these mechanisms are geared to observations in the study area. The inheritance system as described here ensures both inheritance with a successor and without, which both happens. Although in cases of a dissolved household, i.e. cases without a successor, the available land is not equally distributed among the remaining households, but is usually dis-tributed according to internal family hierarchies, the approach of equal portions was the most straightforward method to describe the complicated inheritance structure.