Age structured populations with overlapping generations **

Age is an important factor in many applications because it is related to many genetic (most obviously mating) and environmental factors that influence the evolution of a population. The evolution of age structured populations will lead to overlapping generations because parents can co-exist with their offspring in such a population. Although simuPOP is based on a discrete generation model, it can be used to simulate age structured populations.

To evolve an age structured population, you will need to

• Define an information field age and use it to store age of all individuals. Age is usally assigned randomly at the beginning of a simulation.
• Define a virtual splitter that splits the parental population into several virtual subpopulation. The most important VSP consists of mating individuals (e.g. individuals with age between 20 and 40). Advanced features of virtual splitters can be used to define complex VSPs such as males between age 20 - 40 and females between age 15-30 (use a ProductSplitter to split subpopulations by sex and age, and then a CombinedSplitter to join several smaller VSPs together).
• Use a heterogeneous mating scheme that clones most individuals to the next generation (year) and produce offspring from the mating VSP.

Example ageStructured gives an example of the evolution of age-structured population.

• Information fields ind_id, father_id and mother_id and operators IdTagger and PedigreeTagger are used to track pedigree information during evolution.
• A CloneMating mating scheme is used to copy surviving individuals and a RandomMating mating scheme is used to produce offspring.
• IdTagger and PedigreeTagger are used in the ops parameter of RandomMating because only new offspring should have a new ID and record parental IDs. If you use these operators in the duringOps parameter of the evolve function, individuals copied by CloneMating will have a new ID, and a missing parental ID.
• The resulting population is age-structured so Pedigrees could be extracted from such a population.
• The penetrance function is age dependent. Because this penetrance function is applied to all individuals at each year and an individual will have the disease once he or she is affected, this penetrance function is more or less a hazard function.

Example: Example of the evolution of age-structured population.

>>> import simuPOP as sim
>>> import random
>>> N = 10000
>>> pop = sim.Population(N, loci=1, infoFields=['age', 'ind_id', 'father_id', 'mother_id'])
>>> pop.setVirtualSplitter(sim.InfoSplitter(field='age', cutoff=[20, 50, 75]))
>>> def demoModel(gen, pop):
...     '''A demographic model that keep a constant supply of new individuals'''
...     # number of individuals that will die
...     sim.stat(pop, popSize=True, subPops=[(0,3)])
...     # individuals that will be kept, plus some new guys.
...     return pop.popSize() - pop.dvars().popSize + N / 75
...
>>> def pene(geno, age, ind):
...     'Define an age-dependent penetrance function'
...     # this disease does not occur in children
...     if age < 16:
...         return 0
...     # if an individual is already affected, keep so
...     if ind.affected():
...         return 1
...     # the probability of getting disease increases with age
...     return (0., 0.001*age, 0.001*age)[sum(geno)]
...
>>> def outputstat(pop):
...     'Calculate and output statistics'
...     sim.stat(pop, popSize=True, numOfAffected=True,
...         subPops=[(0, sim.ALL_AVAIL)],
...         vars=['popSize_sp', 'propOfAffected_sp'])
...     for sp in range(3):
...         print('%s: %.3f%% (size %d)' % (pop.subPopName((0,sp)),
...             pop.dvars((0,sp)).propOfAffected * 100.,
...             pop.dvars((0,sp)).popSize))
...     #
...     return True
...
>>>
>>> pop.evolve(
...     initOps=[
...         sim.InitSex(),
...         # random assign age
...         sim.InitInfo(lambda: random.randint(0, 75), infoFields='age'),
...         # random genotype
...         sim.InitGenotype(freq=[0.5, 0.5]),
...         # assign an unique ID to everyone.
...         sim.IdTagger(),
...         sim.PyOutput('Prevalence of disease in each age group:\n'),
...     ],
...     # increase the age of everyone by 1 before mating.
...     preOps=sim.InfoExec('age += 1'),
...     matingScheme=sim.HeteroMating([
...         # all individuals with age < 75 will be kept. Note that
...         # CloneMating will keep individual sex, affection status and all
...         # information fields (by default).
...         sim.CloneMating(subPops=[(0,0), (0,1), (0,2)], weight=-1),
...         # only individuals with age between 20 and 50 will mate and produce
...         # offspring. The age of offspring will be zero.
...         sim.RandomMating(ops=[
...             sim.IdTagger(),                   # give new born an ID
...             sim.PedigreeTagger(),             # track parents of each individual
...             sim.MendelianGenoTransmitter(),   # transmit genotype
...         ],
...         numOffspring=(sim.UNIFORM_DISTRIBUTION, 1, 3),
...         subPops=[(0,1)]),],
...         subPopSize=demoModel),
...     # number of individuals?
...     postOps=[
...         sim.PyPenetrance(func=pene, loci=0),
...         sim.PyOperator(func=outputstat, step=20)
...     ],
...     gen = 200
... )
Prevalence of disease in each age group:
age < 20: 0.381% (size 2628)
20 <= age < 50: 2.504% (size 3953)
50 <= age < 75: 4.814% (size 3282)
age < 20: 0.639% (size 2660)
20 <= age < 50: 26.901% (size 3933)
50 <= age < 75: 50.407% (size 3313)
age < 20: 0.526% (size 2660)
20 <= age < 50: 27.720% (size 3961)
50 <= age < 75: 60.744% (size 3332)
age < 20: 0.489% (size 2660)
20 <= age < 50: 29.624% (size 3990)
50 <= age < 75: 62.121% (size 3300)
age < 20: 0.639% (size 2660)
20 <= age < 50: 28.045% (size 3990)
50 <= age < 75: 63.188% (size 3325)
age < 20: 0.564% (size 2660)
20 <= age < 50: 28.922% (size 3990)
50 <= age < 75: 60.722% (size 3325)
age < 20: 0.714% (size 2660)
20 <= age < 50: 28.371% (size 3990)
50 <= age < 75: 61.774% (size 3325)
age < 20: 0.526% (size 2660)
20 <= age < 50: 29.298% (size 3990)
50 <= age < 75: 60.451% (size 3325)
age < 20: 0.714% (size 2660)
20 <= age < 50: 29.649% (size 3990)
50 <= age < 75: 61.083% (size 3325)
age < 20: 0.414% (size 2660)
20 <= age < 50: 28.897% (size 3990)
50 <= age < 75: 63.218% (size 3325)
200L
>>>
>>> # draw two Pedigrees from the last age-structured population
>>> from simuPOP import sampling
>>> sample = sampling.drawNuclearFamilySample(pop, families=2, numOffspring=(2,3),
...     affectedParents=(1,2), affectedOffspring=(1,3))
>>> sim.dump(sample)
Ploidy: 2 (diploid)
Chromosomes:
1:  (AUTOSOME, 1 loci)
   (1)
Information fields:
age ind_id father_id mother_id
population size: 8 (1 subpopulations with 8 Individuals)
Number of ancestral populations: 0

SubPopulation 0 (), 8 Individuals:
   0: MA 1 | 0 |  41 31100 28012 27744
   1: FA 1 | 1 |  34 31950 27515 26655
   2: FA 1 | 1 |  66 27744 22633 22484
   3: FA 1 | 0 |  74 26655 20957 20911
   4: FU 1 | 0 |  41 31099 28012 27744
   5: FU 0 | 1 |  34 31949 27515 26655
   6: MA 1 | 0 |  64 28012 23909 23470
   7: MU 1 | 1 |  68 27515 24745 21596

>>>

Download ageStructured.py