aRetain {AlleleRetain} | R Documentation |

## Allele Retention, Inbreeding, and Demography

### Description

Simulate the effect of management or demography on allele retention and inbreeding accumulation in bottlenecked populations of animals with overlapping generations.

### Usage

```
aRetain(q0 = 0.05, sourceN = Inf,
startN = 20, startAge = "juvenile", startSR = 0.5, exactSSR= FALSE,
inisurv = c(1,1,1), addN = 0, addyrs = c(0), addSR = 0.5, exactASR = FALSE,
migrN = 0, migrfreq = 1, migrSR = 0.5, exactMSR = FALSE, mpriority = FALSE,
removeL = FALSE, harvN = 0, harvAge = "all", harvyrs = 0, K = 100, Klag = 0,
KAdults = FALSE, reprolag = 0, mature = 1, matingSys = "monogamy",
matingLength = "seasonal", meanMLRS = 1, sdMLRS = 0, reproAgeM = c(1:200),
AgeOnMLRS = "age/age", nMatings = 1, retainBreeders = "male", MaxAge = 25,
SenesAge = 10, adsurvivalF = 0.80, adsurvivalM = 0.80, nonbrsurv = 0.80,
nonbrsurvK = 0.80, juvsurv = 0.80, juvsurvK = 0.80, youngperF = 1.5,
SDypF = 0.25, ypF1 = 1, ypF1yr = 1, MAXypF = 2, MAXypFK = 2,
ypFsex = "female", youngSR = 0.5, trackall = TRUE, GeneCount = "adult",
nyears = 50, nrepl = 100, nreplprint = 10, printplots = FALSE)
```

### Arguments

`q0` |
frequency of rare allele in the source population (range 0-1) |

`sourceN` |
size of source population; must be > startN |

`startN` |
number of starters (or size of bottleneck); not all will become genetic founders; minimum 2 |

`startAge` |
age class ("juvenile", "young adult", or "adult") of starters, supplemental. If "juvenile", all individuals added are assigned age 0; if "young adult", all are assigned age at maturity; if "adult", ages are selected randomly based on the proportion of individuals in the source population expected to be of each age (based on the survival rates and senescence specified below) |

`startSR` |
sex ratio (proportion male) of starters, supplementals, and migrants |

`exactSSR` |
logical: whether startSR gives the exact sex ratio of individuals released |

`inisurv` |
initial survival rate, as a proportion (range 0-1), of individuals released. Given as a vector, where the first value is for starters, the second is for additional releases, and third is for migrants. Annual mortality applies after this value is used. Defaults to 1 for all three groups. |

`addN` |
list of numbers of individuals to release in years soon after population establishment ("supplementals") |

`addyrs` |
list of years in which to release supplementals. Each year corresponds to the number of individuals in the same position in the addN list |

`addSR` |
sex ratio (proportion male) of supplementals; defaults to 0.5 (must be between 0 and 1). This can be either a single value, or a vector, with each element in the vector corresponding to each instance of supplementation (must be the same length as addN) |

`exactASR` |
whether addSR gives the exact sex ratio of individuals released (TRUE) or sexes are assigned randomly based on the probability given by addSR (FALSE); defaults to FALSE. This can be either a single value, or a vector, with each element in the vector corresponding to each instance of supplementation (must be the same length as addN) |

`migrN` |
number of migrants to add |

`migrfreq` |
interval (number of years) at which to add migrN migrants; must be between 1 and nyears, below |

`migrSR` |
sex ratio (proportion male) of supplementals; defaults to 0.5 (must be between 0 and 1) |

`exactMSR` |
whether addSR gives the exact sex ratio of individuals released (TRUE) or sexes are assigned randomly based on the probability given by migrSR (FALSE); defaults to FALSE |

`mpriority` |
logical: whether migrants are given priority over locally produced offspring to recruit into any available breeding vacancies |

`removeL` |
logical: whether to remove the corresponding number of locally produced adults to make room for migrants in the population; only necessary if retainBreeders = "both"/"female"/"male"; will only come into play when population is at K |

`harvN` |
number to be removed in each harvest year |

`harvAge` |
age of individuals to be harvested (as for 'startAge'). If not enough individuals of this age are available, the harvest quota (harvN) will not be filled |

`harvyrs` |
vector of years in which harvest occurs |

`K` |
carrying capacity (population ceiling) |

`Klag` |
number of years for which population is held at or below initial size (breeding still occurs); indicates a prolonged bottleneck |

`KAdults` |
logical: whether K counts only adults, or all individuals (subadults, nonbreeders, helpers) |

`reprolag` |
number of years after establishment for which no reproduction occurs |

`mature` |
average age (in years) at sexual maturity (first breeding) |

`matingSys` |
mating system: "monogamy", "polygyny", or "polygynandry"; to model a polyandrous system, set to "polygyny" and then input female values for the "male" parameters (and male values for the "female" parameters) |

`matingLength` |
"seasonal" or "lifelong"; determines whether individuals retain the same mate from year to year or divorce |

`meanMLRS` |
mean lifetime reproductive success (LRS), in terms of number of matings that produce young (NOT number of offspring) a male gets over his lifetime; including those that never reproduce. Each male will be assigned an individual average from a gamma distribution with this mean and sdMLRS (the shape of the gamma function = (meanMLRS^2)/(sdMLRS^2); scale = (sdMLRS^2)/meanMLRS; see help for R function "rgamma" for more information). The gamma distribution was chosen because of its flexibility in shape appropriate to polygynous mating systems (from strongly right-skewed to nearly symmetrical). The SD:mean ratio is more important than the magnitude of the mean. This individual mean indicates the male's "quality" and will be used to assess his chance of mating, relative to other males present, each year (does not translate directly into actual LRS experienced by that male). Not used if matingSys = "monogamy" |

`sdMLRS` |
among-male standard deviation in LRS; used with meanMLRS as described above |

`reproAgeM` |
list of ages at which males are able to mate successfully |

`AgeOnMLRS` |
expression describing the proportion of LRS achieved by a male at a particular age (for ages contained within reproAgeM), e.g. "-5.4 + 1.5*age - 0.08*age^2"; if there is no effect of age, use the default value of "age/age" (equals 1 so all ages will be assigned the same average, given by meanMLRS) |

`nMatings` |
number of matings per female each year; only used when matingSys = "polygynandry"; must be a whole number |

`retainBreeders` |
should established breeders retain their breeding status from year to year, and prevent young individuals from recruiting if the population is at K? Specify which sex should be retained: "none", "both", "male", or "female". Only used when matingSys = "monogamy." When "none", all new recruits are added to the breeding population; individuals are randomly removed from that pool to truncate the population at K (so new recruits may randomly replace established breeders). When adults will likely survive and prevent new individuals from recruiting, e.g. with territorial species, set this at one of the other values as appropriate for your species. When pairing off widowed or divorced individuals, those of the retained sex(es) that bred previously will be guaranteed a new mate (if available); non-retained adults will compete with new recruits to mate with available adults. If the population is at K, new recruits will only fill vacancies left by adults that died (they will not replace any surviving adults, including females when retainBreeders = "male" and vice versa; i.e. "both" functions the same as "male" and "female" in this part of the model) |

`MaxAge` |
maximum allowable lifespan (in years); can be Inf |

`SenesAge` |
age (in years) after which annual survival will be reduced by senescence. Through this age, adult survival values are set according to adsurvivalF and adsurvivalM (below). After this age, annual survival decreases linearly until MaxAge (at which it is 0): new survival = survival - (survival / (MaxAge - SenesAge)) * (age - SenesAge) |

`adsurvivalF` |
annual survival rate of adult females |

`adsurvivalM` |
annual survival rate of adult males |

`nonbrsurv` |
annual survival rate of nonbreeders (subadults or adults that have never reproduced) |

`nonbrsurvK` |
annual survival rate of nonbreeders when population is at K (used instead of nonbrsurv). If given, subadult survival probability in each year depends on density of the population at the beginning of that year, according to the Beverton-Holt function for density dependence in survival (as in Morris & Doak 2002, Quantitative Conservation Biology): S(E(t)) = S(0)/(1 + beta * E(t)), where S(E(t)) is survival rate at population density E in year t, S(0) is survival when density is near 0, beta is the decline in survival as density increases, and E(t) is population density at time t. "Density" is defined in our model as the proportion of K that has been filled, as there is no spatial information in the model. The model solves for beta according to the user-specified values for nonbrsurv (S(0)) and nonbrsurvK (S at carrying capacity, where E = 1), then uses beta and S(0) to calculate density-dependent survival probability in each year |

`juvsurv` |
first year survival (from the stage described by youngperF, below, to the beginning of the next breeding season) when population is below K |

`juvsurvK` |
first year survival when population is at K (used instead of juvsurv); juvenile survival is density-dependent as for nonbrsurvK |

`youngperF` |
average number of offspring produced per mating each year (averaged over all pairs in population). For a polyandrous female, this is the average number of offspring produced each time she mates with a male (each year): youngperF * nMatings = total average offspring per year. youngperF can be calculated for any reproductive stage (eggs, chicks, independent juveniles) as long as juvsurv indicates the proportion of individuals that survive from this stage to the beginning of the following breeding season |

`SDypF` |
among-individual standard deviation of youngperF, e.g. 0.50 or 2. |

`ypF1` |
where younger breeders have reduced reproductive rates, this can be used to define the reproductive success for first reproductive stage (length of that stage is determined by ypF1yr, below); given as a proportion of youngperF. |

`ypF1yr` |
age after which ypF1 changes to youngperF (e.g. 1 if ypF1 applies to one-year-olds only, or 5 if it applies for the first 5 years and then increases to youngperF from age 6 onward) |

`MAXypF` |
maximum annual number of offspring per individual (e.g. based on biological constraints such as clutch size/renesting) |

`MAXypFK` |
maximum annual number of offspring per individual when population is at K, if different from MAXypF |

`ypFsex` |
which member of a pair limits the reproductive output for the year, based on the biology of the species of interest; can be "male", "female", or "both" (the last will average the male's and female's values) |

`youngSR` |
proportion of offspring that are male |

`trackall` |
logical: whether to track all individuals from the population through the whole simulation; must be TRUE to use indiv.summary or pedigree.summary after running the simulation |

`GeneCount` |
which alleles to count as retained: those in the "adult" population only, or those in "all" individuals (including subadults and other nonbreeders) |

`nyears` |
number of years to run the simulation |

`nrepl` |
number of iterations (replicates) to run |

`nreplprint` |
interval (number of replicates) at which to print a message with the current system time. Allows the user to gauge model progress and to estimate time to completion |

`printplots` |
logical: whether to plot the population growth (number of individuals, as defined by KAdults, present each year) and allele frequency (in the pool defined by GeneCount) as they change over time (TRUE or FALSE). One line will be plotted for each replicate immediately after it runs. Can be used to immediately gauge the demographics of the population (e.g. if it will grow as expected); will slow down the simulation by ~ 10-20 percent. Defaults to FALSE. |

### Details

The user indicates the number of individuals released to establish the population (bottleneck size), along with their age class (adult or juvenile), sex ratio, and post-release survival rate. These individuals can be released all at once or gradually over a period of years. Released individuals are assumed to be unrelated and are randomly assigned genotypes (zero, one, or two copies of a hypothetical neutral allele) according to a user-specified frequency of the allele in the source population. The simulated population can be held at the initial size to simulate a prolonged bottleneck (while reproduction occurs) or the user can specify a post-release lag with no reproduction. Otherwise, released individuals mature and recruit according to user-specified parameters. Species with delayed sexual maturity are modeled by preventing subadults from breeding until a user-specified age. Adults are randomly sorted into monogamous or polygynous breeding pairs, which re-form for multiple matings within one season (in polygynandry systems), remain together seasonally (in monogamous or polygynous systems), or remain together lifelong (in monogamous systems) depending on user-specified settings. Reproduction occurs each year based on individual or population means (depending on settings for individual variation in reproductive output) for the number of offspring produced per pair per year, which can change with age of the parents. Sex is randomly assigned to each offspring according to the user-specified sex ratio for juveniles and offspring inherit alleles from their parents via Mendelian inheritance. When the simulated population reaches the specified carrying capacity, population growth ceases by either preventing recruitment of offspring or removing randomly selected individuals (as indicated by the user). When individuals are removed at random, the user can choose to give priority to remain in the population to established breeders and/or immigrants (if any). Annual survival of individuals is determined by user-specified probabilities for each age class, with optional sex-specific survival rates for adults. The user can choose to incorporate density dependence into juvenile and subadult/nonbreeder survival probabilities and/or to specify senescence effects in survival of adults beyond a certain age.

The model simulates immigration at regular user-specified intervals by adding more individuals from the original source population. Immigrants can be prioritized over locally produced individuals to recruit into breeding vacancies. This scenario may be realistic when most locally produced juveniles would emigrate, or when locally produced juveniles would be removed by managers (e.g. to contribute to other populations or to make room for immigrants). Emigration can be simulated in this model by reducing the survival value for the appropriate age class, assuming emigrants and their descendants do not return to the modeled population.

Frequency of the allele of interest in the simulated population is recorded
after each year of the simulation. The proportion of iterations in which
the allele is retained to the end of the specified time period is
interpreted as the probability of retaining the allele in the population
over that period. The model outputs a census of the simulated
population (adults, subadults/nonbreeders, pairs, founders, and immigrants)
each year, and a list of information for each individual in the simulated
population. The census information can be averaged across replicates with
`aRetain.summary`

. An individual summary function (`indiv.summary`

)
can output pertinent information (e.g. proportion bred, average number that
bred per generation) about individuals of each origin (founder, local, or
immigrant) in the population. A pedigree summary function
(`pedigree.summary`

) can be used to describe accumulation of inbreeding
in the population by calling R package **pedigree**.

See the AlleleRetain Model Guide (available as a PDF file with this installation, or from the model's website at https://sites.google.com/site/alleleretain/) for more details and an example.

### Value

`aRetain`

returns a list of sub-lists, with one sub-list for each replicate
which contains two matrices: one that summarizes the population information for
that replicate (one row for each year; columns = number of adults, number of
breeding females, number of breeding males, number of copies of the rare allele,
number of pairs, number of nonbreeders, number of founders remaining, number of
migrants alive, mean age of breeding pairs), and one that gives pertinent
information for all individuals in that replicate (one row for each individual;
columns = ID, dam, sire, origin [1=starter, 2=supplemental, 3=local,
4=immigrant], birth year, number of years alive in the population, number of
years bred, year added to population). The latter matrix includes all
individuals if `trackall = TRUE`

, or only those alive at the end of the
simulation if `trackall = FALSE`

. Run `aRetain.summary`

,
`indiv.summary`

, and `pedigree.summary`

to generate useful output from
this information (averaged across replicates).

### Author(s)

Emily L. Weiser emily.l.weiser@gmail.com

### References

Weiser, E.L., Grueber, C. E., and I. G. Jamieson. 2012. AlleleRetain: A program to assess management options for conserving allelic diversity in small, isolated populations. Molecular Ecology Resources 12:1161-1167.

### Examples

```
## Simulate rare allele with frequency 0.05 in source population.
## 20 individuals are translocated to establish a new population with carrying
## capacity = 100 individuals. An additional 5 individuals are translocated
## once every 10 years as immigrants. Demographic parameter values are for a
## monogamous passerine bird species with a 5-yr average lifespan. Only 30
## iterations are run so the confidence intervals will be wide.
## Not run:
aR.temp <- aRetain(q0 = 0.05, sourceN = 2000, startN = 20, startAge =
"adult", startSR = 0.5, exactSSR = FALSE, inisurv = 0.90, addN = 0, addyrs
= c(0), migrN = 5, migrfreq = 10, mpriority = FALSE, removeL = FALSE, K =
100, KAdults = FALSE, mature = 1, matingSys = "monogamy", matingLength =
"seasonal", retainBreeders = "male", MaxAge = 16, SenesAge = 5, adsurvivalF =
0.77, adsurvivalM = 0.77, nonbrsurv = 0.70, nonbrsurvK = 0.40, juvsurv = 0.60,
juvsurvK = 0.30, youngperF = 2.85, SDypF = 1.25, MAXypF = 6, MAXypFK = 6,
ypFsex = "female", youngSR = 0.5, trackall = TRUE, GeneCount = "all", nyears =
10, nrepl = 20, nreplprint = 10)
aRetain.summary(aR.temp, GeneCount = "all", alpha=0.05, dropextinct = TRUE)
## End(Not run)
```

*AlleleRetain*version 2.0.2 Index]