aRetain {AlleleRetain}

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 [e-mail]

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)