DOI: 10.5061/dryad.w0vt4b8mq
title: Population fragmentation drives up genetic diversity in signals of individual identity

description: Many species advertise their unique identity to conspecifics using
 dedicated individuality signals: one familiar example is human faces. But
 how unique in the global population do these signals need to be? While
 human faces are highly variable, each person interacts with many fewer
 individuals than are found in the total population. This raises the
 question of how evolutionary mechanisms drive up population-wide diversity
 when selection occurs at such a local level. We use an individual-based
 model in which individuals broadcast their identity and quality in
 separate, genetically-coded signals. Mimicking, for example, scent marking
 mammal species, females in the model assess males using the quality
 signal, then attempt to relocate the highest quality male using his
 identity signal. We ask how population fragmentation affects genetic
 diversity in the individual identity-signalling region under sexual
 selection, predicting one of two opposing outcomes: (1) divided
 populations evolve fewer signal variants globally, since repetition of
 signals is not costly when individuals interact only with local
 conspecifics, or (2) stochasticity in mutation and selection cause
 divergence among subpopulations, increasing the global number of signal
 variants. We show that local selection drives up global genetic diversity
 substantially in fragmented populations, even with extremely low rates of
 dispersal. Because new signal variants arise by mutation and then sweep
 through their subpopulation, a fragmented population has more global
 signal variation. This result furthers our understanding of how high
 levels of diversity in individuality signals are maintained.
description: We use an individual-based
 model of a sexual population with discrete events following Allen
 & Dytham’s (2009) adaptation of the Gillespie (1977) algorithm for
 simulating continuous time models. Extending the single, well-mixed
 population approach of Thom & Dytham (2012), we model a one
 dimensional ring of discrete patches connected by dispersal. An event can
 be either a birth (with possible dispersal to an adjacent population) or a
 death, and time advances after each event. The probability of a death
 event is density dependent and the population size will show stochastic
 logistic growth. We use an equilibrium density of 10,000 individuals
 divided equally across identical patches. The number of patches varies
 from 1 to 50, so the population ranges from 1 patch with 10,000
 equilibrium density, to 2 patches with 5,000 through to 50 patches with an
 equilibrium density of 200. Each individual carries a diploid
 attractiveness locus with alleles that can take any value, and six
 unlinked, diploid loci with four possible alleles at each locus. We
 consider the loci in two groups of three. One group controls signalling
 and the other evolves neutrally under mutation and drift only. There are
 1000 possible unique combinations in each group (10 unique combinations at
 each locus, because genotype AB is phenotypically equivalent to BA), and
 thus 10<sup>3</sup> (1000) possible individuality
 signals. A random
 individual is chosen from the global population of N individuals and an
 event type (either birth or death) is chosen at random. Time moves on an
 average of 1/2N of a time step after each event. If birth is selected and
 the chosen individual is female, she chooses a mate from a random
 selection of 10 individuals from within the same patch. The focal female
 either selects a male on attractiveness criteria (see below) or is
 assigned one at random, with a probability of 0.5 for each. If no males
 are encountered there is no birth, but if a male is encountered then the
 female produces a single offspring. At birth, the new individual is
 randomly assigned a sex (even sex ratio), inherits one allele for each of
 the six marker loci from each parent, and one attractiveness allele from
 each parent. There is no linkage. There is an independent chance of
 mutation for marker and attractiveness alleles. For signalling or neutral
 region mutations, there is a 1:1000 chance that one allele of 12 will
 mutate to one of the three different states. This represents a 1:6000
 mutation rate per locus, which is of the order used in other simulation
 models (Roff 1998). Our mutation rate of 1:500 per locus for
 attractiveness is substantially higher because we assume that
 attractiveness is the product of numerous alleles across the genome, and
 thus that the mutational target is relatively large (Hunt et al. 2004).
 When an attractiveness allele mutates, a random number from a normal
 distribution with a mean of ‑0.02 and standard deviation of 0.02 is added
 to the existing allele with the result that the majority of mutations have
 negative effects on attractiveness. Following Thom & Dytham
 (2012), there is no upper limit on attractiveness. After birth the
 individual has a probability, set by the dispersal rate, of moving to an
 adjacent patch. Patches are arranged in a ring, and dispersal in a
 clockwise or anti-clockwise direction is equally likely. We use dispersal
 rates of 0, 0.0001, 0.001, 0.01, 0.1 and 0.5. Individuals have no more
 than one dispersal event during their lifetime. We used a discrimination rate of
 50<b>%</b> for simulations here, based on previous simulations
 of this system (Thom and Dytham 2012) — females choose the best male in
 half their mating opportunities; the rest of the time, they select
 randomly from males they have encountered. When discriminating, a female
 chooses a mate based on male attractiveness using the sum of the two
 attractiveness alleles. The female rejects all males that have signalling
 loci different from those of the most attractive male, and then chooses a
 mate at random from those remaining. There is no other effect of
 attractiveness or signalling on fecundity, dispersal or mortality, and
 females assess male attractiveness without error. Populations are initiated with
 the number of individuals equal to the equilibrium density (10,000) spread
 randomly across patches. At initiation, each individual has an equal
 chance of being male or female. All markers are set to the same value
 (i.e., there is initially no variation in signalling or neutral loci) and
 each attractiveness allele is assigned a random value drawn from a uniform
 distribution between 0 and 1. We describe a “time step” as the period when
 the number of possible events is twice the population size. We used 100
 realisations for each parameter set tested (the ‘neutral’ model, with
 female discrimination rate set to 0, was replicated 40 times). Simulations
 ran for 50,000 time steps, by which time population dynamics had settled
 into an equilibrium state.
description: There are two datasets, one in which the female discrimination
 function was turned on ("Dytham Thom discriminationON raw
 data.csv") and one with the female discrimination function turned
 off ("Dytham Thom discriminationOFF raw data.csv"). In the
 latter realizations of the model, females chose males entirely at
 random. For both datasets, the column names in order
 are: Dispersal = the dispersal rate (probability of an
 individual moving patch), set at either 0, 0.0001, 0.001, 0.05, 0.1, or
 0.5<br> Rep = Replicate number (100 replicates for discriminationON,
 40 replicates for discriminationOFF)<br> Pop = Population size (the
 target population size was 10,000, maintained through density
 dependence)<br> Npatches = Number of patches - we modelled 1 - 20
 patches, plus the population divided into 25, 30, 35, 40, 45 and 50
 patches<br> Sig_genotypes = Number of signalling genotypes in the
 population<br> Nonsig_genotypes = Number of nonsignalling genotypes
 in the population<br> Mean_quality = Mean quality of males in the
 population (an unbounded value representing quality)<br> Var_quality
 = Variance in male quality quality in the population<br>
 Sig_genos_per_patch = Mean number of signalling genotypes per patch (i.e.
 for Npatches = 1, this is the same as the population-wide signal number,
 for Npatches = 2, it is half, etc).<br> Nsig_genos_per_patch = Mean
 number of non-signalling genotypes per patch