DOI: 10.5061/dryad.zpc866tjk
title: Migration matters in conservation and management: Exploring the 10% rule for demographic independence via simulation

description: Delineating a threshold migration rate for demographic independence is
 important for understanding connectivity among fragmented populations and
 defining management units for conservation and harvest regulation. In
 turn, defining management units is an essential step in sustainable
 management to avoid unintentional depletion of resources managed for
 conservation or harvest. The 10% rule of demographic connectivity is a
 rule of thumb that delineates the threshold of demographic independence
 when the behavior of two populations shifts from synchronous at
 &gt;10% to independent at &lt;10%. However, the accuracy of the
 10% rule to real world scenarios and application to natural resource
 management is unknown. We evaluated the 10% rule using simulation for two
 life history types: Pacific cod, Gadus macrocephalus, a gadid with
 relatively fast growth, and blackspotted rockfish, Sebastes melanostictus,
 a long-lived rockfish species. Results were obtained by simulating a
 real-world tool for evaluating demographic connectivity, positive
 correlation in estimated population sizes. We assessed the effect of
 migration on demographic connectivity on otherwise independent populations
 under one- and two-way migration, and with different population sizes and
 life history parameters. Sensitivity testing showed that positive
 correlation in population size does not occur in roughly a quarter of
 simulations, regardless of the migration rate. When positive correlation
 in population size does occur, mean migration rates over all simulations
 were between 5% and 10%: 0.089 (8.9%) for blackspotted rockfish and 0.058
 (5.8%) for Pacific cod. However, the range of migration resulting in
 demographic connectivity was large, 0.02 – 0.44 for blackspotted rockfish
 and 0.02 – 0.40 for Pacific cod.
description: We evaluated the 10% rule using simulation for two life history
 types: Pacific cod, <em>Gadus macrocephalus</em>, a gadid with
 relatively fast growth, and blackspotted rockfish, <em>Sebastes
 melanostictus</em>, a long-lived rockfish species. Results were
 obtained by simulating a real-world tool for evaluating demographic
 connectivity, positive correlation in estimated population sizes. We
 assessed the effect of migration on demographic connectivity on otherwise
 independent populations under one- and two-way migration, and with
 different population sizes and life history parameters.
description: ## ## Title: Migration matters in conservation and management: Exploring
 the 10% rule for demographic independence via simulation
 https://doi.org/10.5061/dryad.zpc866tjk Description of the data and file
 structure This is a simulation study; therefore, files are provided that
 were used to generate simulated data. Files findsteepness1sexcod.R and
 findsteepness1sexblackspotted.R were used to obtain a steepness parameter
 and F40% that were then used in all other R scripts. Files COV2popsGM.R
 and COV2popsSM.R were used to create data for Table 3, Figures 2 and 3,
 and Figures S1-S3. The following files were also used to simulate data for
 Figure 3: COV2popsSMage0migration.R, COV2popsGMage0migration.R,
 COV2popsSM_maturemigration.R, and COV2popsGM_maturemigration.R. Files
 COV2popsGMobserr.R and COV2popsSMobserr.R were used to create data for
 Figure 4. In the files findsteepness1sexcod.R and
 findsteepness1sexblackspotted.R, we iterated over a reasonable range of
 fishing mortality rates to find the steepness value that maximizes the
 total available catch (TAC) at F35%. TAC is a technical term that refers
 to the maximum amount of fish that can be caught from a specific fishery
 within a year, and F35% refers to the fishing mortality rate that reduces
 the spawning biomass to 35% of its unfished state. Steepness is a measure
 of how much recruitment depends on spawning biomass, and is defined as the
 fraction of recruitment from a virgin population obtained when the
 spawners are at 20% of the unfished level. The values obtained were used
 in the population dynamics models in the other R scripts. Hereafter, SM
 refers to blackspotted rockfish (Sebastes melanostictus) and GM refers to
 Pacific cod (Gadus macrocephalus). The R scripts COV2popsSM.R and
 COV2popsGM.R simulate two populations through time (we simulated
 populations for a 300-year time period, with a 50-year initial burn-in for
 populations to equilibrate, followed by an additional 250 years that
 encompass population stochasticity and allows for long-term dynamics to
 emerge), and calculate the proportion of significant correlations. The
 criterion for demographic dependence was significant correlation in
 population size trajectories over the final 250 years of a 300-year time
 span. This process was repeated over 100 iterations, recording the number
 of significant correlations out of 100 at each migration rate tested.
 Final results were determined for each migration rate by taking the mean
 and variance of significant correlations over the 100 iterations. The
 files COV2popsSMage0migration.R, COV2popsGMage0migration.R,
 COV2popsSM_maturemigration.R, and COV2popsGM_maturemigration.R were
 similar to the files COV2popsSM.R and COV2popsGM.R, except that they
 varied the life stage at which migration takes place. Migration takes
 place at age 0 for "age0migration" files, and in mature
 individuals in the "maturemigration" files. The output of these
 files consists of .csv files with a matrix of mean and variance in
 significant correlations. The proportion of migration tested is listed as
 rownames under the header "m". Migration is shown in two
 directions and one direction each way. The names of the output files also
 include "popstat", which indicates the size of each population,
 and this is specified in the corresponding .R script. Also, output files
 include "exp", which indicates various sensitivities tested, and
 this is also listed in the corresponding .R script. The following is a
 description of the fields found in the output files. m - migration rate
 tested from 0 to .5 in increments of 0.02 All of the following statistics
 represent either a mean or a variance over 100 iterations per migration
 rate, repeated 3 times, and averaged (over the 3 repetitions).
 rowMeans.Mean_mat - the mean proportion of positive correlation tests
 between 2 populations over the final 250 years of a 300 year simulation
 (where population size includes the survey selectivity, as in viewed
 through survey results) in which the populations were significantly
 correlated, with a false discovery rate p-value adjustment applied.
 rowVars.Mean_mat - the variance in the proportion of positive correlation
 tests between 2 populations over the final 250 years of a 300 year
 simulation (where population size includes the survey selectivity, as in
 viewed through survey results) in which the populations were significantly
 correlated, with a false discovery rate p-value adjustment applied.
 rowMeans.Mean_raw_mat - the mean proportion of positive correlation tests
 between 2 populations over the final 250 years of a 300 year simulation in
 which the populations were significantly correlated, with a false
 discovery rate p-value adjustment applied (no survey selectivity applied).
 rowVars.Mean_raw_mat - the variance in the proportion of positive
 correlation tests between 2 populations over the final 250 years of a 300
 year simulation in which the populations were significantly correlated,
 with a false discovery rate p-value adjustment applied (no survey
 selectivity applied). rowMeans.Mig1to2_mat - the mean proportion of
 migrants from 1 to 2 relative to the size of the recipient population,
 population 2. rowVars.Mig1to2_mat - the variance in the proportion of
 migrants from 1 to 2 relative to the size of the recipient population,
 population 2. rowMeans.Mig2to1_mat - the opposite; the mean proportion of
 migrants from population 1 to 2 relative to the size of population 1.
 rowVars.Mig2to1_mat - the variance in the proportion of migrants from
 population 1 to 2 relative to the size of population 1. ## Sharing/Access
 information NA ## Code/Software Software used included R version 4.4.0
 (2024-04-24) and RStudio 2024.04.1 Build 748.