Migration matters in conservation and management: Exploring the 10% rule for demographic independence via simulation
Data files
Dec 31, 2024 version files 428.59 KB
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MigrationData.zip
422.84 KB
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README.md
5.75 KB
Abstract
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 >10% to independent at <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.
README
## 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
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Code/Software
Software used included R version 4.4.0 (2024-04-24) and RStudio 2024.04.1 Build 748.
Methods
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.