the shearing data vertical rather than horizontal. ... St. George shearing data ... that are in the resight data, but are missing from the shearing data:.
Use of the ‘pupR’ package for model-based estimation of northern fur seal pup production Devin Johnson, Rod Towell, and Jason Baker This guide provides a step-by-step code demonstration to use the pupR package as tidyverse group of packages for estimating northern fur seal pup abundance. First, load all the necessary packages:
Raw data structure We begin with data import and rearragement for optimal model fitting. The 2016 NFS pup data can be accessed by the user by typeing the following code to see where the example data is stored: library(pupR)
## pupR 0.0.1 (2017-02-27)
show_data_loc()
## Raw example data located in the following directory: ## /Users/devin.johnson/Library/R/pupR/raw_data/
The data used for this process must look like the 2 data sets in the included directory. The example data may be read into the current R environemtnt using the following command: load_demo_data() head(shear_2016_snp)
## ## ## ## ## ## ##
1 2 3 4 5 6
rookery X0 LUK NA KIT 21 REE NA GOR NA ARD NA MOR 108
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 224 94 NA NA NA NA NA NA NA NA NA NA NA NA 40 60 85 91 66 NA NA NA NA NA NA NA NA NA 108 211 114 106 84 NA 162 174 72 78 6 NA NA NA 153 98 168 70 156 151 NA NA NA NA NA NA NA NA 75 NA NA NA NA NA NA NA NA NA NA NA NA NA 146 144 154 89 175 115 NA NA NA NA NA NA NA NA
head(shear_2016_sng)
## ## ## ## ## ## ##
1 2 3 4 5 6
rookery SOU NOR ERE ECL STA SGZ
X1 X2 X3 X4 X5 98 129 128 NA NA 108 166 176 111 61 246 NA NA NA NA 304 146 NA NA NA 64 12 NA NA NA 150 NA 57 NA NA
head(resight_2016_snp)
## ## ## ## ## ## ##
1 2 3 4 5 6
date rookery section obs resample count 8/12/16 MOR 0 RT 1 2 8/12/16 MOR 0 RT 1 3 8/12/16 MOR 0 RT 1 0 8/12/16 MOR 0 RT 1 2 8/12/16 MOR 0 RT 1 1 8/12/16 MOR 0 RT 1 4
head(resight_2016_sng)
## ## ## ## ## ## ##
1 2 3 4 5 6
date rookery section obs resample count 8/18/16 ECL 1 JTS 1 3 8/18/16 ECL 1 JTS 1 4 8/18/16 ECL 1 JTS 1 2 8/18/16 ECL 1 JTS 1 4 8/18/16 ECL 1 JTS 1 1 8/18/16 ECL 1 JTS 1 0
Note that this is exactly how it is read in from the .csv files. To createw these files, I just cut the appropriate sections out of the SNPdata2016.xlsx and SNGdata2016.xlsx files. The worksheets contailing this data are the pups sheared and resampling sheets. The sheet heading, etc. seem to be different from year-to-year and between island, so, it is up the user to get the .csv files necessary into the same forms. Note, column headings are important and must be exactly the same for the following code to work. However, it is note necessary for the model fitting if you can change the data munging code appropriately. Also, note that the ‘X’ in the shearing data columns was auomatically put there by R , the raw data just has the section numbers as column names.
Data munging Combining and normalizing Now we use the new data packages in R to rearrange the data to use the pupR code to fit the models. We first have to turn the shearing data vertical rather than horizontal. library(tidyverse)
## ## ## ## ##
Loading Loading Loading Loading Loading
tidyverse: tidyverse: tidyverse: tidyverse: tidyverse:
tibble tidyr readr purrr dplyr
## Conflicts with tidy packages ----------------------------------------------
## filter(): dplyr, stats ## ggsave(): ggplot2, cowplot ## lag(): dplyr, stats
# St. Paul shearing data shear_2016_snp %>% gather(section, M, -rookery) %>% filter(!is.na(M)) %>% mutate(section = sapply(strsplit(section, "X", fixed=T), function(x)x[2])) %>% mutate(island = "snp") %>% arrange(rookery, section) -> shear_2016_snp # St. George shearing data shear_2016_sng %>% gather(section, M, -rookery) %>% filter(!is.na(M)) %>% mutate(section = sapply(strsplit(section, "X", fixed=T), function(x)x[2])) %>% mutate(island = "sng") %>% arrange(rookery, section) -> shear_2016_sng rbind(shear_2016_sng, shear_2016_snp) -> shear_2016 head(shear_2016)
## ## ## ## ## ## ##
1 2 3 4 5 6
rookery section M island ECL 1 304 sng ECL 2 146 sng ERE 1 246 sng NOR 1 108 sng NOR 2 166 sng NOR 3 176 sng
Now, we’ll have to sum the resight counts within each section. For the basic occasion-observer model we will then sum over all resight counts within the rookery for each observer and occasion. # St. Paul resight data resight_2016_snp %>% group_by(rookery, section, resample, obs) %>% summarise(., m=sum(count), u=as.integer(n()*25 - m)) %>% ungroup() %>% mutate(island="snp") %>% as.data.frame() -> resight_2016_snp # St. George resight data resight_2016_sng %>% group_by(rookery, section, resample, obs) %>% summarise(., m=sum(count), u=as.integer(n()*25 - m)) %>% ungroup() %>% mutate(island="sng") %>% as.data.frame() -> resight_2016_sng rbind(resight_2016_sng, resight_2016_snp) -> resight_2016 head(resight_2016)
## ## ## ## ## ## ##
1 2 3 4 5 6
rookery section resample obs m u island ECL 1 1 JDB 54 471 sng ECL 1 1 JTS 49 476 sng ECL 1 2 JDB 63 562 sng ECL 1 2 JTS 45 455 sng ECL 2 1 JDB 33 392 sng ECL 2 1 JTS 39 386 sng
Quality control Now we will do a little quality control by checking that all the rookery and sections designations are the same in both the resight and shearing data.frames
shear_sec = transmute(shear_2016, rook_sec=paste(island, rookery, section))[[1]] resight_sec = transmute(resight_2016, rook_sec=paste(island, rookery, section))[[1]] # Check for same section all(resight_sec %in% shear_sec)
## [1] FALSE
all(shear_sec %in% resight_sec)
## [1] FALSE
Therefore we have some mismatches in section and rookery classification. Let find out which ones. These are the sections that are in the resight data, but are missing from the shearing data: unique(resight_sec[!(resight_sec%in%shear_sec)])
## [1] "sng SGZ 2"
"snp REE 67"
"snp REE 1011"
Looks like the number of shear marks for SGZ section 2 were combined with section 1, but, resights were still based on all 3 sections. So, because there does not seem to be good recorded separation between sections 1 and 2 at SGZ, 6 and 7 at REE, and 10 and 11 at REE, we will combine those into a single section in both data.frames. resight_2016 %>% mutate(section_orig=as.character(section), section=ifelse(island=='sng' & rookery=='SGZ' & sect ion_orig%in%c('1','2'), '1/2', section_orig)) %>% mutate(section=ifelse(island=='snp' & rookery=='REE' §ion_orig%in%c('6','7','67'), '6/7', s ection)) %>% mutate(section=ifelse(island=='snp' & rookery=='REE' & section_orig%in%c('10','11','1011'), '1 0/11', section)) -> resight_2016 shear_2016 %>% mutate(section_orig=as.character(section), section=ifelse(island=='sng' & rookery=='SGZ' & secti on_orig%in%c('1','2'), '1/2', section_orig)) %>% mutate(section=ifelse(island=='snp' & rookery=='REE' §ion_orig%in%c('6','7','67'), '6/7', s ection)) %>% mutate(section=ifelse(island=='snp' & rookery=='REE' & section_orig%in%c('10','11','1011'), '1 0/11', section)) -> shear_2016
In the shear_2016 data we have some sections where shear marks were put out, but no resights were recorded. unique(shear_sec[!(shear_sec%in%resight_sec)])
## [1] "sng STA 2" "snp REE 7"
Looks like the resighters only recorded section=1 for resampling at STA. Therefore, all of STA will be combined into 1 section, 1/2 .
resight_2016 %>% mutate(section=ifelse(island=='sng' & rookery=='STA' & section_orig%in%c('1','2'), '1/2', secti on)) -> resight_2016 shear_2016 %>% mutate(section=ifelse(island=='sng' & rookery=='STA' & section_orig%in%c('1','2'), '1/2', sectio n)) -> shear_2016
Now we can check again to make sure all the sections line up shear_sec = transmute(shear_2016, rook_sec=paste(island, rookery, section))[[1]] resight_sec = transmute(resight_2016, rook_sec=paste(island, rookery, section))[[1]] # Check for same section all(resight_sec %in% shear_sec)
## [1] TRUE
all(shear_sec %in% resight_sec)
## [1] TRUE
Alright, everything checks out with sections. Now let’s make sure there is consistancy with respect to observers. unique(resight_2016$obs)
## [1] JDB JTS RRR RT ## Levels: JDB JTS RRR RT
Looks good. I know all those people. Now, let’s go back and make sure all the counts are summed over the new combined sections we’ve defined. resight_2016 %>% group_by(island, rookery, section, resample, obs) %>% summarise(m=sum(m), u=sum(u)) %>% ungroup() %>% mutate(island=factor(island), rookery=factor(rookery), section=factor(section), resample=factor(resample)) %>% as.data.frame() %>% droplevels() -> resight_2016 shear_2016 %>% group_by(island, rookery, section) %>% summarise(M=sum(M)) %>% ungroup() %>% as.data.frame() %>% droplevels() -> shear_2016
The full resulting data is given in the last section ‘Data appendix.’
Model fitting with ‘pupR’ Now we can use the data we just constructed to fit a mark-resight model where detection probablities vary be occasion and observer.
First steps: An observer by occasion model
In this model we seek to account for occasion and observer variablility in the pup detection process. The model is described as follows. Each rookery will be treated separatey, so the description presented here is for a single rookery. The estimates of island total pup production will based on the sum of the rookery estimates.
Model description First, some notation. The following are the observed data = The total number of shear marked pups = number of marked pups counted by observer on occasion = number of unmarked pups counted by observer on occation Now, the parameters of the model are = The total number of unmarked pups in the population = total pup abundance ( ) = probablility that a pup (marked or unmarked) is counted by observer on occasion = probability that a pup is shear marked This model can then be written as the product binomial likelihood
where
. To make the optimization of the likelihood easier, I reparameterized the model as follows:
where
is continuous.
Inference was obtained via MLE using the Hessian matrix of the likelihood for calculation of the appropriate pup production I used
thus,
s. To estimate
.
A little more data manipulation Because I am looking at variation in detection at just the observer by occasion level a little more data manipulation is in order to sum the total number of sheared pups to the rookery level. shear_2016 %>% mutate(island=factor(island)) %>% group_by(island, rookery) %>% summarise(M = sum(M)) %>% ungroup() -> shear_2016_oo resight_2016 %>% group_by(island, rookery, resample, obs) %>% summarize(m=sum(m), u=sum(u)) %>% u ngroup() -> resight_2016_oo shear_2016_oo
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
# A tibble: 19 × 3 island rookery M 1 sng ECL 450 2 sng ERE 246 3 sng NOR 622 4 sng SGZ 207 5 sng SOU 355 6 sng STA 76 7 snp ARD 75 8 snp GOR 796 9 snp KIT 363 10 snp LUK 318 11 snp LZA 608 12 snp MOR 931 13 snp PCL 658 14 snp POL 321 15 snp REE 1115 16 snp TOL 911 17 snp VOS 1546 18 snp ZAP 906 19 snp ZAR 411
resight_2016_oo
## ## ## ## ## ## ## ## ## ## ## ## ## ##
# A tibble: 78 × 6 island rookery resample obs m u 1 sng ECL 1 JDB 87 863 2 sng ECL 1 JTS 88 862 3 sng ECL 2 JDB 99 801 4 sng ECL 2 JTS 76 674 5 sng ERE 1 JDB 59 691 6 sng ERE 1 JTS 45 505 7 sng ERE 2 JDB 51 524 8 sng ERE 2 JTS 44 506 9 sng NOR 1 JDB 145 1180 10 sng NOR 1 JTS 144 1406 # ... with 68 more rows
Wasn’t that easy using dplyr ! I’ll group the two data sets, shear_2016_oo and resight_2016 into a single data set where rows are based on island and rookery. That way I can apply the model fitting to each roookery at once using the functions in the purrr package. resight_2016_oo %>% group_by(island, rookery) %>% nest() %>% left_join(shear_2016_oo) -> resight_2016_oo
## Joining, by = c("island", "rookery")
resight_2016_oo
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
# A tibble: 19 × 4 island rookery 1 sng ECL 411
Notice that there is a row for every (island, rookery) combination. The resample counts are in the data column in which each entry is itself a data set. We can examine these resight data sets just like selecting an entry in a data frame, e.g., for East Reef rookery the resight data is filter(resight_2016_oo, rookery=="ERE") %>% select(data) %>% .[[1]]
## ## ## ## ## ## ## ##
[[1]] # A tibble: 4 × 4 resample obs m u 1 1 JDB 59 691 2 1 JTS 45 505 3 2 JDB 51 524 4 2 JTS 44 506
Note that you have to use the double brackets because the data is actually contained in a single element list. To access the object in the first list element, you need to have the double brackets. we can look at the object that we get with out the double brackets filter(resight_2016_oo, rookery=="ERE") %>% select(data) -> x str(x)
## Classes 'tbl_df', 'tbl' and 'data.frame': 1 obs. of 1 variable: ## $ data:List of 1 ## ..$ :Classes 'tbl_df', 'tbl' and 'data.frame': 4 obs. of 4 variables: ## .. ..$ resample: Factor w/ 3 levels "1","2","3": 1 1 2 2 ## .. ..$ obs : Factor w/ 4 levels "JDB","JTS","RRR",..: 1 2 1 2 ## .. ..$ m : int 59 45 51 44 ## .. ..$ u : int 691 505 524 506
Fitting the model
The function that fits this particular model is fit_oo and we will fit the model to each rookery with the mapping functions of the purrr package. First, you need to create a function that will be applied to each row of the resight_2016_oo data set. resight_2016_oo %>% mutate(., fit = pmap(.,fit_oo)) -> resight_2016_oo resight_2016_oo
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
# A tibble: 19 × 5 island rookery 1 sng ECL 411
Now there is a fitted model associated with each row of the resight data, e.g., in the first row resight_2016_oo[1,5][[1]]
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
[[1]] [[1]]$par theta alpha JDB_1 JTS_1 JDB_2 JTS_2 8.321774 -2.212557 -1.335646 -1.335720 -1.403501 -1.625943 [[1]]$vcv theta alpha JDB_1 JTS_1 JDB_2 JTS_2 theta alpha JDB_1 JTS_1 JDB_2 JTS_2
theta alpha JDB_1 JTS_1 JDB_2 0.002546329 -0.002546321 -0.002898787 -0.002898743 -0.002859188 -0.002546321 0.005011760 0.002898779 0.002898734 0.002859180 -0.002898787 0.002898779 0.004629459 0.003299982 0.003254952 -0.002898743 0.002898734 0.003299982 0.004629415 0.003254902 -0.002859188 0.002859180 0.003254952 0.003254902 0.004594647 -0.002746704 0.002746696 0.003126898 0.003126850 0.003084183 JTS_2 -0.002746704 0.002746696 0.003126898 0.003126850 0.003084183 0.004558467
[[1]]$logLik [1] -34.12472
The get_IS_sample function can now be use to a sample from the posterior distribution of the real parameters for each rookery. resight_2016_oo %>% mutate(SIR=pmap(., get_IS_sample)) -> resight_2016_oo
See, the last column has the sample included. Now lets summarize the posterior sample into some useful estimates. resight_2016_oo %>% mutate(summary=pmap(., summarize_oo)) -> resight_2016_oo select(resight_2016_oo, island, rookery, summary) %>% unnest() %>% as.data.frame() -> results_tbl
## Warning in bind_rows_(x, .id): Unequal factor levels: coercing to character
Here are the Bayes estimates of pup production by rookery and compare the results to the traditional way to estimate production. pupbull = read.csv("/Users/devin.johnson/research/projects/methodology_devel/model_based_pup_prod uction/work/PUPBULL_2016.csv") filter(results_tbl, parameter=="N") %>% left_join(pupbull, by=c("rookery" = "RCOD")) %>% mutate(estimate=ifelse(!is.na(DEADPUPS), estimate+DEADPUPS, estimate)) %>% mutate(CI.lower=ifelse(!is.na(DEADPUPS), CI.lower+DEADPUPS, CI.lower)) %>% mutate(CI.upper=ifelse(!is.na(DEADPUPS), CI.upper+DEADPUPS, CI.upper)) %>% select(-YEAR, -ROOKERY, -contains("BULLS")) -> N_tbl
## Warning in left_join_impl(x, y, by$x, by$y, suffix$x, suffix$y): joining ## factors with different levels, coercing to character vector
N_tbl
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
island rookery parameter estimate se CI.lower CI.upper DEADPUPS sng ECL N 4570 210 4163 4960 NA sng ERE N 3028 184 2685 3400 25 sng NOR N 6299 216 5904 6758 81 sng SGZ N 1860 76 1716 2010 NA sng SOU N 3852 177 3502 4192 41 sng STA N 780 77 639 937 NA snp ARD N 628 66 510 761 NA snp GOR N 7096 271 6596 7638 NA snp KIT N 3518 173 3201 3873 NA snp LUK N 2591 117 2362 2810 103 snp LZA N 5272 208 4882 5697 NA snp MOR N 7805 183 7426 8138 174 snp PCL N 6504 182 6159 6857 NA snp POL N 3175 133 2926 3446 NA snp REE N 10519 258 9994 10986 228 snp TOL N 7088 231 6649 7535 NA snp VOS N 13952 312 13346 14587 NA snp ZAP N 7581 203 7191 7980 NA snp ZAR N 3309 116 3091 3536 152 PUPSBORN SEP 4625 313.5 3025 75.0 6275 57.0 1882 193.0 3891 248.0 792 3.5 640 80.0 7276 136.0 3633 66.5 2559 39.0 5427 109.5 7908 212.5 6667 0.5 3232 83.5 10570 314.0 7381 174.0 14295 393.5 7801 118.0 3252 19.0
ggplot(data=N_tbl) + geom_point(aes(x=PUPSBORN, y=estimate)) + coord_equal() + geom_abline(interc ept = 0, slope = 1) + xlab("Previous method") + ylab("Model-based estimate") + ggtitle("Compariso n of point estimates")
ggplot(data=N_tbl) + geom_point(aes(x=SEP, y=se)) + coord_equal() + geom_abline(intercept = 0, sl ope = 1) + xlab("Previous method") + ylab("Model-based estimate") + ggtitle("Comparison of SE est imates")
Here are the estimates of : filter(results_tbl, !parameter%in%c("N","tau"))
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
island rookery parameter estimate se CI.lower CI.upper sng ECL delta_JDB_1 0.2083330 0.011377570 0.1861339 0.2297150 sng ECL delta_JTS_1 0.2082884 0.011315664 0.1874402 0.2313417 sng ECL delta_JDB_2 0.1972122 0.010833680 0.1765416 0.2190711 sng ECL delta_JTS_2 0.1644383 0.009354653 0.1442692 0.1814432 sng ERE delta_JDB_1 0.2505932 0.017110639 0.2192117 0.2857682 sng ERE delta_JTS_1 0.1838573 0.013035988 0.1598934 0.2095090 sng ERE delta_JDB_2 0.1921587 0.013874811 0.1643338 0.2178673 sng ERE delta_JTS_2 0.1838837 0.013531747 0.1589400 0.2114060 sng NOR delta_JDB_1 0.2134437 0.008991611 0.1959083 0.2308842 sng NOR delta_JTS_1 0.2495495 0.010270138 0.2299610 0.2696299 sng NOR delta_JDB_2 0.2173760 0.009104471 0.1997147 0.2345627 sng NOR delta_JTS_2 0.2373811 0.009801168 0.2186736 0.2566931 sng SGZ delta_JDB_1 0.3501214 0.018172676 0.3144571 0.3854108 sng SGZ delta_JTS_1 0.3500958 0.017959455 0.3147056 0.3843392 sng SGZ delta_JDB_2 0.2288980 0.013376216 0.2040805 0.2559366 sng SGZ delta_JTS_2 0.2829986 0.015646103 0.2522771 0.3140294 sng SGZ delta_JDB_3 0.2691941 0.015316207 0.2407576 0.3006697 sng SGZ delta_JTS_3 0.2558669 0.014462386 0.2285085 0.2844453 sng SOU delta_JDB_1 0.2431438 0.013058542 0.2179358 0.2687373 sng SOU delta_JTS_1 0.2495838 0.013426415 0.2239522 0.2758465 sng SOU delta_JDB_2 0.2170004 0.012176695 0.1940217 0.2415560 sng SOU delta_JTS_2 0.2105279 0.011591839 0.1894357 0.2337656 sng STA delta_JDB_1 0.2589607 0.029451621 0.2054039 0.3217996 sng STA delta_JTS_1 0.2590951 0.029822814 0.2052784 0.3216581 sng STA delta_JDB_2 0.1944457 0.023357464 0.1515490 0.2424679 sng STA delta_JTS_2 0.1943003 0.023535400 0.1512909 0.2438415 snp ARD delta_RRR_1 0.1604183 0.022296004 0.1217954 0.2075166 snp ARD delta_RT_1 0.2009318 0.026363073 0.1505209 0.2534830 snp ARD delta_RRR_2 0.2412268 0.030224611 0.1849250 0.3031398 snp ARD delta_RT_2 0.2416593 0.030605004 0.1807746 0.2985748 snp GOR delta_RRR_1 0.1588508 0.007298386 0.1444877 0.1726620 snp GOR delta_RT_1 0.1410925 0.006837870 0.1267441 0.1538857 snp GOR delta_RRR_2 0.1975481 0.008973296 0.1810361 0.2160151 snp GOR delta_RT_2 0.1447060 0.006887521 0.1313965 0.1580786 snp KIT delta_RRR_1 0.1779828 0.010926699 0.1567878 0.1991888 snp KIT delta_RT_1 0.1779899 0.010915713 0.1570341 0.1992609 snp KIT delta_RRR_2 0.2492769 0.014225718 0.2227780 0.2784767 snp KIT delta_RT_2 0.1852299 0.011165985 0.1657143 0.2093517 snp LUK delta_RRR_1 0.2416081 0.014023670 0.2138232 0.2685263 snp LUK delta_RT_1 0.2515982 0.014573834 0.2244229 0.2811232 snp LUK delta_RRR_2 0.2518183 0.014442833 0.2260879 0.2820331 snp LUK delta_RT_2 0.2316996 0.013859949 0.2051033 0.2590925 snp LZA delta_RRR_1 0.1852454 0.008952653 0.1677992 0.2023230 snp LZA delta_RT_1 0.1851633 0.009021839 0.1684432 0.2031557 snp LZA delta_RRR_2 0.2090670 0.009974918 0.1903347 0.2284057 snp LZA delta_RT_2 0.1853591 0.009067921 0.1677146 0.2032293 snp MOR delta_RRR_1 0.2621589 0.008014394 0.2467792 0.2783795 snp MOR delta_RT_1 0.2656317 0.008257865 0.2486270 0.2806855 snp MOR delta_RRR_2 0.3474607 0.010043324 0.3277668 0.3665149 snp MOR delta_RT_2 0.2918841 0.008600963 0.2749254 0.3083189 snp PCL delta_RRR_1 0.3382731 0.011006887 0.3166804 0.3591249 snp PCL delta_RT_1 0.2731134 0.009405594 0.2538952 0.2911111 snp PCL delta_RRR_2 0.3459630 0.011171940 0.3251386 0.3695298 snp PCL delta_RT_2 0.2807980 0.009671884 0.2600413 0.2981772 snp POL delta_RRR_1 0.2601900 0.013182059 0.2349599 0.2868526 snp POL delta_RT_1 0.2207565 0.011755660 0.1983710 0.2435578
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78
snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp
And, finally,
POL POL REE REE REE REE TOL TOL TOL TOL VOS VOS VOS VOS ZAP ZAP ZAP ZAP ZAR ZAR ZAR ZAR
delta_RRR_2 delta_RT_2 delta_RRR_1 delta_RT_1 delta_RRR_2 delta_RT_2 delta_RRR_1 delta_RT_1 delta_RRR_2 delta_RT_2 delta_RRR_1 delta_RT_1 delta_RRR_2 delta_RT_2 delta_RRR_1 delta_RT_1 delta_RRR_2 delta_RT_2 delta_RRR_1 delta_RT_1 delta_RRR_2 delta_RT_2
0.4103273 0.2681753 0.2599989 0.2479875 0.2601104 0.2016973 0.1377199 0.1164337 0.2578128 0.2119417 0.1936566 0.1990789 0.2527149 0.2347519 0.2971225 0.2540425 0.2575238 0.2145625 0.2773845 0.2616812 0.3013579 0.2535236
0.019200345 0.013807222 0.007800890 0.007502978 0.007861881 0.006357941 0.006127476 0.005441578 0.009884538 0.008411799 0.005461937 0.005721073 0.006674672 0.006272556 0.009591317 0.008344709 0.008717224 0.007345891 0.012896979 0.012457464 0.013748053 0.012055336
0.3726643 0.2411220 0.2455596 0.2343116 0.2446921 0.1894023 0.1263832 0.1060158 0.2389191 0.1962656 0.1831791 0.1871839 0.2396373 0.2221796 0.2784880 0.2384309 0.2410955 0.2001200 0.2527590 0.2372372 0.2742239 0.2288258
0.4475453 0.2947609 0.2754254 0.2635742 0.2752776 0.2140349 0.1502667 0.1273785 0.2776868 0.2283693 0.2043709 0.2093434 0.2660287 0.2469845 0.3154676 0.2711620 0.2748047 0.2292732 0.3034811 0.2864055 0.3281311 0.2755913
the probability that a pup was sheared in each rookery
filter(results_tbl, parameter=="tau")
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
island rookery parameter estimate se CI.lower CI.upper sng ECL tau 0.09864727 0.006257489 0.08572546 0.1100739 sng ERE tau 0.08209930 0.006988685 0.06899728 0.0965124 sng NOR tau 0.10007835 0.005189491 0.08961765 0.1099416 sng SGZ tau 0.11157978 0.008505040 0.09579346 0.1289376 sng SOU tau 0.09336718 0.006380867 0.08090488 0.1060124 sng STA tau 0.09838713 0.014418611 0.07051521 0.1259920 snp ARD tau 0.12069367 0.017985637 0.08710709 0.1572875 snp GOR tau 0.11231302 0.005834882 0.10150917 0.1243331 snp KIT tau 0.10333410 0.007204645 0.08966537 0.1178677 snp LUK tau 0.12827687 0.008909702 0.11050802 0.1452459 snp LZA tau 0.11545057 0.006315647 0.10249513 0.1272765 snp MOR tau 0.12201308 0.004738631 0.11279032 0.1309914 snp PCL tau 0.10110861 0.004657596 0.09159147 0.1100525 snp POL tau 0.10108280 0.006868072 0.08765270 0.1142720 snp REE tau 0.10840129 0.004044791 0.10028776 0.1159639 snp TOL tau 0.12869047 0.005727664 0.11745660 0.1397311 snp VOS tau 0.11079375 0.003656766 0.10337614 0.1175960 snp ZAP tau 0.11963455 0.004974554 0.10995532 0.1294142 snp ZAR tau 0.13043970 0.007585880 0.11649489 0.1465034
Now we can obtain estimates of island-wide production by summing the rookery SIRs.
resight_2016_oo %>% mutate(N_smp = map2(.$SIR, .$M, function(SIR, M) exp(SIR[,1])+M)) -> resight_ 2016_oo resight_2016_oo %>% filter(island=="sng") %>% select(N_smp) %>% .[[1]] %>% Reduce("+",.) -> sng_p rod resight_2016_oo %>% filter(island=="snp") %>% select(N_smp) %>% .[[1]] %>% Reduce("+",.) -> snp_p rod ### St. George round(mean(sng_prod))
## [1] 20242
round(sd(sng_prod))
## [1] 409
round(HPDinterval(mcmc(sng_prod)))
## lower upper ## var1 19400 21007 ## attr(,"Probability") ## [1] 0.95
### St. Paul round(mean(snp_prod))
## [1] 78381
round(sd(snp_prod))
## [1] 729
round(HPDinterval(mcmc(snp_prod)))
## lower upper ## var1 76935 79806 ## attr(,"Probability") ## [1] 0.95
Data appendix ## resight_2016
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
island rookery section resample obs sng ECL 1 1 JDB sng ECL 1 1 JTS sng ECL 1 2 JDB sng ECL 1 2 JTS sng ECL 2 1 JDB sng ECL 2 1 JTS sng ECL 2 2 JDB sng ECL 2 2 JTS sng ERE 1 1 JDB sng ERE 1 1 JTS sng ERE 1 2 JDB sng ERE 1 2 JTS sng NOR 1 1 JDB sng NOR 1 1 JTS sng NOR 1 2 JDB sng NOR 1 2 JTS sng NOR 2 1 JDB sng NOR 2 1 JTS sng NOR 2 2 JDB sng NOR 2 2 JTS sng NOR 3 1 JDB sng NOR 3 1 JTS sng NOR 3 2 JDB sng NOR 3 2 JTS sng NOR 4 1 JDB sng NOR 4 1 JTS sng NOR 4 2 JDB sng NOR 4 2 JTS sng NOR 5 1 JDB sng NOR 5 1 JTS sng NOR 5 2 JDB sng NOR 5 2 JTS sng SGZ 1/2 1 JDB sng SGZ 1/2 1 JTS sng SGZ 1/2 2 JDB sng SGZ 1/2 2 JTS sng SGZ 1/2 3 JDB sng SGZ 1/2 3 JTS sng SGZ 3 1 JTS sng SGZ 3 2 JDB sng SGZ 3 2 JTS sng SGZ 3 3 JDB sng SGZ 3 3 JTS sng SOU 1 1 JDB sng SOU 1 1 JTS sng SOU 1 2 JDB sng SOU 1 2 JTS sng SOU 2 1 JTS sng SOU 2 2 JDB sng SOU 2 2 JTS sng SOU 3 1 JTS sng SOU 3 2 JDB sng SOU 3 2 JTS sng STA 1/2 1 JDB sng STA 1/2 1 JTS sng STA 1/2 2 JDB
m 54 49 63 45 33 39 36 31 59 45 51 44 27 25 28 33 34 34 24 27 45 34 35 39 24 35 25 32 15 16 18 20 85 43 40 45 58 52 15 6 4 4 7 88 36 14 12 38 33 28 23 30 24 20 19 16
u 471 476 562 455 392 386 239 219 691 505 524 506 173 225 272 267 341 366 276 298 255 291 265 286 251 315 275 318 160 209 132 155 565 482 335 405 367 348 110 44 71 71 68 837 264 111 138 387 342 372 202 295 226 180 181 134
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114
sng snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp
STA ARD ARD ARD ARD GOR GOR GOR GOR GOR GOR GOR GOR GOR GOR GOR GOR GOR GOR GOR GOR GOR GOR GOR GOR GOR GOR GOR GOR KIT KIT KIT KIT KIT KIT KIT KIT KIT KIT KIT KIT KIT KIT KIT KIT KIT KIT KIT KIT KIT KIT KIT KIT LUK LUK LUK LUK LUK
1/2 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 1 1 1 1 2
2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1
JTS RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR
13 14 17 18 14 28 26 28 17 22 19 27 24 50 35 58 47 6 4 10 6 15 14 16 21 8 8 14 8 4 5 2 1 3 3 3 3 11 15 24 20 15 13 27 12 18 12 17 13 12 15 20 18 62 60 56 46 15
137 86 108 132 136 247 224 222 158 228 206 273 201 325 290 517 328 44 46 40 19 85 61 84 104 67 67 111 92 21 20 23 24 22 22 47 47 89 110 151 105 135 112 223 138 182 188 158 137 113 110 180 132 413 365 369 329 110
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172
snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp
LUK LUK LUK LZA LZA LZA LZA LZA LZA LZA LZA LZA LZA LZA LZA LZA LZA LZA LZA LZA LZA LZA LZA LZA LZA LZA LZA MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR MOR PCL PCL PCL
2 2 2 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 1 1 1
1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2
RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR
22 24 25 2 5 5 4 11 12 10 12 23 25 17 15 19 14 17 11 22 22 16 13 38 27 64 60 17 16 27 28 37 38 40 33 61 64 47 37 53 54 69 50 23 20 45 23 31 34 57 53 13 13 59 41 39 35 37
178 176 175 48 45 45 46 114 163 65 63 177 175 108 85 106 86 108 89 153 178 159 137 262 223 486 440 183 184 298 297 288 337 310 267 414 361 328 313 322 346 356 275 177 180 280 202 269 266 443 372 112 112 291 234 311 265 313
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230
snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp
PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL PCL POL POL POL POL POL POL POL POL REE REE REE REE REE REE REE REE REE REE REE REE REE REE REE REE REE REE REE REE REE REE REE REE REE
1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 1 1 1 1 2 2 2 2 1 1 1 1 10/11 10/11 10/11 10/11 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6/7
2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1
RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR
38 23 18 20 15 14 7 12 11 23 30 36 30 33 31 38 24 38 30 41 35 47 34 42 34 33 25 55 31 54 48 72 55 10 15 18 23 25 21 10 11 68 50 44 31 19 19 21 20 52 34 20 15 16 14 21 16 45
262 152 107 130 110 136 68 113 114 227 220 314 245 342 294 362 251 387 320 409 340 428 316 383 316 267 200 445 219 471 427 728 545 140 110 257 202 125 129 90 89 457 450 356 319 181 181 204 130 348 241 230 135 159 136 154 109 405
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288
snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp
REE REE REE REE REE REE REE REE REE REE REE TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL TOL VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS
6/7 6/7 6/7 8 8 8 8 9 9 9 9 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 1 1 1 1 10 10 10 10 11 11 11 11 12 12 12
1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2
RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR
48 54 34 36 40 74 64 32 40 9 12 3 4 10 6 4 5 10 8 6 5 20 15 15 12 58 38 12 11 27 19 20 20 37 32 32 29 39 34 29 16 46 35 16 17 22 22 4 6 9 4 11 12 11 11 19 22 24
402 446 291 314 360 576 461 243 260 91 113 47 71 115 69 46 45 90 92 19 20 80 85 60 38 292 237 88 89 148 131 205 155 288 218 218 196 261 241 171 109 304 240 134 133 153 153 46 44 66 71 64 88 89 89 181 178 226
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346
snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp
VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP
12 13 13 13 13 14 14 14 14 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5
2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1
RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR RT RRR
18 57 56 68 53 36 45 52 43 8 9 10 5 16 12 21 34 23 20 39 32 30 24 20 19 43 39 48 50 18 28 27 30 12 9 20 12 14 20 15 16 13 7 15 12 24 25 22 27 18 16 24 23 42 35 29 24 24
182 443 369 557 497 314 330 423 382 42 66 65 70 109 88 154 241 177 180 386 318 220 226 155 156 382 411 427 350 82 122 173 170 113 116 155 138 86 105 110 109 62 43 85 88 126 125 153 148 107 109 201 177 233 190 221 176 301
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369
snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp
## shear_2016
ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR
5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 1 1 1 1 2 2 2 2
1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2
RT 25 225 RRR 40 310 RT 31 194 RRR 54 371 RT 50 325 RRR 22 153 RT 19 156 RRR 52 423 RT 33 317 RRR 36 339 RT 32 243 RRR 51 349 RT 38 362 RRR 34 266 RT 29 246 RRR 101 599 RT 81 569 RRR 103 647 RT 85 540 RRR 20 155 RT 18 157 RRR 23 177 RT 18 157
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
island rookery section M sng ECL 1 304 sng ECL 2 146 sng ERE 1 246 sng NOR 1 108 sng NOR 2 166 sng NOR 3 176 sng NOR 4 111 sng NOR 5 61 sng SGZ 1/2 150 sng SGZ 3 57 sng SOU 1 98 sng SOU 2 129 sng SOU 3 128 sng STA 1/2 76 snp ARD 1 75 snp GOR 1 153 snp GOR 2 98 snp GOR 3 168 snp GOR 4 70 snp GOR 5 156 snp GOR 6 151 snp KIT 0 21 snp KIT 1 40 snp KIT 2 60 snp KIT 3 85 snp KIT 4 91 snp KIT 5 66 snp LUK 1 224 snp LUK 2 94 snp LZA 1 55 snp LZA 2 85 snp LZA 3 110 snp LZA 4 105 snp LZA 5 95 snp LZA 6 158 snp MOR 0 108 snp MOR 1 146 snp MOR 2 144 snp MOR 3 154 snp MOR 4 89 snp MOR 5 175 snp MOR 6 115 snp PCL 1 106 snp PCL 2 62 snp PCL 3 55 snp PCL 4 103 snp PCL 5 81 snp PCL 6 131 snp PCL 7 120 snp POL 1 178 snp POL 2 143 snp REE 1 108 snp REE 10/11 84 snp REE 2 211 snp REE 3 114 snp REE 4 106
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92
snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp snp
REE REE REE REE TOL TOL TOL TOL TOL TOL TOL TOL VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS VOS ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAP ZAR ZAR
5 6/7 8 9 1 2 3 4 5 6 7 8 1 10 11 12 13 14 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 1 2
84 162 174 72 60 53 68 144 107 148 156 175 88 24 68 94 321 194 44 67 128 99 155 97 79 88 51 111 113 144 96 152 131 108 320 91
