Bayesian Multivariate Autoregressive State-Space models - MARSS in Jags
Context
Species interactions are fascinating. To study them we often have to analyse time series of counts. Counts are challenging because of observation errors, lack of independence and spatial heterogeneity. State-space models are often used to deal with these issues. However, state-space models are complex statistical tools and are not easy to manipulate.
Eli Holmes, Mark Scheuerell and Eric Ward share electronic books and courses on the analysis of time series, including material on state-space models. They introduce MARSS models (MARSS = Multivariate Autoregressive State-Space) as a flexible framework to analyse time series of counts, and provide a package called MARSS to implement these models.
Check it out, these resources are awesome!
Holmes, Scheuerell and Ward also have a great book on the analysis of time series, in which they illustrate the frequentist approach with their package MARSS and the Bayesian approach with Jags and Stan. Regarding species interactions more specifically, Eli Holmes has a dedicated course in which she asks how interactions change over time, and how environmental change affect interactions, and she uses state-space models to answer these questions.
Below I will use Jags to reproduce an example from the package MARSS user's guide.
Models
Multivariate state-space models can be written as:
Briefly speaking, is a vector of observed log counts for each species,
is for the true log abundances,
is a matrix that captures species interactions,
the process error,
the observation error,
is a vector of intrinsic growth rate for each species. There are many variations of this model. For example, we may wish to incorporate environmental covariates. More details can be found in the
MARSS user's guide that you can easily access by typing in the following command.
RShowDoc("UserGuide", package="MARSS")Chapter 14 on the Estimation of species interaction strengths with and without covariates will be of much interest to us. You can easily get the code and data that come with this chapter by typing in the following command.
RShowDoc("Chapter_SpeciesInteractions.R", package="MARSS")Now let's get to it. We will use a dataset from a landmark paper on MARSS by Ives et al. (2003) entitled Estimating community stability and ecological interactions from time-series data and published in the journal Ecological Monographs.
Read in and visualize data
Prerequisites.
library(tidyverse)
theme_set(theme_light())
library(janitor)
library(lubridate)
library(MARSS)Load in the plankton data. Only use the plankton, daphnia, and non-daphnia.
data(ivesDataByWeek)
dat <- ivesDataByWeek %>%
as_tibble() %>%
clean_names() %>% # clean column names
select(large_phyto, small_phyto, daphnia, non_daphnia) %>% # select species
mutate(across(where(is.double), log)) %>% # log transform all columns
mutate(across(where(is.double), scale, scale = FALSE)) %>% # center all columns
clean_names() # clean column names
dat## # A tibble: 269 x 4
## large_phyto[,1] small_phyto[,1] daphnia[,1] non_daphnia[,1]
## <dbl> <dbl> <dbl> <dbl>
## 1 0.152 -0.504 -1.22 -1.63
## 2 0.383 -0.271 -0.906 -1.68
## 3 0.491 -0.222 -0.582 -1.04
## 4 -0.538 -0.820 -1.32 -0.664
## 5 -0.394 -0.649 -0.853 -1.20
## 6 -1.44 -0.704 -1.71 -0.748
## 7 -1.42 -0.893 -0.847 -1.03
## 8 -1.17 -0.688 -1.13 -1.18
## 9 -0.739 -0.611 -2.22 -1.61
## 10 NA NA NA NA
## # … with 259 more rows
Plot all data.
dat %>%
mutate(week = row_number()) %>% # add week id
pivot_longer(large_phyto:non_daphnia,
values_to = "log_biomass",
names_to = "species") %>%
ggplot() +
aes(x = week, y = log_biomass, color = species) +
geom_line() +
labs(x = "Week",
y = "Biomass (log)",
color = "Species") +
geom_hline(yintercept = 0, lty = "dashed") +
expand_limits(x = 0)
Plot by species.
dat %>%
mutate(week = row_number()) %>% # add week id
pivot_longer(large_phyto:non_daphnia,
values_to = "log_biomass",
names_to = "species") %>%
ggplot() +
aes(x = week, y = log_biomass) +
geom_line() +
labs(x = "Week",
y = "Biomass (log)") +
geom_hline(yintercept = 0, lty = "dashed", color = "gray70") +
expand_limits(x = 0) +
facet_wrap(~species)
MARSS model in the frequentist framework
We consider a model with the following assumptions:
- All phytoplankton share the same process variance.
- All zooplankton share the same process variance.
- Phytoplankton and zooplankton have different measurement variances.
- Measurement errors are independent.
- Process errors are independent.
We fit this model with the MARSS package. We need to specify the ingredients first.
Q <- matrix(list(0), 4, 4)
diag(Q) <- c("Phyto", "Phyto", "Zoo", "Zoo")
R <- matrix(list(0), 4, 4)
diag(R) <- c("Phyto", "Phyto", "Zoo", "Zoo")
plank.model.0 <- list(
B = "unconstrained", U = "zero", Q = Q,
Z = "identity", A = "zero", R = R,
x0 = "unequal", tinitx = 1
)
plank.model.0## $B
## [1] "unconstrained"
##
## $U
## [1] "zero"
##
## $Q
## [,1] [,2] [,3] [,4]
## [1,] "Phyto" 0 0 0
## [2,] 0 "Phyto" 0 0
## [3,] 0 0 "Zoo" 0
## [4,] 0 0 0 "Zoo"
##
## $Z
## [1] "identity"
##
## $A
## [1] "zero"
##
## $R
## [,1] [,2] [,3] [,4]
## [1,] "Phyto" 0 0 0
## [2,] 0 "Phyto" 0 0
## [3,] 0 0 "Zoo" 0
## [4,] 0 0 0 "Zoo"
##
## $x0
## [1] "unequal"
##
## $tinitx
## [1] 1
Then we fit the model.
kem.plank.0 <- dat %>%
t() %>%
MARSS(model = plank.model.0)## Success! abstol and log-log tests passed at 301 iterations.
## Alert: conv.test.slope.tol is 0.5.
## Test with smaller values (<0.1) to ensure convergence.
##
## MARSS fit is
## Estimation method: kem
## Convergence test: conv.test.slope.tol = 0.5, abstol = 0.001
## Estimation converged in 301 iterations.
## Log-likelihood: -410.8999
## AIC: 869.7998 AICc: 873.3501
##
## Estimate
## R.Phyto 0.41998
## R.Zoo 0.06767
## B.(1,1) 0.76682
## B.(2,1) 0.18777
## B.(3,1) -0.42591
## B.(4,1) -0.32672
## B.(1,2) 0.28961
## B.(2,2) 0.51355
## B.(3,2) 2.28596
## B.(4,2) 1.35405
## B.(1,3) -0.01823
## B.(2,3) 0.00521
## B.(3,3) 0.49159
## B.(4,3) -0.21804
## B.(1,4) 0.13090
## B.(2,4) -0.04494
## B.(3,4) 0.38885
## B.(4,4) 0.83103
## Q.Phyto 0.11955
## Q.Zoo 0.17140
## x0.X.large_phyto 0.20698
## x0.X.small_phyto 0.01609
## x0.X.daphnia -1.13943
## x0.X.non_daphnia -1.69203
## Initial states (x0) defined at t=1
##
## Standard errors have not been calculated.
## Use MARSSparamCIs to compute CIs and bias estimates.
We may get the estimates in a more readable format. For example, let's have a look to the interactions. We denote LP for large phytoplankton, SP for small phytoplankton, D for Daphnia and ND for non-Daphnia. These estimates describe the effect of the density of species j on the per capita growth rate of species i.
B.0 <- coef(kem.plank.0, type = "matrix")$B[1:4, 1:4]
rownames(B.0) <- colnames(B.0) <- c("LP", "SP", "D", "ND")
print(B.0, digits = 2)## LP SP D ND
## LP 0.77 0.29 -0.0182 0.131
## SP 0.19 0.51 0.0052 -0.045
## D -0.43 2.29 0.4916 0.389
## ND -0.33 1.35 -0.2180 0.831
The effect of species j on species i is given by the cell at i-th row and j-th column. The B matrix suggests that SP has a possitive effect on D (2.29).
In the diagonal, we have the strenght of density-dependence: if species i is density-independent, then equals 1; smaller
means more density dependence.
MARSS model in the Bayesian framework
Let's try to reproduce these results in a Bayesian framework with Jags.
library(R2jags)Let's explore the scaled gama prior for precision which gives us the scaled half-t prior for the standard deviation in Jags. Check out this presentation by Martyn Plummer for more details.
LaplacesDemon::rhalft(1000, scale = 1, nu = 10) %>%
as_tibble() %>%
ggplot(aes(value)) +
geom_histogram(fill = "white", color = "black")
Write the model.
jagsscript <- cat("
model {
# Estimate the initial state vector of population abundances
for(i in 1:nSpecies) {
X[i,1] ~ dnorm(0,1) # weakly informative normal prior
xknot[i] <- X[i,1]
}
# B matrix of interactions
B[1, 1] <- alpha[1]
B[1, 2] <- alpha[2]
B[1, 3] <- alpha[3]
B[1, 4] <- alpha[4]
B[2, 1] <- alpha[5]
B[2, 2] <- alpha[6]
B[2, 3] <- alpha[7]
B[2, 4] <- alpha[8]
B[3, 1] <- alpha[9]
B[3, 2] <- alpha[10]
B[3, 3] <- alpha[11]
B[3, 4] <- alpha[12]
B[4, 1] <- alpha[13]
B[4, 2] <- alpha[14]
B[4, 3] <- alpha[15]
B[4, 4] <- alpha[16]
for (k in 1:16){
alpha[k] ~ dunif(-1, 1)
}
# Autoregressive process
for(t in 2:nYears) {
for(i in 1:nSpecies) {
predX[i,t] <- inprod(B[i,], X[,t-1])
X[i,t] ~ dnorm(predX[i,t], tauQ[species[i]])
}
}
tauQ[1] ~ dscaled.gamma(1, 10)
tauQ[2] ~ dscaled.gamma(1, 10)
Qp <- 1 / tauQ[1]
Qd <- 1 / tauQ[2]
# Observation model
for(t in 1:nYears) {
for(i in 1:nSpecies) {
counts[i,t] ~ dnorm(X[i,t], tauR[species[i]])
}
}
tauR[1] ~ dscaled.gamma(1, 10)
tauR[2] ~ dscaled.gamma(1, 10)
Rp <- 1 / tauR[1]
Rd <- 1 / tauR[2]
}
",file="marss-jags.txt")Put the data in a list, specify the parameters to monitor.
tdat <- t(dat)
jags.data <- list(counts = tdat,
nSpecies = nrow(tdat),
nYears = ncol(tdat),
species = c(1, 1, 2, 2))
jags.params <- c("Qp", "Qd", "xknot","alpha", "Rp", "Rd", "X")
model.loc <- "marss-jags.txt" # name of the txt fileNow run Jags!
mod_1 <- jags(jags.data,
parameters.to.save = jags.params,
model.file = model.loc,
n.chains = 2,
n.burnin = 2500,
n.thin = 1,
n.iter = 5000) ## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 363
## Unobserved stochastic nodes: 1809
## Total graph size: 3530
##
## Initializing model
Inspect estimates. Probably needs to run it longer to improve n.eff. For illustration purpose, that'll do.
mod_1## Inference for Bugs model at "marss-jags.txt", fit using jags,
## 2 chains, each with 5000 iterations (first 2500 discarded)
## n.sims = 5000 iterations saved
## mu.vect sd.vect 2.5% 25% 50% 75% 97.5% Rhat n.eff
## Qd 0.243 0.099 0.095 0.169 0.226 0.302 0.475 1.044 42
## Qp 0.272 0.107 0.120 0.200 0.254 0.320 0.579 1.516 6
## Rd 0.163 0.071 0.022 0.116 0.160 0.206 0.315 1.155 41
## Rp 0.344 0.105 0.012 0.296 0.351 0.408 0.521 1.359 14
## X[1,1] 0.212 0.462 -0.717 -0.084 0.205 0.516 1.119 1.005 5000
## X[2,1] -0.194 0.364 -0.896 -0.446 -0.201 0.048 0.532 1.017 93
## X[3,1] -0.914 0.369 -1.597 -1.167 -0.935 -0.671 -0.134 1.003 1400
## X[4,1] -1.378 0.351 -2.018 -1.619 -1.398 -1.161 -0.631 1.001 5000
## X[1,2] 0.114 0.409 -0.717 -0.160 0.129 0.394 0.913 1.012 130
## X[2,2] -0.007 0.327 -0.632 -0.240 -0.014 0.214 0.629 1.008 210
## X[3,2] -0.997 0.318 -1.645 -1.200 -0.991 -0.788 -0.379 1.002 5000
## X[4,2] -1.361 0.321 -1.946 -1.586 -1.372 -1.154 -0.707 1.006 280
## X[1,3] 0.037 0.398 -0.738 -0.232 0.044 0.319 0.806 1.035 49
## ...
## X[1,268] 0.511 0.380 -0.244 0.263 0.515 0.757 1.259 1.008 200
## X[2,268] 0.307 0.317 -0.316 0.098 0.310 0.520 0.924 1.002 950
## X[3,268] 0.257 0.315 -0.387 0.047 0.267 0.470 0.857 1.003 570
## X[4,268] -0.252 0.291 -0.817 -0.441 -0.256 -0.062 0.321 1.001 5000
## X[1,269] 0.846 0.440 -0.018 0.542 0.846 1.158 1.654 1.057 32
## X[2,269] 0.638 0.420 -0.200 0.360 0.642 0.934 1.443 1.017 100
## X[3,269] -0.058 0.336 -0.700 -0.282 -0.075 0.161 0.647 1.012 150
## X[4,269] -0.153 0.327 -0.797 -0.364 -0.152 0.056 0.503 1.002 1400
## alpha[1] 0.599 0.160 0.239 0.501 0.616 0.711 0.870 1.038 170
## alpha[2] 0.150 0.221 -0.248 0.005 0.129 0.284 0.660 1.286 9
## alpha[3] 0.022 0.070 -0.108 -0.027 0.019 0.069 0.163 1.143 15
## alpha[4] 0.143 0.100 -0.049 0.074 0.142 0.209 0.336 1.030 70
## alpha[5] 0.102 0.172 -0.195 -0.021 0.092 0.215 0.446 1.072 170
## alpha[6] 0.566 0.175 0.211 0.450 0.568 0.685 0.894 1.070 40
## alpha[7] 0.037 0.078 -0.096 -0.022 0.031 0.088 0.200 1.021 230
## alpha[8] -0.097 0.114 -0.314 -0.175 -0.094 -0.021 0.135 1.044 41
## alpha[9] -0.067 0.218 -0.532 -0.198 -0.068 0.092 0.338 1.079 34
## alpha[10] 0.877 0.140 0.456 0.839 0.923 0.967 0.997 1.180 32
## alpha[11] 0.527 0.106 0.313 0.458 0.532 0.597 0.726 1.155 18
## alpha[12] 0.519 0.167 0.212 0.407 0.503 0.617 0.887 1.024 110
## alpha[13] -0.141 0.167 -0.487 -0.255 -0.131 -0.034 0.171 1.081 41
## alpha[14] 0.738 0.138 0.451 0.642 0.745 0.839 0.976 1.075 40
## alpha[15] -0.198 0.079 -0.362 -0.247 -0.198 -0.145 -0.041 1.159 15
## alpha[16] 0.839 0.103 0.619 0.772 0.851 0.922 0.992 1.154 16
## xknot[1] 0.212 0.462 -0.717 -0.084 0.205 0.516 1.119 1.005 5000
## xknot[2] -0.194 0.364 -0.896 -0.446 -0.201 0.048 0.532 1.017 93
## xknot[3] -0.914 0.369 -1.597 -1.167 -0.935 -0.671 -0.134 1.003 1400
## xknot[4] -1.378 0.351 -2.018 -1.619 -1.398 -1.161 -0.631 1.001 5000
## deviance 455.623 157.971 -39.036 427.024 495.739 546.645 624.539 1.413 9
##
## For each parameter, n.eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor (at convergence, Rhat=1).
##
## DIC info (using the rule, pD = var(deviance)/2)
## pD = 10854.9 and DIC = 11310.5
## DIC is an estimate of expected predictive error (lower deviance is better).
Check convergence.
traceplot(mod_1,
ask = FALSE,
varname = c("Qp", "Qd", "xknot","alpha", "Rp", "Rd"))
Get Q and R estimates and compare to MLEs.
mod_1$BUGSoutput$mean$Qd## [1] 0.2428883
mod_1$BUGSoutput$mean$Qp## [1] 0.2716571
mod_1$BUGSoutput$mean$Rd## [1] 0.1629837
mod_1$BUGSoutput$mean$Rp## [1] 0.3437218
kem.plank.0$coef['Q.Zoo']## Q.Zoo
## 0.1713966
kem.plank.0$coef['Q.Phyto']## Q.Phyto
## 0.1195536
kem.plank.0$coef['R.Zoo']## R.Zoo
## 0.06767447
kem.plank.0$coef['R.Phyto']## R.Phyto
## 0.4199771
Get init X estimates and compare to MLEs.
mod_1$BUGSoutput$mean$xknot## [1] 0.2115938 -0.1937940 -0.9135877 -1.3777157
kem.plank.0$coef['x0.X.large_phyto']## x0.X.large_phyto
## 0.2069771
kem.plank.0$coef['x0.X.small_phyto']## x0.X.small_phyto
## 0.01608991
kem.plank.0$coef['x0.X.daphnia']## x0.X.daphnia
## -1.139434
kem.plank.0$coef['x0.X.non_daphnia']## x0.X.non_daphnia
## -1.692034
Get B estimates and compare to MLEs.
round(matrix(mod_1$BUGSoutput$mean$alpha, byrow = TRUE, ncol = 4) ,2)## [,1] [,2] [,3] [,4]
## [1,] 0.60 0.15 0.02 0.14
## [2,] 0.10 0.57 0.04 -0.10
## [3,] -0.07 0.88 0.53 0.52
## [4,] -0.14 0.74 -0.20 0.84
print(B.0, digits = 2)## LP SP D ND
## LP 0.77 0.29 -0.0182 0.131
## SP 0.19 0.51 0.0052 -0.045
## D -0.43 2.29 0.4916 0.389
## ND -0.33 1.35 -0.2180 0.831
Compare observed counts and estimated abundances.
pivot_dat <- dat %>%
mutate(week = row_number()) %>%
pivot_longer(large_phyto:non_daphnia,
values_to = "log_biomass",
names_to = "species")
mod_1$BUGSoutput$sims.matrix %>%
as_tibble() %>%
pivot_longer(cols = everything(), values_to = "value", names_to = "parameter") %>%
filter(str_detect(parameter, "X")) %>%
mutate(species = rep(rep(unique(pivot_dat$species), 269),5000),
week = as.numeric(rep(gl(269, 4),5000))) %>%
group_by(parameter, species, week) %>%
summarize(medianN = median(value),
lci = quantile(value, probs = 2.5/100),
uci = quantile(value, probs = 97.5/100)) %>%
arrange(week) %>%
ggplot() +
geom_ribbon(aes(x = week, y = medianN, ymin = lci, ymax = uci), fill = "red", alpha = 0.3) +
geom_line(aes(x = week, y = medianN), lty = "dashed", color = "red") +
geom_point(data = pivot_dat, aes(x = week, y = log_biomass)) +
labs(x = "Week",
y = "Biomass (log)") +
geom_hline(yintercept = 0, lty = "dashed", color = "gray70") +
expand_limits(x = 0) +
facet_wrap(~species, scales = "free_y")
Yet to be done
Getting closer to Ives' et al (2003) results
We are far from the estimates that Ives and colleagues obtained in their paper. This is because we do not fit the same model. In Chapter 14 on the Estimation of species interaction strengths with and without covariates of the MARSS package user's guide, additionnal steps are given to fit models more similar to Ives' model.
Tackle a more complex problem
At some stage, I would like to analyse the data from this paper A multi-decade time ser ies of kelp forest community structure at San Nicolas Island, California (USA).
These data are analysed in Eli Holmes' course on estimating interactions starting at slide 31. Below are some preliminary descriptive analyses.
When you go on the data paper webpage, you have the raw data and the metadata.
Broadly speaking, we have:
- 7 sites around the island
- Biannual surveys from 1980-2011 (n= 63)
- Divers collect data on:
- Fish (59 spp)
- Inverts (14 spp)
- Kelps (6 spp)
Get sea otter (Enhydra lutris) counts.
ind_otters <- read_csv("http://www.esapubs.org/archive/ecol/E094/244/Table2_independent_sea_otters.csv") %>%
clean_names() %>%
mutate(date = mdy(date),
year = year(date)) %>%
select(-date) %>%
pivot_longer(cols = west:south, values_to = "counts", names_to = "region") %>%
add_column(stage = "independent")
pup_otters <- read_csv("http://www.esapubs.org/archive/ecol/E094/244/Table3_sea_otter_pups.csv") %>%
clean_names() %>%
mutate(date = mdy(year),
year = year(date)) %>%
select(-date) %>%
pivot_longer(cols = west:south, values_to = "counts", names_to = "region") %>%
add_column(stage = "pup")
otters <- bind_rows(ind_otters, pup_otters)Visualize.
otters %>%
count(year, region, wt = counts) %>%
ggplot() +
aes(x = year, y = n, fill = region) +
geom_col() +
labs(y = "# otters",
fill = "Region")
Now let's get the counts for all species.
Benthic fishes first.
benthicfish_raw <- read_csv("http://www.esapubs.org/archive/ecol/E094/244/Benthic%20fish%20density%20raw%20data.csv")
benthicfish <- benthicfish_raw %>%
clean_names() %>%
mutate(date = mdy(date),
year = year(date)) %>%
# separate(date, c("year", "month", "day"), "-")
select(station, year, species_code, adult_density, juv_density)
#dat %>% View()
benthicfish %>% count(station) # 7 stations/sites## # A tibble: 7 x 2
## station n
## <dbl> <int>
## 1 1 9731
## 2 2 9361
## 3 3 9361
## 4 4 9731
## 5 5 9361
## 6 6 9509
## 7 7 5365
benthicfish %>% count(year) # 30 years## # A tibble: 30 x 2
## year n
## <dbl> <int>
## 1 1981 888
## 2 1982 1998
## 3 1983 2035
## 4 1984 1295
## 5 1985 2220
## 6 1986 2405
## 7 1987 2590
## 8 1988 2590
## 9 1989 2590
## 10 1990 1295
## # … with 20 more rows
benthicfish %>% count(species_code) # 37 species## # A tibble: 37 x 2
## species_code n
## <dbl> <int>
## 1 1002 1687
## 2 1003 1687
## 3 1011 1687
## 4 1012 1687
## 5 1014 1687
## 6 1016 1687
## 7 1017 1687
## 8 1018 1687
## 9 1019 1687
## 10 1020 1687
## # … with 27 more rows
midwaterfish_raw <- read_csv("http://www.esapubs.org/archive/ecol/E094/244/Midwater%20fish%20density%20raw%20data.csv")
midwaterfish <- midwaterfish_raw %>%
clean_names() %>%
mutate(date = mdy(date),
year = year(date)) %>%
# separate(date, c("year", "month", "day"), "-")
select(station, year, species_code, adult_density, juv_density)
#dat %>% View()
midwaterfish %>% count(station) # 7 stations/sites## # A tibble: 7 x 2
## station n
## <dbl> <int>
## 1 1 15635
## 2 2 15045
## 3 3 15045
## 4 4 15576
## 5 5 15281
## 6 6 15340
## 7 7 8555
midwaterfish %>% count(year) # 30 years## # A tibble: 30 x 2
## year n
## <dbl> <int>
## 1 1981 1770
## 2 1982 3481
## 3 1983 3245
## 4 1984 2360
## 5 1985 3540
## 6 1986 3835
## 7 1987 4130
## 8 1988 4130
## 9 1989 4130
## 10 1990 2065
## # … with 20 more rows
midwaterfish %>% count(species_code) # 59 species## # A tibble: 59 x 2
## species_code n
## <dbl> <int>
## 1 1001 1703
## 2 1002 1703
## 3 1003 1703
## 4 1004 1703
## 5 1005 1703
## 6 1006 1703
## 7 1008 1703
## 8 1009 1703
## 9 1010 1703
## 10 1011 1703
## # … with 49 more rows
benthicover_raw <- read_csv("http://www.esapubs.org/archive/ecol/E094/244/Benthic%20cover%20raw%20data.csv")
benthicover <- benthicover_raw %>%
clean_names() %>%
mutate(date = mdy(date),
year = year(date)) %>%
# separate(date, c("year", "month", "day"), "-")
select(station, year, species_code, cover)
#dat %>% View()
benthicover %>% count(station) # 7 stations/sites## # A tibble: 7 x 2
## station n
## <dbl> <int>
## 1 1 84546
## 2 2 81620
## 3 3 81312
## 4 4 87780
## 5 5 85470
## 6 6 83160
## 7 7 45738
benthicover %>% count(year) # 31 years## # A tibble: 31 x 2
## year n
## <dbl> <int>
## 1 1980 9240
## 2 1981 18480
## 3 1982 18480
## 4 1983 16786
## 5 1984 13706
## 6 1985 18480
## 7 1986 20020
## 8 1987 21406
## 9 1988 21560
## 10 1989 21406
## # … with 21 more rows
benthicover %>% count(species_code) # 154 species## # A tibble: 154 x 2
## species_code n
## <chr> <int>
## 1 0000 3569
## 2 0002 3569
## 3 0012 3569
## 4 0025 3569
## 5 0029 3569
## 6 0030 3569
## 7 0045 3569
## 8 0046 3569
## 9 0047 3569
## 10 0048 3569
## # … with 144 more rows
benthicover %>% count(cover) # 21 levels## # A tibble: 21 x 2
## cover n
## <dbl> <int>
## 1 0 518132
## 2 5 13063
## 3 10 5393
## 4 15 3089
## 5 20 2083
## 6 25 1555
## 7 30 1167
## 8 35 903
## 9 40 740
## 10 45 612
## # … with 11 more rows
benthicdensity_raw <- read_csv("http://www.esapubs.org/archive/ecol/E094/244/Benthic%20density%20raw%20data.csv")
benthicdensity <- benthicdensity_raw %>%
clean_names() %>%
mutate(date = mdy(date),
year = year(date)) %>%
# separate(date, c("year", "month", "day"), "-")
select(station, year, species_code, density)
#dat %>% View()
benthicdensity %>% count(station) # 7 stations/sites## # A tibble: 7 x 2
## station n
## <dbl> <int>
## 1 1 5187
## 2 2 5035
## 3 3 5035
## 4 4 5415
## 5 5 5320
## 6 6 5054
## 7 7 2869
benthicdensity %>% count(year) # 31 years## # A tibble: 31 x 2
## year n
## <dbl> <int>
## 1 1980 570
## 2 1981 1140
## 3 1982 1140
## 4 1983 1007
## 5 1984 798
## 6 1985 1121
## 7 1986 1235
## 8 1987 1330
## 9 1988 1330
## 10 1989 1330
## # … with 21 more rows
benthicdensity %>% count(species_code) # 19 species## # A tibble: 19 x 2
## species_code n
## <chr> <int>
## 1 0024 1785
## 2 0029 1785
## 3 0030 1785
## 4 0066 1785
## 5 0067 1785
## 6 0075 1785
## 7 0081 1785
## 8 0082 1785
## 9 0085 1785
## 10 0089 1785
## 11 0092 1785
## 12 0152 1785
## 13 0553 1785
## 14 0556 1785
## 15 0557 1785
## 16 0558 1785
## 17 0574 1785
## 18 0575 1785
## 19 0589 1785
giantkelp_raw <- read_csv("http://www.esapubs.org/archive/ecol/E094/244/Giant%20kelp%20size%20frequency.csv")
giantkelp <- giantkelp_raw %>%
clean_names() %>%
mutate(date = mdy(date),
year = year(date))
giantkelp## # A tibble: 14,037 x 8
## station period date swath kelp_id hold_fast stipe_count year
## <dbl> <dbl> <date> <chr> <chr> <dbl> <dbl> <dbl>
## 1 1 1 1980-08-27 10R 1_2_111 NA NA 1980
## 2 1 1 1980-08-27 10R 1_2_113 NA NA 1980
## 3 1 1 1980-08-27 10R 1_2_125 NA NA 1980
## 4 1 1 1980-08-27 10R 1_2_134 NA NA 1980
## 5 1 1 1980-08-27 10R 1_2_141 NA NA 1980
## 6 1 1 1980-08-27 10R 1_2_150 NA NA 1980
## 7 1 1 1980-08-27 22R 1_4_112 NA NA 1980
## 8 1 1 1980-08-27 22R 1_4_146 NA NA 1980
## 9 1 1 1980-08-27 32L 1_5_77 NA NA 1980
## 10 1 1 1980-08-27 32L 1_5_96 NA NA 1980
## # … with 14,027 more rows
Modeling is yet to come.
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