Introduction

In 2000, the Santa Barbara Coastal Term Ecological Long-Term Research (SBC LTER) program was established to better understand kelp forest ecosystems in southern California. Spiny lobsters (Panulirus interruptus, Figure 1), which are the focus of many SBC LTER studies, are important predators in giant kelp forests (Reed, 2019). Monitoring lobster abundance, size, and fishing pressure are all part of an annual, on-going study that started in 2012. Studies were conducted at five sites near Santa Barbara County: Carpinteria, Isla Vista, Arroyo Quemado, Mohawk, and Naples (Figure 2). On January 1, 2012, Marine Protected Areas (MPAs) were established at Isla Vista and Naples.

Figure 1: California spiny lobsters (Panulirus interruptus) emerging from under a rock. Photo credit: Ed Bierman, Wikipedia.

MPAs are sections of the ocean reserved for conservation of ecosystems, habitats, and species (WildAid, 2018). While MPAs allow some activities within their borders, one of their main goals is to increase wildlife populations by restricting or eliminating removal of species (WildAid, 2018). This report examines how lobster size and abundance has changed in two MPAs compared to three non-MPAs along the Santa Barbara Coast.

Figure 2: Map of the five locations lobster surveys took place. Survey sites from left to right: Arroyo Quemado, Naples (MPA), Isla Vista (MPA), Mohawk, Carpinteria.

Data and Methods

Data for spiny lobster abundance and size was collected by divers from the months of August to December from 2012 to 2018 by the Santa Barbara Coastal Long-Term Ecological Research (LTER). Lobster counts and sizes were based on visual observations from a diver searching 2.5m areas on opposite sides of a 60m transect tape. For more information on collection methods and spatial information, please see the metadata.

Counts and sizes (mm) of lobsters were visually compared in MPAs and Non-MPAs. The differences in mean lobster size in MPAs and non-MPAs were compared by two-sample t-tests (\(\alpha\) = 0.05 throughout). To measure the magnitude of the difference between the means, we calculated the effect size using Cohen’s d. All analyses and figures were prepared using R software version 3.6.1. Collaboration between authors was done using GitHub.

Results

Result A: Changes in lobster abundance by site (2012 - 2018)

The impact of creating MPAs on lobster abundance can be seen in Figure 3. Isla Vista had the highest number of lobster observations in 2018 and one of the greatest increases in abundance. From 2012 to 2018 Isla Vista lobster abundance increased from 26 to 946 observations, an increase of approximately 3,500%. While the 2018 lobster abundance at the Naples MPA was not as high as the Isla Vista MPA (n2018=298), Naples had a larger percent increase (over 4,800% increase) from 2012-2018. This dramatic increase may be attributed to the very small number of observed lobsters at Naples in 2012 (n2012=6). Comparatively, lobster abundance at the non-MPA sites - Carpinteria, Arroyo Quemado, and Mohawk - only experienced a 339%, 98%, and 42% increase from 2012-2018, respectively.

The total number of lobsters in MPAs increased over 3,700% from 32 lobster observations in 2012 to 1,244 lobster observations in 2018. In the three non-MPA study sites, the total number of observed lobsters increased 182% from 199 lobsters in 2012 to 561 lobsters in 2018.

# Install packages

library(tidyverse)
library(janitor)
library(here)
library(tidyr)
library(kableExtra)
library(effsize)
library(dplyr)

# Read in data and clean/wrangle
# Assign site name to 4 letter site code
# Create new column for MPA status

lobster_abundance_sbc <- read_csv(here::here("data", "lobster_abundance_sbc_lter.csv"),
                                  na = "-99999") %>%
  janitor::clean_names() %>%  
  mutate(site_name_long = case_when(
    site %in% c("CARP") ~ "Carpinteria" ,
    site %in% c("IVEE") ~ "Isla Vista",
    site %in% c("AQUE") ~ "Arroyo Quemado",
    site %in% c("MOHK") ~ "Mohawk", 
    site %in% c("NAPL") ~ "Naples"))  %>% 
  mutate(MPA = case_when( 
    site %in% c("IVEE", "NAPL") ~ "MPA",
    site %in% c("AQUE", "CARP", "MOHK") ~ "Non MPA"))
# annual lobster sub data set

annual_lobsters <- lobster_abundance_sbc %>% 
  group_by(site_name_long, year, MPA) %>% 
  summarise(yearly_lobsters=sum(count)) 
 
# graph of annual lobster counts from 2012 - 2018

ggplot(annual_lobsters, aes(x=year, y=yearly_lobsters)) +
  geom_line(aes(color=site_name_long), show.legend = FALSE) +
  geom_point(aes(color = site_name_long), show.legend = FALSE) + 
  theme_minimal() +
  labs(x = "\nYear", y = "Annual Number of Observed Lobsters\n", 
       title="Annual Lobster Abundance from 2012-2018\n") +
  coord_cartesian(clip="off", 
                  xlim=c(2012,2018)) +
  theme(plot.margin=unit(c(1,10,1,1), "lines"),
        plot.title = element_text(hjust=0.5),
        legend.position = "right",
        legend.title=element_blank()) +
  scale_fill_discrete(name= "MPA Status") +
  scale_color_manual(values = c("black", "black", "maroon", "black", "maroon")) +
  scale_x_continuous(lim=c(2012, 2018), 
                     expand=c(0,0)) +
  scale_y_continuous(lim=c(0, 1000), 
                     expand=c(0,0),
                     breaks=seq(0,1000, by=250)) +
  annotate("text", label= "Isla Vista (MPA)", 
           x = Inf, 
           y = 940, 
           size = 3,
           hjust = -0.1,
           vjust = 0,
           color = "maroon") +
  annotate("text", label = "Naples (MPA)",
           x = Inf,
           y = 270,
           size = 3,
           hjust = -0.2,
           vjust = 0,
           color = "maroon") +
  annotate("text", label = "Arroyo Quemado",
           x = Inf,
           y = 33,
           size = 3,
           hjust = -0.1,
           vjust = 0) +
  annotate("text", label = "Mohawk",
           x = Inf,
           y = 145,
           size = 3,
           hjust = -0.2,
           vjust = 0) +
  annotate("text", label = "Carpinteria",
           x = Inf,
           y = 330,
           size = 3,
           hjust = -0.18,
           vjust = 0)

Figure 3. Lobster counts in MPAs (red) and non-MPAs (black) from 2012 to 2018. MPA lobster counts in 2012 were close to zero, and increased to over 250 individuals at Naples MPA and over 800 individuals at the Isla Vista MPA. Non-MPAs also experienced higher lobster counts in 2018 compared to 2012, however, the results were not as significant to those in MPA sites. Data: SBC LTER.

Result B: Lobster size distribution shifts, 2012 vs 2018

The lobster size distribution in the five study sites in 2012 and 2018 is shown in Figure 4. Lobster size distribution has stayed relatively constant for two non-MPAs in 2012 and 2018: Carpinteria (n2012= 78, n2018=343) and Mohawk (n2012= 83, n2018=164). The lobster sizes followed a normal distribution at both sites, however only observed lobster sizes at Carpinteria exerienced no change in means (2012: 74.4mm \(\pm\) 1.65mm, 2018: 74.5mm \(\pm\) 0.6mm) (mean \(\pm\) SE); Mohawk experienced a decline in means (2012: 77.3mm \(\pm\) 1.2mm, 2018: 72.4mm \(\pm\) 0.7mm). The other MPA, Arroyo Quemado (n2012=38, mean2012=71mm, SE2012=1.7mm), had a slightly right-skewed distribution in 2012. However, in 2018 lobster sizes in Arroyo Quemado followed a normal distribution like the other non-MPAs, but had no change in mean lobster size.

In 2012, lobster sizes at both MPAs, Isla Vista (n2012=26) and Naples (n2012=6), were right skewed. Isla Vista lobsters had an average size of 66.1mm \(\pm\) 2.4mm and lobsters at Naples had an average size of 73mm \(\pm\) 4.8mm. However, in 2018 the distribution of lobster sizes (Isla Vista n2018=946, Naples n2018=298) followed a normal distribution that is similar to that of the other non-MPA sites in 2018 and both experienced an increase in mean lobster sizes (Isla Vista: 76.6mm \(\pm\) 0.4mm, Naples: 80.5mm \(\pm\) 0.5mm)

In 2018, all sites followed a normal distribution. Naples had the largest mean lobster size in 2018 and Isla Vista had the second largest mean lobster size. Naples, Isla Vista, and Arroyo Quemado had the three smallest sample sizes in 2012, which could account for the skewed distribution. Likely, the larger number of observations 2018 displayed the true population distribution for all the sites.

# Uncount lobster observations
lobster_abundance_tidy <- lobster_abundance_sbc %>%
  tidyr::uncount(count)

# sub-data: keep only years 2012 and 2018
lobster_size <- lobster_abundance_tidy %>%
  filter(year %in% c("2012", "2018"))%>% 
  mutate(year=as.character(year)) ### this code added becuase ggplot wouldnt recognize our year column correctly (would display color based on year aesthetic). Changing the values to characters helped over come this error

# determine sample size for each class/year
num_observations <- lobster_size %>% 
  group_by(site) %>% 
  count(year)

# determine mean, SD, SE for each site in 2012 and 2018
site_stats <- lobster_size %>% 
  group_by(year, site) %>% 
  summarize(means=mean(size_mm),
            n= n(),
            sd=sd(size_mm),
            se=sd/sqrt(n)) 
  
# graph for distrmibution of lobster sizes in 2012 and 2018 
ggplot(lobster_size, 
       aes(x=size_mm)) +
  geom_density(aes(fill=year), 
               position='identity', 
               alpha=0.5) +
  theme_minimal() +
  labs(x="Size (mm)", y="Density\n", 
       title="Change in lobster size distribution between 2012 and 2018") +
  theme(plot.title = element_text(hjust=0.5)) +
  scale_x_continuous(lim=c(30, 130),
                     expand=c(0,0),
                     breaks=seq(30,120, by=20)) +
  scale_y_continuous(lim=c(0, 0.06),
                     expand=c(0,0)) +
  facet_wrap(~site_name_long, scales="free_x") +
  scale_fill_discrete(name="Year")

Figure 4: The change in lobster size (mm) distributions at five sites on the California coast in 2012 (pink) and 2018 (blue). All sites except Mohawk and Carpinteria experienced an increase in size of observed lobsters between 2012 and 2018. Both MPAs, Isla Vista and Naples, were right skewed in 2012. Arroyo Quemado was the only non-MPA that did not follow a normal distribution. All sites followed normal distribution in 2018 and all means averaged around 75mm. Data: SBC LTER.

Result C: Is there a difference between mean lobster sizes at MPA vs non-MPA sites in 2012 and 2018?

Table 1. Results from two sample t-tests comparing mean lobster sizes at MPA and non-MPA sites in 2012 and 2018. Data: SBC LTER.

# data from 1: mean and standard deviation for MPA and non MPAs in 2012 and 2018
lobster_size_stats <- lobster_size %>% 
  group_by(year, MPA) %>% 
  summarize(Mean=mean(size_mm), 
            Standard_Deviation=sd(size_mm))


# data frame 2: sample size for MPA and non MPAs in 2012 and 2018
num_observations <- annual_lobsters %>%
    group_by(MPA, year) %>% 
    summarize(sample_size=sum(yearly_lobsters)) %>% 
    ungroup(year) %>% 
    mutate(year=as.character(year)) %>% 
    dplyr::filter(year %in% c("2018", "2012"))  # fixed it!!

# merge data frames 
lobster_size_table_merged <- inner_join(lobster_size_stats, num_observations, by=c("MPA", "year"))

# create table with mean, standard deviation, and sample size for MPA and non MPAs in 2012 and 2018
lobster_table <- lobster_size_table_merged %>%
  kable(col.names = c("Year", 
                    "MPA status",
                    "Mean lobster size (mm)",
                    "Standard deviation",
                    "Sample population"),
                digits=2) %>%
  kable_styling(bootstrap_options = "striped",
                full_width = F, 
                position="center") %>%
  add_header_above(c("Mean lobster sizes at MPA vs Non-MPA sites in 2012 and 2018" = 5)) 

lobster_table
Mean lobster sizes at MPA vs Non-MPA sites in 2012 and 2018
Year MPA status Mean lobster size (mm) Standard deviation Sample population
2012 MPA 67.38 12.15 32
2012 Non MPA 74.92 12.41 199
2018 MPA 77.57 11.70 1244
2018 Non MPA 73.62 10.09 561

2012 observations for mean lobster sizes between MPA (67.38mm) and non-MPA sites (74.92mm) differed significantly (t(42.09) = -3.25, p = 0). The medium effect size (-0.6) indicates it is likely the there was a significant difference between mean lobster sizes at MPA and non-MPA sites in 2012, despite the large difference in smaple sizes.

For observations in 2018, mean lobster sizes between MPA (77.57mm) and non-MPA sites (73.62mm) differed significantly (t(1239.51) = 7.31, p = 0). To measure the magnitude of the difference between MPA and non-MPA sites in 2018, we calcualted the effect size. A moderate effect size (0.4) indicates that though the difference in means was more difficult to observe, there was indeed a difference between population means.

In MPA sites, the difference in mean lobster size observations in 2012 (67.38mm) and 2018 (77.57mm) differed significantly (t(32.5) = -4.69, p = 0). The large effect size (-0.9) calculated for MPA sites indicates that there was a substantial difference in lobster means in 2012 and 2018.

The difference in mean lobster sizes in non-MPA sites in 2012 (74.92mm) and 2018 (73.62mm) did not differ (t(296.01) = 1.33, p = 0.18). The actual difference between means was 1.3 mm. A small effect size (0.1) confirms that there is not enough evidence to determine that these two populations have different means.

Summary

It is worth noting that all size observations recorded by divers were visually estimated. These types of measurements are likely more erroneous and should be subject to more scrutiny during data analysis than measurements conducted with a device.

Citations

Bierman, Ed (2016). California spiny lobster. Wikipedia. https://en.wikipedia.org/wiki/California_spiny_lobster.

Reed D. (2019). SBC LTER: Reef: Abundance, size and fishing effort for California Spiny Lobster (Panulirus interruptus), ongoing since 2012. Environmental Data Initiative. https://doi.org/10.6073/pasta/a593a675d644fdefb736750b291579a0. Date accessed 11/13/2019.

SBC LTER. Santa Barbara Coastal LTER: About SBC LTER. https://sbclter.msi.ucsb.edu/. Date accessed 11/15/2019.

WildAid (2018). Marine Protected Areas 101. https://wildaid.org/marine-protected-areas-101/. Date accessed 11/15/2019.