Recreating Figure 2.1 in Ecological Detective

There are many different hypotheses that can explain the basic relationship between two variables. Figure 2.1 in the Ecologial Detective suggest 4 possible models. The models have no parameter values. Try to iteratively find the parameter values to get your figure to look like the one in Figure 2.1.

S <- seq(1,15, by = 1)  # 1:15
Null_hypothesis<- 2.5

our_data <- data.frame(S = S, Null = Null_hypothesis)
our_data$Model_A <- 0.5 *S
our_data$Model_B <- (0.9 *S)/(1 + 0.1*S)
our_data$Model_C <- 1.8 *S * exp(-0.18*S)

plot_labels = data.frame(x = c(14,14,8, 4), y = c(7.5,5.5,2.75,3.5), labels = c("Model A", "Model B", "NULL", "Model C"))


ggplot() +
  geom_line(data = our_data,aes(x = S, y = Null), colour="black") +
  geom_line(data = our_data,aes(x = S, y = Model_A), colour="blue") +
  geom_line(data = our_data,aes(x = S, y = Model_B), colour="green") +
  geom_line(data = our_data,aes(x = S, y = Model_C), colour="red") +
  geom_text(data = plot_labels, aes(x=x, y= y, label = labels)) +
  coord_cartesian(ylim = c(0,9), xlim = c(0, 16), expand = FALSE) +
  scale_x_continuous(breaks = seq(0,16,by=2)) +
  scale_y_continuous(breaks = seq(1,8,by=1)) +
  labs(x = "Flock size", y = "Consumption rate") +
  theme_bw()

plot of chunk unnamed-chunk-2

Probability and probability models

  • Ecological data (and most other kinds of data) involve different levels of randomness
  • Most models represent the mean of the population

  • Comparing models requires understanding the probability of individual observations (based on the distribution)

  • Most people understand the normal or Gaussian distribution, but htere are many, many different types of distributions

WORD OF ADVICE: Always plot your data

fish_data <- read_csv("https://raw.githubusercontent.com/chrischizinski/MWFWC_FishR/master/CourseMaterial/data/wrkshp_data.csv")
## Parsed with column specification:
## cols(
##   .default = col_character(),
##   WaterbodyCode = col_integer(),
##   Area = col_integer(),
##   MethodCode = col_integer(),
##   surveydate = col_datetime(format = ""),
##   Station = col_integer(),
##   Effort = col_integer(),
##   SpeciesCode = col_integer(),
##   LengthGroup = col_integer(),
##   FishCount = col_integer(),
##   FishLength = col_integer(),
##   FishWeight = col_integer(),
##   Age = col_integer(),
##   Edge = col_integer(),
##   Annulus1 = col_integer(),
##   Annulus2 = col_integer(),
##   Annulus3 = col_integer(),
##   Annulus4 = col_integer(),
##   Annulus5 = col_integer(),
##   Annulus6 = col_integer(),
##   Annulus7 = col_integer()
##   # ... with 2 more columns
## )
## See spec(...) for full column specifications.
glimpse(fish_data)
## Observations: 16,527
## Variables: 43
## $ WaterbodyCode <int> 4113, 4113, 4113, 4113, 4113, 4113, 4113, 4113, ...
## $ Area          <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
## $ MethodCode    <int> 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, ...
## $ surveydate    <dttm> 2014-10-29 05:00:00, 2014-10-29 05:00:00, 2014-...
## $ Station       <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, ...
## $ Effort        <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
## $ SpeciesCode   <int> 730, 730, 730, 730, 730, 730, 730, 730, 730, 730...
## $ LengthGroup   <int> 100, 120, 140, 150, 160, 170, 180, 190, 200, 210...
## $ FishCount     <int> 1, 1, 1, 2, 2, 3, 6, 6, 3, 3, 2, 3, 2, 1, 2, 1, ...
## $ FishLength    <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ FishWeight    <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Age           <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Edge          <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus1      <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus2      <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus3      <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus4      <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus5      <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus6      <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus7      <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus8      <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus9      <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus10     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus11     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus12     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus13     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus14     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus15     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus16     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus17     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus18     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus19     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus20     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus21     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus22     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus23     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus24     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus25     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus26     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus27     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus28     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus29     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ Annulus30     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
fish_data %>% 
  select(WaterbodyCode:Age) %>% 
  mutate(Age = as.numeric(Age)) %>% 
  filter(!is.na(Age),
         WaterbodyCode == 4999,
         SpeciesCode %in% c(780)) -> FishAge  

glimpse(FishAge)
## Observations: 82
## Variables: 12
## $ WaterbodyCode <int> 4999, 4999, 4999, 4999, 4999, 4999, 4999, 4999, ...
## $ Area          <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
## $ MethodCode    <int> 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, ...
## $ surveydate    <dttm> 2013-09-24 05:00:00, 2013-09-24 05:00:00, 2013-...
## $ Station       <int> 2, 2, 2, 2, 4, 4, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, ...
## $ Effort        <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
## $ SpeciesCode   <int> 780, 780, 780, 780, 780, 780, 780, 780, 780, 780...
## $ LengthGroup   <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ FishCount     <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ FishLength    <int> 248, 232, 195, 264, 262, 258, 96, 256, 233, 243,...
## $ FishWeight    <int> 198, 154, 104, 242, 230, 210, 8, 218, 172, 168, ...
## $ Age           <dbl> 7, 3, 2, 4, 6, 5, 1, 4, 5, 6, 5, 3, 3, 3, 3, 3, ...

Let’s look at distribution plots of FishLength and Age

ggplot(data = FishAge) + 
  geom_histogram(aes(x = Age), binwidth = 1, fill = "green", colour = "black") +
  theme_bw()

plot of chunk unnamed-chunk-4

ggplot(data = FishAge,aes(x = Age)) + 
  geom_histogram(aes(y = ..density..),binwidth = 1, fill = "green", colour = "black") +
  geom_density(colour = "red", fill = "red", alpha = 0.5) +
  theme_bw()

plot of chunk unnamed-chunk-4

ggplot(data = FishAge) +
  geom_histogram(aes(x = FishLength), binwidth = 10, fill = "red", colour = "black" ) + 
  theme_bw()

plot of chunk unnamed-chunk-4

ggplot(data = FishAge) +
  geom_violin(aes(x = "", y = FishLength), fill = "red", colour = "black" ) + 
  theme_bw()

plot of chunk unnamed-chunk-4

ggplot(data = FishAge) +
  geom_point(aes(x = "", y = FishLength), position = "jitter") +
  geom_boxplot(aes(x = "", y = FishLength), fill = "red", colour = "black", alpha = 0.25, outlier.colour = NA) + 
  theme_bw()

plot of chunk unnamed-chunk-4