Time series plots from vectors

Perhaps the most basic type of plot to make is a TIME SERIES PLOT

x-axis is …

time ## y-axis is …
something that changes over time

Example time series

Time series plot - Wolves of Yellowstone NP

Some classic time series plots

Classic time series

R comes packaged with some time series plots in a special format

Can be plotted in 2 easy steps

R comes packaged with some time series plots in a special format

data(lynx) # load data
plot(lynx)

Most data in R is stored on 1 of 2 DATA STRUCTURES

VECTORS

like columns in a spreadsheet

DATA FRAMES

like a whole spreadsheet

Vectors are like the COLUMNS of a spreadsheet

##    year.1.15.
## 1        1995
## 2        1996
## 3        1997
## 4        1998
## 5        1999
## 6        2000
## 7        2001
## 8        2002
## 9        2003
## 10       2004
## 11       2005
## 12       2006
## 13       2007
## 14       2008
## 15       2009

Vectors are conceptually like columns, but printed in R in a ROW

year

##  [1] 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
## [16] 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020

Dataframes are like a whole spreadsheet

and are printed out like a spreadsheet

##    year packs wolves
## 1  1995   3.0     21
## 2  1996   9.0     51
## 3  1997   9.0     86
## 4  1998  11.0    112
## 5  1999  11.0    118
## 6  2000   8.0    119
## 7  2001  10.0    132
## 8  2002  14.0    148
## 9  2003  13.5    174
## 10 2004  16.0    171
## 11 2005  13.0    118
## 12 2006  13.0    136
## 13 2007  11.0    171
## 14 2008  12.0    124
## 15 2009  14.0     96

Time series plots are made from 2 VECTORS of data

Time

year

##  [1] 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
## [16] 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020

Thing that’s changing over time

wolves

##  [1]  21  51  86 112 118 119 132 148 174 171 118 136 171 124  96  97  98  83  95
## [20] 104  98 108  97  80  94 123

The 2 vectors MUST be the same length

R’s length() command determines the number of elements in a vector
(also works on some other things)

length(year)

## [1] 26

length(wolves)

## [1] 26

We can TEST FOR EQUALITY of lengths

Test for equality: ==
== is an R function
= is a different R function (That I don’t use)
= is also used within arguments

length(year) == length(wolves)

## [1] TRUE

If 2 vectors are different length then returns FALSE

I made a vector of different length

# the vector
wolves_wrong

## [1]  21  51  86 112 118 119

# its length
length(wolves_wrong)

## [1] 6

If 2 vectors are different length then returns FALSE

I can compare it to the length of year
use the function “==”

length(year) == length(wolves_wrong)

## [1] FALSE

How would this operation be phrased in words?

length(year) == length(wolves_wrong)

## [1] FALSE

This is asking the question “Does 26 = 6”

26 == 6

## [1] FALSE

`plot()` he defaults are blah

DEFAULTS are the initial settings of a function

changes to what functions do are set via ARGUEMENTS
DEFAULTS are the initial settings of arguements
do not need to be explicitly set

Some improvements

ALL of this is specified by CODE

Some more improvements

ALL of this is specified by CODE

Many plots in base R can be made with the `plot()` command

This is just base R!
… and for time series, scatterplots, and some others
Other plots have specialized functions, such as hist for histograms
ggplot and ggpubr use completely different functions

plot(wolves ~ year)

A TITLE is added with `main = ...`

These are handy for keeping your work labeled…
… But plots in papers usually don’t have them
main = ... allows you to set the title

plot(wolves ~ year, main = "A plot made with plot()")

The `plot()` command can plot points, lines or both

the default is for points

“p” = points
“l” = line
“b” = points and lines
NOTE: letter must be in QUOTES

The `plot()` command can plot points, lines or both

par(mfrow = c(2,2), mar = c(2,2,4,1)) #ignore this line
plot(wolves ~ year, main = "(default)") # default
plot(wolves ~ year, type = "p", main = "type = 'p'") # type  = "p"
plot(wolves ~ year, type = "l", main = "type = 'p'") # type  = 'l'
plot(wolves ~ year, type = "b", main = "type = 'b'") # type  = "l"

`col = ...` set the COLOR

The default is black
NOTE: number NOT in quotes

par(mfrow = c(2,2), mar = c(2,2,4,1)) #ignore this line
plot(wolves ~ year, main = "(default)") # default
plot(wolves ~ year, col = 1, main = "col = 1") # black
plot(wolves ~ year, col = 2, main = "col = 2") # red
plot(wolves ~ year, col = 3, main = "col = 3") # green

For points, `pch = ...` sets the type of point

Just have to remember this
NOTE: numbers NOT in quotes

par(mfrow = c(2,2), mar = c(2,2,4,1)) #ignore this line
plot(wolves ~ year, main = "(default)") 
plot(wolves ~ year, pch = 2, main = "pch = 2")
plot(wolves ~ year, pch = 10, main = "pch = 3") 
plot(wolves ~ year, pch = 16, main = "pch = 16")

My favorite `pch` values are in the teens

Just have to remember this
NOTE: numbers NOT in quotes

par(mfrow = c(2,2), mar = c(2,2,4,1)) #ignore this line
plot(wolves ~ year, pch = 15,  main = "pch = 15") 
plot(wolves ~ year, pch = 16, main = "pch = 16")
plot(wolves ~ year, pch = 17, main = "pch = 17") 
plot(wolves ~ year, pch = 18, main = "pch = 18")

Multiple arguments can be combined

What is the argument for the type of point?
What is the argument for color?
What is the argument for lines and points?
What is the argument for the title?

Multiple arguments can be combined

xlab = ... sets x-axis label
ylab = ... sets y- axis label
NOTE: labels in QUOTES!

par(mfrow = c(1,1), mar = c(4,4,4,4)) # ignore this
plot(wolves ~ year, pch = 16,  col = 2, type = "b",
     xlab = "Year",
     ylab = "Wolves (N)")

NOTE: ggplot2 is a TOTALLY different way to do things

main function is ggplot()
doesn’t work on vectors, must use dataframes

ggplot(data = wolves,
       aes(y = packs, x = year)) +
  geom_point() + 
  geom_line()

Vectors are made with the `c()` function

packs  <- c( 3, 9,  9,11,  11, 8,10,14,13.5,16,
             13,13,11,12,  14,11,10,10,10,  11,
             10,11,11, 9,   8, 9)

EACH element within the vector separated by a comma `,`

packs  <- c( 3, 9,  9,11, 11, 8,10,14,13.5,16,
             13,13,11,12, 14,11,10,10,10,  11,
             10,11,11, 9,  8, 9)

Long vectors often split between lines

Spaces ok too - I use them to line things up

packs  <- c( 3, 9,  9,11, 11, 8,10,14,13.5,16,
             13,13,11,12, 14,11,10,10,10,  11,
             10,11,11, 9, 8, 9)

Vectors can contain text

Text MUST be in quotes

wolf_names  <- c("white fang", "fluffy", "bingo","minnie", "percy")

Single ELEMENTS of a vector accessed using BRACKETS

aka BRACKET NOTATION

# names
wolf_names  <- c("white fang", "fluffy", "bingo","minnie", "percy")

# first name - uses 1 (not 0!)
wolf_names[1]

## [1] "white fang"

# 2nd names name - starts at 1 (not 0!)
wolf_names[2]

## [1] "fluffy"

Multple ELEMENTS of a vector accessed using :

# first two
wolf_names[1:2]

## [1] "white fang" "fluffy"

# 2nd two
wolf_names[2:3]

## [1] "fluffy" "bingo"

This is called INDEXING

“The index for ‘fluffy’ is 2”

wolf_names[2]

## [1] "fluffy"

MUST have 2 values when using `:`

ERRORS

wolf_names[1:]

wolf_names[:2]

Can call everything if you want

wolf_names[1:5]

## [1] "white fang" "fluffy"     "bingo"      "minnie"     "percy"

Can call everything BUT the 1st like this

wolf_names[2:5]

## [1] "fluffy" "bingo"  "minnie" "percy"

First real programming trick

ready for it?

Use NEGATIVE INDEXING to drop elements

Drop just 1st

wolf_names[-1]

## [1] "fluffy" "bingo"  "minnie" "percy"

Drop just 2nd

wolf_names[-2]

## [1] "white fang" "bingo"      "minnie"     "percy"

Next real programming trick - can “pass” vectors of indices to vectors

what does that mean?

A vector

wolf_names  <- c("white fang", "fluffy", "bingo","minnie", "percy")

a vector element via an index value

wolf_names[1]

## [1] "white fang"

2 vector elements via an index values

wolf_names[1:2]

## [1] "white fang" "fluffy"

a vector of indices

i <- c(1,2)

2 vector elements via a vector of indices

wolf_names[i]

## [1] "white fang" "fluffy"

I can make a vector of numbers 2 ways

I will usually use the first for clarity

i1 <- c(1, 2, 3)

i2 <- c(1:3)

How do I test for equality of the two vectors

length(i1) == length(i2)

## [1] TRUE

Operations on vectors can be VECTORIZED

Some vectors

DNA <- c("A","T","C","G")

RNA <- c("A","U","C","G")

Their length

length(DNA)

## [1] 4

length(RNA)

## [1] 4

The equality of their lengths

length(DNA) == length(RNA)

## [1] TRUE

Access 1st elements

DNA[1]

## [1] "A"

RNA[1]

## [1] "A"

Equality of first elements

DNA[1] == RNA[1]

## [1] TRUE

Access 2nd elements

DNA[2]

## [1] "T"

RNA[2]

## [1] "U"

IN-Equality of 2nd elements

DNA[2] == RNA[2]

## [1] FALSE

Assess equality of ALL elements

the function == has been applied to each pair of elements
this is a VECTORIZED operation

DNA == RNA

## [1]  TRUE FALSE  TRUE  TRUE

VECTORIZED operations are common in R

taking the log of something is very common in math, stats, ML, bio…

natural log = `log()` in R

log base 10 = `log10()`

log base 2 = `lo2g()`

log(10)

## [1] 2.302585

log10(10)

## [1] 1

log2(10)

## [1] 3.321928

Functions can be applied to entire vectors

VECTORIZED operations are common in R

log(wolves)

##        year    packs   wolves
## 1  7.598399 1.098612 3.044522
## 2  7.598900 2.197225 3.931826
## 3  7.599401 2.197225 4.454347
## 4  7.599902 2.397895 4.718499
## 5  7.600402 2.397895 4.770685
## 6  7.600902 2.079442 4.779123
## 7  7.601402 2.302585 4.882802
## 8  7.601902 2.639057 4.997212
## 9  7.602401 2.602690 5.159055
## 10 7.602900 2.772589 5.141664
## 11 7.603399 2.564949 4.770685
## 12 7.603898 2.564949 4.912655
## 13 7.604396 2.397895 5.141664
## 14 7.604894 2.484907 4.820282
## 15 7.605392 2.639057 4.564348
## 16 7.605890 2.397895 4.574711
## 17 7.606387 2.302585 4.584967
## 18 7.606885 2.302585 4.418841
## 19 7.607381 2.302585 4.553877
## 20 7.607878 2.397895 4.644391
## 21 7.608374 2.302585 4.584967
## 22 7.608871 2.397895 4.682131
## 23 7.609367 2.397895 4.574711
## 24 7.609862 2.197225 4.382027
## 25 7.610358 2.079442 4.543295
## 26 7.610853 2.197225 4.812184

Math can be done on entire vectors

The average wolf it 95 pounds

Wolf BIOMASS each year

wolves*95

##      year  packs wolves
## 1  189525  285.0   1995
## 2  189620  855.0   4845
## 3  189715  855.0   8170
## 4  189810 1045.0  10640
## 5  189905 1045.0  11210
## 6  190000  760.0  11305
## 7  190095  950.0  12540
## 8  190190 1330.0  14060
## 9  190285 1282.5  16530
## 10 190380 1520.0  16245
## 11 190475 1235.0  11210
## 12 190570 1235.0  12920
## 13 190665 1045.0  16245
## 14 190760 1140.0  11780
## 15 190855 1330.0   9120
## 16 190950 1045.0   9215
## 17 191045  950.0   9310
## 18 191140  950.0   7885
## 19 191235  950.0   9025
## 20 191330 1045.0   9880
## 21 191425  950.0   9310
## 22 191520 1045.0  10260
## 23 191615 1045.0   9215
## 24 191710  855.0   7600
## 25 191805  760.0   8930
## 26 191900  855.0  11685

Yellowstone NP is 3500 suare miles

Wolves per square mile

wolves / 3500

##         year        packs     wolves
## 1  0.5700000 0.0008571429 0.00600000
## 2  0.5702857 0.0025714286 0.01457143
## 3  0.5705714 0.0025714286 0.02457143
## 4  0.5708571 0.0031428571 0.03200000
## 5  0.5711429 0.0031428571 0.03371429
## 6  0.5714286 0.0022857143 0.03400000
## 7  0.5717143 0.0028571429 0.03771429
## 8  0.5720000 0.0040000000 0.04228571
## 9  0.5722857 0.0038571429 0.04971429
## 10 0.5725714 0.0045714286 0.04885714
## 11 0.5728571 0.0037142857 0.03371429
## 12 0.5731429 0.0037142857 0.03885714
## 13 0.5734286 0.0031428571 0.04885714
## 14 0.5737143 0.0034285714 0.03542857
## 15 0.5740000 0.0040000000 0.02742857
## 16 0.5742857 0.0031428571 0.02771429
## 17 0.5745714 0.0028571429 0.02800000
## 18 0.5748571 0.0028571429 0.02371429
## 19 0.5751429 0.0028571429 0.02714286
## 20 0.5754286 0.0031428571 0.02971429
## 21 0.5757143 0.0028571429 0.02800000
## 22 0.5760000 0.0031428571 0.03085714
## 23 0.5762857 0.0031428571 0.02771429
## 24 0.5765714 0.0025714286 0.02285714
## 25 0.5768571 0.0022857143 0.02685714
## 26 0.5771429 0.0025714286 0.03514286

Math can be done using variable

Make variables with constants

wolve_weight <- 95
YNP_size <- 3500

Do math using varibales

wolves/wolve_weight

##        year      packs    wolves
## 1  21.00000 0.03157895 0.2210526
## 2  21.01053 0.09473684 0.5368421
## 3  21.02105 0.09473684 0.9052632
## 4  21.03158 0.11578947 1.1789474
## 5  21.04211 0.11578947 1.2421053
## 6  21.05263 0.08421053 1.2526316
## 7  21.06316 0.10526316 1.3894737
## 8  21.07368 0.14736842 1.5578947
## 9  21.08421 0.14210526 1.8315789
## 10 21.09474 0.16842105 1.8000000
## 11 21.10526 0.13684211 1.2421053
## 12 21.11579 0.13684211 1.4315789
## 13 21.12632 0.11578947 1.8000000
## 14 21.13684 0.12631579 1.3052632
## 15 21.14737 0.14736842 1.0105263
## 16 21.15789 0.11578947 1.0210526
## 17 21.16842 0.10526316 1.0315789
## 18 21.17895 0.10526316 0.8736842
## 19 21.18947 0.10526316 1.0000000
## 20 21.20000 0.11578947 1.0947368
## 21 21.21053 0.10526316 1.0315789
## 22 21.22105 0.11578947 1.1368421
## 23 21.23158 0.11578947 1.0210526
## 24 21.24211 0.09473684 0.8421053
## 25 21.25263 0.08421053 0.9894737
## 26 21.26316 0.09473684 1.2947368

wolves/YNP_size

##         year        packs     wolves
## 1  0.5700000 0.0008571429 0.00600000
## 2  0.5702857 0.0025714286 0.01457143
## 3  0.5705714 0.0025714286 0.02457143
## 4  0.5708571 0.0031428571 0.03200000
## 5  0.5711429 0.0031428571 0.03371429
## 6  0.5714286 0.0022857143 0.03400000
## 7  0.5717143 0.0028571429 0.03771429
## 8  0.5720000 0.0040000000 0.04228571
## 9  0.5722857 0.0038571429 0.04971429
## 10 0.5725714 0.0045714286 0.04885714
## 11 0.5728571 0.0037142857 0.03371429
## 12 0.5731429 0.0037142857 0.03885714
## 13 0.5734286 0.0031428571 0.04885714
## 14 0.5737143 0.0034285714 0.03542857
## 15 0.5740000 0.0040000000 0.02742857
## 16 0.5742857 0.0031428571 0.02771429
## 17 0.5745714 0.0028571429 0.02800000
## 18 0.5748571 0.0028571429 0.02371429
## 19 0.5751429 0.0028571429 0.02714286
## 20 0.5754286 0.0031428571 0.02971429
## 21 0.5757143 0.0028571429 0.02800000
## 22 0.5760000 0.0031428571 0.03085714
## 23 0.5762857 0.0031428571 0.02771429
## 24 0.5765714 0.0025714286 0.02285714
## 25 0.5768571 0.0022857143 0.02685714
## 26 0.5771429 0.0025714286 0.03514286

When two vectors are used in an operation their elements are compared PAIRWISE

Vectors of wolves and number of packs at same time

wolves[1:5]

## [1]  21  51  86 112 118

packs[1:5]

## [1]  3  9  9 11 11

year[1:5]

## [1] 1995 1996 1997 1998 1999

Number of wolves and packs year 1

wolves[1]

## [1] 21

packs[1]

## [1] 3

Wolves per pack

21/3

## [1] 7

Wolves per pack via index values

math jargon: dividing one SCALAR by another SCALAR

wolves[1]/packs[1]

## [1] 7

Wolves per pack for ALL YEARS

A vectorized operation

wolves/packs

##  [1]  7.000000  5.666667  9.555556 10.181818 10.727273 14.875000 13.200000
##  [8] 10.571429 12.888889 10.687500  9.076923 10.461538 15.545455 10.333333
## [15]  6.857143  8.818182  9.800000  8.300000  9.500000  9.454545  9.800000
## [22]  9.818182  8.818182  8.888889 11.750000 13.666667

Wolves per pack 1st 2 years

Using `:`

wolves[1:2]/packs[1:2]

## [1] 7.000000 5.666667

Using indices in a vector via `c()`

i <- c(1,2)
wolves[i]

## [1] 21 51

Using raw index

wolves[c(1,2)]/packs[c(1,2)]

## [1] 7.000000 5.666667

Wolves per pack ignoring just first year

wolves[-1]/packs[-1]

##  [1]  5.666667  9.555556 10.181818 10.727273 14.875000 13.200000 10.571429
##  [8] 12.888889 10.687500  9.076923 10.461538 15.545455 10.333333  6.857143
## [15]  8.818182  9.800000  8.300000  9.500000  9.454545  9.800000  9.818182
## [22]  8.818182  8.888889 11.750000 13.666667

Time series plots from vectors

Perhaps the most basic type of plot to make is a TIME SERIES PLOT

x-axis is …

Example time series

Some classic time series plots

R comes packaged with some time series plots in a special format

R comes packaged with some time series plots in a special format

Most data in R is stored on 1 of 2 DATA STRUCTURES

VECTORS

DATA FRAMES

Vectors are like the COLUMNS of a spreadsheet

Vectors are conceptually like columns, but printed in R in a ROW

Dataframes are like a whole spreadsheet

Time series plots are made from 2 VECTORS of data

The 2 vectors MUST be the same length

We can TEST FOR EQUALITY of lengths

If 2 vectors are different length then returns FALSE

If 2 vectors are different length then returns FALSE

How would this operation be phrased in words?

This is asking the question “Does 26 = 6”

plot() he defaults are blah

DEFAULTS are the initial settings of a function

Some improvements

Some more improvements

Many plots in base R can be made with the plot() command

A TITLE is added with main = ...

The plot() command can plot points, lines or both

the default is for points

The plot() command can plot points, lines or both

col = ... set the COLOR

For points, pch = ... sets the type of point

My favorite pch values are in the teens

Multiple arguments can be combined

Multiple arguments can be combined

Multiple arguments can be combined

NOTE: ggplot2 is a TOTALLY different way to do things

Vectors are made with the c() function

EACH element within the vector separated by a comma ,

Long vectors often split between lines

Spaces ok too - I use them to line things up

Vectors can contain text

Text MUST be in quotes

Single ELEMENTS of a vector accessed using BRACKETS

aka BRACKET NOTATION

Multple ELEMENTS of a vector accessed using :

This is called INDEXING

“The index for ‘fluffy’ is 2”

MUST have 2 values when using :

ERRORS

Can call everything if you want

Can call everything BUT the 1st like this

First real programming trick

Use NEGATIVE INDEXING to drop elements

Next real programming trick - can “pass” vectors of indices to vectors

A vector

a vector element via an index value

2 vector elements via an index values

a vector of indices

2 vector elements via a vector of indices

I can make a vector of numbers 2 ways

I will usually use the first for clarity

How do I test for equality of the two vectors

Operations on vectors can be VECTORIZED

Some vectors

Their length

The equality of their lengths

Access 1st elements

Equality of first elements

Access 2nd elements

IN-Equality of 2nd elements

Assess equality of ALL elements

VECTORIZED operations are common in R

taking the log of something is very common in math, stats, ML, bio…

natural log = log() in R

log base 10 = log10()

log base 2 = lo2g()

Functions can be applied to entire vectors

VECTORIZED operations are common in R

Math can be done on entire vectors

The average wolf it 95 pounds

`plot()` he defaults are blah

Many plots in base R can be made with the `plot()` command

A TITLE is added with `main = ...`

The `plot()` command can plot points, lines or both

The `plot()` command can plot points, lines or both

`col = ...` set the COLOR

For points, `pch = ...` sets the type of point

My favorite `pch` values are in the teens

Vectors are made with the `c()` function

EACH element within the vector separated by a comma `,`

MUST have 2 values when using `:`

natural log = `log()` in R

log base 10 = `log10()`

log base 2 = `lo2g()`

Using `:`

Using indices in a vector via `c()`