Life Tables and Suvivorship Curves

- Question One -

Based upon the first figure, the numner of life births increased since the 1920s (possibly due to improvements in techonlogy), but the birth rate has decreased since the 1920s. This could be becaused with improvements in technology and education of women, the rate of births each year would decrease. A population rate of 2 would mean a stagnant growth because it takes two people people to produce offspring so a fertility rate of two would just make up for the two parents after they died, never increasing just remaining stagnant in growth. Considering most rates are slightly above, at, or below 2 when it comes to fertility rates, that must mean the US population is remaining somewhat steady or increasing only slightly. I predict that in the next few decades the population will decline.

- Question Two -

Protecting nesting sites would most likely allow crude birth rates and total fertility of a population to increase, which could increase populations if the population has the habitat to support their growing population. The issues with shifting this is that if we don’t focus on adult habitats, then we aren’t protecting habitat that could support a growing youth population from the protected nesting sites. Also, it can be hard to protect nesting sites because you would have to also prevent preadtors from eating eggs/young. This can be hard because how would you keep predators out, by reducing populations? When you reduce predator populations, its prey will increase.

- Question Three -

A cohort life table would be better for following barnacle or plant populations because they are both reqruited into populations during a defined time interval. A size-based/stage-based life table would be best to describe cats or horses becuase they are best described by size or developmental stage than by age.

- Question Four -

Type 1 curve would best represent human populations, type 2 would be represent birds, and type 3 would best represent trees for example. A type 1 curve would mean that members of a population have a high survival when young, but mortality increases dramatically towards the end of life. A type 1 population would put a lot of energy into raising their young, but after they are fully developed they put in less energy. Type 2 curves represent a population that has a constant mortality rate with age. A type 2 population would put in less and less energy into raising their young at a constant decreasing rate. Type 3 curves represent populations that high higher morality when individuals are young and older individuals survive better. A type 3 population would most likely reproduce a lot of young and have less energy exerted towards keep their young alive, but as more young die off then more energy is exerted into keeping the young that survived alive.

- Question Five -

Population A

survivor2 <- read.csv("/Users/nicole/Downloads/survivorship.csv")
survivor22 <- subset(survivor2, type == "A")

#graph section and labeling- replace this title with each population 
title <- "Population A"

survivor22$lx <- survivor22$Sx / survivor22[1,3] #lx for the Type B subset

survivor22$Sxplus1 <- lead(survivor22$Sx, n= 1L) #Sx+1 variable

survivor22$gx <- survivor22$Sxplus1 / survivor22$Sx

# Survivorship curve plot 

plot(lx ~ age_x, data= survivor22, log = "y", main = title) #log scale 

## Warning in xy.coords(x, y, xlabel, ylabel, log): 1 y value <= 0 omitted
## from logarithmic plot

Figure: This is a survivorship curve plot on a log scale for Population A.

Population B

survivor <- read.csv("/Users/nicole/Downloads/survivorship.csv")

#there are three populations given in the dataset 
#subset the dataframe to analyze each population 

survivor <- subset(survivor, type == "B")

#graph section and labeling- replace this title with each population 
title <- "Population B"

survivor$lx <- survivor$Sx / survivor[1,3] #lx for the Type B subset

survivor$Sxplus1 <- lead(survivor$Sx, n= 1L) #Sx+1 variable

survivor$gx <- survivor$Sxplus1 / survivor$Sx

# Survivorship curve plot 

plot(lx ~ age_x, data= survivor, log = "y", main = title) #log scale 

## Warning in xy.coords(x, y, xlabel, ylabel, log): 1 y value <= 0 omitted
## from logarithmic plot

Figure: This is a survivorship curve plot on a log scale for Population B.

Population C

survivor3 <- read.csv("/Users/nicole/Downloads/survivorship.csv")
survivor33 <- subset(survivor2, type == "C")

#graph section and labeling- replace this title with each population 
title <- "Population C"

survivor33$lx <- survivor33$Sx / survivor33[1,3] #lx for the Type C subset

survivor33$Sxplus1 <- lead(survivor33$Sx, n= 1L) #Sx+1 variable

survivor33$gx <- survivor33$Sxplus1 / survivor33$Sx

# Survivorship curve plot 

plot(lx ~ age_x, data= survivor33, log = "y", main = title) #log scale 

## Warning in xy.coords(x, y, xlabel, ylabel, log): 1 y value <= 0 omitted
## from logarithmic plot

Figure: This is a survivorship curve plot on a log scale for Population C.

Population A fits a type 2 model of survivorship, population B represents a type 3 model of survivorship, and population C represents a type 1 model of survivorship. From this, one can assume that population A has a mortality rate that is constant with age, showing that as organisms get older they decay at a constant rate. Population B has higher mortality rates when individuals are young and then older individuals have better survivorship when they are older. Population C has higher survival in individuals when they are young, but mortality increases dramatically at the end of individuals’ lives.

- Question Six -

Population A

# Population A
title <- "Population A"
plot(gx ~ age_x, data = survivor22, main = title)

Figure: Age-specific survivorship curve for the population.

Population B

#Population B 
title <- "Population B"
plot(gx ~ age_x, data = survivor, main = title)

Figure: Age-specific survivorship curve for the population.

Population C

title <- "Population C"
#Population C
plot(gx ~ age_x, data = survivor33, main = title)

Figure: Age-specific survivorship curve for the population.

For population A the graph means that the survivorship is the same at each age at 0.5. Population B has increasing survivorship until age 4, then survivorship is around the same until it drops at the end of the populations’ life. Population C has relatively stable surivorship until age 4 where the survivorship begins to drop until a low at age 10.

- Question Seven -

Population A

# Population A
title <- "Population A"
plot(ex ~ age_x, data = survivor22, main = title)

Figure: Life expectancy curve for the population.

Population B

#Population B 
title <- "Population B"
plot(ex ~ age_x, data = survivor, main = title)

Figure: Life expectancy curve for the population for the population.

Population C

title <- "Population C"
#Population C
plot(ex ~ age_x, data = survivor33, main = title)

Figure: Life expectancy curve for the population for the population.

For population A, life expectancy is stable at 1.5 until age 6 where life expectancy starts to drop. Thus, life expectancy is is stable until the population reaches age 6 where life expencancy decreases. Population B has very low life expectancy at birth but it increases dramatically until age 4 where then life expectancy dramatically decreses incrementally until age 10, where it hits a low. Population C has a very high life expectancy at birth, which then declines until it hits a constant rate at age 8-10.

- Question Eight -

Population A

#Population A
survivor22$Ro <- survivor22$lx * survivor22$bx

sum(survivor22$Ro)

## [1] 0.9417969

title <- "Population A"
plot(Ro ~ age_x, data = survivor22, main = title)

Figure: A graph displaying net reproductive rate of the population.

Population B

#Population B
survivor$Ro <- survivor$lx * survivor$bx

sum(survivor$Ro)

## [1] 0.88487

title <- "Population B"
plot(Ro ~ age_x, data = survivor, main = title)

Figure: A graph displaying net reproductive rate of the population.

Population C

#Population C
survivor33$Ro <- survivor33$lx * survivor33$bx

sum(survivor33$Ro)

## [1] 5.479

title <- "Population C"
plot(Ro ~ age_x, data = survivor33, main = title)

Figure: A graph displaying net reproductive rate of the population.

Population A is declining because Ro is less than 1. Population B is declining because Ro is less than 1. Population C is growing exponentially because Ro is greater than 1. Age specific survivorship and fecundity are interrelated because if a population has lower survivorship at birth, then less individuals will reach maturity represent fecundity numbers. If a population has very high survivorship at birth, more individuals will reach maturity and contribute to fecundity.

- Question Nine -

Population A

#Population A 

G_A <- sum(survivor22$lx * survivor22$bx * survivor22$age_x) / sum(survivor22$lx * survivor22$bx)
G_A

## [1] 3.367897

sumRoA <- sum(survivor22$Ro)
sumRoA

## [1] 0.9417969

rA <- log(sumRoA)/G_A
rA

## [1] -0.01780507

#Calculate population size at any time interval 

NoA <- 2048 #pop size 

tA <- 100 #time interval 

populationA_size_t <- NoA * exp(rA * tA)
populationA_size_t

## [1] 345.1957

Population B

#Population B 

G_B <- sum(survivor$lx * survivor$bx * survivor$age_x) / sum(survivor$lx * survivor$bx)
G_B

## [1] 5.843288

sumRoB <- sum(survivor$Ro)

rB <- log(sumRoB)/G_B
rB

## [1] -0.02093249

#Calculate population size at any time interval 

NoB <- 10000 #pop size 

tB <- 100 #time interval 

populationB_size_t <- NoB * exp(rB * tB)
populationB_size_t

## [1] 1232.86

Population C

#Population C

G_C <- sum(survivor33$lx * survivor33$bx * survivor33$age_x) / sum(survivor33$lx * survivor33$bx)
G_C

## [1] 3.934477

sumRoC <- sum(survivor33$Ro)

rC <- log(sumRoC)/G_C
rC

## [1] 0.4323122

#Calculate population size at any time interval 

NoC <- 1000 #pop size 

tC <- 100 #timei interval 

populationC_size_t <- NoC * exp(rC * tC)
populationC_size_t

## [1] 5.957746e+21

Population A: - generation time: 3.4 - intrinsic rate of increase: -0.018 - pop size after 100 generations: 345.1957

Population B: - generation time: 5.8 - intrinsic rate of increase: -0.021 - pop size after 100 generations: 1232.86

Population C: - generation time: 3.9 - intrinsic rate of increase: 0.43 - pop size after 100 generations: 5.957746e+21

- Question Ten -

Conservationists can use life tables to see which time period of a populations lifespan they are the most at risk or have the highest mortality rate or when a threatened population has the best survivorship in order to prioritize different habitats or conservation efforts during certain time spans of a population’s life. Using these tables, we can determine which time interval of an endangered population’s life is most meaningful for conservation efforts and can then apply management strategies during time periods that would optimize the survival of a population.