dhindsa_20729365_level1guided
Aman Dhindsa
27/09/2020
Question 1.
Human population has been growing at an exponential rate. Our current population size is estimated to be about 7.8 billion people with an annual growth rate of 1.05% (Worldometers, 2020). As our population grows, we use up more land, resources, and release more waste product on to the planet. This has a profound effect on wildlife. 
Figure 1. Human population growth and extinction rate
As our population grows, more species become extinct. In fact, scientist across the globe agree that we are currently living in an anthropogenically caused mass extinction event,
Moreover, we have unleashed a mass extinction event, the sixth in roughly 540 million years, wherein many current life forms could be annihilated or at least committed to extinction by the end of this century. (Ripple et al., 2017)
Species such as the polar bear, Ursus maritimus, are a prime example of how our current existence pushes wildlife to the brink of extinction (USGS, 2020).
Question 2.
setwd("~/Desktop/BIOL 458 R")
end.species<-read.csv("lab1endangered.csv",header=TRUE,sep=",")
popsize<-read.csv("lab1pop.csv",header=TRUE,sep=",")
#make enough space for 2 y-axis
par(mar = c(5, 4, 4, 4) + 0.3)
#plot human pop size
plot(popsize$year,popsize$population.size/1000000, xlab="Year",ylab="Human population size (in millions)",xlim=c(1960,2020),ylim=c(0,40),col="red",pch=19,main="Human Population Size in Canada and COSEWIC Endangered Species over time",type="l")
#human population projection
abline(lm(popsize$population.size/1000000~popsize$year),col="green")
#plot endangered speices
par(new=TRUE)
plot(end.species$year,end.species$COSEWIC.recognized.species,axes=FALSE,ylab="",xlab="",col="blue",pch=19,type="l")
#add second axis
axis(side=4,at=pretty(range(end.species$COSEWIC.recognized.species)))
mtext("COSEWIC recognized species",side=4,line=3)
#legend
legend("topleft", legend=c("Recorded Canadian population size","Projected Canadian population size","Recorded COSEWIC endangered species"),col=c("red","green","blue"), lty=1, cex=0.6)
Figure 2. Canadian Population Size and COSEWIC Endangered Species
Based on the trend displayed in Figure 2, we can see that rising population size in Canada has corresponded with a rising number of endangered species. Additionally, the projected population size is an under estimate compared to the real population of 37.8 million in Canada today (Worldometers,2020)
Question 3.
The population density of the Juglans cinerea now is 0.03. This was calculated using the equation, \[\begin{eqnarray} N_t= N_o * \lambda^t\\ \\ N_{10}= 0.2 \frac{individuals}{m^2} * 0.8282 \frac{individuals}{individual*year}^{10 years}\\ \\ N_{10}= 0.03 \frac{indivuals}{m^2}\\ \end{eqnarray}\]
Question 4.
#import datatable into r
setwd("~/Desktop/BIOL 458 R")
UScases<-read.csv("UScases.csv",header=TRUE,sep=",")
Date<-UScases$Date
Cases<-UScases$Cases
#i want to estimate population growth for only the last 60 days
Nt1<-tail(Cases,60)
Nt<-UScases[(length(Cases)-60):(length(Cases)-1),2]
lamt=Nt1/Nt
#arithmetic mean
lamA<-mean(lamt)
#geometric mean
r<-mean(log(lamt))
lamG<-exp(mean(log(lamt)))
#error
error<-sd(lamt)/sqrt(length(lamt))Question 5.
The population growth rate for US covid-19 cases from July, 9th 2020 to September 6th, 2020 is 0.012 +/- 610^{-4}
Question 6.
The estimated growth rate of 0.012 (r value >1) implies that covid-19 cases are still growing. The total number of people infected is still growing, and at an exponential rate.
Question 7.
Figure 3. Covid-19 Cases in the United States
Question 8.
##
## Call:
## lm(formula = Cases/1e+06 ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.7343 -0.6352 -0.2981 0.6573 1.3778
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.582e+02 1.148e+01 -39.93 <2e-16 ***
## x 2.502e-02 6.241e-04 40.09 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7165 on 249 degrees of freedom
## Multiple R-squared: 0.8658, Adjusted R-squared: 0.8653
## F-statistic: 1607 on 1 and 249 DF, p-value: < 2.2e-16
Figure 4. Regression Diagnostic Plots
The regression summary provided us with coefficients of 0.025 and -458. These tell us the slope and intercept of the line we plotted in figure 3.
The p-value of <2.2e-16 tells us that there is a statistically significant relationship between time (predictor variable) and covid-19 cases in the US (response variable). We can reject our null hypothesis of the linear regression. The adjusted R-squared value of 0.865 tells us that not all of the variance in covid-19 cases was explained by time. Many points differed from the best fit line.
The residuals vs fitted plot gives us an idea of how the residuals were distributed. There is a distinct “U-shaped” trend present. Our model initially underestimated cases, then it overestimated cases, and then began underestimating cases once again. The assumption that this relationship is linear is not being met.
The normal Q-Q plot test the normality of the residual. We can see our data is not normally distributed since the residuals do not lie on the dashed line. The assumption that the residual error is distributed normally is not being met.
The scale-location plot shows the square root of the standardized residuals. There is a clear trend present. Our data is likely not linearly correlated.
Lastly, the residuals vs leverage plot shows us each data points leverage in the regression result. We can see that there is a large number of data points that are at a distance greater than 1.
Question 9.
A p-value over 0.05 is not statistically significant, therefore we would fail to reject the null hypothesis of the linear regression. I.e. there is a significant chance that our slope is 0 and there is no relationship between covid-19 cases and time. An R-squared value of 0.85 would be almost identical to the one we already got, but because there is a high p-value the R-squared cannot be used to make any conclusions.
Work Cited
Ripple WJ, Wolf C, Newsome TM, Galetti M, Alamgir M, Crist E, Mahmoud MI, Laurance WF (13 November 2017). “World Scientists’ Warning to Humanity: A Second Notice” (PDF). BioScience. 67 (12): 1026–1028.
Scott, J.M. 2008. Threats to Biological Diversity: Global,Contental,Local. U.S. Geological Survey, Idaho Cooperative Fish and Wildlife, Research Unit, University of Idaho.
USGS. 2020. Adaptive Managment for Threatened and Endangered Species. Retrieved from: https://www.usgs.gov/centers/pwrc/science/adaptive-management-threatened-and-endangered-species?qt-science_center_objects=0#qt-science_center_objects
Worldometers. 2020. World Population. Retrieved from: https://www.worldometers.info/world-population/ and https://www.worldometers.info/world-population/canada-population/