Finish predraft of Discussion and +ch4.

Chapter2.tex

@@ -72,7 +72,7 @@ \section{Introduction}
 
 
 
-\subsection{General Intro}
+\tmpsection{General Intro}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % A basic introduction to the field,
 % comprehensible to a scientist in any discipline.
@@ -101,7 +101,7 @@ \subsection{General Intro}
 Maganga \emph{et al.} found that distribution fragmentation predicts viral richness \cite{maganga2014bat}, but \cite{gay2014parasite} finds the opposite relationship. 
 While the data set in \cite{gay2014parasite} is larger, the analysis in \cite{maganga2014bat} is much more focused on fragmentation.
 Genetic correlates of population structure have also been used.
-Turmelle \emph{et al.} \cite{turmelle2009correlates}, in a small analysis, find that high $F_{st}$ (i.e. a structured population) correlates with high richness.
+Turmelle \emph{et al.} \cite{turmelle2009correlates}, in a small analysis, find that high $F_{st}$ (\emph{i.e.} a structured population) correlates with high richness.
 However, they do not account for the widely different spatial scales found in population structure studies, nor do they deal with the differences between $F_{ST}$, $\phi_{ST}$ and other measures appropriately. 
 
 Empirical, correlative studies are often contradictory due to small sample sizes, noisy data and because empirical relationships often do not extrapolate well to other taxa (though see \cite{kamiya2014determines} for a meta-analysis).
@@ -255,10 +255,10 @@ \section{Methods}
 $\mu$ & Death rate & Per year per individual & 0.05\\
 %$d_I$ & Infectious death rate & Additional deaths per day per individual&\\
 $\rho$ & No. pathogens && 2\\
-$p$ &  Pathogen index i.e. $p\in\{1,2\}$ for pathogens 1 and 2 & &\\
-$q$ & Disease class i.e., $q\in\{1,2,12\}$&\\
+$p$ &  Pathogen index \emph{i.e.} $p\in\{1,2\}$ for pathogens 1 and 2 & &\\
+$q$ & Disease class \emph{i.e.}, $q\in\{1,2,12\}$&\\
 %$\mathcal{V}$ & Neighbourhood of a node &&\\
-$t, t^\prime$ & Time and time plus waiting time i.e., $t+\delta$ & Days&\\
+$t, t^\prime$ & Time and time plus waiting time \emph{i.e.}, $t+\delta$ & Days&\\
 $k_i$ & Degree of node $i$ &&\\
 $\delta$ & Waiting time until next event & Days&\\
 $\alpha$ & Cross immunity & Proportion& 0.1\\
@@ -615,7 +615,7 @@ \section{Discussion}
 
 These results imply that if population structure does in fact affect pathogen richness \cite{maganga2014bat, turmelle2009correlates, gay2014parasite} it must occur by a mechanism other than the one studied here.
 Therefore it is not the spread and persistance of a newly evolved pathogen that is facilitated by population structure.
-Other mechanisms that should be examined include reduced competitive exclusion of already established pathogens or increased invasion of less closely and less strongly competiting pathogens, perhaps mediated by ecological competition of pathogens (i.e. reducuction of the susceptible pool by disease induced mortality).
+Other mechanisms that should be examined include reduced competitive exclusion of already established pathogens or increased invasion of less closely and less strongly competiting pathogens, perhaps mediated by ecological competition of pathogens (\emph{i.e.} reducuction of the susceptible pool by disease induced mortality).
 Furthermore, single pathogen dynamics could have an important role such as population structure causing a much slower, asynchronous epidemic preventing acquired herd immunity \cite{plowright2011urban}.
 
 Given that we find no affect of population structure on the ability of a new pathogen to invade, this host trait is not useful for predicting the probability that a wild species has many pathogens.

Chapter3.tex

@@ -18,7 +18,7 @@ \section{Abstract}
 
 % Theory led.
 
-The pattern of contacts between individuals (i.e. population structure) has long been known to strongly affect epidemic processes.
+The pattern of contacts between individuals (\emph{i.e.} population structure) has long been known to strongly affect epidemic processes.
 Theory suggests that population structure can promote pathogen richness while the ecological literature generally assumes it will decrease richness.
 
 
@@ -371,7 +371,7 @@ \subsection{Population stucture data}
 I converted all $F_{ST}$ value to migration using $M = (1-F_{ST})/8F_{ST}$.
 This removes the $(0, 1)$ bounds of $F_{ST}$ and is more easily interpretable though the results are unaffected. 
 These two measures of population structure were analysed separately as the number of subspecies has 196 data points while there is only $F_{ST}$ data for 22 bat species.
-For the subspecies analysis all bat species in \textcite{luis2013comparison} were used (i.e. all species with at least one known virus species).
+For the subspecies analysis all bat species in \textcite{luis2013comparison} were used (\emph{i.e.} all species with at least one known virus species).
 However, for the gene flow analysis, all bat species with suitable $F_{ST}$ estimates were used.
 As this included some species not present in \textcite{luis2013comparison} this includes some bat species with zero known virus species. 
 
@@ -732,7 +732,7 @@ \subsection{Study limitations}
 
 The relationship between population structure and pathogen richness suggests that population structure has a least some potential as being predictive of high pathogen richness and therefore of a species likelihood of being a reservoir of a potentially zoonotic pathogen. 
 However given that it is difficult to measure population structure and given that the relationship appears to be weak at best, this trait on it's own is unlikely to be useful in predicting zoonotic risk.
-However, as a number of other factors are also associated with pathogen richness (body mass and to a lesser extent range size here but also other traits elsewhere), using a combination traits in a predictive (i.e. machine learning) framework has potential to be used in prioritising zoonotic disease surveillance.
+However, as a number of other factors are also associated with pathogen richness (body mass and to a lesser extent range size here but also other traits elsewhere), using a combination traits in a predictive (\emph{i.e.} machine learning) framework has potential to be used in prioritising zoonotic disease surveillance.
 The main hurdle in this approach is finding a way to validate models---due to the study effort bias in current data, predictive models will also be biased.
 
 The relationship between pathogen richness and population structure also has implications for habitat fragmentation and range shifts due to global change.

Chapter4.tex

@@ -3,8 +3,15 @@
 
 
 
+\begin{knitrout}
+\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe}
 
 
+{\ttfamily\noindent\bfseries\color{errorcolor}{\#\# Error in library(extrafont): there is no package called 'extrafont'}}
+
+{\ttfamily\noindent\bfseries\color{errorcolor}{\#\# Error in as.vector(y): object 'theme\_tcdl' not found}}\end{kframe}
+\end{knitrout}
+
 
 
 
@@ -308,26 +315,26 @@ \subsection{Metapopulation model}
 \tmpsection{Overview}
 
 
-I used two-pathogen, metapopulation SIR model to compare the roles of demograhic parameters on pathogen species richness.
-Specifically I let two identical pathogens (and endemic pathogen and an invading pathogen) compete.
+I used a two-pathogen, metapopulation SIR model to compare the roles of demograhic parameters on pathogen species richness.
+Specifically I let two identical pathogens---an endemic pathogen and an invading pathogen---compete.
 I used presistence or not of the second pathogen as my response variable.
-I test whether population abundance is more important than population density.
-I then test whether colony size or the number of colonies is the more important component of population abundance.
+I tested whether population abundance is more important than population density.
+I then tested whether colony size or the number of colonies is the more important component of population abundance.
 The multpathogen SIR model is identical to that in Chapter \ref{ch:sims1} and is implemented in R \cite{R}.
 
 
 
 In each simulation the population is seeded with 20 individuals infected with pathogen 1 in each colony. 
 Pathogen 1 is then allowed to spread and reach equilibrium. 
-After \ensuremath{7\times 10^{5}} events, 5 individuals infected with pathogen 2 are added to one colony. 
+After \ensuremath{7\times 10^{5}} events, 5 individuals infected with pathogen 2 are added to one randomly selected colony. 
 After another \ensuremath{3\times 10^{5}} events the invasion of pathogen 2 is considered successful if any individuals with pathogen 2 still remain.
 
 \subsection{Dependant variables}
 
 Three dependant variables were varied: colony size, number of colonies and area.
 From these parameters, population abundance and population density can be calculated.
 The default values of these parameters was a population size of 8000 individuals split into 20 colonies of 400.
-The default area of the simulations was 
+The default area of the simulations was \ensuremath{10^{4}}.
 
 Three sets of simulations were run.
 First, colony size was varied using values 100, 200, 400, 800 and \ensuremath{1.6\times 10^{3}}.
@@ -342,7 +349,7 @@ \subsection{Dependant variables}
 The metapopulation structure was created for each simulation by randomly placing colonies in space (Figure~\ref{fig:colonyNetworkPlots}).
 The spatial scale of the simulations vary between \ensuremath{2.5\times 10^{3}} and \ensuremath{4\times 10^{4}} km$^2$ (space is given in kilometers even though they are oin fact arbitrary units for simplicity).
 This corresponds to square areas with sides of 50 to 200 km).
-Dispersal can only occur between two colonies if they are within 100 kilometers of each other i.e. they are connected nodes in the metapopulation network.
+Dispersal can only occur between two colonies if they are within 100 kilometers of each other \emph{i.e.} they are connected nodes in the metapopulation network.
 The number of connections each colony has is called its degree, $k$.
 How well connected the metapopulation network is overall is measured by the mean degree, $\bar{k}$.
 This does not guarentee that the population is fully connected but as the endemic pathogen is seeded in all colonies, the invading pathogen cannot be seeded into a fully susceptible colony.
@@ -407,7 +414,7 @@ \section{Results}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 At the default parameter settings, the probability of invasion and establishment of the second pathogen, $P(I)$,  was rare ($\beta = 0.1,\: P(I) = 0.02;\: \beta = 0.2,\: P(I) = \ensuremath{3.33\times 10^{-3}};\: \beta = 0.3,\: P(I) = 0.06$).
-Although there is no clear pattern, these proportions are significantly different ($\chi^2$ test: $\chi^2 = 17.21,\: \text{df} = 2,\: p = \ensuremath{1.83\times 10^{-4}}$).
+Although there is no clear, directional relationship, these proportions are significantly different ($\chi^2$ test: $\chi^2 = 17.21,\: \text{df} = 2,\: p = \ensuremath{1.83\times 10^{-4}}$).
 
 In 37 simulations, both of the pathogens went extinct.
 This did not depend on transmission rate ($\chi^2$ test: $\chi^2 = 1.51,\: \text{df} = 2,\: p = 0.47$).
@@ -427,8 +434,8 @@ \subsection{Population density or abundance}
 
 \subsection{Colony size or number of groups}
 
-To test whether colony size or the number of colonies is the more important component of population abundance, I compared the regression coefficients of the multiple regressions fitted to simulation results (Figure~\ref{fig:plotTransMeans}).
-Increasing colony size or the number of colonies increases the probability of invasion but this affect is much stronger for colony size (Table~\ref{t:regrCoefs}).
+To test whether colony size or the number of colonies is the more important component of population abundance, I compared the regression coefficients, $b_2$ and $b_3$, of the multiple regressions fitted to simulation results (Figure~\ref{fig:plotTransMeans}).
+Increasing colony size or the number of colonies increases the probability of invasion but this affect is much stronger and more statistically significant, for colony size (Table~\ref{t:regrCoefs}).
 Therefore the simulations support the hypothesis that colony size is the more important component of population size, though colony number does still increase the probability of invasion.
 
 
@@ -505,7 +512,7 @@ \subsection{Global change}
 However these changes might affect range size \cite{thomas2004extinction}, population abundance \cite{craigie2010large}, population connectivity \cite{} or group size \cite{lehmann2010apes, zunino2007habitat, manor2003impact, atwood2006influence} to different extents.
 My results suggest that pathogen communities will response differently depending on the change although it should be noted that the mechanism here---invasion of a new pathogen---is possibly more relevant in the longer term.
 In short, species suffering reductions in groups size \cite{lehmann2010apes, zunino2007habitat, manor2003impact, atwood2006influence} are predicted to experience decreases in pathogen richness in the long term.
-Species that are experience increases in group size \cite{lehmann2010apes} would be expected gain new pathogen species more quickly.
+Species that are experiencing increases in group size \cite{lehmann2010apes} would be expected gain new pathogen species more quickly.
 In contrast, species suffering range contractions \cite{thomas2004extinction} and decreases in abundance \cite{craigie2010large} are expected to experience smaller changes in pathogen richness.
 
 
@@ -548,13 +555,24 @@ \subsection{Assumptions and limitation}
 
 \tmpsection{Further correlations between factors}
 
+I have used the simple relationships between demographic factors (density = abundance / area for exmaples) to illustrate that these are tightly linked.
+In order to isolate the affects of these factors I have assumed these simple relationships hold; to examine density without altering abundance I have fixed abundance and manipulated area.
+However in reality these are likely to covary both and between species and within species across time.
+Therefore, these quantities are certainly linked, they cannot be assumed to have simple linear relationships and should not be used as proxies of each other without further examination.
+For exampleiIt is expected that group size increases with range size \cite{}.
+Similarly it is unlikely that a species whose range size decreases will not experience a decrease in total abundance as well; the range contraction is likely to occur over generations rather than a simple squeezing of the existing individuals into a smaller area.
+
+
 %For instance, various relationships between group size and home range size exist (Macdonald 1983). Kruuk and Macdonald (1985) predict that home range behaviour in group living species should conform to one of two strategies. They should either expand their range to encompass sufficient additional resources to support more group members (expansionism) or increase group size only up to the size that can be sustained on the resources within the smallest economically defendable range needed to support the minimum social unit (contractionism). http://onlinelibrary.wiley.com/enhanced/doi/10.1111/j.1600-0587.2009.05745.x
 % Badger Group size versus territory size http://onlinelibrary.wiley.com/doi/10.1034/j.1600-0706.2001.950208.x/abstract
 
 
 \subsection{Conclusions}
 
-
+Overall I have shown that while a number of demographic factors are intrinsically linked, they have different affects on the rate at which new pathogens will invade.
+I found that abundance, not density, has the stronger impact on the ability of a pathogen to invade.
+Furthermore, species with large groups are likely to harbour more pathogens than species with many, smaller groups.
+Due to the correlations between these factors, they are particularly hard to study within a comparative framework; this highlights the utility of mechanistic models.