\relax \citation{May:2006lr} \citation{Berlow:2004yq,Vandermeer:2006fj} \@writefile{toc}{\contentsline {chapter}{\numberline {7}An Introduction to Food Webs}{211}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{lof}{\contentsline {figure}{\numberline {7.1}{\ignorespaces Two representations of a food web with 4 nodes and 8 directed links. The link label ``v'' indicates the proportion of $P$'s diet comprised of $R$.}}{211}} \newlabel{fig:web}{{7.1}{211}} \@writefile{toc}{\contentsline {section}{\numberline {7.1}Food Web Characteristics}{211}} \citation{May:2006lr} \citation{Cohen1990d} \citation{Dunne2002} \citation{Cohen1990d,Hubbell2001,Williams2000a} \citation{MacArthur1967,Rosenzweig1995} \citation{Post:2002bs} \citation{Pimm1977} \citation{Post:2002bs} \citation{May1973ab} \citation{May:2006lr} \citation{May1973ab,May1972} \@writefile{toc}{\contentsline {section}{\numberline {7.2}Food chain length --- an emergent property}{214}} \@writefile{toc}{\contentsline {subsection}{\numberline {7.2.1}Multi-species Lotka--Volterra notation}{214}} \newlabel{eq:compact}{{7.1}{214}} \@writefile{toc}{\contentsline {subsection}{\numberline {7.2.2}Background}{214}} \newlabel{A}{{7.2a}{215}} \newlabel{sub@A}{{(a)}{a}} \newlabel{E}{{7.2b}{215}} \newlabel{sub@E}{{(b)}{b}} \newlabel{B}{{7.2c}{215}} \newlabel{sub@B}{{(c)}{c}} \@writefile{lof}{\contentsline {figure}{\numberline {7.2}{\ignorespaces Three of the six webs investigated by Pimm and Lawton (1977).}}{215}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {}}}{215}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {}}}{215}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(c)}{\ignorespaces {}}}{215}} \newlabel{fig:PLABE}{{7.2}{215}} \newlabel{eq:IS}{{7.2}{215}} \newlabel{eq:1}{{7.3}{215}} \citation{Pimm1978} \citation{Pimm1977,Pimm1978} \citation{Pimm1977} \citation{McCann1998,McCann1997} \@writefile{lof}{\contentsline {figure}{\numberline {7.3}{\ignorespaces \relax \fontsize {9}{11}\selectfont \abovedisplayskip 8.5\p@ plus3\p@ minus4\p@ \abovedisplayshortskip \z@ plus2\p@ \belowdisplayshortskip 4\p@ plus2\p@ minus2\p@ \def \leftmargin \leftmargini \parsep \z@ plus\p@ minus\p@ \topsep 6\p@ plus2\p@ minus4\p@ \itemsep \z@ {\leftmargin \leftmargini \parsep \z@ plus\p@ minus\p@ \topsep 6\p@ plus2\p@ minus4\p@ \itemsep \z@ }\belowdisplayskip \abovedisplayskip Relation between the average interaction strength and the number of species able to coexist (here directed connectance is $C_D = 0.3$). The line represents the maximum number of species that are predicted to be able to coexist at equilibrium. Fewer species could coexist, but, on average, more species cannot coexist at equilibrium.}}{216}} \newlabel{fig:may1}{{7.3}{216}} \citation{Pimm1977} \citation{May1973ab} \@writefile{toc}{\contentsline {section}{\numberline {7.3}Implementing Pimm and Lawton's Methods}{217}} \citation{May1972} \citation{McCann1997} \@writefile{lof}{\contentsline {figure}{\numberline {7.4}{\ignorespaces Perturbations at the equilibrium tend to dissipate more rapidly (more negative dominant eigenvalues) with greater intraspecific negative density dependence (\textsf {IntraDD}) and greater interspecifiic interaction strength (\textsf {I}). This graph also demonstrates the independence of \textsf {IntraDD} and \textsf {I} in these simulations.}}{220}} \newlabel{fig:pairsA}{{7.4}{220}} \citation{Pimm1977} \newlabel{hA}{{7.5a}{221}} \newlabel{sub@hA}{{(a)}{a}} \newlabel{hE}{{7.5b}{221}} \newlabel{sub@hE}{{(b)}{b}} \newlabel{hB}{{7.5c}{221}} \newlabel{sub@hB}{{(c)}{c}} \@writefile{lof}{\contentsline {figure}{\numberline {7.5}{\ignorespaces Histograms for three of the six food chains (A, E, and B) used by Pimm and Lawton.}}{221}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Four level chain}}}{221}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Two level chain}}}{221}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(c)}{\ignorespaces {Four levels + omnivory}}}{221}} \newlabel{fig:RTHist}{{7.5}{221}} \@writefile{toc}{\contentsline {section}{\numberline {7.4}Shortening the Chain}{221}} \newlabel{hE}{{7.4}{222}} \@writefile{lof}{\contentsline {figure}{\numberline {7.6}{\ignorespaces For a food chain with two levels, and three basal species, perturbation growth rate ($\lambda _1$) declines with increasing intraspecific negative density dependence (\textsf {IntraDD}) and is unrelated to predator-prey interaction strengths.}}{222}} \newlabel{fig:E1}{{7.6}{222}} \@writefile{toc}{\contentsline {section}{\numberline {7.5}Adding Omnivory}{222}} \@writefile{toc}{\contentsline {subsection}{\numberline {7.5.1}Comparing Chain A versus B}{223}} \citation{Pimm1977} \@writefile{lof}{\contentsline {figure}{\numberline {7.7}{\ignorespaces Comparing the distributions of return times for chain \textbf {A} and \textbf {B}. "Density" is probability density. The distribution of return times for chain \textbf {A} is the solid black line, and the distribution of return times for chain \textbf {B} is the dashed red line.}}{224}} \newlabel{fig:histsAB}{{7.7}{224}} \citation{Pimm1977,Pimm1978} \citation{Huxel1998,McCann1997} \citation{Polis1991} \citation{McCann1998,McCann1997} \@writefile{toc}{\contentsline {section}{\numberline {7.6}Re-evaluating Take-Home Messages}{225}} \citation{Kingsland:1985kx} \citation{Bolker2003a} \citation{Bakker:1999qa,Byers:2006bs} \citation{Thompson:2007uq} \citation{McCann1998,Vandermeer:2006fr} \citation{Pimm1978} \@writefile{toc}{\contentsline {section}{\numberline {7.7}Summary}{226}} \@writefile{toc}{\contentsline {section}{Problems}{226}} \newlabel{prob4}{{7.2}{226}} \@setckpt{Chap07/Chapter07}{ \setcounter{page}{227} \setcounter{equation}{3} \setcounter{enumi}{6} \setcounter{enumii}{0} \setcounter{enumiii}{0} \setcounter{enumiv}{0} \setcounter{footnote}{7} \setcounter{mpfootnote}{0} \setcounter{part}{3} \setcounter{section}{7} \setcounter{subsection}{0} \setcounter{subsubsection}{0} \setcounter{paragraph}{0} \setcounter{subparagraph}{0} \setcounter{figure}{7} \setcounter{table}{0} \setcounter{chapter}{7} \setcounter{theorem}{0} \setcounter{prob}{2} \setcounter{merk}{0} \setcounter{pp@next@reset}{0} \setcounter{parentequation}{0} \setcounter{float@type}{4} \setcounter{KVtest}{0} \setcounter{subfigure}{0} \setcounter{subfigure@save}{3} \setcounter{lofdepth}{1} \setcounter{subtable}{0} \setcounter{subtable@save}{0} \setcounter{lotdepth}{1} \setcounter{FancyVerbLine}{6} }