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<span>Toggle Proposed explanations for the law subsection</span> </button> <ul id="toc-Proposed_explanations_for_the_law-sublist" class="vector-toc-list"> <li id="toc-Historical_context_and_the_2⁄3_scaling_surface_law" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Historical_context_and_the_2⁄3_scaling_surface_law"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Historical context and the <span><span>2</span>⁄<span>3</span></span> scaling surface law</span> </div> </a> <ul id="toc-Historical_context_and_the_2⁄3_scaling_surface_law-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kleiber's_contribution" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kleiber's_contribution"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Kleiber's contribution</span> </div> </a> <ul id="toc-Kleiber's_contribution-sublist" class="vector-toc-list"> </ul> </li> <li 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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Approximate power law relating animal metabolic rate to mass</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Kleiber1947.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Kleiber1947.svg/330px-Kleiber1947.svg.png" decoding="async" width="330" height="226" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Kleiber1947.svg/495px-Kleiber1947.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/Kleiber1947.svg/660px-Kleiber1947.svg.png 2x" data-file-width="707" data-file-height="484" /></a><figcaption>Kleiber's plot comparing body size to metabolic rate for a variety of species.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </figcaption></figure> <p><b>Kleiber's law</b>, named after <a href="/wiki/Max_Kleiber" title="Max Kleiber">Max Kleiber</a> for his biology work in the early 1930s, states, after many observation that, for a vast number of animals, an animal's <a href="/wiki/Basal_metabolic_rate" title="Basal metabolic rate">Basal Metabolic Rate</a> scales to the <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num">3</span>⁄<span class="den">4</span></span> power of the animal's mass.<sup id="cite_ref-hilgardia_2-0" class="reference"><a href="#cite_note-hilgardia-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>More precisely : posing w = mass of the animal in kilograms, then BMR = 70w<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ^{3/4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ^{3/4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b5cae8ba79e4c8bc8d4a780f0c0664c9a3b9d34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:2.698ex; height:2.676ex;" alt="{\displaystyle ^{3/4}}"></span> kilocalories per day, or BMR = 3.4w<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ^{3/4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ^{3/4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b5cae8ba79e4c8bc8d4a780f0c0664c9a3b9d34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:2.698ex; height:2.676ex;" alt="{\displaystyle ^{3/4}}"></span> watts.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Thus, over the same time span, a cat having a mass 100 times that of a mouse will consume only about 32 times the energy the mouse uses. </p><p>Presently is unclear if the value of the exponent in Kleiber's law is correct, in part because the law currently lacks a single theoretical explanation that is entirely satisfactory. </p><p>More recently, Kleiber's law has also been shown to apply in <a href="/wiki/Plants" class="mw-redirect" title="Plants">plants</a>,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> suggesting that Kleiber's observation is much more general </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Proposed_explanations_for_the_law">Proposed explanations for the law</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kleiber%27s_law&action=edit&section=1" title="Edit section: Proposed explanations for the law"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kleiber's law, like many other biological <a href="/wiki/Allometric_law" class="mw-redirect" title="Allometric law">allometric laws</a>, is a consequence of the <a href="/wiki/Physics" title="Physics">physics</a> and/or <a href="/wiki/Geometry" title="Geometry">geometry</a> of <a href="/wiki/Circulatory_system" title="Circulatory system">circulatory systems</a> in biology.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Max Kleiber first discovered the law when analyzing a large number of independent studies on respiration within individual species.<sup id="cite_ref-hilgardia_2-1" class="reference"><a href="#cite_note-hilgardia-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Kleiber expected to find an exponent of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">2</span>⁄<span class="den">3</span></span> (for reasons explained below), and was confounded by the discovery of a <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">3</span>⁄<span class="den">4</span></span> exponent. </p> <div class="mw-heading mw-heading3"><h3 id="Historical_context_and_the_2⁄3_scaling_surface_law"><span id="Historical_context_and_the_2.E2.81.843_scaling_surface_law"></span>Historical context and the <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">2</span>⁄<span class="den">3</span></span> scaling surface law</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kleiber%27s_law&action=edit&section=2" title="Edit section: Historical context and the 2⁄3 scaling surface law"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Before Kleiber's observation of the 3/4 power scaling, a 2/3 power scaling was largely anticipated based on the "surface law",<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> which states that the basal metabolism of animals differing in size is nearly proportional to their respective body surfaces. This surface law reasoning originated from simple geometrical considerations. As organisms increase in size, their volume (and thus mass) increases at a much faster rate than their surface area. Explanations for <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">2</span>⁄<span class="den">3</span></span>-scaling tend to assume that metabolic rates scale to avoid <a href="/wiki/Heat_exhaustion" title="Heat exhaustion">heat exhaustion</a>. Because bodies lose heat passively via their surface but produce heat metabolically throughout their mass, the metabolic rate must scale in such a way as to counteract the <a href="/wiki/Square%E2%80%93cube_law" title="Square–cube law">square–cube law</a>. Because many physiological processes, like heat loss and nutrient uptake, were believed to be dependent on the surface area of an organism, it was hypothesized that metabolic rate would scale with the 2/3 power of body mass.<sup id="cite_ref-surfaceLaw1_7-0" class="reference"><a href="#cite_note-surfaceLaw1-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Rubner (1883) first demonstrated the law in accurate respiration trials on dogs.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Kleiber's_contribution"><span id="Kleiber.27s_contribution"></span>Kleiber's contribution</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kleiber%27s_law&action=edit&section=3" title="Edit section: Kleiber's contribution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Max Kleiber challenged this notion in the early 1930s. Through extensive research on various animals' metabolic rates, he found that a 3/4 power scaling provided a better fit to the empirical data than the 2/3 power.<sup id="cite_ref-hilgardia_2-2" class="reference"><a href="#cite_note-hilgardia-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> His findings provided the groundwork for understanding allometric scaling laws in biology, leading to the formulation of the <a href="/w/index.php?title=Metabolic_Scaling_Theory&action=edit&redlink=1" class="new" title="Metabolic Scaling Theory (page does not exist)">Metabolic Scaling Theory</a> and the later work by West, Brown, and Enquist, among others. </p><p>Such an argument does not address the fact that different organisms exhibit different shapes (and hence have different <a href="/wiki/Surface-area-to-volume_ratio" title="Surface-area-to-volume ratio">surface-area-to-volume ratios</a>, even when scaled to the same size). Reasonable estimates for organisms' surface area do appear to scale linearly with the metabolic rate.<sup id="cite_ref-History_9-0" class="reference"><a href="#cite_note-History-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Exponent_3⁄4"><span id="Exponent_3.E2.81.844"></span>Exponent <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">3</span>⁄<span class="den">4</span></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kleiber%27s_law&action=edit&section=4" title="Edit section: Exponent 3⁄4"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Geoffrey_West" title="Geoffrey West">West</a>, <a href="/wiki/James_Brown_(ecologist)" title="James Brown (ecologist)">Brown</a>, and <a href="/wiki/Brian_Enquist" class="mw-redirect" title="Brian Enquist">Enquist</a>, (hereafter WBE) proposed a general theory for the origin of many <a href="/wiki/Allometry" title="Allometry">allometric scaling laws</a> in biology. According to the WBE theory, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">3</span>⁄<span class="den">4</span></span>-scaling arises because of efficiency in nutrient distribution and transport throughout an organism. In most organisms, metabolism is supported by a circulatory system featuring branching tubules (i.e., plant vascular systems, insect tracheae, or the human cardiovascular system). WBE claim that (1) metabolism should scale proportionally to nutrient flow (or, equivalently, total fluid flow) in this circulatory system and (2) in order to minimize the energy dissipated in transport, the volume of fluid used to transport nutrients (i.e., blood volume) is a fixed fraction of body mass. <sup id="cite_ref-WBEModel_10-0" class="reference"><a href="#cite_note-WBEModel-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> The model assumes that the energy dissipated is minimized and that the terminal tubes do not vary with body size. It provides a complete analysis of numerous anatomical and physiological scaling relations for circulatory systems in biology that generally agree with data.<sup id="cite_ref-WBEModel_10-1" class="reference"><a href="#cite_note-WBEModel-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> More generally, the model predicts the structural and functional properties of vertebrate cardiovascular and respiratory systems, plant vascular systems, insect tracheal tubes, and other distribution networks. </p><p>They then analyze the consequences of these two claims at the level of the smallest circulatory tubules (capillaries, alveoli, etc.). Experimentally, the volume contained in those smallest tubules is constant across a wide range of masses. Because fluid flow through a tubule is determined by the volume thereof, the total fluid flow is proportional to the total number of smallest tubules. Thus, if <span class="texhtml mvar" style="font-style:italic;">B</span> denotes the basal metabolic rate, <span class="texhtml mvar" style="font-style:italic;">Q</span> the total fluid flow, and <span class="texhtml mvar" style="font-style:italic;">N</span> the number of minimal tubules,<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B\propto Q\propto N{\text{.}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>∝</mo> <mi>Q</mi> <mo>∝</mo> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>.</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B\propto Q\propto N{\text{.}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3670c1b4361e058bb3be08075cbf918cf477da9" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.51ex; height:2.509ex;" alt="{\displaystyle B\propto Q\propto N{\text{.}}}"></span> Circulatory systems do not grow by simply scaling proportionally larger; they become <a href="/wiki/Fractal" title="Fractal">more deeply nested</a>. The depth of nesting depends on the <a href="/wiki/Fractal_dimension" title="Fractal dimension">self-similarity exponents</a> of the tubule dimensions, and the effects of that depth depend on how many "child" tubules each branching produces. Connecting these values to macroscopic quantities depends (very loosely) on a precise model of tubules. WBE show that if the tubules are well-approximated by rigid cylinders, then, to prevent the fluid from <a href="/wiki/Incompressible_flow" title="Incompressible flow">"getting clogged"</a> in small cylinders, the total fluid volume <span class="texhtml mvar" style="font-style:italic;">V</span> satisfies<sup id="cite_ref-Reformulated_11-0" class="reference"><a href="#cite_note-Reformulated-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N^{4}\propto V^{3}{\text{.}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>∝</mo> <msup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>.</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N^{4}\propto V^{3}{\text{.}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72ade7c110e5d7469414ac6ef6c3df9f4b951989" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.894ex; height:2.676ex;" alt="{\displaystyle N^{4}\propto V^{3}{\text{.}}}"></span> (Despite conceptual similarities, this condition is inconsistent with <a href="/wiki/Murray%27s_law" title="Murray's law">Murray's law</a>)<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Because blood volume is a fixed fraction of body mass,<sup id="cite_ref-WBEModel_10-2" class="reference"><a href="#cite_note-WBEModel-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B\propto M^{\frac {3}{4}}{\text{.}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>∝</mo> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>.</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B\propto M^{\frac {3}{4}}{\text{.}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a361d5b7c5193d3906b78996434405a65bf23b2" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.744ex; height:3.509ex;" alt="{\displaystyle B\propto M^{\frac {3}{4}}{\text{.}}}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Non-power-law_scaling">Non-power-law scaling</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kleiber%27s_law&action=edit&section=5" title="Edit section: Non-power-law scaling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The WBE theory predicts that the scaling of metabolism is not a strict power law but rather should be slightly curvilinear. The 3/4 exponent only holds exactly in the limit of organisms of infinite size. As body size increases, WBE predict that the scaling of metabolism will converge to a ~3/4 scaling exponent.<sup id="cite_ref-WBEModel_10-3" class="reference"><a href="#cite_note-WBEModel-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Indeed, WBE predicts that the metabolic rates of the smallest animals tend to be greater than expected from the power-law scaling (see Fig. 2 in Savage et al. 2010 <sup id="cite_ref-Savageetal_13-0" class="reference"><a href="#cite_note-Savageetal-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> ). Further, Metabolic rates for smaller animals (birds under 10 kg [22 lb], or insects) typically fit to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">2</span>⁄<span class="den">3</span></span> much better than <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">3</span>⁄<span class="den">4</span></span>; for larger animals, the reverse holds.<sup id="cite_ref-Empirics_14-0" class="reference"><a href="#cite_note-Empirics-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> As a result, log-log plots of metabolic rate versus body mass can "curve" slightly upward, and fit better to quadratic models.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> In all cases, local fits exhibit exponents in the <span class="texhtml">[<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">2</span>⁄<span class="den">3</span></span>,<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">3</span>⁄<span class="den">4</span></span>]</span> range.<sup id="cite_ref-ArbNetworks_16-0" class="reference"><a href="#cite_note-ArbNetworks-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Elaborated_and_Modified_circulatory_models">Elaborated and Modified circulatory models</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kleiber%27s_law&action=edit&section=6" title="Edit section: Elaborated and Modified circulatory models"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Elaborations of the WBE model predict <i>larger</i> scaling exponents, worsening the discrepancy with observed data.<sup id="cite_ref-Savage18787686_17-0" class="reference"><a href="#cite_note-Savage18787686-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> see also, <sup id="cite_ref-Empirics_14-1" class="reference"><a href="#cite_note-Empirics-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup>). However, one can retain a similar theory by relaxing WBE's assumption of a nutrient transport network that is both <a href="/wiki/Fractal" title="Fractal">fractal</a> and circulatory. Different networks are less efficient in that they exhibit a lower scaling exponent. Still, a metabolic rate determined by nutrient transport will always exhibit scaling between <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">2</span>⁄<span class="den">3</span></span> and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">3</span>⁄<span class="den">4</span></span>.<sup id="cite_ref-ArbNetworks_16-1" class="reference"><a href="#cite_note-ArbNetworks-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> WBE argued that fractal-like circulatory networks are likely under strong <a href="/wiki/Stabilizing_selection" title="Stabilizing selection">stabilizing selection</a> to evolve to minimize energy used for transport. If selection for greater metabolic rates is favored, then smaller organisms will prefer to arrange their networks to scale as <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">2</span>⁄<span class="den">3</span></span>. Still, selection for larger-mass organisms will tend to result in networks that scale as <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">3</span>⁄<span class="den">4</span></span>, which produces the observed curvature.<sup id="cite_ref-Savage_2004_19-0" class="reference"><a href="#cite_note-Savage_2004-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Modified_thermodynamic_models">Modified thermodynamic models</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kleiber%27s_law&action=edit&section=7" title="Edit section: Modified thermodynamic models"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An alternative model notes that metabolic rate does not solely serve to generate heat. Metabolic rate contributing solely to useful work should scale with power 1 (linearly), whereas metabolic rate contributing to heat generation should be limited by surface area and scale with power <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">2</span>⁄<span class="den">3</span></span>. Basal metabolic rate is then the <a href="/wiki/Convex_combination" title="Convex combination">convex combination</a> of these two effects: if the proportion of useful work is <span class="texhtml mvar" style="font-style:italic;">f</span>, then the basal metabolic rate should scale as <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B=f\cdot kM+(1-f)\cdot k'M^{\frac {2}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>=</mo> <mi>f</mi> <mo>⋅</mo> <mi>k</mi> <mi>M</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>f</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <msup> <mi>k</mi> <mo>′</mo> </msup> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B=f\cdot kM+(1-f)\cdot k'M^{\frac {2}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b740312d7806f89ab9063c3def9e5730e265bc86" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:29.214ex; height:4.009ex;" alt="{\displaystyle B=f\cdot kM+(1-f)\cdot k'M^{\frac {2}{3}}}"></span> where <span class="texhtml mvar" style="font-style:italic;">k</span> and <span class="texhtml"><i>k</i><span class="nowrap" style="padding-left:0.15em;">′</span></span> are constants of proportionality. <span class="texhtml"><i>k</i><span class="nowrap" style="padding-left:0.15em;">′</span></span> in particular describes the <a href="/w/index.php?title=Meeh_factor&action=edit&redlink=1" class="new" title="Meeh factor (page does not exist)">surface area ratio</a> of organisms and is approximately <span class="texhtml">0.1 kJ·h<sup>−1</sup>·g<sup>−2/3</sup></span>;<sup id="cite_ref-balles_20-0" class="reference"><a href="#cite_note-balles-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> typical values for <span class="texhtml mvar" style="font-style:italic;">f</span> are 15-20%.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> The theoretical maximum value of <span class="texhtml mvar" style="font-style:italic;">f</span> is 21%, because the efficiency of <a href="/wiki/Glucose_oxidation_reaction" class="mw-redirect" title="Glucose oxidation reaction">glucose oxidation</a> is only 42%, and half of the <a href="/wiki/Adenosine_triphosphate" title="Adenosine triphosphate">ATP</a> so produced is wasted.<sup id="cite_ref-balles_20-1" class="reference"><a href="#cite_note-balles-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Criticism_of_explanations">Criticism of explanations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kleiber%27s_law&action=edit&section=8" title="Edit section: Criticism of explanations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kozłowski and Konarzewski have argued against attempts to explain Kleiber's law via any sort of limiting factor because metabolic rates vary by factors of 4-5 between rest and activity. Hence, any limits that affect the scaling of the <i>basal</i> metabolic rate would make elevated metabolism — and hence all animal activity — impossible.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> WBE conversely argue that natural selection can indeed select for minimal transport energy dissipation during rest, without abandoning the ability for less efficient function at other times.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>Other researchers have also noted that Kozłowski and Konarzewski's criticism of the law tends to focus on precise structural details of the WBE circulatory networks but that the latter are not essential to the model.<sup id="cite_ref-Reformulated_11-1" class="reference"><a href="#cite_note-Reformulated-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Experimental_support">Experimental support</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kleiber%27s_law&action=edit&section=9" title="Edit section: Experimental support"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Analysis_of_variance" title="Analysis of variance">Analyses of variance</a> for a variety of physical variables suggest that although most variation in basal metabolic rate is determined by mass, additional variables with significant effects include body temperature and taxonomic order.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p><p>A 1932 work by Brody calculated that the scaling was approximately 0.73.<sup id="cite_ref-History_9-1" class="reference"><a href="#cite_note-History-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p><p>A 2004 analysis of field metabolic rates for mammals conclude that they appear to scale with exponent 0.749.<sup id="cite_ref-Savage_2004_19-1" class="reference"><a href="#cite_note-Savage_2004-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Generalizations">Generalizations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kleiber%27s_law&action=edit&section=10" title="Edit section: Generalizations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kleiber's law has been reported to interspecific comparisons and has been claimed not to apply at the intraspecific level.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> The taxonomic level that body mass metabolic allometry should be studied has been debated <sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> Nonetheless, several analyses suggest that while the exponents of the Kleiber's relationship between body size and metabolism can vary at the intraspecific level, statistically, intraspecific exponents in both plants and animals tend to cluster around 3/4.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="In_other_kingdoms">In other kingdoms</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kleiber%27s_law&action=edit&section=11" title="Edit section: In other kingdoms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A 1999 analysis concluded that biomass production in a given plant scaled with the <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">3</span>⁄<span class="den">4</span></span> power of the plant's mass during the plant's growth,<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> but a 2001 paper that included various types of unicellular photosynthetic organisms found scaling exponents intermediate between 0.75 and 1.00.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> Similarly, a 2006 paper in <i>Nature</i> argued that the exponent of mass is close to 1 for plant seedlings, but that variation between species, phyla, and growth conditions overwhelm any "Kleiber's law"-like effects.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> But, metabolic scaling theory can successfully resolve these apparent exceptions and deviations. For finite-size corrections in networks with both area-preserving and area-increasing branching, the WBE model predicts that fits to data for plants yield scaling exponents that are steeper than 3/4 in small plants but then converge to 3/4 in larger plants (see <sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Savage18787686_17-1" class="reference"><a href="#cite_note-Savage18787686-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>). </p> <div class="mw-heading mw-heading3"><h3 id="Intra-organismal_results">Intra-organismal results</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kleiber%27s_law&action=edit&section=12" title="Edit section: Intra-organismal results"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Because cell protoplasm appears to have constant density across a range of organism masses, a consequence of Kleiber's law is that, in larger species, less energy is available to each cell volume. Cells appear to cope with this difficulty via choosing one of the following two strategies: smaller cells or a slower cellular metabolic rate. <a href="/wiki/Neuron" title="Neuron">Neurons</a> and <a href="/wiki/Adipocytes" class="mw-redirect" title="Adipocytes">adipocytes</a> exhibit the former; every other type of cell, the latter.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> As a result, different organs exhibit different allometric scalings (see table).<sup id="cite_ref-History_9-2" class="reference"><a href="#cite_note-History-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><table class="wikitable sortable"> <caption> Allometric scalings for <a href="/wiki/Basal_metabolic_rate" title="Basal metabolic rate">BMR</a>-vs.-mass in human tissue </caption> <tbody><tr> <th>Organ</th> <th>Scaling exponent </th></tr> <tr> <td>Brain</td> <td>0.7 </td></tr> <tr> <td>Kidney</td> <td>0.85 </td></tr> <tr> <td>Liver</td> <td>0.87 </td></tr> <tr> <td>Heart</td> <td>0.98 </td></tr> <tr> <td>Muscle</td> <td>1.0 </td></tr> <tr> <td>Skeleton</td> <td>1.1 </td></tr></tbody></table></dd></dl> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kleiber%27s_law&action=edit&section=13" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Allometric_law" class="mw-redirect" title="Allometric law">Allometric law</a></li> <li><a href="/wiki/Evolutionary_physiology" title="Evolutionary physiology">Evolutionary physiology</a></li> <li><a href="/wiki/Metabolic_theory_of_ecology" title="Metabolic theory of ecology">Metabolic theory of ecology</a></li> <li><a href="/wiki/Scaling_law" class="mw-redirect" title="Scaling law">Scaling law</a></li> <li><a href="/wiki/Rate-of-living_theory" title="Rate-of-living theory">Rate-of-living theory</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kleiber%27s_law&action=edit&section=14" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFKleiber1947" class="citation journal cs1">Kleiber M (October 1947). 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"Re-examination of the "3/4-law" of metabolism". <i>Journal of Theoretical Biology</i>. <b>209</b> (1): 9–27. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/physics/0007096">physics/0007096</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001JThBi.209....9D">2001JThBi.209....9D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1006%2Fjtbi.2000.2238">10.1006/jtbi.2000.2238</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/11237567">11237567</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:9168199">9168199</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Theoretical+Biology&rft.atitle=Re-examination+of+the+%223%2F4-law%22+of+metabolism&rft.volume=209&rft.issue=1&rft.pages=9-27&rft.date=2001-03&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A9168199%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2001JThBi.209....9D&rft_id=info%3Aarxiv%2Fphysics%2F0007096&rft_id=info%3Apmid%2F11237567&rft_id=info%3Adoi%2F10.1006%2Fjtbi.2000.2238&rft.aulast=Dodds&rft.aufirst=PS&rft.au=Rothman%2C+DH&rft.au=Weitz%2C+JS&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKleiber%27s+law" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKolokotronesDeedsFontana2010" class="citation journal cs1">Kolokotrones T, Deeds EJ, Fontana W (April 2010). "Curvature in metabolic scaling". <i>Nature</i>. <b>464</b> (7289): 753–6. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2010Natur.464..753K">2010Natur.464..753K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnature08920">10.1038/nature08920</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/20360740">20360740</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4374163">4374163</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Curvature+in+metabolic+scaling&rft.volume=464&rft.issue=7289&rft.pages=753-6&rft.date=2010-04&rft_id=info%3Adoi%2F10.1038%2Fnature08920&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4374163%23id-name%3DS2CID&rft_id=info%3Apmid%2F20360740&rft_id=info%3Abibcode%2F2010Natur.464..753K&rft.aulast=Kolokotrones&rft.aufirst=T&rft.au=Deeds%2C+EJ&rft.au=Fontana%2C+W&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKleiber%27s+law" class="Z3988"></span> <br />But note that a quadratic curve has undesirable theoretical implications; see <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMacKay2011" class="citation journal cs1">MacKay NJ (July 2011). "Mass scale and curvature in metabolic scaling. Comment on: T. Kolokotrones et al., curvature in metabolic scaling, Nature 464 (2010) 753-756". <i>Journal of Theoretical Biology</i>. <b>280</b> (1): 194–6. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011JThBi.280..194M">2011JThBi.280..194M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.jtbi.2011.02.011">10.1016/j.jtbi.2011.02.011</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/21335012">21335012</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Theoretical+Biology&rft.atitle=Mass+scale+and+curvature+in+metabolic+scaling.+Comment+on%3A+T.+Kolokotrones+et+al.%2C+curvature+in+metabolic+scaling%2C+Nature+464+%282010%29+753-756&rft.volume=280&rft.issue=1&rft.pages=194-6&rft.date=2011-07&rft_id=info%3Apmid%2F21335012&rft_id=info%3Adoi%2F10.1016%2Fj.jtbi.2011.02.011&rft_id=info%3Abibcode%2F2011JThBi.280..194M&rft.aulast=MacKay&rft.aufirst=NJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKleiber%27s+law" class="Z3988"></span></span> </li> <li id="cite_note-ArbNetworks-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-ArbNetworks_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ArbNetworks_16-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBanavarMosesBrownDamuth2010" class="citation journal cs1">Banavar JR, Moses ME, Brown JH, Damuth J, Rinaldo A, Sibly RM, Maritan A (September 2010). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2936637">"A general basis for quarter-power scaling in animals"</a>. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. <b>107</b> (36): 15816–20. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2010PNAS..10715816B">2010PNAS..10715816B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.1009974107">10.1073/pnas.1009974107</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2936637">2936637</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/20724663">20724663</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+National+Academy+of+Sciences+of+the+United+States+of+America&rft.atitle=A+general+basis+for+quarter-power+scaling+in+animals&rft.volume=107&rft.issue=36&rft.pages=15816-20&rft.date=2010-09&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC2936637%23id-name%3DPMC&rft_id=info%3Apmid%2F20724663&rft_id=info%3Adoi%2F10.1073%2Fpnas.1009974107&rft_id=info%3Abibcode%2F2010PNAS..10715816B&rft.aulast=Banavar&rft.aufirst=JR&rft.au=Moses%2C+ME&rft.au=Brown%2C+JH&rft.au=Damuth%2C+J&rft.au=Rinaldo%2C+A&rft.au=Sibly%2C+RM&rft.au=Maritan%2C+A&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC2936637&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKleiber%27s+law" class="Z3988"></span></span> </li> <li id="cite_note-Savage18787686-17"><span class="mw-cite-backlink">^ <a href="#cite_ref-Savage18787686_17-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Savage18787686_17-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSavageDeedsFontana2008" class="citation journal cs1">Savage VM, Deeds EJ, Fontana W (September 2008). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2518954">"Sizing up allometric scaling theory"</a>. <i>PLOS Computational Biology</i>. <b>4</b> (9): e1000171. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008PLSCB...4E0171S">2008PLSCB...4E0171S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1371%2Fjournal.pcbi.1000171">10.1371/journal.pcbi.1000171</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2518954">2518954</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/18787686">18787686</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=PLOS+Computational+Biology&rft.atitle=Sizing+up+allometric+scaling+theory&rft.volume=4&rft.issue=9&rft.pages=e1000171&rft.date=2008-09&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC2518954%23id-name%3DPMC&rft_id=info%3Apmid%2F18787686&rft_id=info%3Adoi%2F10.1371%2Fjournal.pcbi.1000171&rft_id=info%3Abibcode%2F2008PLSCB...4E0171S&rft.aulast=Savage&rft.aufirst=VM&rft.au=Deeds%2C+EJ&rft.au=Fontana%2C+W&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC2518954&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKleiber%27s+law" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFApolEtienneOlff2008" class="citation journal cs1">Apol ME, Etienne RS, Olff H (2008). <a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-2435.2008.01458.x">"Revisiting the evolutionary origin of allometric metabolic scaling in biology"</a>. <i>Functional Ecology</i>. <b>22</b> (6): 1070–1080. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008FuEco..22.1070A">2008FuEco..22.1070A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-2435.2008.01458.x">10.1111/j.1365-2435.2008.01458.x</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Functional+Ecology&rft.atitle=Revisiting+the+evolutionary+origin+of+allometric+metabolic+scaling+in+biology&rft.volume=22&rft.issue=6&rft.pages=1070-1080&rft.date=2008&rft_id=info%3Adoi%2F10.1111%2Fj.1365-2435.2008.01458.x&rft_id=info%3Abibcode%2F2008FuEco..22.1070A&rft.aulast=Apol&rft.aufirst=ME&rft.au=Etienne%2C+RS&rft.au=Olff%2C+H&rft_id=https%3A%2F%2Fdoi.org%2F10.1111%252Fj.1365-2435.2008.01458.x&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKleiber%27s+law" class="Z3988"></span></span> </li> <li id="cite_note-Savage_2004-19"><span class="mw-cite-backlink">^ <a href="#cite_ref-Savage_2004_19-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Savage_2004_19-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSavageGilloolyWoodruffWest2004" class="citation journal 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(1997), which derives a model for the mammalian arterial system, predicts that smaller mammals should show consistent deviations in the direction of higher metabolic rates than expected from <span class="texhtml"><i>M</i><sup><sup>3</sup>⁄<sub>4</sub></sup></span> scaling. 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title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Biological+scaling%3A+does+the+exception+prove+the+rule%3F&rft.volume=445&rft.issue=7127&rft.pages=E9-10%2C+discussion+E10-1&rft.date=2007-02&rft_id=info%3Adoi%2F10.1038%2Fnature05548&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A43905935%23id-name%3DS2CID&rft_id=info%3Apmid%2F17268426&rft_id=info%3Abibcode%2F2007Natur.445....9E&rft.aulast=Enquist&rft.aufirst=BJ&rft.au=Allen%2C+AP&rft.au=Brown%2C+JH&rft.au=Gillooly%2C+JF&rft.au=Kerkhoff%2C+AJ&rft.au=Niklas%2C+KJ&rft.au=Price%2C+CA&rft.au=West%2C+GB&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKleiber%27s+law" class="Z3988"></span> and associated responses </span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSavageAllenBrownGillooly2007" class="citation journal cs1">Savage VM, Allen AP, Brown JH, Gillooly JF, Herman AB, Woodruff WH, West GB (March 2007). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1838666">"Scaling of number, size, and metabolic rate of cells with body size in mammals"</a>. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. <b>104</b> (11): 4718–23. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007PNAS..104.4718S">2007PNAS..104.4718S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.0611235104">10.1073/pnas.0611235104</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1838666">1838666</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17360590">17360590</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+National+Academy+of+Sciences+of+the+United+States+of+America&rft.atitle=Scaling+of+number%2C+size%2C+and+metabolic+rate+of+cells+with+body+size+in+mammals&rft.volume=104&rft.issue=11&rft.pages=4718-23&rft.date=2007-03&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1838666%23id-name%3DPMC&rft_id=info%3Apmid%2F17360590&rft_id=info%3Adoi%2F10.1073%2Fpnas.0611235104&rft_id=info%3Abibcode%2F2007PNAS..104.4718S&rft.aulast=Savage&rft.aufirst=VM&rft.au=Allen%2C+AP&rft.au=Brown%2C+JH&rft.au=Gillooly%2C+JF&rft.au=Herman%2C+AB&rft.au=Woodruff%2C+WH&rft.au=West%2C+GB&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1838666&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKleiber%27s+law" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kleiber%27s_law&action=edit&section=15" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRau2002" class="citation journal cs1">Rau AR (September 2002). 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Washington, D.C.: Joseph Henry Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780309096812" title="Special:BookSources/9780309096812"><bdi>9780309096812</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=In+the+Beat+of+a+Heart&rft.place=Washington%2C+D.C.&rft.pub=Joseph+Henry+Press&rft.date=2006&rft.isbn=9780309096812&rft.aulast=Whitfield&rft.aufirst=J&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Finbeatofheart00whit&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKleiber%27s+law" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGlazier2010" class="citation journal cs1">Glazier DS (February 2010). 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Archived from <a rel="nofollow" class="external text" href="http://courses.missouristate.edu/mcb095f/bio121/lab/Respiration/of_mice_and_elephants.htm">the original</a> on 3 December 2008.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Of+mice+and+Elephants&rft.date=1999-01-12&rft.aulast=Johnson&rft.aufirst=G&rft_id=http%3A%2F%2Fcourses.missouristate.edu%2Fmcb095f%2Fbio121%2Flab%2FRespiration%2Fof_mice_and_elephants.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKleiber%27s+law" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWoolley" class="citation web cs1">Woolley T. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170522031206/http://www.numberphile.com/videos/kleibers.html">"3/4 and Kleiber's Law"</a>. <i>Numberphile</i>. <a href="/wiki/Brady_Haran" title="Brady Haran">Brady Haran</a>. Archived from <a rel="nofollow" class="external text" href="http://www.numberphile.com/videos/kleibers.html">the original</a> on 2017-05-22<span class="reference-accessdate">. Retrieved <span class="nowrap">2013-04-01</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Numberphile&rft.atitle=3%2F4+and+Kleiber%27s+Law&rft.aulast=Woolley&rft.aufirst=T&rft_id=http%3A%2F%2Fwww.numberphile.com%2Fvideos%2Fkleibers.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKleiber%27s+law" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmil2000" class="citation journal cs1">Smil, V. (2000). <a rel="nofollow" class="external text" href="https://www.nature.com/articles/35001159">"Laying down the law"</a>. <i>Nature</i>. <b>403</b> (6770): 597. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000Natur.403..597S">2000Natur.403..597S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F35001159">10.1038/35001159</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10688176">10688176</a>.</cite><span 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href="/wiki/Template_talk:Modelling_ecosystems" title="Template talk:Modelling ecosystems"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Modelling_ecosystems" title="Special:EditPage/Template:Modelling ecosystems"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Ecology:_Modelling_ecosystems:_Trophic_components" style="font-size:114%;margin:0 4em"><a href="/wiki/Ecology" title="Ecology">Ecology</a>: <a href="/wiki/Ecosystem_model" title="Ecosystem model">Modelling ecosystems</a>: <a href="/wiki/Trophic_level" title="Trophic level">Trophic</a> components</div></th></tr><tr><th scope="row" class="navbox-group" style="width:7.5em">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abiotic_component" title="Abiotic component">Abiotic component</a></li> <li><a href="/wiki/Abiotic_stress" title="Abiotic stress">Abiotic stress</a></li> <li><a href="/wiki/Behavioral_ecology" title="Behavioral ecology">Behaviour</a></li> <li><a href="/wiki/Biogeochemical_cycle" title="Biogeochemical cycle">Biogeochemical cycle</a></li> <li><a href="/wiki/Biomass_(ecology)" title="Biomass (ecology)">Biomass</a></li> <li><a href="/wiki/Biotic_component" class="mw-redirect" title="Biotic component">Biotic component</a></li> <li><a href="/wiki/Biotic_stress" title="Biotic stress">Biotic stress</a></li> <li><a href="/wiki/Carrying_capacity" title="Carrying capacity">Carrying capacity</a></li> <li><a href="/wiki/Competition_(biology)" title="Competition (biology)">Competition</a></li> <li><a href="/wiki/Ecosystem" title="Ecosystem">Ecosystem</a></li> <li><a href="/wiki/Ecosystem_ecology" title="Ecosystem ecology">Ecosystem ecology</a></li> <li><a href="/wiki/Ecosystem_model" title="Ecosystem model">Ecosystem model</a></li> <li><a href="/wiki/Green_world_hypothesis" title="Green world hypothesis">Green world hypothesis</a></li> <li><a href="/wiki/Keystone_species" title="Keystone species">Keystone species</a></li> <li><a href="/wiki/List_of_feeding_behaviours" title="List of feeding behaviours">List of feeding behaviours</a></li> <li><a href="/wiki/Metabolic_theory_of_ecology" title="Metabolic theory of ecology">Metabolic theory of ecology</a></li> <li><a href="/wiki/Productivity_(ecology)" title="Productivity (ecology)">Productivity</a></li> <li><a href="/wiki/Resource_(biology)" title="Resource (biology)">Resource</a></li> <li><a href="/wiki/Restoration_ecology" class="mw-redirect" title="Restoration ecology">Restoration</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.5em"><a href="/wiki/Autotroph" title="Autotroph">Producers</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Autotroph" title="Autotroph">Autotrophs</a></li> <li><a href="/wiki/Chemosynthesis" title="Chemosynthesis">Chemosynthesis</a></li> <li><a href="/wiki/Chemotroph" title="Chemotroph">Chemotrophs</a></li> <li><a href="/wiki/Foundation_species" title="Foundation species">Foundation species</a></li> <li><a href="/wiki/Kinetotroph" title="Kinetotroph">Kinetotrophs</a></li> <li><a href="/wiki/Mixotroph" title="Mixotroph">Mixotrophs</a></li> <li><a href="/wiki/Myco-heterotrophy" title="Myco-heterotrophy">Myco-heterotrophy</a></li> <li><a href="/wiki/Mycotroph" title="Mycotroph">Mycotroph</a></li> <li><a href="/wiki/Organotroph" title="Organotroph">Organotrophs</a></li> <li><a href="/wiki/Photoheterotroph" title="Photoheterotroph">Photoheterotrophs</a></li> <li><a href="/wiki/Photosynthesis" title="Photosynthesis">Photosynthesis</a></li> <li><a href="/wiki/Photosynthetic_efficiency" title="Photosynthetic efficiency">Photosynthetic efficiency</a></li> <li><a href="/wiki/Phototroph" title="Phototroph">Phototrophs</a></li> <li><a href="/wiki/Primary_nutritional_groups" title="Primary nutritional groups">Primary nutritional groups</a></li> <li><a href="/wiki/Primary_production" title="Primary production">Primary production</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.5em"><a href="/wiki/Consumer_(food_chain)" title="Consumer (food chain)">Consumers</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Apex_predator" title="Apex predator">Apex predator</a></li> <li><a href="/wiki/Bacterivore" title="Bacterivore">Bacterivore</a></li> <li><a href="/wiki/Carnivore" title="Carnivore">Carnivores</a></li> <li><a href="/wiki/Chemoorganotroph" class="mw-redirect" title="Chemoorganotroph">Chemoorganotroph</a></li> <li><a href="/wiki/Foraging" title="Foraging">Foraging</a></li> <li><a href="/wiki/Generalist_and_specialist_species" title="Generalist and specialist species">Generalist and specialist species</a></li> <li><a href="/wiki/Intraguild_predation" title="Intraguild predation">Intraguild predation</a></li> <li><a href="/wiki/Herbivore" title="Herbivore">Herbivores</a></li> <li><a href="/wiki/Heterotroph" title="Heterotroph">Heterotroph</a></li> <li><a href="/wiki/Heterotrophic_nutrition" title="Heterotrophic nutrition">Heterotrophic nutrition</a></li> <li><a href="/wiki/Insectivore" title="Insectivore">Insectivore</a></li> <li><a href="/wiki/Mesopredator" title="Mesopredator">Mesopredators</a></li> <li><a href="/wiki/Mesopredator_release_hypothesis" title="Mesopredator release hypothesis">Mesopredator release hypothesis</a></li> <li><a href="/wiki/Omnivore" title="Omnivore">Omnivores</a></li> <li><a href="/wiki/Optimal_foraging_theory" title="Optimal foraging theory">Optimal foraging theory</a></li> <li><a href="/wiki/Planktivore" title="Planktivore">Planktivore</a></li> <li><a href="/wiki/Predation" title="Predation">Predation</a></li> <li><a href="/wiki/Prey_switching" title="Prey switching">Prey switching</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.5em"><a href="/wiki/Decomposer" title="Decomposer">Decomposers</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chemoorganoheterotrophy" class="mw-redirect" title="Chemoorganoheterotrophy">Chemoorganoheterotrophy</a></li> <li><a href="/wiki/Decomposition" title="Decomposition">Decomposition</a></li> <li><a href="/wiki/Detritivore" title="Detritivore">Detritivores</a></li> <li><a href="/wiki/Detritus" title="Detritus">Detritus</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.5em"><a href="/wiki/Microorganism#Habitats_and_ecology" title="Microorganism">Microorganisms</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Archaea" title="Archaea">Archaea</a></li> <li><a href="/wiki/Bacteriophage" title="Bacteriophage">Bacteriophage</a></li> <li><a href="/wiki/Lithoautotroph" title="Lithoautotroph">Lithoautotroph</a></li> <li><a href="/wiki/Lithotroph" title="Lithotroph">Lithotrophy</a></li> <li><a href="/wiki/Marine_microorganisms" title="Marine microorganisms">Marine</a></li> <li><a href="/wiki/Microbial_cooperation" title="Microbial cooperation">Microbial cooperation</a></li> <li><a href="/wiki/Microbial_ecology" title="Microbial ecology">Microbial ecology</a></li> <li><a href="/wiki/Microbial_food_web" title="Microbial food web">Microbial food web</a></li> <li><a href="/wiki/Microbial_intelligence" title="Microbial intelligence">Microbial intelligence</a></li> <li><a href="/wiki/Microbial_loop" title="Microbial loop">Microbial loop</a></li> <li><a href="/wiki/Microbial_mat" title="Microbial mat">Microbial mat</a></li> <li><a href="/wiki/Microbial_metabolism" title="Microbial metabolism">Microbial metabolism</a></li> <li><a href="/wiki/Phage_ecology" title="Phage ecology">Phage ecology</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.5em"><a href="/wiki/Food_web" title="Food web">Food webs</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biomagnification" title="Biomagnification">Biomagnification</a></li> <li><a href="/wiki/Ecological_efficiency" title="Ecological efficiency">Ecological efficiency</a></li> <li><a href="/wiki/Ecological_pyramid" title="Ecological pyramid">Ecological pyramid</a></li> <li><a href="/wiki/Energy_flow_(ecology)" title="Energy flow (ecology)">Energy flow</a></li> <li><a href="/wiki/Food_chain" title="Food chain">Food chain</a></li> <li><a href="/wiki/Trophic_level" title="Trophic level">Trophic level</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.5em">Example webs</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Lake_ecosystem#Trophic_relationships" title="Lake ecosystem">Lakes</a></li> <li><a href="/wiki/River_ecosystem#Trophic_relationships" title="River ecosystem">Rivers</a></li> <li><a href="/wiki/Soil_food_web" title="Soil food web">Soil</a></li> <li><a href="/wiki/Tritrophic_interactions_in_plant_defense" title="Tritrophic interactions in plant defense">Tritrophic interactions in plant defense</a></li> <li><a href="/wiki/Marine_food_web" title="Marine food web">Marine food webs</a> <ul><li><a href="/wiki/Cold_seep" title="Cold seep">cold seeps</a></li> <li><a href="/wiki/Hydrothermal_vent#Biological_communities" title="Hydrothermal vent">hydrothermal vents</a></li> <li><a href="/wiki/Intertidal_ecology" title="Intertidal ecology">intertidal</a></li> <li><a href="/wiki/Kelp_forest#Trophic_ecology" title="Kelp forest">kelp forests</a></li> <li><a href="/wiki/North_Pacific_Gyre" title="North Pacific Gyre">North Pacific Gyre</a></li> <li><a href="/wiki/Ecology_of_the_San_Francisco_Estuary#Food_web" title="Ecology of the San Francisco Estuary">San Francisco Estuary</a></li> <li><a href="/wiki/Tide_pool" title="Tide pool">tide pool</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.5em">Processes</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ascendency" title="Ascendency">Ascendency</a></li> <li><a href="/wiki/Bioaccumulation" title="Bioaccumulation">Bioaccumulation</a></li> <li><a href="/wiki/Cascade_effect_(ecology)" title="Cascade effect (ecology)">Cascade effect</a></li> <li><a href="/wiki/Climax_community" title="Climax community">Climax community</a></li> <li><a href="/wiki/Competitive_exclusion_principle" title="Competitive exclusion principle">Competitive exclusion principle</a></li> <li><a href="/wiki/Consumer%E2%80%93resource_interactions" title="Consumer–resource interactions">Consumer–resource interactions</a></li> <li><a href="/wiki/Copiotroph" title="Copiotroph">Copiotrophs</a></li> <li><a href="/wiki/Dominance_(ecology)" title="Dominance (ecology)">Dominance</a></li> <li><a href="/wiki/Ecological_network" title="Ecological network">Ecological network</a></li> <li><a href="/wiki/Ecological_succession" title="Ecological succession">Ecological succession</a></li> <li><a href="/wiki/Energy_quality" title="Energy quality">Energy quality</a></li> <li><a href="/wiki/Energy_systems_language" title="Energy systems language">Energy systems language</a></li> <li><a href="/wiki/F-ratio_(oceanography)" title="F-ratio (oceanography)">f-ratio</a></li> <li><a href="/wiki/Feed_conversion_ratio" title="Feed conversion ratio">Feed conversion ratio</a></li> <li><a href="/wiki/Feeding_frenzy" title="Feeding frenzy">Feeding frenzy</a></li> <li><a href="/wiki/Mesotrophic_soil" title="Mesotrophic soil">Mesotrophic soil</a></li> <li><a href="/wiki/Nutrient_cycle" title="Nutrient cycle">Nutrient cycle</a></li> <li><a href="/wiki/Oligotroph" title="Oligotroph">Oligotroph</a></li> <li><a href="/wiki/Paradox_of_the_plankton" title="Paradox of the plankton">Paradox of the plankton</a></li> <li><a href="/wiki/Trophic_cascade" title="Trophic cascade">Trophic cascade</a></li> <li><a href="/wiki/Trophic_mutualism" title="Trophic mutualism">Trophic mutualism</a></li> <li><a href="/wiki/Trophic_state_index" title="Trophic state index">Trophic state index</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.5em">Defense,<br />counter</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Animal_coloration" title="Animal coloration">Animal coloration</a></li> <li><a href="/wiki/Anti-predator_adaptation" title="Anti-predator adaptation">Anti-predator adaptations</a></li> <li><a href="/wiki/Camouflage" title="Camouflage">Camouflage</a></li> <li><a href="/wiki/Deimatic_behaviour" title="Deimatic behaviour">Deimatic behaviour</a></li> <li><a href="/wiki/Herbivore_adaptations_to_plant_defense" title="Herbivore adaptations to plant defense">Herbivore adaptations to plant defense</a></li> <li><a href="/wiki/Mimicry" title="Mimicry">Mimicry</a></li> <li><a href="/wiki/Plant_defense_against_herbivory" title="Plant defense against herbivory">Plant defense against herbivory</a></li> <li><a href="/wiki/Shoaling_and_schooling#Predator_avoidance" title="Shoaling and schooling">Predator avoidance in schooling fish</a></li></ul> </div></td></tr></tbody></table></div><div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Ecology:_Modelling_ecosystems:_Other_components" style="padding:3px"><table class="nowraplinks hlist mw-collapsible uncollapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Modelling_ecosystems" title="Template:Modelling ecosystems"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Modelling_ecosystems" title="Template talk:Modelling ecosystems"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Modelling_ecosystems" title="Special:EditPage/Template:Modelling ecosystems"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Ecology:_Modelling_ecosystems:_Other_components" style="font-size:114%;margin:0 4em"><a href="/wiki/Ecology" title="Ecology">Ecology</a>: <a href="/wiki/Ecosystem_model" title="Ecosystem model">Modelling ecosystems</a>: Other components</div></th></tr><tr><th scope="row" class="navbox-group" style="width:7.5em"><a href="/wiki/Population_ecology" title="Population ecology">Population<br />ecology</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abundance_(ecology)" title="Abundance (ecology)">Abundance</a></li> <li><a href="/wiki/Allee_effect" title="Allee effect">Allee effect</a></li> <li><a href="/wiki/Consumer-resource_model" title="Consumer-resource model">Consumer-resource model</a></li> <li><a href="/wiki/Depensation" title="Depensation">Depensation</a></li> <li><a href="/wiki/Ecological_yield" title="Ecological yield">Ecological yield</a></li> <li><a href="/wiki/Effective_population_size" title="Effective population size">Effective population size</a></li> <li><a href="/wiki/Intraspecific_competition" title="Intraspecific competition">Intraspecific competition</a></li> <li><a href="/wiki/Logistic_function" title="Logistic function">Logistic function</a></li> <li><a href="/wiki/Malthusian_growth_model" title="Malthusian growth model">Malthusian growth model</a></li> <li><a href="/wiki/Maximum_sustainable_yield" title="Maximum sustainable yield">Maximum sustainable yield</a></li> <li><a href="/wiki/Overpopulation" title="Overpopulation">Overpopulation</a></li> <li><a href="/wiki/Overexploitation" title="Overexploitation">Overexploitation</a></li> <li><a href="/wiki/Population_cycle" title="Population cycle">Population cycle</a></li> <li><a href="/wiki/Population_dynamics" title="Population dynamics">Population dynamics</a></li> <li><a href="/wiki/Population_model" title="Population model">Population modeling</a></li> <li><a href="/wiki/Population_size" title="Population size">Population size</a></li> <li><a href="/wiki/Lotka%E2%80%93Volterra_equations" title="Lotka–Volterra equations">Predator–prey (Lotka–Volterra) equations</a></li> <li><a href="/wiki/Recruitment_(biology)" title="Recruitment (biology)">Recruitment</a></li> <li><a href="/wiki/Small_population_size" title="Small population size">Small population size</a></li> <li><a href="/wiki/Ecological_stability" title="Ecological stability">Stability</a> <ul><li><a href="/wiki/Ecological_resilience" title="Ecological resilience">Resilience</a></li> <li><a href="/wiki/Resistance_(ecology)" title="Resistance (ecology)">Resistance</a></li></ul></li> <li><a href="/wiki/Random_generalized_Lotka%E2%80%93Volterra_model" title="Random generalized Lotka–Volterra model">Random generalized Lotka–Volterra model</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.5em">Species</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biodiversity" title="Biodiversity">Biodiversity</a></li> <li><a href="/wiki/Density_dependence" title="Density dependence">Density-dependent inhibition</a></li> <li><a href="/wiki/Ecological_effects_of_biodiversity" title="Ecological effects of biodiversity">Ecological effects of biodiversity</a></li> <li><a href="/wiki/Ecological_extinction" title="Ecological extinction">Ecological extinction</a></li> <li><a href="/wiki/Endemism" title="Endemism">Endemic species</a></li> <li><a href="/wiki/Flagship_species" title="Flagship species">Flagship species</a></li> <li><a href="/wiki/Ordination_(statistics)" title="Ordination (statistics)">Gradient analysis</a></li> <li><a href="/wiki/Bioindicator" title="Bioindicator">Indicator species</a></li> <li><a href="/wiki/Introduced_species" title="Introduced species">Introduced species</a></li> <li><a href="/wiki/Invasive_species" title="Invasive species">Invasive species</a> / <a href="/wiki/Native_species" title="Native species">Native species</a></li> <li><a href="/wiki/Latitudinal_gradients_in_species_diversity" title="Latitudinal gradients in species diversity">Latitudinal gradients in species diversity</a></li> <li><a href="/wiki/Minimum_viable_population" title="Minimum viable population">Minimum viable population</a></li> <li><a href="/wiki/Unified_neutral_theory_of_biodiversity" title="Unified neutral theory of biodiversity">Neutral theory</a></li> <li><a href="/wiki/Occupancy%E2%80%93abundance_relationship" title="Occupancy–abundance relationship">Occupancy–abundance relationship</a></li> <li><a href="/wiki/Population_viability_analysis" title="Population viability analysis">Population viability analysis</a></li> <li><a href="/wiki/Priority_effect" title="Priority effect">Priority effect</a></li> <li><a href="/wiki/Rapoport%27s_rule" title="Rapoport's rule">Rapoport's rule</a></li> <li><a href="/wiki/Relative_abundance_distribution" title="Relative abundance distribution">Relative abundance distribution</a></li> <li><a href="/wiki/Relative_species_abundance" title="Relative species abundance">Relative species abundance</a></li> <li><a href="/wiki/Species_diversity" title="Species diversity">Species diversity</a></li> <li><a href="/wiki/Species_homogeneity" title="Species homogeneity">Species homogeneity</a></li> <li><a href="/wiki/Species_richness" title="Species richness">Species richness</a></li> <li><a href="/wiki/Species_distribution" title="Species distribution">Species distribution</a></li> <li><a href="/wiki/Species%E2%80%93area_relationship" title="Species–area relationship">Species–area curve</a></li> <li><a href="/wiki/Umbrella_species" title="Umbrella species">Umbrella species</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.5em">Species<br />interaction</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Antibiosis" title="Antibiosis">Antibiosis</a></li> <li><a href="/wiki/Biological_interaction" title="Biological interaction">Biological interaction</a></li> <li><a href="/wiki/Commensalism" title="Commensalism">Commensalism</a></li> <li><a href="/wiki/Community_(ecology)" title="Community (ecology)">Community ecology</a></li> <li><a href="/wiki/Ecological_facilitation" title="Ecological facilitation">Ecological facilitation</a></li> <li><a href="/wiki/Interspecific_competition" title="Interspecific competition">Interspecific competition</a></li> <li><a href="/wiki/Mutualism_(biology)" title="Mutualism (biology)">Mutualism</a></li> <li><a href="/wiki/Parasitism" title="Parasitism">Parasitism</a></li> <li><a href="/wiki/Storage_effect" title="Storage effect">Storage effect</a></li> <li><a href="/wiki/Symbiosis" title="Symbiosis">Symbiosis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.5em"><a href="/wiki/Spatial_ecology" title="Spatial ecology">Spatial<br />ecology</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biogeography" title="Biogeography">Biogeography</a></li> <li><a href="/wiki/Cross-boundary_subsidy" title="Cross-boundary subsidy">Cross-boundary subsidy</a></li> <li><a href="/wiki/Cline_(biology)" title="Cline (biology)">Ecocline</a></li> <li><a href="/wiki/Ecotone" title="Ecotone">Ecotone</a></li> <li><a href="/wiki/Ecotype" title="Ecotype">Ecotype</a></li> <li><a href="/wiki/Disturbance_(ecology)" title="Disturbance (ecology)">Disturbance</a></li> <li><a href="/wiki/Edge_effects" title="Edge effects">Edge effects</a></li> <li><a href="/wiki/Foster%27s_rule" title="Foster's rule">Foster's rule</a></li> <li><a href="/wiki/Habitat_fragmentation" title="Habitat fragmentation">Habitat fragmentation</a></li> <li><a href="/wiki/Ideal_free_distribution" title="Ideal free distribution">Ideal free distribution</a></li> <li><a href="/wiki/Intermediate_disturbance_hypothesis" title="Intermediate disturbance hypothesis">Intermediate disturbance hypothesis</a></li> <li><a href="/wiki/Insular_biogeography" title="Insular biogeography">Insular biogeography</a></li> <li><a href="/wiki/Land_change_modeling" title="Land change modeling">Land change modeling</a></li> <li><a href="/wiki/Landscape_ecology" title="Landscape ecology">Landscape ecology</a></li> <li><a href="/wiki/Landscape_epidemiology" title="Landscape epidemiology">Landscape epidemiology</a></li> <li><a href="/wiki/Landscape_limnology" title="Landscape limnology">Landscape limnology</a></li> <li><a href="/wiki/Metapopulation" title="Metapopulation">Metapopulation</a></li> <li><a href="/wiki/Patch_dynamics" title="Patch dynamics">Patch dynamics</a></li> <li><a href="/wiki/R/K_selection_theory" title="R/K selection theory"><i>r</i>/<i>K</i> selection theory</a></li> <li><a href="/wiki/Resource_selection_function" title="Resource selection function">Resource selection function</a></li> <li><a href="/wiki/Source%E2%80%93sink_dynamics" title="Source–sink dynamics">Source–sink dynamics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.5em"><a href="/wiki/Ecological_niche" title="Ecological niche">Niche</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ecological_niche" title="Ecological niche">Ecological niche</a></li> <li><a href="/wiki/Ecological_trap" title="Ecological trap">Ecological trap</a></li> <li><a href="/wiki/Ecosystem_engineer" title="Ecosystem engineer">Ecosystem engineer</a></li> <li><a href="/wiki/Species_distribution_modelling" title="Species distribution modelling">Environmental niche modelling</a></li> <li><a href="/wiki/Guild_(ecology)" title="Guild (ecology)">Guild</a></li> <li><a href="/wiki/Habitat" title="Habitat">Habitat</a> <ul><li><a href="/wiki/Marine_habitat" title="Marine habitat">marine habitats</a></li></ul></li> <li><a href="/wiki/Limiting_similarity" title="Limiting similarity">Limiting similarity</a></li> <li><a href="/wiki/Niche_apportionment_models" title="Niche apportionment models">Niche apportionment models</a></li> <li><a href="/wiki/Niche_construction" title="Niche construction">Niche construction</a></li> <li><a href="/wiki/Niche_differentiation" class="mw-redirect" title="Niche differentiation">Niche differentiation</a></li> <li><a href="/wiki/Ontogenetic_niche_shift" title="Ontogenetic niche shift">Ontogenetic niche shift</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.5em"><a href="/wiki/Non-trophic_networks" title="Non-trophic networks">Other<br />networks</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Assembly_rules" title="Assembly rules">Assembly rules</a></li> <li><a href="/wiki/Bateman%27s_principle" title="Bateman's principle">Bateman's principle</a></li> <li><a href="/wiki/Bioluminescence" title="Bioluminescence">Bioluminescence</a></li> <li><a href="/wiki/Ecological_collapse" class="mw-redirect" title="Ecological collapse">Ecological collapse</a></li> <li><a href="/wiki/Ecological_debt" title="Ecological debt">Ecological debt</a></li> <li><a href="/wiki/Ecological_debt" title="Ecological debt">Ecological deficit</a></li> <li><a href="/wiki/Energy_flow_(ecology)" title="Energy flow (ecology)">Ecological energetics</a></li> <li><a href="/wiki/Ecological_indicator" title="Ecological indicator">Ecological indicator</a></li> <li><a href="/wiki/Ecological_threshold" title="Ecological threshold">Ecological threshold</a></li> <li><a href="/wiki/Ecosystem_diversity" title="Ecosystem diversity">Ecosystem diversity</a></li> <li><a href="/wiki/Emergence" title="Emergence">Emergence</a></li> <li><a href="/wiki/Extinction_debt" title="Extinction debt">Extinction debt</a></li> <li><a class="mw-selflink selflink">Kleiber's law</a></li> <li><a href="/wiki/Liebig%27s_law_of_the_minimum" title="Liebig's law of the minimum">Liebig's law of the minimum</a></li> <li><a href="/wiki/Marginal_value_theorem" title="Marginal value theorem">Marginal value theorem</a></li> <li><a href="/wiki/Thorson%27s_rule" title="Thorson's rule">Thorson's rule</a></li> <li><a href="/wiki/Xerosere" title="Xerosere">Xerosere</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.5em">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Allometry" title="Allometry">Allometry</a></li> <li><a href="/wiki/Alternative_stable_state" title="Alternative stable state">Alternative stable state</a></li> <li><a href="/wiki/Balance_of_nature" title="Balance of nature">Balance of nature</a></li> <li><a href="/wiki/Biological_data_visualization" title="Biological data visualization">Biological data visualization</a></li> <li><a href="/wiki/Ecological_economics" title="Ecological economics">Ecological economics</a></li> <li><a href="/wiki/Ecological_footprint" title="Ecological footprint">Ecological footprint</a></li> <li><a href="/wiki/Ecological_forecasting" title="Ecological forecasting">Ecological forecasting</a></li> <li><a href="/wiki/Environmental_humanities" title="Environmental humanities">Ecological humanities</a></li> <li><a href="/wiki/Ecological_stoichiometry" title="Ecological stoichiometry">Ecological stoichiometry</a></li> <li><a href="/wiki/Ecopath" title="Ecopath">Ecopath</a></li> <li><a href="/wiki/Ecosystem_based_fisheries" class="mw-redirect" title="Ecosystem based fisheries">Ecosystem based fisheries</a></li> <li><a href="/wiki/Endolith" title="Endolith">Endolith</a></li> <li><a href="/wiki/Evolutionary_ecology" title="Evolutionary ecology">Evolutionary ecology</a></li> <li><a href="/wiki/Functional_ecology" title="Functional ecology">Functional ecology</a></li> <li><a href="/wiki/Industrial_ecology" title="Industrial ecology">Industrial ecology</a></li> <li><a href="/wiki/Macroecology" title="Macroecology">Macroecology</a></li> <li><a href="/wiki/Microecosystem" title="Microecosystem">Microecosystem</a></li> <li><a href="/wiki/Natural_environment" title="Natural environment">Natural environment</a></li> <li><a href="/wiki/Regime_shift" title="Regime shift">Regime shift</a></li> <li><a href="/wiki/Sexecology" title="Sexecology">Sexecology</a></li> <li><a href="/wiki/Systems_ecology" title="Systems ecology">Systems ecology</a></li> <li><a href="/wiki/Urban_ecology" title="Urban ecology">Urban ecology</a></li> <li><a href="/wiki/Theoretical_ecology" title="Theoretical ecology">Theoretical ecology</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><a href="/wiki/Outline_of_ecology" title="Outline of ecology">Outline of ecology</a></div></td></tr></tbody></table></div>    </div><noscript><img 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