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Encyclopedia of Evolution 4

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Density-dependent selection is a special type of natural selection in which survival and reproduction depend on the population density of other individuals of the same species. Density in this context can be thought of as the number of other individuals nearby. The action of den­ sity-dependent selection may be influenced by the vary­ ing density of neighbors during different life stages. For instance, insect survival from egg to adult may depend on the density of larvae, whereas the number of eggs laid by females may vary with adult density.

Development of Logistic Theory. Robert MacAr­ thur (1962) was the first to develop the mathematical relationship between ecological theories of population growth and the effect of natural selection at different densities. MacArthur accomplished this with the aid of the logistic equation of population growth: This ecolog­ ical model states that populations at low densities will grow exponentially at the intrinsic rate of population growth (r). The logistic model also assumes that, as a population becomes more crowded, the rate of growth declines. The population ceases to grow when it reaches its carrying capacity (K), which is the equilibrium popu­ lation size.

Classical theories of natural selection measured fit­ ness by calculating the intrinsic rate of growth (r) of a population. This parameter tends to be maximized by maximizing fertility and survival at low population den­ sity. MacArthur extended this idea by suggesting that, at high population density, the population size at carrying capacity (K) would be an appropriate measure of fitness. This theory has sometimes been referred to as r and K selection, drawing from the two parameters of the lo­ gistic equation. In 1971, Roughgarden generalized these ideas by suggesting that fitness may be equated with per capita rates of reproduction and population growth. An example of this theory is shown in Figure �t low popu­ lation density, natural selection will favor the increase and ultimate fixation of the >A allele because the � homozygotes have highest fitness. However, at high den­ sity, natural selection would favor increases in the alter­ native �allele. Most importantly, the outcome of evo­ lution depends on the density of the environment.

Trade-offs at Low and High Densities. A key to this theory is the idea of trade-offs. As illustrated in Fig­ ure 1, the genotype that is best at low density has the lowest fitness at high density and vice versa. If these types of trade-offs did not exist, then there would be one best genotype for all environments. Although there are

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55 no first principles that can be invoked to prove that 56 trade-offs exist, there are some simple arguments that 57 suggest this is a reasonable assumption. Martin Cody 58 (1966), first developed this idea in the context of life 59 history evolution. Cody argued that all organisms must 60 contend with limited amounts of time and energy. As 61 soon as they devote more of their time and energy to, 62 say, reproduction, they will have less time and energy 63 for other activities, such as competiting for food. 64 If the trade-off assumption is valid, those populations 65 that have evolved to grow fastest at low density should 66 do poorly at high density and vice versa These ideas 67 have been tested by maintaining populations of fruit flies 68 (Drosophila mewnogaster) at very low and very high 69 densities. After eight generations of evolution, the popu- 70 lation growth rates of the high- and low-density adapted 71 populations differentiated, and the predicted trade-offs 72 were observed (Figure 2). 73 These populations of fruit flies have been studied in 7 4 more detail to determine which traits changed to cause 75 the observed differences in population growth rates. At 76 least three larval behavioral traits become differentiated 77 between the low- and high-density populations. The 78 high-density populations show elevated larval feeding 79 rates compared to the low-density populations. In fruit 80 flies, it is known that high feeding rates translate into 81 increased competitive ability for limited food, which is 82 certainly at a premium in crowded environments. How- 83 ever, larvae with high feeding rates show reduced sur- · 84 vival at low density. Feeding rates then explain, at least 85 in part, the trade-offs observed in Figure 2. When pop- 86 ulations of fruit flies adapted to high larval densities are 87 moved back to low densities, the flies' feeding rates rap- 88 idly evolve to a lower level, presumably as a conse- 89 quence of the reduced survival of fast feeders at low 90 density. Individuals from populations adapted to high 91 density also move greater distances while foraging com- 92 pared to individuals from populations adapted to low 93 density. Finally, larvae from populations that have 94 evolved at high densities are less likely to metamor- 95 phose into adults (pupate) on the surface of the food 96 and tend to crawl farther from the food surface in search 97 of a pupation site. This altered behavior also improves 98 survival because larvae that pupate on the surface of the 99 food in crowded cultures showed greatly elevated mor- 1 00 tality rates. 101 Development of Verbal Theory. At the same time 102 as MacArthur and Roughgarden were developing their 1 03 quantitative theories of density-dependent natural selec- 104 tion, an extensive verbal theory of rand K selection was 105 developed. A verbal theory is simply one in which the 106 major assumptions and conclusions are argued in words 107 without reliance on formal mathematics. Verbal theories 108 are acceptable ways of developing ideas in biology. 109 However, the logic supporting the conclusions of verbal 110 theories is not always as obvious as it is with mathe- 111 matical theories. The verbal theories of rand K selection 112 suggested populations that evolved at high density,

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113 called K-selected, should be composed of individuals 114 with increased competitive ability, larger body size, de- 115 layed reproduction, and repeated reproduction over 116 many years, or iteroparity. Populations evolved at low 117 density, or r-selected, under this theory would display 118 the opposite set of charactertstics: reduced competitive 119 ability, small body size, high levels of reproduction early 120 in life, and survival over fewer reproductive years. 121 Many of the logical flaws with the verbal theory of r 122 and K selection quickly became obvious to many sci- 123 entists. For instance, the mathematical theories devel- 124 oped by Roughgarden and MacArthur do not have adults 125 of different ages; instead, all reproduction takes place 126 at a single instant in time. The verbal theories mistak- 127 enly inferred that the evolution of high carrying capac- 128 ities would lead to adults surviving and reproducing over 129 many years. The demise of the verbal theory was sig- 130 naled by a series of review papers by Steven Stearns in 131 1976 and 1977 that clearly revealed many of the flaws in 132 the verbal theory. 133 Studies of Wtld Populations. How important is 134 density-dependent natural selection in wild popula- 135 tions? This has been a difficult question to answer for 136 several reasons. Much of the early empirical work fo- 137 cused on natural populations that were thought to have 138 experienced different density environments. Any differ- 139 ence among these populations in charactertstics like fer- 140 tility and competitive ability was then attributed to den- 141 sity-dependent natural selection. The problem with 142 these types of studies is that historical information on 143 the past density conditions of populations was often an- 144 ecdotal or incomplete. Likewise, because these natural 145 populations were not under human control, it was often 146 impossible to rule out other factors, such as predation 147 and herbivory, that may have systematically differed be- 148 tween populations. Despite these problems, there are 149 some well-studied natural populations where density- 150 dependent selection is important. 151 Soay sheep in Scotland, for example, show pheno- 152 typic differences in coat color and horn type. Both of 153 these characteristics are under single- or two-locus ge- 154 netic control. Paul Moorcroft and his colleagues (1996) 155 showed that females with dark coats and small twisted 156 horns survived better at low densities than females with 157 light coats and untwisted horns. However, at high popu- 158 lation densities the advantage was reversed. Because 159 population densities vary dramatically in the studied 160 populations, density-dependent selection is probably im- 161 portant for the maintenance of the genetic polymer- 162 phisms in horn shape and coat color. 163 Populations that grow according to the logistic model 164 are expected ultimately to reach an equilibrium size 165 equal to the carrying capacity. However, depending on 166 the characteristics of the population, the approach to 167 this equilibrium can be gradual and smooth, or it may 168 be oscillatory, with the population overshooting and un- 169 dershooting the carrying capacity by decreasing 170 amounts each generation, or some populations may

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171 never settle down to the equilibrium predicted by the 172 logistic equation. These different scenarios reflect dif- 173 ferent kinds of population stability. Just as density-de- 17 4 pendent natural selection may affect population growth 175 rates, it may also affect the stability of population size. 176 Population stability is an important area of biological 177 research because the long-term persistence of popula- 178 tions, especially endangered species, can be affected by 179 their tendency to fluctuate or stabilize. Theoretical work 180 has come up with conflicting predictions. In some cases, 181 density-dependent selection can lead to increased sta- 182 bility of a population, whereas in other cases, stability 183 decreased. There has been one large experiment per- 184 formed with fruit flies. In this study, fruit flies were 185 placed in an environment that caused the population 186 size to fluctuate. Despite evidence of substantial genetic 187 change in these populations as they adapted to the sue- 188 cessive environments, none of these changes appear to 189 have affected the stability of the populations. In this 190 case, the evolution of density-dependent traits did not 191 affect the stability of population size. 192 [See also Fitness; Life History Theory: An Overview; 193 Demography; Genetic Polymorphism; Population Ge- 194 netics.]

me BIBLIOGRAPHY 197 Cody, M. "A General Theory of Clutch Size.• Evolution 20 (1966): 198 174-184. 199 MacArthur, R. H. "Some Generalized Theorems of Natural Selec- 200 tion. • Proceedings of the National Academy of Sciences USA 201 48 (1962): 1893-1897. In this classic paper, MacArthur proposes 202 that fitness be measured by the carrying capacity of the logistic 203 equation at high densities. 204 MacArthur, R. H., and E. 0. Wilson. The Theory of Island Bio- 205 geography. Princeton, N.J., 1967. The authors not only develop 206 the ideas of r and K selection but consider many other inter- 207 esting problems in ecology that influenced research in this area 208 for the next twenty years. 209 Moorcroft, P. R., S. D. Albon, J. M. Pemberton, I. R. Stevenson, and 210 T. H. Cluton-Brock. "Density-dependent Selection in a Fluctu- 211 ating Ungulate Population," Proceedings of the Royal Society 212 of LcmdonB 263 (1996): 31-38. 213 Mueller, L. D. "Theoretical and Empirical examination of Density- 214 dependent Natural Selection." Annual Review of Ecol.ogy and 215 Systematics 28 (1997): 269-288. This is a recent review of sci- 216 entific research in this area 217 Mueller, L. D., and F. J. Ayala "Trade-off between r-selection and 218 K-selection in Drosophila Populations," Proceedings of the Na- 219 tional Academy of Sciences USA 78 (1981): 1303-1305. The 220 authors demonstrate trade-off in population growth rates due 221 to density-dependent natural selection. 222 Mueller, L. D., and A Joshi. Stabuity in Model Populations. Prince- 223 ton, N.J., 2000. Reviews some of the mathematical aspects of 224 population stability analysis and discusses experimental re- 225 search with fruit files on the evolution of stability. 226 Roughgarden, J. "Density-dependent Natural Selection." Ecowgy 52 227 (1971): 453-468. Develops the basic theory and predictions of 228 density-dependent natural selection in a straightforward, clear 229 fashion. 230 Stearns, S. C. "Life History Tactics: A Review of the ideas." Quar- 231 terly Review of Biowgy 51 (1976): 3-47. 232 Stearns, S. C. "The Evolution of Life History Traits: A Critique of 233 the Theory and Review of the Data" Annual Review of Ecow!JY

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234 and Systematics 8 (1977): 145-171. 235 - LAURENCE D. MUELLER 236 237

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Per-Capita Growth Rates

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Population Density

Density-Dependent Selection. F1GURE 1. Per-capita growth rates (fitness) for three genotypes. At low density, the A,A, homozygote has the highest fitness whereas at high density, the A2A2 homozygote has the highest fitness. The heterozygote has intermediate fitness at all densities. (Laurence D. Mueller).

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15 Density-Dependent Selection. FIGURE 2. The per-capita 16 growth rates for populations of fruit flies (Drosophila 17 me/anogaster) that have evolved at either very low density or 18 very high density. The populations that had adapted to low 19 densities for eight generations were tested at one low 20 density (10 adults) and two high densities (500 and 7500 21 adults). The same tests were carried out simultaneously on 22 the populations that had been maintained at very high 23 densities. (Laurence D. Mueller.) 24 25 26 27