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Intra-clade predation facilitates the evolution of larger body size
e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 533–539
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Intra-clade predation facilitates the evolution of larger body size Katsuhiko Yoshida ∗ Biodiversity Conservation Research Project, National Institute for Environmental Studies, 16-2 Onogawa, Tsukuba, Ibaraki 305-8506, Japan
a r t i c l e
i n f o
a b s t r a c t
Article history:
A computer simulation based on a food web model was used to examine whether
Received 10 May 2005
predator–prey interactions facilitate the evolution of larger body size, and if so, what con-
Received in revised form 22
ditions accelerate the body size increase. If predator species were assumed to feed only on
December 2005
smaller prey species, the evolution of larger body size was driven in the food web model.
Accepted 9 February 2006
Intra-clade predation (predator–prey relationship within a same clade) accelerated the body
Published on line 20 March 2006
size increase in the simulation. When predators and prey belong to the same clade, they tend to have similar body sizes; even a slight increase in prey body size reduces predation.
Keywords:
Moreover, in such a case, the former prey readily becomes a predator of its former predator,
Intra-clade predation
because their feeding preferences and characters are similar to each other. Such a reversal
Evolution
of predator–prey relationship forces a stepwise increase in the body size of both species
Body size
in a positive feed back process. The conditions needed for the positive feed back process
Food web model
may exist just after the K/T mass extinction. Thus, the process suggested in this study might explain the rapid evolution of larger body size in mammals at the beginning of the Paleocene. © 2006 Elsevier B.V. All rights reserved.
1.
Introduction
Since Cope (1887) suggested that the body size of animals tends to increase in a particular evolutionary lineage, the evolution of larger body size has been controversial. In the course of this controversy, studies have revealed that the Cope’s socalled rule is not always true (e.g. Stanley, 1973). However, the question of what factor(s) contribute to evolutionary increases in body size is still being argued (Atkinson and Sibly, 1997; Gould, 1997; Alroy, 1998; Bokma, 2001; Burness et al., 2001; Stern, 2001; Belk and Houston, 2002; Maurer, 2002; Knouft and Page, 2003). Several researchers have noted that an animal with a large body size can more easily maintain its body temperature than smaller animals simply because of its larger volume (Bergmann, 1847; Mayr, 1956; Stanley, 1973). Indeed, within
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most mammalian groups, body size tends to increase with increasing latitude (a phenomenon known as Bergmann’s rule, Bergmann, 1847). Other studies focused on the fact that most clades are founded by an ancestor with a small body, because large species became extinct in mass extinction events, such as P/T and K/T boundaries (Raup, 1991; Hayami, 1997; Alroy, 1998). Consequently, the average body size in each clade has inevitably increased along its evolutionary lineage (Stanley, 1973; Alroy, 1998). Other studies suggested the importance of primary production; that is, the body size of animals often increases where and when primary production is high (Burness et al., 2001; Maurer, 2002). In addition, large body size has evolutionary advantages for reproduction (Brown et al., 1993), predation, developing high intelligence with a large brain and having a long life span (Newell, 1949; Kurten, 1953; Rensch, 1959; Gould, 1966; Stanley, 1973). Stanley (1973) said
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that whether the body size of a given species will increase or decrease may be depend on whether the mean size in the original population is smaller or larger than the optimum body size in the niche of the species. Perhaps, the optimum body size is decided by the influence of several factors mentioned above. In food webs, predators are generally larger than prey ´ (Veina, 1985; Warren and Lawton, 1987; Cohen et al., 1993; Pahl-Wostl, 1997; Neubert et al., 2000; Jennings et al., 2001). Thus, the predator–prey relationship is considered to be an important factor in the evolution of larger body size (Stanley, 1973). Few studies examined the details of this process, in part because predator–prey interactions cannot be traced on an evolutionary time scale. In recent years, a few researchers have begun to extract detailed evidence of predation from the fossil record (e.g. Kowalewski and Kelley, 2002; Kelley et al., 2003), but there is not yet sufficient data to trace evolutionary changes in predator–prey relationships. In the present study, computer simulations of the evolution of a model food web (Yoshida, 2002, 2003a) were performed to examine whether predator–prey interactions facilitate the evolution of larger body size, and, if so, what conditions accelerate the evolution.
web, a predator species feeds on a prey species, if the character of the prey is within the range of the feeding preference of the predator. The character of the prey and the feeding preference of the predator are described by arrays of 10 elements, D and A, respectively. Each element of D and A (D[k] and A[k]: the kth element of D and A, respectively) is randomly chosen from the interval [0,100.0]. The range of feeding preference (P) is randomly chosen from the interval [0,10.0]. Whether a predatory species i feeds on a prey species j is judged as follows. First, the number of elements of Dj that satisfy the following condition is counted: Ai [k] − Pi < Dj [k] < Ai [k] + Pi ,
(2)
2.
Methods
where Ai[k] and Dj[k] are the kth elements of A of species i and D of species j, respectively. Next, the number of elements of Dj satisfying the above condition is compared with a random number chosen from the interval [0,10.0]. If the former is larger, species i can feed on species j; that is, aij > 0. In the initial setting, the value of aij is randomly chosen from [0,0.2]. If characters of two plant species are similar to each other, these plants compete with each other. Whether plant species a hinders the growth of plant species b is judged by the same manner described above; that is, the number of elements of Db that satisfy the following condition is counted:
2.1.
Outline of the system
Da [k] − Ca < Db [k] < Da [k] + Ca ,
This study is based on Yoshida (2002, 2003a) food web model. In this model, a food web is represented by the following multidimensional Lotka-Volterra equations:
⎛
⎞
dMi aij Mj ⎠ , = M i ⎝r i + dt n
i = 1, . . . , n
(1)
j=1
where Mi and Mj are the total biomass of species i and j, respectively; ri is the intrinsic growth rate of species i; n is the number of species in the system; aij is the effect of species j on species i. As a result of the calculation, if the total biomass of a species becomes smaller than the individual body size of the species (w, the biomass of one individual of the species), the species becomes extinct. In the initial setting, the value of w is randomly chosen for each species from the interval [0,0.03], and the initial biomass of a species is set to 0.1. In the initial state, the model food web consists of 50 animal and 50 plant species. Each of the 100 initial species is a founder of a clade, which is defined as a group of species derived from a common founder species. Each clade in the model food web is phylogenetically independent of the others. The value of the intrinsic growth rate (r) of a plant species is randomly chosen from the interval [0,2.0], reflecting the fact that plant species conduct primary production. In contrast, r of an animal species is set to zero; that is, an animal species cannot increase its biomass without feeding on other species.
2.2.
Construction of inter-specific interactions
The manner of construction of inter-specific interactions is based on Yoshida (2002, 2003a,b) model. In the model food
(3)
where C is the sensitivity to competition. Next, the number of elements of Dj satisfying the above condition is compared with a random number chosen from the interval [0,10.0]. If, in the initial setting, species a hinders the growth of plant species b (aba < 0), the value of aba is randomly chosen from [−0.2,0]. Diagonal elements of the interaction matrix, aii , represent intra-specific competition coefficients. In this model, plant species with large r values are assumed to suffer from severe intra-specific competition (Yoshida, 2003a). If species i is a plant species, aii is calculated by the following equation: aii = −0.3 −
2.3.
ri × 0.7. 4.0
(4)
Appearance of new species
At every 100 steps, a new species is derived from a randomly chosen species in the model food web. The total biomass of the new species is set to 5% of that of its ancestor species. Variables of the new species are set by adding small values (slight mutations) to those of its ancestor. The values are given for the variables by random numbers drawn from Gaussian distributions with mean 0. The standard deviations of the Gaussian distributions are based on the evolutionary rate (E) of the ancestor; E for each element of A and D, 0.3E for P, 0.1E for r, 0.1E for E and 0.003E for w. In the initial setting, the value of E is drawn from a Gaussian distribution with mean 1.0 and standard deviation 0.1. These standard deviations are set not to exceed 10% of the maximum of each variable. Gradual evolution is thereby realized in the model. Inter-specific interactions of the new species are decided by adding slight mutations to those of its ancestor species. When the new species is judged to feed on one of the prey of
e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 533–539
the ancestor species (using Eq. (2)), the coefficient of interaction between the new species and the prey is set by adding the absolute value of a random number to that between the ancestor and the prey. The random number is drawn from a Gaussian distribution, with mean 0 and standard deviation 0.1E of the new species. When a new species is judged not to feed on a prey of the ancestor, the coefficient of interaction between them is set by subtracting the absolute value of a Gaussian random number (with mean 0 and standard deviation 0.1E of the prey) from the coefficient of interaction between the ancestor and the prey. The coefficient of interaction between the new species and a predator of the ancestor is set in the same manner. Inter-specific interactions between the new species and other species that are neither predator nor prey of the ancestor are decided by the same manner as in the initial setting. At every 500 steps, a new founder species emerges in the system and establishes a new clade. Plant and animal founders appear alternately. Variables and interactions of the new founder species are given in the same manner as in the initial setting. In this study, simulations with 200,000 steps were iterated 20 times. In each simulation, 2100 species (100 initial species and 2000 species appearing during a run: 200,000/100 = 2000) and 500 clades (100 initial clades and 400 clades appearing during a run: 200,000/500 = 400) emerged, and half of them animals. Data for 21,000 animal species (1050 × 20) and 5000 animal clades (500/2 × 20) were analyzed.
2.4.
Assumptions with regard to body size
Because predators are usually larger than their prey in natural ´ communities (Veina, 1985; Warren and Lawton, 1987; Cohen et al., 1993; Pahl-Wostl, 1997; Neubert et al., 2000; Jennings et al., 2001), this relationship was fixed as a rule in the present model (hereafter “the body size assumption”). Animal species can feed on plant species regardless of the body size assumption; however, larger animals are at an advantage over smaller ones, because larger animals can feed on a greater number of prey species. Larger animals, however, generally need much food and larger home ranges than do smaller ones (Palomares and Caro, 1999). Therefore, larger animals experience more severe intraspecific competition than do smaller ones. In the present model, this disadvantage is represented by an intra-specific competition coefficient of species i (aii ) given by the following equation: aii = −0.3 −
wi × 0.7, K
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In this study, three types of simulations were conducted: one with the body size assumption and another without it, and the other without intra-clade simulation (predator–prey relationships within a clade intra-clade predation were assumed to be forbidden). In simulations without the body size assumption or intra-clade predation, K (Eq. (5)) was always set to 0.3.
2.5.
Reality of the food web model
In order to show the reality of a food web model, it is necessary to compare properties of model food web with those of real webs, as Williams and Martinez (2000), Cattin et al. (2004) and Rossberg et al. (2005) did. As a result of comparison, mean values of parameters calculated were quite close to those of real food webs (see Fig. 1 in Yoshida, in press). This result shows the reality of the model.
3.
Results
3.1. Temporal changes in the species diversity and the connectance in the model food web Within the first 100 steps in all simulations, the total species diversity in the model food web decreased from 100 to about 60 species (Fig. 1). Except in simulations without the body size assumption, the total species diversity increased gradually with time (Fig. 1). In the simulations with the body size assumption, a small K value was likely to maintain a high species diversity (Fig. 1). The total species diversity was smallest with the body size assumption and K = 0.3 (about 95 species) and was largest without intra-clade predation (about 150 species, Fig. 1). The evolution of the evolution of predator–prey interactions cannot be examined reliably in the model food web with a low species diversity, because, in such a model, the freedom
(5)
where wi is the body size of species i and K is a constant. If the value of K is small, it is relatively difficult for an animal species to evolve larger body size. As mentioned in Section 1, having a large body size could be advantageous for various life-history traits other than predator–prey interactions. However, those advantages are not considered in order to highlight the effects of predator–prey interaction. In this context, a constant value of r = 0 is assigned to all animal species; that is, all animal species in the model have the same metabolic rate.
Fig. 1 – Temporal changes in species diversity (total number of species) in the model food web. Each data point illustrates the average of 20 simulations. Data are plotted every 4000 steps.
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Fig. 2 – Temporal change in the mean body size in each model food web. See caption of Fig. 1. Fig. 3 – Number of clades involving huge species. of diet choice is restricted severely. The present model with very high species diversity (Fig. 1) can avoid such a problem.
3.2. web
Temporal change in body size in the model food
In the simulation without the body size assumption, the mean body size in the model food web did not change significantly from the initial state: with the body size assumption, however, the mean body size increased with time (Fig. 2). As supposed in Eq. (5), the mean body size tended to increase with the K value, but there was no significant difference in the mean body size between the simulations at K = 0.3 and 0.5 (Fig. 2). In the simulation without intra-clade predation, the mean body size in the model was lower than in any of the simulations with the body size assumption (Fig. 2), even though the K value was set to 0.3. In some simulations, some species achieved a body size larger than 0.06 (four times of the initial value of the mean body size in the model food web). With the body size assumption at K = 0.3, 39 of the 5000 animal clades that emerged in 20 iterations involved such huge species. Among them, intra-clade predation existed in 38 clades. On the other hand, in the simulations without the body size assumption, only four clades involving huge species arose (2 -test: p < 0.001, 2 = 28.49, degree of freedom = 1). The simulations without intra-clade predation generated only 11 clades involving huge species (2 -test: p < 0.001, 2 = 15.68, degree of freedom = 1) (Fig. 3). These results of the simulations suggest that the evolution of larger body size rarely occurred without the body size assumption (i.e. predators not assumed to be larger than prey), and intra-clade predation accelerated the evolution of larger body size.
3.3. Characteristics of predator–prey interaction of clades involving huge species Focused on the result of simulations with the body size assumption at K = 0.3, the body size of the species belonging
to clades involving huge species were compared with those of their predatory species. The difference in body size between predator and prey was significantly smaller in the case of intraclade predation than in the case of inter-clade predation, in which the predator and prey do not belong to a same clades (Fig. 4, p < 0.001, Kolmogorov–Smirnov test). The difference in cumulative relative frequency between the two distributions was largest between 0.01 and 0.012 (the difference = 0.139: Fig. 4). In order to clarify the difference in the predator–prey interactions between clades with and without the evolution of
Fig. 4 – Cumulative relative frequency curves of the difference in body size between predator and prey species. The total number of predator–prey pairs, the mean difference in body size between predator and prey, and the standard deviation of the difference are 16,204, 0.00985, 0.00887 in cases of intra-clade predation and 13,456, 0.012, 0.012 in inter-clade predation, respectively.
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Fig. 5 – The ratio of intra-clade predation to the number of predators. Data for clades involving (upper column) and not involving (lower column) huge species are shown.
larger body size, focusing on the result of simulations with the body size assumption (K = 0.3), properties of predator–prey interactions in 39 clades involving huge species were compared with those of 43 clades which do not involved huge species although they were favored with sufficient chances for the evolution of larger body size. They survived for more than 100,000 steps included more than 10 species each at maximum diversity. One of the conspicuous properties of the predator–prey interactions in the clades involving huge species was a high rate of intra-clade predation: the rate was twice that of the clades not involving huge species (Fig. 5). The clades involving huge species also had a higher frequency of reversals of predator–prey relationship: a descendant species evolved to feed on a predator of the ancestor. The clades involving huge species were larger than twice the frequency of the clades not involving huge species (Fig. 6). 57.6% of the reversals of predator–prey relationship observed in the clades involving huge species were intra-clade predations, and the percentage was significantly larger than 51.1% of those in the clades not involving huge species (p < 0.001, 2 -test, 2 = 12.71, degree of freedom = 1). These results indicate that reversal of predator–prey relationship was closely related to the evolution of larger body size, especially in the case of intra-clade predation.
Fig. 6 – Reversal of predator–prey relationship. Each column represents the proportion of reversals of predator–prey relationships. The hatched area in each column represents intra-clade predation. Of the 8252 predator–prey pairs in the clades involving huge species, reversal of predator–prey relationship occurred in 5065 pairs, among which 2916 cases represented intra-clade predation (57.6%). Of the 9299 predator–prey pairs without huge species, such a reversal occurred in only 2558 pairs, among which 1308 cases represented intra-clade predation (51.1%).
Fig. 7 – Schematic diagram of the evolution of larger body size in predator–prey relationship. Solid arrows represent predator–prey relationships, and broken ones represent ancestor–descendant relationships. The size of each figure is an index of body size. In the case of intra-clade predation (A), species tend to have small size differences. Species c, which is a slightly larger descendant of a, can feed on b, which is a predator of a. In the same manner, d can feed on c. Iterations of such reversals of predation drives the stepwise evolution of larger body size. In the case of inter-clade predation (B), the evolution of larger body size is not driven, because the initial difference in body size between predator and prey tends to be large.
4.
Discussion
4.1.
Evolution of larger body size in the model food web
The results of this study indicate that the model food web with the body size assumption facilitated the evolution of larger body size (Fig. 2). In addition, intra-clade predation accelerated the evolution of larger body size (Figs. 2 and 3). How intra-clade predation forces body size to increase can be explained by the small difference in body size between predator and prey in the case of intra-clade predation (Fig. 4): the small difference is derived from the fact that species belonging to a same clade have similar properties. In the model food web based on the body size assumption, a species can defend itself against its predator if it evolves to a larger size than the predator. In many cases of intra-clade predation, a prey species can readily attain the critical size via a slight increase in body size (Fig. 7A). In addition, species belonging to the same clade have similar feeding preferences. Therefore, in the case of intra-clade predation, if a descendant of a prey species becomes larger than a predator, the descendant is likely to feed on the predator (Fig. 7A); thus, reversal of predator–prey relationship commonly occurs (Fig. 6). To sum up, if intra-clade predation is assumed, a slight increase in body size profits the species in terms of both anti-predatory and predation strategies, causing a positive feedback process (Fig. 7A) and producing many reversals of predator–prey relationships in intra-clade predation (Fig. 6). In this way, species go up a flight of stairs toward large body size.
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In contrast, in the inter-clade case, the difference in body size between predator and prey tends to be large (Fig. 4). If a prey species is much smaller than its predator, a gradual increase in body size barely changes its ability to defend against predation (Fig. 7B). Therefore, reversal of predator-prey relationship is rare in inter-clade predation (Figs. 6 and 7B). In other words, in the case of inter-clade predation, the stairs are to sharp for the prey species to ascend (Fig. 7B). In addition, in inter-clade predation, even if the prey species does evolve to become larger than the predator, reversal of predator–prey relationship would still be rare, because the feeding preference of the former prey scarcely meets the properties of the former predator having no phylogenetic relation to the prey.
4.2.
Has the real world ever seen this process?
The model results suggest that two conditions are necessary for the evolution of larger body size in predator–prey systems: the existence of intra-clade predations (as shown in Fig. 6, inter-clade predation is not forbidden), and a small difference in body size between predator and prey (there is no very large predator). In the present world, the process occurs rarely, because the difference in body size between predator and prey are mainly so large that a prey species can not evolve to be larger than its predator by a gradual increase in ´ body size (Veina, 1985; Warren and Lawton, 1987; Cohen et al., 1993; Pahl-Wostl, 1997; Neubert et al., 2000; Jennings et al., 2001). However, the conditions might have been met just after the K/T mass extinction. There were no large-bodied animals in terrestrial food webs at the beginning of the Paleocene, because large animals such as dinosaurs had become extinct (e.g. Raup, 1991; Alroy, 1998). Fortunately, ancestral mammals survived the mass extinction, and most of them were about the size of rats (Savage and Long, 1986; Ji et al., 2002; Tomida et al., 2002; Weil, 2002). Therefore, the difference in body size among mammals in that period was very small. As inferred from tooth morphology, most Cretaceous mammals are considered to have had a carnivorous diet (e.g. Savage and Long, 1986; Tomida et al., 2002). For example, Eomia, that is the oldest eutherian mammal (Ji et al., 2002), is considered to have been a carnivore or insectivore (Weil, 2002). Cimolestids mammals, which survived the K/T mass extinction, are also considered to have been carnivores or insectivores (Robertson et al., 2004). In addition, judging from the fact that many present-day mammalian predators feed on mammalian prey, mammals apparently meet the feeding preference of mammals themselves. Therefore, intra-clade predation could have occurred in ancestral mammalian clades just after the K/T mass extinction. However, there is no direct evidence of intra-clade predation in mammals just after the K/T mass extinction. Moreover, it is risky for a predator to attack a prey whose body size is similar to its own. However, during that period, ancestral mammals may not have been a position to pick and choose, because they probably suffered from severe starvation owing to the winter like conditions caused by a meteor impact (e.g. Alvarez et al., 1980). In addition, small-bodied mammals, which have high metabolic rates, cannot survive on food without a high assimilation efficiency (Begon et al.,
1996). Therefore, ancestral mammals during that period might have dared to attack prey of similar size, despite of the danger of counterattack. The evolution of larger body size in mammals that occurred at the beginning of the Paleocene might have been facilitated by the process suggested in this study. When the difference in adult body size between predator and prey is slight, the predator could avoid the risk of counterattack by attacking juveniles of the prey species, a case that may appear to violate the body size assumption. Even in this situation, however, the larger species is at an advantage, because adults of the larger species are not preyed on by the smaller species and they produce offspring without the risk of predation. Therefore, the body size assumption could be extended to include such a case, although the rate of body size increase in such a case may be smaller than that in the present simulation with the body size assumption. Intra-clade predation and the resultant positive feedback process cannot explain the evolution of larger body size in herbivorous animals, because the reversal of predator–prey relationship between carnivore and herbivore does not occur. However, the result of the present study shows that, without the positive feedback process, the evolution of larger body size does not go on rapidly (Figs. 2 and 3). As shown by Alroy (1998), the maximum body size of mammal rapidly increased just after the K/T mass extinction, and after that, the evolutionary rate of maximum body size became low. This fact could be interpreted: while intra-clade predation existed, the larger body size evolved rapidly, and, after the predator–prey relationships between carnivorous and herbivorous mammals were established, the speed of the evolution of larger body size slowed down.
5.
Conclusion
The results of simulations based on a food web model with the assumption that predators are larger than prey indicate that intra-clade predation accelerates the evolution of larger body size. Because species belonging to the same clade have similar characteristics, predator and prey have similar body sizes and feeding preferences. Therefore, in cases of intraclade predation, a prey can easily avoid predation by evolving a slightly increased body size, and reversal of predator–prey relationship occurs frequently. Consequently, natural selection would favor stepwise increases in body size between intra-clade predator and prey species. The conditions needed for this scenario, namely the existence of intra-clade predation between species of similar body sizes, might have existed just after the K/T mass extinction. Thus, the rapid evolution of larger body size in mammals at the beginning of the Paleocene could be explained by the process suggested in the present study.
Acknowledgements I especially thank Takao Ubukata, Akio Takenaka and Naoko Egi for their enthusiastic guidance and critical reading of the first draft.
ecological modelling
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Kowalewski, M., Kelley, P.H., 2002. The fossil record of predation. Paleont. Soc. Sp. Pap. 8, 398. Kurten, B., 1953. On the variation and population dynamics of fossil and recent mammal populations. Acta Zool. Fen. 76, 1–122. Maurer, B.A., 2002. Big thinking. Nature 415, 489–491. Mayr, E., 1956. Geographical character gradients and climatic adaptation. Evolution 10, 105–108. Neubert, M.G., Blumenshine, S.C., Duplisea, D.E., Jonsson, T., Rashleigh, B., 2000. Body size and food web structure: testing the equiprobability assumption and the cascade model. Oecologia 123, 241–251. Newell, N.D., 1949. Phyletic size increase -an important trend illustrated by fossil invertebrates. Evolution 3, 103–124. Pahl-Wostl, C., 1997. Dynamic structure of a food web model: comparison with a food chain model. Ecol. Modell. 100, 103–123. Palomares, F., Caro, T.M., 1999. Interspecific killing among mammalian carnivores. Am. Nat. 153, 492–508. Raup, D.M., 1991. Extinction: Bad Genes of Bad Luck. W.W. Norton & Company Inc., New York, 210 pp. Rensch, B., 1959. Evolution Above the Species Level. Columbia University Press, New York, 419 pp. Robertson, D.S., McKenna, M.C., Toon, O.B., Hope, S., Lillegraven, J.A., 2004. Survival in the first hours of the Cenozoic. Geol. Soc. Am. Bull. 116, 760–768. Rossberg, A.G., Matsuda, H., Amemiya, T., Itoh, K., 2005. An explanatory model for food-web structure and evolution. Ecol. Complex 2, 312–321. Savage, R.J.G., Long, M.R., 1986. Mammal Evolution: An Illustrated Guide. British Museum (Natural History), London, 258 pp. Stanley, S.M., 1973. An explanation for Cope’s rule. Evolution 27, 1–26. Stern, D., 2001. Body-size evolution: how to evolve a mammoth moth. Curr. Biol. 11, R917–R919. Tomida, Y., Itou, A., Okamoto, Y., 2002. Illustrated Encyclopaedia of Extinct Mammals. Maruzen Co. Ltd., Tokyo, 222 pp. ´ Veina, A.F., 1985. Empirical relationship between predator and prey size among terrestrial vertebrate predators. Oecologia 67, 555–565. Warren, P.H., Lawton, J.H., 1987. Invertebrate predator-prey body size relationship: an explanation for upper triangular food webs and patterns in food web structure? Oecologia 74, 231–235. Weil, A., 2002. Upwards and onwards. Nature 416, 798–799. Williams, R.J., Martinez, N.D., 2000. Simple rule yield complex food webs. Nature 404, 180–183. Yoshida, K., 2002. Long survival of “living fossils” with low taxonomic diversities in an evolving food web. Paleobiology 28, 464–473. Yoshida, K., 2003a. Evolutionary dynamics of species diversity in an interaction web. Ecol. Modell. 163, 131–143. Yoshida, K., 2003b. Dynamics of evolutionary patterns of clades in food web system model. Ecol. Res. 18, 625–637. Yoshida, K. Effect of the intensity of stochastic disturbance on temporal diversity patterns—a simulation study in evolutionary time scale. Ecol. Modell., in press.
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Intra-clade predation facilitates the evolution of larger body size Katsuhiko Yoshida ∗ Biodiversity Conservation Research Project, National Institute for Environmental Studies, 16-2 Onogawa, Tsukuba, Ibaraki 305-8506, Japan
a r t i c l e
i n f o
a b s t r a c t
Article history:
A computer simulation based on a food web model was used to examine whether
Received 10 May 2005
predator–prey interactions facilitate the evolution of larger body size, and if so, what con-
Received in revised form 22
ditions accelerate the body size increase. If predator species were assumed to feed only on
December 2005
smaller prey species, the evolution of larger body size was driven in the food web model.
Accepted 9 February 2006
Intra-clade predation (predator–prey relationship within a same clade) accelerated the body
Published on line 20 March 2006
size increase in the simulation. When predators and prey belong to the same clade, they tend to have similar body sizes; even a slight increase in prey body size reduces predation.
Keywords:
Moreover, in such a case, the former prey readily becomes a predator of its former predator,
Intra-clade predation
because their feeding preferences and characters are similar to each other. Such a reversal
Evolution
of predator–prey relationship forces a stepwise increase in the body size of both species
Body size
in a positive feed back process. The conditions needed for the positive feed back process
Food web model
may exist just after the K/T mass extinction. Thus, the process suggested in this study might explain the rapid evolution of larger body size in mammals at the beginning of the Paleocene. © 2006 Elsevier B.V. All rights reserved.
1.
Introduction
Since Cope (1887) suggested that the body size of animals tends to increase in a particular evolutionary lineage, the evolution of larger body size has been controversial. In the course of this controversy, studies have revealed that the Cope’s socalled rule is not always true (e.g. Stanley, 1973). However, the question of what factor(s) contribute to evolutionary increases in body size is still being argued (Atkinson and Sibly, 1997; Gould, 1997; Alroy, 1998; Bokma, 2001; Burness et al., 2001; Stern, 2001; Belk and Houston, 2002; Maurer, 2002; Knouft and Page, 2003). Several researchers have noted that an animal with a large body size can more easily maintain its body temperature than smaller animals simply because of its larger volume (Bergmann, 1847; Mayr, 1956; Stanley, 1973). Indeed, within
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most mammalian groups, body size tends to increase with increasing latitude (a phenomenon known as Bergmann’s rule, Bergmann, 1847). Other studies focused on the fact that most clades are founded by an ancestor with a small body, because large species became extinct in mass extinction events, such as P/T and K/T boundaries (Raup, 1991; Hayami, 1997; Alroy, 1998). Consequently, the average body size in each clade has inevitably increased along its evolutionary lineage (Stanley, 1973; Alroy, 1998). Other studies suggested the importance of primary production; that is, the body size of animals often increases where and when primary production is high (Burness et al., 2001; Maurer, 2002). In addition, large body size has evolutionary advantages for reproduction (Brown et al., 1993), predation, developing high intelligence with a large brain and having a long life span (Newell, 1949; Kurten, 1953; Rensch, 1959; Gould, 1966; Stanley, 1973). Stanley (1973) said
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that whether the body size of a given species will increase or decrease may be depend on whether the mean size in the original population is smaller or larger than the optimum body size in the niche of the species. Perhaps, the optimum body size is decided by the influence of several factors mentioned above. In food webs, predators are generally larger than prey ´ (Veina, 1985; Warren and Lawton, 1987; Cohen et al., 1993; Pahl-Wostl, 1997; Neubert et al., 2000; Jennings et al., 2001). Thus, the predator–prey relationship is considered to be an important factor in the evolution of larger body size (Stanley, 1973). Few studies examined the details of this process, in part because predator–prey interactions cannot be traced on an evolutionary time scale. In recent years, a few researchers have begun to extract detailed evidence of predation from the fossil record (e.g. Kowalewski and Kelley, 2002; Kelley et al., 2003), but there is not yet sufficient data to trace evolutionary changes in predator–prey relationships. In the present study, computer simulations of the evolution of a model food web (Yoshida, 2002, 2003a) were performed to examine whether predator–prey interactions facilitate the evolution of larger body size, and, if so, what conditions accelerate the evolution.
web, a predator species feeds on a prey species, if the character of the prey is within the range of the feeding preference of the predator. The character of the prey and the feeding preference of the predator are described by arrays of 10 elements, D and A, respectively. Each element of D and A (D[k] and A[k]: the kth element of D and A, respectively) is randomly chosen from the interval [0,100.0]. The range of feeding preference (P) is randomly chosen from the interval [0,10.0]. Whether a predatory species i feeds on a prey species j is judged as follows. First, the number of elements of Dj that satisfy the following condition is counted: Ai [k] − Pi < Dj [k] < Ai [k] + Pi ,
(2)
2.
Methods
where Ai[k] and Dj[k] are the kth elements of A of species i and D of species j, respectively. Next, the number of elements of Dj satisfying the above condition is compared with a random number chosen from the interval [0,10.0]. If the former is larger, species i can feed on species j; that is, aij > 0. In the initial setting, the value of aij is randomly chosen from [0,0.2]. If characters of two plant species are similar to each other, these plants compete with each other. Whether plant species a hinders the growth of plant species b is judged by the same manner described above; that is, the number of elements of Db that satisfy the following condition is counted:
2.1.
Outline of the system
Da [k] − Ca < Db [k] < Da [k] + Ca ,
This study is based on Yoshida (2002, 2003a) food web model. In this model, a food web is represented by the following multidimensional Lotka-Volterra equations:
⎛
⎞
dMi aij Mj ⎠ , = M i ⎝r i + dt n
i = 1, . . . , n
(1)
j=1
where Mi and Mj are the total biomass of species i and j, respectively; ri is the intrinsic growth rate of species i; n is the number of species in the system; aij is the effect of species j on species i. As a result of the calculation, if the total biomass of a species becomes smaller than the individual body size of the species (w, the biomass of one individual of the species), the species becomes extinct. In the initial setting, the value of w is randomly chosen for each species from the interval [0,0.03], and the initial biomass of a species is set to 0.1. In the initial state, the model food web consists of 50 animal and 50 plant species. Each of the 100 initial species is a founder of a clade, which is defined as a group of species derived from a common founder species. Each clade in the model food web is phylogenetically independent of the others. The value of the intrinsic growth rate (r) of a plant species is randomly chosen from the interval [0,2.0], reflecting the fact that plant species conduct primary production. In contrast, r of an animal species is set to zero; that is, an animal species cannot increase its biomass without feeding on other species.
2.2.
Construction of inter-specific interactions
The manner of construction of inter-specific interactions is based on Yoshida (2002, 2003a,b) model. In the model food
(3)
where C is the sensitivity to competition. Next, the number of elements of Dj satisfying the above condition is compared with a random number chosen from the interval [0,10.0]. If, in the initial setting, species a hinders the growth of plant species b (aba < 0), the value of aba is randomly chosen from [−0.2,0]. Diagonal elements of the interaction matrix, aii , represent intra-specific competition coefficients. In this model, plant species with large r values are assumed to suffer from severe intra-specific competition (Yoshida, 2003a). If species i is a plant species, aii is calculated by the following equation: aii = −0.3 −
2.3.
ri × 0.7. 4.0
(4)
Appearance of new species
At every 100 steps, a new species is derived from a randomly chosen species in the model food web. The total biomass of the new species is set to 5% of that of its ancestor species. Variables of the new species are set by adding small values (slight mutations) to those of its ancestor. The values are given for the variables by random numbers drawn from Gaussian distributions with mean 0. The standard deviations of the Gaussian distributions are based on the evolutionary rate (E) of the ancestor; E for each element of A and D, 0.3E for P, 0.1E for r, 0.1E for E and 0.003E for w. In the initial setting, the value of E is drawn from a Gaussian distribution with mean 1.0 and standard deviation 0.1. These standard deviations are set not to exceed 10% of the maximum of each variable. Gradual evolution is thereby realized in the model. Inter-specific interactions of the new species are decided by adding slight mutations to those of its ancestor species. When the new species is judged to feed on one of the prey of
e c o l o g i c a l m o d e l l i n g 1 9 6 ( 2 0 0 6 ) 533–539
the ancestor species (using Eq. (2)), the coefficient of interaction between the new species and the prey is set by adding the absolute value of a random number to that between the ancestor and the prey. The random number is drawn from a Gaussian distribution, with mean 0 and standard deviation 0.1E of the new species. When a new species is judged not to feed on a prey of the ancestor, the coefficient of interaction between them is set by subtracting the absolute value of a Gaussian random number (with mean 0 and standard deviation 0.1E of the prey) from the coefficient of interaction between the ancestor and the prey. The coefficient of interaction between the new species and a predator of the ancestor is set in the same manner. Inter-specific interactions between the new species and other species that are neither predator nor prey of the ancestor are decided by the same manner as in the initial setting. At every 500 steps, a new founder species emerges in the system and establishes a new clade. Plant and animal founders appear alternately. Variables and interactions of the new founder species are given in the same manner as in the initial setting. In this study, simulations with 200,000 steps were iterated 20 times. In each simulation, 2100 species (100 initial species and 2000 species appearing during a run: 200,000/100 = 2000) and 500 clades (100 initial clades and 400 clades appearing during a run: 200,000/500 = 400) emerged, and half of them animals. Data for 21,000 animal species (1050 × 20) and 5000 animal clades (500/2 × 20) were analyzed.
2.4.
Assumptions with regard to body size
Because predators are usually larger than their prey in natural ´ communities (Veina, 1985; Warren and Lawton, 1987; Cohen et al., 1993; Pahl-Wostl, 1997; Neubert et al., 2000; Jennings et al., 2001), this relationship was fixed as a rule in the present model (hereafter “the body size assumption”). Animal species can feed on plant species regardless of the body size assumption; however, larger animals are at an advantage over smaller ones, because larger animals can feed on a greater number of prey species. Larger animals, however, generally need much food and larger home ranges than do smaller ones (Palomares and Caro, 1999). Therefore, larger animals experience more severe intraspecific competition than do smaller ones. In the present model, this disadvantage is represented by an intra-specific competition coefficient of species i (aii ) given by the following equation: aii = −0.3 −
wi × 0.7, K
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In this study, three types of simulations were conducted: one with the body size assumption and another without it, and the other without intra-clade simulation (predator–prey relationships within a clade intra-clade predation were assumed to be forbidden). In simulations without the body size assumption or intra-clade predation, K (Eq. (5)) was always set to 0.3.
2.5.
Reality of the food web model
In order to show the reality of a food web model, it is necessary to compare properties of model food web with those of real webs, as Williams and Martinez (2000), Cattin et al. (2004) and Rossberg et al. (2005) did. As a result of comparison, mean values of parameters calculated were quite close to those of real food webs (see Fig. 1 in Yoshida, in press). This result shows the reality of the model.
3.
Results
3.1. Temporal changes in the species diversity and the connectance in the model food web Within the first 100 steps in all simulations, the total species diversity in the model food web decreased from 100 to about 60 species (Fig. 1). Except in simulations without the body size assumption, the total species diversity increased gradually with time (Fig. 1). In the simulations with the body size assumption, a small K value was likely to maintain a high species diversity (Fig. 1). The total species diversity was smallest with the body size assumption and K = 0.3 (about 95 species) and was largest without intra-clade predation (about 150 species, Fig. 1). The evolution of the evolution of predator–prey interactions cannot be examined reliably in the model food web with a low species diversity, because, in such a model, the freedom
(5)
where wi is the body size of species i and K is a constant. If the value of K is small, it is relatively difficult for an animal species to evolve larger body size. As mentioned in Section 1, having a large body size could be advantageous for various life-history traits other than predator–prey interactions. However, those advantages are not considered in order to highlight the effects of predator–prey interaction. In this context, a constant value of r = 0 is assigned to all animal species; that is, all animal species in the model have the same metabolic rate.
Fig. 1 – Temporal changes in species diversity (total number of species) in the model food web. Each data point illustrates the average of 20 simulations. Data are plotted every 4000 steps.
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Fig. 2 – Temporal change in the mean body size in each model food web. See caption of Fig. 1. Fig. 3 – Number of clades involving huge species. of diet choice is restricted severely. The present model with very high species diversity (Fig. 1) can avoid such a problem.
3.2. web
Temporal change in body size in the model food
In the simulation without the body size assumption, the mean body size in the model food web did not change significantly from the initial state: with the body size assumption, however, the mean body size increased with time (Fig. 2). As supposed in Eq. (5), the mean body size tended to increase with the K value, but there was no significant difference in the mean body size between the simulations at K = 0.3 and 0.5 (Fig. 2). In the simulation without intra-clade predation, the mean body size in the model was lower than in any of the simulations with the body size assumption (Fig. 2), even though the K value was set to 0.3. In some simulations, some species achieved a body size larger than 0.06 (four times of the initial value of the mean body size in the model food web). With the body size assumption at K = 0.3, 39 of the 5000 animal clades that emerged in 20 iterations involved such huge species. Among them, intra-clade predation existed in 38 clades. On the other hand, in the simulations without the body size assumption, only four clades involving huge species arose (2 -test: p < 0.001, 2 = 28.49, degree of freedom = 1). The simulations without intra-clade predation generated only 11 clades involving huge species (2 -test: p < 0.001, 2 = 15.68, degree of freedom = 1) (Fig. 3). These results of the simulations suggest that the evolution of larger body size rarely occurred without the body size assumption (i.e. predators not assumed to be larger than prey), and intra-clade predation accelerated the evolution of larger body size.
3.3. Characteristics of predator–prey interaction of clades involving huge species Focused on the result of simulations with the body size assumption at K = 0.3, the body size of the species belonging
to clades involving huge species were compared with those of their predatory species. The difference in body size between predator and prey was significantly smaller in the case of intraclade predation than in the case of inter-clade predation, in which the predator and prey do not belong to a same clades (Fig. 4, p < 0.001, Kolmogorov–Smirnov test). The difference in cumulative relative frequency between the two distributions was largest between 0.01 and 0.012 (the difference = 0.139: Fig. 4). In order to clarify the difference in the predator–prey interactions between clades with and without the evolution of
Fig. 4 – Cumulative relative frequency curves of the difference in body size between predator and prey species. The total number of predator–prey pairs, the mean difference in body size between predator and prey, and the standard deviation of the difference are 16,204, 0.00985, 0.00887 in cases of intra-clade predation and 13,456, 0.012, 0.012 in inter-clade predation, respectively.
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Fig. 5 – The ratio of intra-clade predation to the number of predators. Data for clades involving (upper column) and not involving (lower column) huge species are shown.
larger body size, focusing on the result of simulations with the body size assumption (K = 0.3), properties of predator–prey interactions in 39 clades involving huge species were compared with those of 43 clades which do not involved huge species although they were favored with sufficient chances for the evolution of larger body size. They survived for more than 100,000 steps included more than 10 species each at maximum diversity. One of the conspicuous properties of the predator–prey interactions in the clades involving huge species was a high rate of intra-clade predation: the rate was twice that of the clades not involving huge species (Fig. 5). The clades involving huge species also had a higher frequency of reversals of predator–prey relationship: a descendant species evolved to feed on a predator of the ancestor. The clades involving huge species were larger than twice the frequency of the clades not involving huge species (Fig. 6). 57.6% of the reversals of predator–prey relationship observed in the clades involving huge species were intra-clade predations, and the percentage was significantly larger than 51.1% of those in the clades not involving huge species (p < 0.001, 2 -test, 2 = 12.71, degree of freedom = 1). These results indicate that reversal of predator–prey relationship was closely related to the evolution of larger body size, especially in the case of intra-clade predation.
Fig. 6 – Reversal of predator–prey relationship. Each column represents the proportion of reversals of predator–prey relationships. The hatched area in each column represents intra-clade predation. Of the 8252 predator–prey pairs in the clades involving huge species, reversal of predator–prey relationship occurred in 5065 pairs, among which 2916 cases represented intra-clade predation (57.6%). Of the 9299 predator–prey pairs without huge species, such a reversal occurred in only 2558 pairs, among which 1308 cases represented intra-clade predation (51.1%).
Fig. 7 – Schematic diagram of the evolution of larger body size in predator–prey relationship. Solid arrows represent predator–prey relationships, and broken ones represent ancestor–descendant relationships. The size of each figure is an index of body size. In the case of intra-clade predation (A), species tend to have small size differences. Species c, which is a slightly larger descendant of a, can feed on b, which is a predator of a. In the same manner, d can feed on c. Iterations of such reversals of predation drives the stepwise evolution of larger body size. In the case of inter-clade predation (B), the evolution of larger body size is not driven, because the initial difference in body size between predator and prey tends to be large.
4.
Discussion
4.1.
Evolution of larger body size in the model food web
The results of this study indicate that the model food web with the body size assumption facilitated the evolution of larger body size (Fig. 2). In addition, intra-clade predation accelerated the evolution of larger body size (Figs. 2 and 3). How intra-clade predation forces body size to increase can be explained by the small difference in body size between predator and prey in the case of intra-clade predation (Fig. 4): the small difference is derived from the fact that species belonging to a same clade have similar properties. In the model food web based on the body size assumption, a species can defend itself against its predator if it evolves to a larger size than the predator. In many cases of intra-clade predation, a prey species can readily attain the critical size via a slight increase in body size (Fig. 7A). In addition, species belonging to the same clade have similar feeding preferences. Therefore, in the case of intra-clade predation, if a descendant of a prey species becomes larger than a predator, the descendant is likely to feed on the predator (Fig. 7A); thus, reversal of predator–prey relationship commonly occurs (Fig. 6). To sum up, if intra-clade predation is assumed, a slight increase in body size profits the species in terms of both anti-predatory and predation strategies, causing a positive feedback process (Fig. 7A) and producing many reversals of predator–prey relationships in intra-clade predation (Fig. 6). In this way, species go up a flight of stairs toward large body size.
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In contrast, in the inter-clade case, the difference in body size between predator and prey tends to be large (Fig. 4). If a prey species is much smaller than its predator, a gradual increase in body size barely changes its ability to defend against predation (Fig. 7B). Therefore, reversal of predator-prey relationship is rare in inter-clade predation (Figs. 6 and 7B). In other words, in the case of inter-clade predation, the stairs are to sharp for the prey species to ascend (Fig. 7B). In addition, in inter-clade predation, even if the prey species does evolve to become larger than the predator, reversal of predator–prey relationship would still be rare, because the feeding preference of the former prey scarcely meets the properties of the former predator having no phylogenetic relation to the prey.
4.2.
Has the real world ever seen this process?
The model results suggest that two conditions are necessary for the evolution of larger body size in predator–prey systems: the existence of intra-clade predations (as shown in Fig. 6, inter-clade predation is not forbidden), and a small difference in body size between predator and prey (there is no very large predator). In the present world, the process occurs rarely, because the difference in body size between predator and prey are mainly so large that a prey species can not evolve to be larger than its predator by a gradual increase in ´ body size (Veina, 1985; Warren and Lawton, 1987; Cohen et al., 1993; Pahl-Wostl, 1997; Neubert et al., 2000; Jennings et al., 2001). However, the conditions might have been met just after the K/T mass extinction. There were no large-bodied animals in terrestrial food webs at the beginning of the Paleocene, because large animals such as dinosaurs had become extinct (e.g. Raup, 1991; Alroy, 1998). Fortunately, ancestral mammals survived the mass extinction, and most of them were about the size of rats (Savage and Long, 1986; Ji et al., 2002; Tomida et al., 2002; Weil, 2002). Therefore, the difference in body size among mammals in that period was very small. As inferred from tooth morphology, most Cretaceous mammals are considered to have had a carnivorous diet (e.g. Savage and Long, 1986; Tomida et al., 2002). For example, Eomia, that is the oldest eutherian mammal (Ji et al., 2002), is considered to have been a carnivore or insectivore (Weil, 2002). Cimolestids mammals, which survived the K/T mass extinction, are also considered to have been carnivores or insectivores (Robertson et al., 2004). In addition, judging from the fact that many present-day mammalian predators feed on mammalian prey, mammals apparently meet the feeding preference of mammals themselves. Therefore, intra-clade predation could have occurred in ancestral mammalian clades just after the K/T mass extinction. However, there is no direct evidence of intra-clade predation in mammals just after the K/T mass extinction. Moreover, it is risky for a predator to attack a prey whose body size is similar to its own. However, during that period, ancestral mammals may not have been a position to pick and choose, because they probably suffered from severe starvation owing to the winter like conditions caused by a meteor impact (e.g. Alvarez et al., 1980). In addition, small-bodied mammals, which have high metabolic rates, cannot survive on food without a high assimilation efficiency (Begon et al.,
1996). Therefore, ancestral mammals during that period might have dared to attack prey of similar size, despite of the danger of counterattack. The evolution of larger body size in mammals that occurred at the beginning of the Paleocene might have been facilitated by the process suggested in this study. When the difference in adult body size between predator and prey is slight, the predator could avoid the risk of counterattack by attacking juveniles of the prey species, a case that may appear to violate the body size assumption. Even in this situation, however, the larger species is at an advantage, because adults of the larger species are not preyed on by the smaller species and they produce offspring without the risk of predation. Therefore, the body size assumption could be extended to include such a case, although the rate of body size increase in such a case may be smaller than that in the present simulation with the body size assumption. Intra-clade predation and the resultant positive feedback process cannot explain the evolution of larger body size in herbivorous animals, because the reversal of predator–prey relationship between carnivore and herbivore does not occur. However, the result of the present study shows that, without the positive feedback process, the evolution of larger body size does not go on rapidly (Figs. 2 and 3). As shown by Alroy (1998), the maximum body size of mammal rapidly increased just after the K/T mass extinction, and after that, the evolutionary rate of maximum body size became low. This fact could be interpreted: while intra-clade predation existed, the larger body size evolved rapidly, and, after the predator–prey relationships between carnivorous and herbivorous mammals were established, the speed of the evolution of larger body size slowed down.
5.
Conclusion
The results of simulations based on a food web model with the assumption that predators are larger than prey indicate that intra-clade predation accelerates the evolution of larger body size. Because species belonging to the same clade have similar characteristics, predator and prey have similar body sizes and feeding preferences. Therefore, in cases of intraclade predation, a prey can easily avoid predation by evolving a slightly increased body size, and reversal of predator–prey relationship occurs frequently. Consequently, natural selection would favor stepwise increases in body size between intra-clade predator and prey species. The conditions needed for this scenario, namely the existence of intra-clade predation between species of similar body sizes, might have existed just after the K/T mass extinction. Thus, the rapid evolution of larger body size in mammals at the beginning of the Paleocene could be explained by the process suggested in the present study.
Acknowledgements I especially thank Takao Ubukata, Akio Takenaka and Naoko Egi for their enthusiastic guidance and critical reading of the first draft.
ecological modelling
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