The relationship between the duration of food web evolution and the vulnerability to biological invasion

ecological complexity 5 (2008) 86–98

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The relationship between the duration of food web evolution and the vulnerability to biological invasion§ Katsuhiko Yoshida * Population Ecology Section, Environmental Biology Division, National Institute for Environmental Studies, 16-2 Onogawa, Tsukuba, Ibaraki 305-8506 Japan

article info

abstract

Article history:

I conducted computer simulations of food web evolution and investigated the relationship

Received 10 January 2007

between the duration of food web evolution and the vulnerability to biological invasion.

Received in revised form

Model food webs without evolution consisted of animal species with a limited number of

28 June 2007

prey species and producer species with small intrinsic growth rates. Because these species

Accepted 28 June 2007

were not resistant to predation pressure, model food webs without evolution were vulner-

Published on line 20 March 2008

able to invasion of powerful omnivores, which had a wide range of feeding preference and a high ecological efficiency. In model food webs without evolution, the number of animal

Keywords:

species depending on producer species was small. Therefore, if a producer species invaded

Food web evolution

and disturbed the base of such food webs, few animal species became extinct. However,

Food web structure

model food webs with a long time evolution had a structure that a small number of producer

Biological invasion

species supported a large number of animal species. When a producer species invaded and

Computer simulation

disturbed the base of such food webs in this state, many species became extinct by an

Vulnerability to biological invasion

indirect effect. The mean number of prey species of animal species and the mean intrinsic growth rate of producer species increased rapidly in the early stage of evolution. Therefore, in the early stage of food web evolution, food webs were temporarily resistant to invasion of powerful omnivores. However, this resistibility was not maintained for a long time. The result of this study strongly suggests that food webs change with time, and consequently the vulnerability to invasion changes with time. # 2008 Elsevier B.V. All rights reserved.

1.

Introduction

Biological invasion is one of the most serious environmental problems in the world. In order to develop more efficient conservation measures, we must reveal what kinds of species are dangerous for what kinds of community before invasions occur. However, this is hard to investigate by means of experiments or observations in the real world. In some countries with invasive alien species acts, we cannot conduct experiments freely. Even if experiments of invasion are possible, such experiments are very dangerous, because, if §

experimental species happen to escape, some of them may be dangerous invaders. In addition, we must usually wait for a long time to obtain results of experiments or observations in the real world. Therefore, computer simulations using hypothetical community models are very useful. Why are invasive species dangerous? Although interspecific interactions in recipient communities are selected via long-term evolution, invasive species suddenly establish inter-specific interaction without evolutionary processes (Washitani and Yahara, 1996). Then, species vulnerable to invasive species easily become extinct (Frankel and Soule´,

This study is partially supported by Global Environmental Research Fund, Ministry of the Environment, Government of Japan (the study for ecological risk assessment and management of the invasive alien species; representative, Koichi Goka). * Tel.: +81 298 50 2443; fax: +81 29 850 2586. E-mail address: [email protected]. 1476-945X/$ – see front matter # 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ecocom.2008.02.002

ecological complexity 5 (2008) 86–98

1981; Clarke et al., 1984; Hadfield, 1986; Savage, 1987; Griffiths et al., 1993; Rodda et al., 1999; Hasegawa, 1999). Therefore, to assess the risk of biological invasion, the evolutionary background of species and communities should be considered. Each community has its own evolutionary history. For example, some communities on stable continents evolved for a very long time, whereas communities on newly appeared volcanic islands or recently destroyed by catastrophic disturbance (e.g. Thornton et al., 1988; Bush and Whittaker, 1991; Fridriksson and Magnu´sson, 1992; Thornton, 1996; Whittaker et al., 1999) have only short histories. Community structure changes with time, and consequently the vulnerability to invasion may change. Therefore, to assess the risk of biological invasion, we must reveal the relationship between food web evolution and the vulnerability to biological invasion. For this purpose, a community model on an evolutionary time scale is necessary. In recent years, great progress in community models incorporating evolutionary dynamics has been made (Caldarelli et al., 1998; Happel and Stadler, 1998; Amaral and Meyer, 1999; Drossel et al., 2001, 2004; Yoshida, 2002, 2003a, 2006a,b; Tokita and Yasutomi, 2003; Chowdhury and Stauffer, 2004; Rossberg et al., 2005, 2006; Ito and Ikegami, 2006). While some of the models incorporating population dynamics (Caldarelli et al., 1998; Happel and Stadler, 1998; Drossel et al., 2001, 2004; Yoshida, 2002, 2003a, 2006a,b; Tokita and Yasutomi, 2003; Chowdhury and Stauffer, 2004; Ito and Ikegami, 2006) and others not (Amaral and Meyer, 1999; Rossberg et al., 2005, 2006), the former type of models are preferable for the purpose of this study, because only invasive species which increase their number of individuals after invasion have strong impacts on a recipient community. In addition, for simulations of invasive species, models must solve the problem how to construct interactions between species which have never met each other. For solving this problem, it is useful to construct inter-specific interactions based on abstract characters of species (Caldarelli et al., 1998; Drossel et al., 2001, 2004; Yoshida, 2002, 2003a, 2006a,b; Rossberg et al., 2006; Ito and Ikegami, 2006), because, by this method, interspecific interactions can be constructed regardless of the previous histories of species. In addition, because this method can be utilized in all cases of construction of interactions, all inter-specific interactions in the model are equivalent. Therefore, the effect of biological invasion can be assessed accurately. In this study, I conducted a computer simulation of food web evolution by using a modified Yoshida (2002, 2003a, 2006a,b) model, which satisfies the above conditions, and investigated the relationship between the duration of food web evolution and the vulnerability to biological invasion.

2.

Methods

2.1.

Outline of the food web model

The food web model in this study is constructed by modifying my previous food web model. I modified the original model by dividing animals into herbivores (consume producer species),

87

carnivores (consume animal species), and omnivores (consume both animal and producer species), and by adding ecological efficiency, which is assumed to have an inverse relationship to the range of feeding preference (see Section 2.5). In addition, all animal species have negative intrinsic growth rates (see Eq. (3)). In the food web model in this study, inter-specific interactions are determined based on characters of species. Food webs in the model evolve via evolution and immigration of species. Population dynamics is represented by using a simple form Lotka–Volterra equation. The idea for the construction of interactions, that interspecific interactions are determined based on characters of species, is also adopted in the Niche Model (Williams and Martinez, 2000), the Web World Model (Caldarelli et al., 1998; Drossel et al., 2001, 2004), the Matching Model (Rossberg et al., 2005), and the Speciation Model (Rossberg et al., 2006). In the Niche Model, inter-specific interactions are determined based on one-dimensional niche space, and species having a larger niche value are assumed to feed on others having a smaller value. These assumptions may restrict the direction of species evolution, although the model does not consider evolution of species. On the other hand, in my model, inter-specific interactions are determined based on 10-dimensional niche space. Thereby, species can evolve more freely. The Niche Model (Williams and Martinez, 2000), the Matching Model (Rossberg et al., 2005), and the Speciation Model (Rossberg et al., 2006) are known for well reproducing various topological features of real food webs. However, since these models do not incorporate population dynamics, these cannot be utilized for studies for phenomena related to fluctuations of the number of individuals or the amount of biomass, for example, the phenomenon that species invading with a small number of individuals affect recipient ecosystems after those invasive species increase their population. In the Web World Model (Caldarelli et al., 1998; Drossel et al., 2001, 2004) and my model, inter-specific interactions are determined based on characters of species. In addition, both models incorporate population dynamics. One of the differences between these models is in the manner of species evolution. In the Web World Model, characters of a new species born via speciation are set by copying those of its ancestor and replacing one of the copied characters with a new one. This model of evolution allows saltationary evolution. On the other hand, in my model, values of characters for species always evolve gradually. As a consequent, phylogenetically related species have similar characters. Thus, this model can represent phylogenetic constraint in a biologically meaningful manner. The newly developed Web World Model (Web World Model II: Drossel et al., 2001, 2004) incorporated a non-linear functional response for describing population dynamics and optimal foraging theory for the construction of inter-specific interaction, both of which are not incorporated my model. Then, at first glance, my model seems to be unrealistic. However, the means of statistics describing the resultant food webs in my model were closer to the means of real food webs than that in the Web World Model II (Yoshida, 2006c). As

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mentioned earlier (Yoshida, 2006c), this result does not deny the validity of the Web World Model II but supports the reality of my model.

2.2.

Basic structure of the food web model

A food web in this model is represented by the following multidimensional Lotka–Volterra equations: 0 1 n X dMi ¼ ei Mi @ri þ ai j M j A; dt j¼1

(1)

where Mi and Mj are the total biomasses of species i and j, respectively, ei the ecological efficiency of species I, ri the intrinsic growth rate of species I, n the number of species in the food web and aij is the effect of species j on species i (Values of variables, except for r for animal species and e, are summarized in Table 1). On a computer, the actual calculation is done by using the Euler method with the step size 0.001: 0 Mi ðt þ DtÞ ¼ Mi ðtÞ þ Dt  eMi ðtÞ@ri þ

n X

1

ai j M j ðtÞA;

(2)

Table 1 – Variables for species Variable M w r (plant) D[k] A[k] P C E aij aji

Initial value 0.1 [0, 0.003] [0, 2] [0, 100] [0, 100] [1, 10] [2, 10] (1.0, 0.1) [0, 0.2] aij

Variables for descendant VA/20 VA + (0, 0.0003E) VA + (0,0.1E) VA + (0,E) VA + (0,E) VA + (0,0.3E) VA + (0,0.3E) VA +(0,0.1E) VA +(0,0.1E) aij

For definitions of variables, see the text. Initial value: values assigned to variables for species in the initial setting of food web (see the text) and founder species immigrating from outside a food web, values assigned to variables for new species born by speciation; [0–10]: random number uniformly distributed between 0 and 10, (0, E): Gaussian random number with mean 0, S.D. E, VA: the value of each variable for ancestor species.

of 10 elements. The decision whether a predatory species i feeds on a prey species j is made by counting the number of elements of D that satisfy the following condition:

j¼1

Ai ½k  Pi < D j ½k < Ai ½k þ Pi ; where Mi(t) is the total biomass of species i at a given time t; and Dt = 0.001. In this study, 1000 Euler steps are defined as 1 time unit. 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. A model food web consists of animal and producer species. Animal species are divided into herbivores (consume producer species), carnivores (consume animal species), and omnivores (consume both animal and producer species). Producer species conduct primary production and grow on their own. The intrinsic growth rate (r) of producer species is assigned a positive value (Table 1). In contrast, animal species cannot survive without feeding on other species. Thus, r of an animal species is set by the following equation: ri ¼ 0:15 

wi  0:35; 0:03

(3)

that is, the biomass of an animal species decreases because of natural death of individuals, metabolism, and so on. The simulation begins with 50 animal and 50 producer 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.

where Ai[k] and Dj[k] are the kth elements of A of species i and D of species j, respectively; Pi is the range of feeding preference of species i. If the number of elements is larger, the probability that species i can feed on species j is larger. The final decision is made by using a random number uniformly distributed in [0, 10]. If the random number is smaller than the number of elements of Dj that satisfies the above condition, predatory species i is decided to be able to feed on prey species j. In this case, aij, which is the effect of species i on species j, is assigned a positive value (see also Fig. 1 in Yoshida, 2003b), and aji, which is the effect of species j on species i, is set to aij. In this model, larger animals are assumed to feed on smaller animals, because predators are usually larger than their prey in natural communities (Ve´zina, 1985; Warren and Lawton, 1987; Cohen et al., 1993; Pahl-Wostl, 1997; Neubert et al., 2000; Jennings et al., 2001). This assumption is also incorporated in the Cascade Model (Cohen et al., 1990). On the other hand, animal species can feed on producer species regardless of body size. In the model, producer species are assumed to hinder each other’s growth when they have similar characters (Yoshida, 2003a). Whether producer species a hinders producer species b is decided in the same manner as described above; that is, the number of elements of Db that satisfy the following condition is counted: Da ½k  Ca < Db ½k < Da ½k þ Ca ;

2.3.

(4)

(5)

Construction of inter-specific interactions

The construction of trophic links is explained in detail using an example case in which a predatory species i tries to feed on a prey species j. If properties of species j match the feeding preference of species i, species i can feed on species j. The properties of species j, and the feeding preference of species i are represented by Dj and Ai, respectively, both of which are arrays

where C is the sensitivity to competition and is randomly chosen from the interval [2.0, 10.0]. 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 number of elements of Dj satisfying the above condition is larger than the random number, species a hinders the growth of producer species b (aba < 0); that is, the value of aba is randomly chosen from [0.2, 0].

ecological complexity 5 (2008) 86–98

The diagonal elements of the interaction matrix, aii, represent intra-specific competition coefficients. In this model, producer species with large r values are assumed to suffer from severe intra-specific competition (Yoshida, 2003a). Thus, if species i is a producer species, aii is calculated by the following equation: aii ¼ 0:3 

ri  0:7 4:0

(6)

In this model, animals with larger body size are assumed to experience more severe intra-specific competition than do smaller ones, because larger animals generally need more food and larger home ranges than do smaller ones (Palomares and Caro, 1999). Thus, aii of animal species is set according to the following equation: aii ¼ 0:15 

2.4.

wi  0:35: 0:03

(7)

Evolution of a model community

Model food webs in this study are constructed via the evolution of species. At every 100 time units, a species in the food web is randomly chosen. A part of the population of this species is separated from the main population and becomes a new species. The total biomass of the new species is set to 5% of that of its ancestor species. The parameters of the new species are set by adding slight mutations to those of its ancestor. The degrees of mutations are given 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; that is, E for each element of A and D, 0.3E for P, 0.1E for r, 0.1E for E, and 0.0003E 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 new species are decided by adding slight mutations to those of its ancestor species. When a new species is judged to feed on one of the prey of the ancestor species by Eq. (4), the interaction coefficient 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 species of the ancestor, the interaction coefficient 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 interaction coefficient between the ancestor and the prey. The interaction coefficient 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 do not interact with the ancestor are decided by the same manner as in the initial setting. At every 500 time units, a new species immigrates to the food web and establishes a new clade. Immigrations of a producer, omnivore, herbivore, and carnivore occur in turn.

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Variables and interactions of the new founder species are set in the same manner as for the initial setting.

2.5.

Ecological efficiency

Animal species can use a fraction of the biomass gained via predation for their growth of population. In this study, I assumed that an animal species specializing to feed on a limited number of prey species can utilized its prey species more effectively than those not specializing. Then, the ecological efficiency, e, is defined as K/P, where K is a constant and P is the range of feeding preference. The upper limit of the ecological efficiency is set to 1.0. When omnivores feed on producer species, K is set to 1. Because animals are efficient food (Begon et al., 1996), K is set to 2, when omnivores feed on animals. Herbivores and carnivores specialize for feeding on producer species and animals, respectively. Then, K for these types of species is twice that for omnivores. In the simulation of invasion, another type of animal species, powerful omnivore, is introduced. A powerful omnivore has a wide range of feeding preference (P is fixed to 20), and a high ecological efficiency, which is twice that of usual omnivores.

2.6.

Simulation of invasion

For the simulation of invasion, I prepared nine types of recipient food webs by varying the duration of evolution: recipient food webs with 0, 20,000, 40,000, 60,000, 80,000, 100,000, 120,000, 160,000 and 200,000 time units evolution, respectively (Food webs with 0 time unit evolution are called food webs without evolution). After evolution, recipient food webs were left for 10,000 time units, in order to relax the effect of the last speciation. One species with a very small biomass (0.01, one tenth of the biomass assigned to species in the initial setting) invades a recipient community. Invasions of producers, omnivores, herbivores, carnivores and powerful omnivores occur in turn. The parameter values for invaders except for body size (w) are set in the same manner as the initial setting of model food webs. The value of w for powerful omnivore is randomly chosen from the interval [0.005, 0.01]; that is, powerful omnivores tend to invade as top predators. The value of w for other animal species is randomly chosen from the interval [0, 0.007]. The effect of the invasion is monitored for 1000 time units. After that, the model is reset to the state before invasion, and the next species invades. In one simulation of a recipient community, producers, omnivores, herbivores, carnivores, and powerful omnivores each invade 18 times, and this simulation set is iterated 30 times for each type of recipient food webs. Thus, a total of 2700 (5  18  30) invasions were investigated in each type of recipient food webs.

3.

Result

3.1.

Food web structure

I compared the means of statistics characterizing model food webs after an evolution over 200,000 time units with the

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means of 14 real food webs (Pimm and Lawton, 1980; Baird and Ulanowics, 1989; Warren, 1989; Hall and Raffaelli, 1991; Martinez, 1991; Polis, 1991; Goldwasser and Roughgarden, 1993; Huxham et al., 1996; Schneider, 1997; Yodzis, 1998; Cristian and Luczkovich, 1999; Martinez et al., 1999; Hori and Noda, 2001; Woodward and Hildrew, 2001). The degree of difference in each parameter between real and model food webs is measured in terms of the standard deviation of each parameter for the model food web (Williams and Martinez, 2000). Fig. 1 represents the result of this comparison between real and model food webs. As compared with models without population dynamics (e.g. Williams and Martinez, 2000; Cattin et al., 2004; Rossberg et al., 2005, 2006), models incorporating population dynamics (e.g. Caldarelli et al., 1998; Drossel et al., 2001, 2004; Yoshida, 2002, 2003a, 2006a,b; Tokita and Yasutomi, 2003; Chowdhury and Stauffer, 2004; Ito and Ikegami, 2006) are, because of the complexity of such models (Yoshida, 2006c), hard to control with regard to the topology of resultant food web. Consequently, the resultant model food webs are not as similar to real food webs. In particular, the difference in the ratio of animal/producer was remarkable (Fig. 1, Table 2), indicating that too many producer species existed in the model food web. The high value of %B (fraction of producer species) in the model food web also suggests this interpretation. This large difference can be understood by the tendency that, in real food webs, producer species tend to be highly lumped or resolved to a coarser taxonomic level (Briand and Cohen, 1984; Paine, 1988; Hall and Raffaelli, 1991,1994; Polis, 1991; Martinez, 1993), although all species can be distinguished in the model food web. This tendency artificially increases the ratio of animal/producer. In fact, the ratio of animal/producer in a few real food webs, in which producer species are finely resolved taxonomically, were close to or much lower than for the model food webs (Little Rock Lake: 1.89 (Martinez, 1991); the Hiura rocky intertidal: 2.07 (Hori and

Noda, 2001); Tuesday Lake: 1.00 (Cohen et al., 2003)). Therefore, the large difference in the ratio of animal/producer between real and model food webs does not deny the realism of the model.

3.2.

Just after the beginning of the simulations, the species diversity in food webs suddenly decreased from 100 to about 60 (Fig. 2a), due to the initial instability of such systems (Gardner and Ashby, 1970; May, 1972; Tokita and Yasutomi, 1999; Yoshida, 2003b). During the following 40,000 time units, the species diversity rapidly increased toward about 100. After that, while the rate of increase of species diversity became low, the species diversity continued to increase and finally reached 120 (Fig. 2a). Food webs became complex with time. The link density rapidly increased toward a plateau of around 7 at 80,000 time units (Fig. 2b). The pattern of temporal change in the maximum food chain length was similar to that in the link density, whereas it exhibited large fluctuations (Fig. 2c). The ratio of animal/producer increased rapidly during the first 40,000 time units, indicating that the diversity of animal species increased rapidly. In the stage after 40,000 time units, the ratio of animal/producer was maintained at a constant value (Fig. 2d). While the ratio of animal/producer increased rapidly, interactions related to animal species developed remarkably. The mean number of prey species per animal species increased rapidly during the first 20,000 time units (Fig. 2e). The mean number of herbivorous animal species per producer species increased rapidly during the first 40,000 time units (Fig. 2f). The pattern of temporal change in the intrinsic growth rate, r, of producer species was similar to that in the mean number of herbivorous animal species per producer species (Fig. 2f and g), indicating that producer species with low growth rates cannot survive under high grazing pressure. These results indicate that food webs developed rapidly during the first 40,000 time units. After that, food webs changed slowly. Of the variables shown in Fig. 2, link density, the maximum food chain length, and the ratio of animal/ producer stopped increasing at around 80,000 time units (Fig. 2b–d). The generality and the mean number of herbivorous animal species per producer species stopped increasing at around 120,000 time units (Fig. 2e and f). However, the species diversity and intrinsic growth rate of producer species continued to increase through 200,000 time units. In addition, link density and the ratio of animal/producer began to increase near the end of simulation once again (Fig. 2b and d). These results indicate that food webs reached a semiequilibrium state between 80,000 and 120,000 time units. However, food webs were not completed and continued to develop through 200,000 time units.

3.3. Fig. 1 – Degree of difference between real and model food webs. The horizontal axis represents absolute values of the degree of difference between model and real food webs (for details, see the text). The vertical axis represents properties for food web in order of the value of the difference. For properties, see the explanation for Table 2.

Temporal changes in food web structure

Features of invasive species

Fig. 3 represents the number of prey species of animal species invading the food webs with 200,000 time units evolution. Powerful omnivores, which tended to invade as top predators and have a wide range of feeding preference, fed on a much larger number of prey species than the others (Fig. 3).

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Table 2 – Properties of food web Real food webs

Animal/producer %I  I %B %T  I log(no. chains) %I  B Diversity %I Generality Max. chain length %T  B Vulnerability Herbivorous animal/producer Predator/prey S.D. of chain length Link density %T

Model food web with 200,000 time units evolution

Mean

S.D.

Mean

S.D.

17.28 0.51 0.16 0.25 2.55 0.19 70.60 0.64 8.11 9.82 0.05 6.16 13.40 1.07 1.32 6.77 0.20

24.46 0.26 0.14 0.16 0.36 0.14 43.41 0.22 5.08 3.54 0.08 3.55 17.73 0.24 0.34 4.26 0.13

1.95 0.08 0.35 0.08 2.94 0.52 118.23 0.41 11.57 5.97 0.32 7.52 18.66 0.88 1.02 7.56 0.24

0.32 0.06 0.04 0.04 0.11 0.11 16.46 0.09 1.49 1.67 0.15 0.89 3.69 0.15 0.38 0.97 0.10

Difference (real  model) 47.54 7.16 4.76 4.07 3.40 3.08 2.89 2.71 2.32 2.31 1.82 1.53 1.43 1.27 0.81 0.81 0.47

S.D., standard deviation; animal/producer, the ratio of animal species to producer species; diversity, number of species in a food web; %T, %I, %B: fractions of top (T, species without predator), intermediate (I, species with both predator and prey), and basal (B, producer) species; %T  I, %T  B, %I  I, %I  B, fractions of interactions between the types of species; log(no. chains), log10 of the number of predator–prey links; generality, the mean number of prey species per animal species; vulnerability, the mean number of predatory species per species; max. chain length, the maximum food chain length in a food web; S.D. of chain length, the S.D. of food chain length in a food web; herbivorous animal/ producer, mean number of herbivorous animal species per producer species; predator/prey, (T + I)/(I + B); link density, (number of predator– prey links)/(diversity). Parameters are in order of the value of the difference between real and model food web (difference real-model). For the difference, see text.

Fig. 4 represents the probability of successful invasion in the food webs with 200,000 time units evolution. An invasion is regarded to be successful, if an invasive species survives for 1000 time units after invasion. The probability of successful invasion of animal species was closely related to the number of prey species of animal species (Figs. 3 and 4). Producer species had a high probability of successful invasion (Fig. 4), because they could survive without depending on other species.

3.4.

Effects of invasion

Fig. 5 represents the probability of severe extinction event caused by a single invasion. A severe extinction event is defined as one where more than 5% of all species in a recipient food web become extinct. For the food webs without evolution, powerful omnivores were the most dangerous (Fig. 5a). On the contrary, for food webs with 200,000 time units evolution, producer species were as dangerous as powerful omnivores (Fig. 5b). In the most severe extinction events, 17.6% and 18.6% of all species in a food web were eliminated by a single invasion of a producer and a powerful omnivore, respectively. When a producer species invaded food webs with 200,000 time units evolution, 3.25 animal species, on average, became extinct, but only 0.41 producer species (Fig. 6). This result indicates that animal species tended to become extinct by the indirect effect of producer invasion: the biomasses of a number of resident plant species fluctuated by competition with invasive plant species, and many animal populations were affected by the fluctuations and became extinct. Focusing on producers and powerful omnivores, I investigated temporal changes in the fraction of species eliminated

by a single invasion (Fig. 7). The fraction of animal species eliminated by an invasion of a producer species increased rapidly from 10,000 to 40,000 time units, and after that it maintained a constant value (Fig. 7a). This pattern is very similar to the patterns of temporal changes in parameters of the model food webs shown in Fig. 2. The fraction of producer species eliminated by an invasion of a producer species was much lower than that of animal species (Fig. 7a). It increased slowly until 120,000 time units and maintained a constant value in the later stage (Fig. 7a). The fractions of animal and producer species eliminated by an invasion of a powerful omnivore were the highest at 0 time unit (Fig. 7b). Those rates decreased suddenly between 10,000 and 20,000 time units (Fig. 7b). The fraction of animal species eliminated by an invasion of a powerful omnivore increased rapidly from 20,000 to 40,000 time units. In the following stage, the fraction remained at 4%, which was equal to the fraction of animal species eliminated by an invasion of producer species (Fig. 7a and b). The fraction of producer species eliminated by an invasion of powerful omnivore increased slowly until 80,000 time units and maintained a constant value in the following stage (Fig. 7b).

4.

Discussion

4.1.

Food web evolution

The model food webs in this study became complex with time (species diversity, trophic level, inter-specific interactions, Fig. 2). Such a tendency was frequently observed in other food web models (Caldarelli et al., 1998; Drossel et al., 2001, 2004;

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Fig. 2 – Temporal changes in parameters for food web. (a) Diversity, (b) link density, (c) the maximum food chain length, (d) the ratio of animal/producer species, (e) generality (the mean number of prey species per animal species), (f) the number of herbivorous animal species per producer species and (g) intrinsic growth rate of producer species. Vertical axes represent value of these parameters, and horizontal ones represent time units. Error bars represent standard deviations. For properties, see Table 2.

Tokita and Yasutomi, 2003; Chowdhury and Stauffer, 2004; Ito and Ikegami, 2006). Another feature of the model food webs, the ratio of animal/producer species was higher at the beginning of evolution (Fig. 2d). The reason is that, of the initial 100 species (50 animal and 50 producer species), producer species tended to survive, because they could grow without depending on other species. Are such patterns of food web evolution observed in the real world? The pattern of the development of a food web has been well observed on the Krakatau Islands, on which the community was completely destroyed by the catastrophic volcanic eruption in 1883 (Thornton et al., 1988; Bush and Whittaker, 1991; Whittaker et al., 1999), although the food web

on the Krakatau Islands after the volcanic eruption has been developed mainly by species immigration not by evolution. A number of works reported that the species diversity on the Krakatau Islands increased with time (Thornton et al., 1988; Bush and Whittaker, 1991; Fridriksson and Magnu´sson, 1992; Thornton, 1996; Whittaker et al., 1999). In addition, the colonization pattern of animal species suggests that the trophic level became higher with time (Thornton, 1996). Animal species cannot survive without primary production of producer species. Therefore, it is quite natural that the diversity of producer species is higher than that of animal species in the early stage of food web evolution. Bush and Whittaker (1991) showed that the species diversity of butterfly

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Fig. 3 – The mean number of prey species of animal species which invaded the model food web with 200,000 time units evolution. Error bars represent standard deviation.

increased after that of higher plant increased. This data seems to coincide with the result of the model. However, the data reported by Partomihardjo et al. (2004) does not coincide with that reported by Bush and Whittaker (1991): the temporal pattern of species diversity of vascular plant was very similar to that of butterfly. Because of this inconsistency, whether the diversity of producer species was higher in the beginning of the real food web cannot be judged. There is a possibility that the latter result is derived from the geographical condition of the Krakatau Islands; that is, there was no time lag between the colonization of producer species and that of animal species, because the Krakatau Islands are very close to the mainland of Sumatra and Java, which are the sources of species (Bush and Whittaker, 1991). Southwood (1961) showed a statistically significant linear correlation between the number of insect species associated with British trees and the number of Quaternary fossil records

Fig. 4 – The fraction of successful invasions to food webs with 200,000 time units evolution.

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of these trees. Birks (1980) also reported the same tendency. This tendency has been well quoted as part of the ‘‘geologic-time hypothesis’’ (Opler, 1974). This tendency seems to be compatible with the results of this study that the link density, the ratio of animal/producer species, the mean number of herbivorous animal species per producer species, and that of prey species per animal species increased with time (Fig. 2b, d–f). However, this tendency has not been proven yet. Birks (1980), Rosenzweig (1995), and Bra¨ndle and Brandl (2001) pointed out that this tendency was not statistically significant when the data of trees introduced by human activity was removed. This result might be derived from the data that the number of insect species related to such tree species was very small (Birks, 1980). Consequently, the tendency becomes obscure when the data of such tree species are removed. It can be considered that there was not enough time for insects to adapt to recently introduced trees, because the increase of human activity is a recent event in geologic-time. Therefore, further studies are necessary whether the data of trees introduced by human activity should be removed or not. In addition to the problem concerning human activity, Kennedy and Southwood (1984) suggested, based on a multivariate analysis, that time was not the principal factor controlling the number of insect species utilizing tree species (the principal factor was the abundance of trees). Therefore, it should be concluded that time is only one of the factors controlling the evolution of inter-specific interaction.

4.2.

Temporal changes in the vulnerability to invasion

The model food webs with 200,000 time units evolution were particularly vulnerable to invasion of powerful omnivores and producers (Fig. 5b). On the contrary, other types of invasive species rarely lead to severe extinction events (Fig. 5b). One of the reasons was the low probability of successful invasion of these species (Fig. 4), which was calculated based on the total number of invasions. In addition, as compared with powerful omnivores, these types of species fed on a small number of prey species (Fig. 5). Therefore, they could not have a strong impact on the recipient food webs. The effect of the invasion of producer species on the food webs without evolution was small (Figs. 5a and 7a). However, it became more severe with time (Fig. 7a). In particular, after 40,000 time units, it was as severe as that for powerful omnivores (Fig. 7). In addition, it is notable that the temporal pattern of the fraction of animal species eliminated by an invasion of producer species coincided with that of the ratio of animal/producer species (Figs. 2d and 7a). In the beginning of the food web evolution, producer species were fed on by a limited number of animal species (Figs. 2f and 8a), and the trophic level was low (Figs. 2c and 8a). Then, even if an invasive producer species disturbed the base of recipient food webs, few animal species were affected. Therefore, severe extinction events did not occur (Figs. 5a and 7a). However, the number of animal species increased and the trophic level became higher with time (Fig. 2c and d). Consequently, food webs became less stable; that is, a small number of producer species supported a large number of animal species (Figs. 2d and 8b). Therefore, when an invasive producer species disturbed the base of a food web, many

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Fig. 5 – The probability of severe extinction events caused by a single invasion. A severe extinction event is defined as one where more than 5% of all species in the recipient community become extinct caused by a single invasion. (a) Food webs without evolution (with 0 time unit evolution) and (b) those with 200,000 time units evolution.

animal species became extinct by the indirect effect of the producer species invasion. The most dangerous type of invader for the food webs without evolution was powerful omnivore (Fig. 5a). Because species in the food webs without evolution were not selected via predation pressure, producer species had low intrinsic growth rates (Fig. 2g), and animal species fed on a small number of prey species (Fig. 2e). Such species cannot resist the predation pressure from powerful omnivores. Therefore, severe extinction tended to be induced by powerful omnivore (Fig. 5a). However, during the period from 10,000 to 20,000 time units, the number of prey species per animal species and the mean intrinsic growth rate of producer species increased rapidly (Fig. 2e and g). Therefore, the food webs during this period became resistant to invasion of powerful omnivores (Fig. 7b). Although the number of prey species per animal species increased after 30,000 time units (Fig. 2e), the ratio of animal species eliminated by an invasion of a powerful omnivore increased again (Fig. 7b). This phenomenon was related to the rapid increase of the ratio of animal/producer species until 40,000 time units (Fig. 2d). Powerful omnivores feed not only on animal species but also on producer species. Therefore, if an invasive powerful omnivore disturbed the base of food webs with a high ratio of animal/producer species by

Fig. 6 – The mean numbers of producer and animal species eliminated by a single invasion of a producer species. Error bars represent standard deviation.

predation, many animal species became extinct by the same processes as for the invasion of a producer species. This interpretation was supported by the results that the fraction of animal species eliminated by an invasion of a powerful omnivore was almost equal to that by producer species (Fig. 7a and b). The fraction of producer species eliminated by an invasion of a powerful omnivore decreased until 20,000 time units (Fig. 7b). This decline related to the rapid increase of the intrinsic growth rate, r, of producer species (Fig. 2g), while the numbers of herbivorous animal species per producer species and prey species per animal species were still low in the period (Fig. 2f). The intrinsic growth rate of producer species increased after 30,000 time units (Fig. 2g). However, the predation pressure on producer species in food webs also increased rapidly (Fig. 2d and f). Therefore, producer species easily went extinct when additional predation pressure was added by an invasion of a powerful omnivore. The predation pressure on producer species in food webs remained constant after 80,000 time units (Fig. 2d and f). Consequently, the ratio of producer species eliminated by an invasion of a powerful omnivore also maintained a constant value in the same period (Fig. 7b). In this way, the vulnerability to invasion of powerful omnivores was closely related to rapid changes in the food web structure in the early stage of food web evolution. The relationship between the resistibility to invasion and food web evolution was investigated by Post and Pimm (1983), Drake (1990), Law and Morton (1996). In their simulations, food webs evolved by repeated invasion of species which were randomly chosen from a finite species pool. They showed that the resistibility to invasion increased with the duration of food web evolution. This is somewhat inconsistent with the result of this study, since food webs in this study became vulnerable to invasion of producer species (Fig. 7). The cause of this difference may be in the manner of simulation. Using a finite species pool for food web evolution limits the capability of evolution. Then, food webs easily approach the most stable combination of species. In addition,

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Fig. 7 – Temporal changes of the fraction of species eliminated by invasion. (a) Effect of an invasion of a producer species and (b) that of a powerful omnivore species. Negative values of the fraction represent species successfully invading the model food web without extinction of resident species.

Happel and Stadler (1998) and Tokita and Yasutomi (2003) showed that large and complicated food webs could not be constructed only by repeated invasion of species. Therefore, food webs evolved only by invasion did not reach the climax state (e.g. Fig. 2) achieved by the model in this study incorporating speciation.

4.3.

Direction of further studies

Species in the model were so simplified that they were classified only according to their feeding types. Other ways of classification based on other detailed properties were impossible. Thus, species in the model could not be related to real taxonomic groups (e.g. mammals, reptiles, insects and so on). This is a problem in the comparison between the result of this study and empirical data. I analyzed the frequency of feeding type of animal species invading Japan using a database (Invasive species database published by National Institute for Environmental studies, Japan (2003)), in which the feeding type of 228 animal species are described. When the data was analyzed regardless of taxonomic classification, omnivorous invasive species were the most frequent (Fig. 9a). This result was similar to that of simulations in this study (Fig. 4). When the data was compiled

according to taxonomic classification, similar results were obtained in mammals, birds, and fishes (Fig. 9b, c and f). However, carnivorous invasive species were most frequent among reptiles and amphibia, and herbivorous invasive species were the most frequent among insects (Fig. 9d, e and g), contrasting the simulation results (Fig. 4). The database is not completed and is still being updated. There is a possibility of some biases. For example, most insect species in the database are agricultural pests, and this may increase the frequency of herbivorous insect species. This result faces us with new problems. One is a detailed analysis of empirical data. Continuously updating the database, we should clarify what properties of each taxonomic group determine the frequency of feeding types of invasive species in each group. The model should be modified correspondingly. There are two directions for modifying the model. One is to incorporate detailed properties of species, which are the cause of the difference among taxonomic groups shown in Fig. 9. This modification may reinforce the reality of the model. However, such a modification complicates the model, and consequently, the behaviors of the model may become hard to be understood and sometimes become less realistic (e.g. Ludwig and Walters, 1985). The other direction would be to specialize the model to

Fig. 8 – Schematic figures of model food webs.

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Fig. 9 – Frequency of feeding types of invasive species. Based on the invasive species database released by the National Institute for Environmental Studies, Japan (2003). Numbers shown in parentheses represent the total number of species in each category.

represent some particular taxonomic group. Such a modification reinforces the reality of the model while keeping it simple. However, its generality is lost. For example, a model specialized to mammals cannot be applied to reptiles. Neither direction of modification is inferior. Either type of model is necessary for each purpose. In further works, we must carefully choose a model according to our purpose (Iwasa et al., 1987, 1989).

5.

Concluding remarks

Elton (1958) stated that complex ecosystems are resistant to biological invasion. This statement was not supported by the result of my simulations. As food webs became complex with time, food webs became vulnerable to invasion of producer species (Fig. 7a), because of the unstable structure (the ratio of animal/producer species) of food webs with long time evolution (Fig. 2d). Elton’s (1958) statement was true in the early stage of food web evolution. Before 20,000 time units, the food web became resistant with the increase of the food web complexity (Figs. 2

and 7b). The reason was that, during this period, the number of prey species of animal species and the mean intrinsic growth rate of producer species increased (Fig. 2e and g), whereas the predation pressure on producer species was still weak (Fig. 2d and f). However, this resistibility was not maintained for a long time. As the ratio of animal/producer species rapidly increased until 40,000 time units, the vulnerability to the invasion of powerful omnivores increased again (Fig. 7b) due to the same process of extinction caused by the invasion of producer species; that is, when an invasive powerful omnivore disturbed the base of the food web by predation with a high ratio of animal/producer species, many animal species depending on producer species tended to become extinct. Because the relationship between the time scale of the real world and the model is unclear, it is also not cleared how many years are necessary for real food webs to reach an equilibrium state, which corresponds to the stage after 80,000 or 120,000 time units in the model food web (Fig. 2). However, clarifying the relationship between time scales of real world and model may continue to be very difficult, because evolutionary rate of species vary with space, time, and species (Westoll, 1949; Stanley, 1979; Futuyma, 1986; Martin et al., 1992).

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The result of this study strongly suggests that food webs change with time, and consequently, the vulnerability to invasion changes with time. If there is a fact that a measure against biological invasion is effective at a certain time, the fact does not assure that the measure is effective in the future, too. In particular, because food webs recently established change rapidly, such food webs should be monitored continuously, and measures against biological invasion should be changed flexibly.

Acknowledgements This paper is based on a presentation given at the international workshop ‘‘Advances in food-web theory and its application to ecological risk assessment’’ held in Yokohama on 13th, and 14th September 2006. I specially thanks to Axel G. Rossberg and Reiichiro Ishii for co-organizing the workshop and giving me the opportunity of presenting this work. I also thanks to Axel G. Rossberg for giving me fruitful comments on the manuscript. This study is partially supported by Global Environmental Research Fund, Ministry of the Environment, Government of Japan (the study for ecological risk assessment and management of the invasive alien species; representative, Koichi Goka).

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