45

Predicting Changes in Ecosystems after Eradication ofInvasive Species through Computer Simulations
Katsuhiko YOSHIDA
Center for Environmental Biology and Ecosystem Studies, National Institute for Environmental Studies
16-2 Onogawa, Tsukuba, Ibaraki 305-8506, Japan
E-mail: kyoshida@nies.go.jp

Abstract
Projects to restore ecosystems have been conducted in various regions. To assess the effects of theseprojects, studies have been launched to predict changes in ecosystems by constructing mathematical models
to reproduce target ecosystems and performing computer simulations. When an entire ecosystem including
many species is the target, models using differential equations are often used to calculate population dynamics
of the species constituting the ecosystem. When interactions among species are reproduced, the types ofinteractions are determined based on previous studies and experts’ opinions. Since it often happens that thestrength of interactions cannot be measured, multiple models with randomly determined strengths ofinteractions are prepared to perform simulations to select a model that satisfies the requirements. After that,simulations of eradication of invasive species are performed to predict the outcome. This is the generalprocedure. A plurality of simulations has predicted that if there are multiple invasive species, eradicating these
species simultaneously will be effective for restoring the ecosystem efficiently. However, since simultaneous
eradication has a larger impact on ecosystems, monitoring must continue even after eradication andappropriate measures taken. Furthermore, since the models are still in the course of development, a framework
is required to feed data obtained from monitoring into the models to improve them further.
Key words :	ecosystem change, eradication, invasive species, prediction, simulation

1. Introduction
Biological Invasion is one of the most serious
environmental problems. This is also true in the
Ogasawara Islands. On several of these islands, thevegetation has been destroyed due to grazing damage byferal goats. Large areas of bare ground have spread(Fig. 1; Hata et al., 2007; Kachi, 2010). Therefore,
projects to restore the ecosystems, such as eradication ofinvasive species, have been conducted in various regions(in the Ogasawara Islands, eradication of feral goats iscomplete except for on Chichi-Jima Island). One of themost severe problems is that it is often impossible topredict with ease places where effects will appear in an
ecosystem when invasive species are eradicated, because
multiple species interact within the ecosystem. Several
studies have pointed out that various problems may occur
after eradication (e.g., meso-predator release: Courchamp
et al., 1999; increase of another invasive species: Osawa
et al., 2015; negative impacts on native species via interspecific interactions: Ballari et al., 2016). Moreover, thelong-term effects of eradication are mostly unclear.
Accordingly, attempts to reproduce an ecosystem to be
managed on a computer and assess the effects throughGlobal Environmental Research
23/2019: 045-051
printed in Japan

Fig. 1 P hotograph of Nakoudo-Jima Island in the Ogasawara
Islands, taken in June 2012. Photographer: Katsuhiko Yoshida.

simulations to manipulate the ecosystem, such as
removals or additions of species, have been initiated tocheck for unexpected harmful effects (Caut et al., 2007;
Raymond et al., 2011; Bode et al., 2015, 2017; Baker etal., 2017, 2019; Yoshida et al., 2019). Such studies would
be useful especially for the Ogasawara Islands, because©2019 AIRES

46

K. YOSHIDA

unexpected harmful effects are not acceptable inecosystems on islands registered as a Natural World
Heritage site.
Although theoretical studies on removals or
additions of species have been conducted over many
years (Pimm, 1980; Zavaleta et al., 2001; Quince et al.,2005), these previous studies have been conducted using
relatively simple hypothetical ecosystems because thepurpose was to understand the general and fundamental
behavior of ecosystems. In recent years, however, several
studies have tried to construct simulation models
reproducing real, complex ecosystems and to predictchanges after manipulation due to the necessity of
ecosystem management. In this paper, such trends inrecent years are reviewed and future directions are
discussed.

2. Basic Structure of Ecosystem Models
Many species interact with each other in any
ecosystem, being intertwined like a web. To construct anecosystem model, these interactions must be expressedmathematically. Differential equation models, often using
Lotka–Volterra equations (Lotka, 1920 1922a 1922b,
1925; Volterra, 1926, 1928), have long been used for such
expressions. Many ecosystem models are based on theseequations (Caut et al., 2007; Raymond et al., 2011; Bodeet al., 2015, 2017; Baker et al., 2017, 2019; Yoshida etal., 2019).
Ecosystems can be easily reproduced using a Lotka–
Volterra equation. The Lotka–Volterra equation ispresented in the following form:dMi= ri Mi + ∑ Nj=1 aijMi Mj,
dt

(1)

where Mi and Mj are the biomass (or the number ofindividuals) of species i and j, respectively; ri is theintrinsic growth rate of species i; N is the total number of
species within a system; and aij is the interaction
coefficient representing the strength of influence ofspecies j on species i. This equation is often used in thisform but there are many variations depending on thetarget ecosystem for the purpose of study as described
below. When actually performing a calculation, theequation is expressed in the form of a matrix of N rows
and N columns in a computer as shown below:

…
…
…
…

a11 a12…a1N
a21 a22…a2N

aN1 aN 2…aNN

Combinations of symmetric components allow easy
expression of various types of interactions observed in an
actual ecosystem (Table 1). For example, when aij ispositive and aji is negative, species i derives benefit from
species j but species j is damaged by species i; therefore,

Table 1 
Combinations of positive and negative interaction
coefficients and types of interactions represented by them.

aij

aji

+

-

predator-prey--competiton++

mutualism+

0commensalism-

0amensalism

00

no interaction

aij represents the strength of influence of species j on species i and aji
represents the converse. Various types of interactions observed inecosystems can be represented by combinations of positive and negativevalues of aij and aji.

this combination represents a predator–prey relationshipin which species i preys on species j. The diagonalcomponent aii is the influence on itself, representing intraspecific competition.
The Lotka–Volterra equations have many variations
depending on the target ecosystem or the purpose.
Famous variations include Holling Type II, which takes
handling time when organisms eat their prey into
consideration, and Holling Type III, which introduces theeffect of increasing difficulty for predators to find theirprey or starting to search for other prey when the prey
population decreases (Holling, 1959, 1965). Carrying
capacity may be included in the equation, although notincluded in equation (1) above, or the equation may
become complicated due to incorporation of various
parameters that reproduce detailed properties of species
to be handled such as proliferation of potential of
constituent species and preferences of predators forcertain prey. This tendency is particularly strong when an
ecosystem with a small number of species, such as asystem with three species, is considered (Caut et al.,2007; Bode et al., 2015). However, in studies in whichecosystems with many species are targeted, simple
Lotka–Volterra equations are often used (Raymond et al.,2011; Baker et al., 2017, 2019; Bode et al., 2017). This isbecause it is difficult to actually collect detailed data ofmany species. Another reason is that the coexistence ofall species constituting a target ecosystem is relatively
easy to model using simple Lotka–Volterra equations.
Although the Holling Type II function is observed mostoften in the real world (Begon & Mortimer, 1981), thisequation is not often used when considering ecosystems
with many species because it is extremely difficult toreproduce the coexistence of multiple species whensimulations use the Holling Type II function (Yoshida,unpublished data). If all the species constituting a target
ecosystem cannot coexist, such a model cannot be
regarded as a successful one.

Predicting Ecosystem Changes through Simulations

3. How to Reproduce Ecosystems
This section describes how to reproduce a target
ecosystem with a differential equation model, the mostcommon type used.
Procedures for reproducing an ecosystem are quite
common and proceed as follows (Fig. 2): (1) set the
species constituting the target ecosystem; (2) set theproperties of the constituent species; (3) set theinteractions; (4) calculate the population dynamics ofeach species by performing provisional simulations; and(5) select a model satisfying the requirements as a resultof the simulation. Item (1) is determined using previous
studies, literature and observations as references. Items(2) and (3) are also determined in the same way as item
(1) using previous studies and literature data as
references, but many species that have not been
sufficiently studied are also included in an ecosystemwith a large number of species. Therefore, although not
published as papers, opinions of experts are often used as
references to determine these items (Caut et al., 2007;
Raymond et al., 2011; Bode et al., 2015, 2017; Baker etal., 2017, 2019; Yoshida et al., 2019). The model of Bodeet al. (2017) was constructed with an emphasis
particularly on such opinions. Bode et al. (2017) held
workshops multiple times with the participation of not
only researchers from universities but also a wide variety
of experts including government officials, representativesof non-governmental organizations (NGOs) andenvironmental volunteers. They then summarized theopinions from the experts to determine whether
interactions between species and interactions withenvironmental elements such as the amount of rainfall
would have positive or negative effects on the respective

47

species. Furthermore, Bode et al. (2017) also summarized
opinions concerning how environmental changes andanthropogenic impacts influence interactions among
species and interactions with environmental elements,
and constructed a model to predict the effects on
ecosystems.
Opinions of experts, however, are often not
quantitative and sometimes information simply cannot be
obtained. In particular, it is extremely difficult to obtain
actual measurement values for the strength of interactions
between species. In such a case, a small number ofparameter sets that can reproduce the target ecosystems
well are selected from a larger number of parameter sets,
the values of which are randomly determined ((4) and (5)in Fig. 2, Table 2). What is required first for selection of
the parameter set is that all species constituting theTable 2 Detailed procedure of (5) in Fig. 2.
Literature

Raymond Bodeet al.
et al.
(2011)(2015)

Bodeet al.
(2017)

Yoshidaet al.
(2019)

Total number ofparameter sets
examined(*1)

2 million

1 billion

500 (*2)

Number of selectedparameter sets

1000

15000

10000

1

Additional criteriaof selection

suitable
Best fit
for experts’ to real
opiniondata(*1): the total number of parameter sets examined is unknown. Raymond etal. (2011) repeated a process of confirming stability of a system byperforming simulations giving the strength of interactions randomly until
1000 parameter sets that allowed stable coexistence of all the species were
found. (*2): for each parameter set, 200 simulations with different
interaction matrix were conducted.

Fig. 2 Procedure for reproducing a target ecosystem.
A model to reproduce an ecosystem is created by following the procedure described in this figure. Information
to be used in each step is shown in the dotted line frame. For details of procedure (5), see Table 2.

48

K. YOSHIDA

ecosystem to be reproduced can coexist. This is common
to all studies
Several studies have adopted other criteria forparameter selection. Bode et al. (2017) selected those thatshowed behavior with respect to environmental changes
and anthropogenic disturbances as predicted by experts
who had participated in the workshops. Baker et al.
(2017) selected parameter sets that reproduced the
behavior observed in an ecosystem in Yellowstone
National Park after the introduction of wolves. Yoshida etal. (2019) selected one parameter set with the highest
ability to reproduce the actual measured values of thevegetation ratios on Nakoudo-Jima Island in the
Ogasawara Islands (Hata et al., 2007).

4. Types of Models
Although “model” is one word, models can bedivided into various types depending on the elements tobe emphasized when modeling. Masuda (1991)
mentioned three elements for constructing a model,
likening them to the three primary colors of light (red,green and blue) (Fig. 3): realistic variables, global domain
and basic understanding. “Realistic variables” (R) showcorrespondence to physical variables in the real world. A
model emphasizing this element will necessarily
introduce a process that works in the real world. “Global
domain” (G) means the model constructed is of anautonomous world, i.e., not a cutaway part of a world (acutaway part does not move autonomously), and models
the target world in its entirety. “Basic understanding” (B)means being able to explain the cause-and-effectrelationships in a model. This element may be restated as
being able to understand the model simply and clearly.
An ideal model would have these three elements but
is impossible to achieve. Therefore, two of these elements
are adopted for many models. A toy model adopts G andB, and represents the entire world with a small number ofvariables (processes). Ecosystem models that reproduce
multiple species by the Lotka–Volterra equation(Raymond et al., 2011; Bode et al., 2017; Baker et al.,2017, 2019) belong to this type. A process model adopts
B and R, and represents cause-and-effect relationships in
a cutaway portion of an ecosystem using realistic
variables. Models of Caut et al. (2007) and Bode et al.
(2015), which cut away a portion of a motif from within
an ecosystem and adopt a plurality of realistic variables,
belong to this type. A full model adopts R and G, andrepresents the entire world by combining realistic
processes. This type of model has the advantage that it iseasily seen as realistic. A representative example of thismodel is the global circulation model. Among theecosystem models introduced in this paper, only themodel of Yoshida et al. (2019) belongs to the full modeltype. This model includes material circulation processes
such as decomposition processes of excrement, remains

Fig. 3 Classification of simulation models (after Masuda, 1991).
The models introduced in this study are classified according to thecategories of Masuda (1991). Numbers in parentheses correspond to eachmodel: (1) Caut et al. (2007), (2) Raymond et al. (2011), (3) Bode et al.
(2015), (4) Bode et al. (2017), (5) Baker et al. (2017), (6) Baker et al.
(2019) and (7) Yoshida et al. (2019). For other items, refer to the text.

and dead leaves; the detritus food chain; and plant growth
based on nutrient contents. It not only describesinteractions among organisms simply by the Lotka–
Volterra equation but also introduces many processes that
actually work in ecosystems, such as preferences for prey
based on characteristics of the constituent species,changes in prey menus based on the optimum foraging
theory, and scrambling for places among plants or
seabirds.
Each model has disadvantages. The toy model isnecessarily an abstract model because of its structure.
Therefore, it makes comparison with reality difficult, andconsequently, it generally makes it difficult to gain abroad understanding. The process model is suitable fortracking modeled phenomena in a narrow range, butcannot explain behavior outside this narrow range. The
full model is necessarily a complicated model, and so it
makes it difficult to understand the cause-and-effectrelationships of phenomena occurring within the model.
Furthermore, it also causes practical problems in that agreat amount of effort is required for its construction andthe amount of time required for simulation becomes
longer.

5.	Changes in Ecosystems after Eradication ofInvasive Species
This section introduces knowledge for eradication ofinvasive species obtained from studies using theecosystem simulations introduced above.
As in the Ogasawara Islands, there are many known
cases of multiple invasive species. Thus, whether it would
be better to eradicate each of the species individually orPredicting Ecosystem Changes through Simulations
multiple species simultaneously must be clarified.
Therefore, several simulation studies have targeted suchcases (Caut et al., 2007; Raymond et al., 2011; Bode etal., 2015; Yoshida et al., 2019). A conclusion common tothese studies is that there is a greater restorative effect on
ecosystems when multiple invasive species are
simultaneously eradicated. If invasive species are
eradicated individually, there is a possibility that theremaining species will become unconstrained andincrease in biomass, causing unnecessary disturbances tothe ecosystem (Raymond et al., 2011; Yoshida et al.,2019). These results from simulations are also
corroborated by actual observations (Zavaleta et al.,
2001; Coomes et al., 2003; Johnson et al., 2007; Hoare etal., 2007; Griffiths, 2011; Innes & Saunders, 2011; Glenet al., 2013; Osawa et al., 2015).
However, since eradication of invasive species itself
is a disturbance to an ecosystem, the intensity of the
disturbance increases when multiple species are
eradicated at the same time. Therefore, it may become
difficult to predict the behavior of the ecosystem after
eradication. In an example by Yoshida et al. (2019), therestorative effect on the ecosystem certainly became
larger when non-native goats and rats were eradicatedsimultaneously from Nakoudo-Jima Island, but theecosystem entered a bi-stable state, that is, there was a
possibility of completely opposite results, in which thewhole island following eradication would change toforest or grassland (Fig. 4). Furthermore, although rare, it
was also suggested that, in an ecosystem containing a49

large area of invasive white popinac (Leucaena
leucocephala), where the overall diversity level was low
and oligotrophication was advancing, the vegetation
could be destroyed as a consequence of simultaneous
eradication of goats and rats (Yoshida et al., 2019).
Therefore, monitoring should be continued, and theecosystem appropriately managed to prevent extreme
events.
It generally takes time, effort and money to eradicate
multiple species simultaneously, so this can be impossible
in some cases (Bode et al., 2015). In fact, on NakoudoJima Island, only goats have been eradicated, while rats
and white popinac have not yet been eradicated.
Furthermore, if the order of eradication is mistaken,
species to be conserved could be adversely affected(Okochi, 2009). In such a case, it is necessary to
determine a schedule of the best order for eradication. For
example, Bode et al., (2015) showed that it was better toeradicate the predator side first when the invasive species
were in a predator–prey relationship. However, aphenomenon called meso-predator release (Courchamp etal., 1999), in which a rapid increase in intermediate
predators caused by eradication of top predators causes
secondary damage to the ecosystem, may be assumed insome cases; thus, careful responses are required according
to the circumstances of the target ecosystem. It is very
important in actual eradication projects to maximize theeffects of eradication and ecosystem restoration with alimited budget, so this will be a main theme in modellingstudies.

Fig. 4 Frequency distribution contour map for combinations of grassland and forest areas.
The horizontal axes on the left and the right sides show the grassland (%) and forest (%) areas,
respectively. The frequency is indicated by the colors shown in the legend on the right side. The
distribution is concentrated in two places: an extremity where grassland accounts for less than 10%
and forest accounts for 90% or higher; and an extremity where grassland accounts for 90% or higher
and forest accounts for less than 10%.

50

K. YOSHIDA

6. Future Directions

Acknowledgments

Future prediction studies using ecosystem models
have just started. The models are not perfect yet and, insome cases, the actual changes in ecosystems are notconsistent with the predictions. For example, Yoshida etal. (2019) predicted that all of Nakoudo-Jima Island
would revert to forest when only goats were eradicated.
Although the forested area has increased, it is at a muchslower rate than predicted by the model and bare groundstill remains (Hata et al., 2019). Furthermore, the invasive
white popinac has been increasing. In this regard,
inhibition of seedling colonization due to soil erosion andeffects such as exposure of oligotrophic subsoil havebeen indicated (Hata et al., 2019). These elements were
not included in the model used by Yoshida et al. (2019).
However, I never recommend adding processes andparameters to models indiscriminately. It is not always
true that a correct model can be constructed by making acomplex model with the introduction of many realistic
processes (Iwasa, 1990). In a well-known example, thebehavior of a model became unstable and the accuracy of
its predictions was actually lower when the model was
made more complex (Ludwig & Walters, 1985). On theother hand, models that are too simple sometimes
produce incorrect results (Matsuda, 1996). A good model
is one with the degree of complexity appropriate for the
purpose (Akçakaya et al., 1999). We should keep this in
mind.
Models are still being developed, so would bedesirable to construct a research system including a
positive feedback loop by which feedback of information
obtained from monitoring can be provided to models toimprove them and make their predictions more accurate(Fig. 5). If a positive feedback loop like this can beconstructed, it will help us conserve ecosystems
effectively and be able to understand them better.

I give special thanks to Naoki Kachi for giving me
this opportunity and guiding me to the Ogasawara
Islands, Hiroyuki Yokomizo for helping prepare thismanuscript, and Kenji Hata, Kazuto Kawakami, Syuntaro
Hiradate, and Takeshi Osawa for guiding me to the
Ogasawara Islands. This study was partly supported by
grant-in-aid for scientific research A (No. 24710038,
25241025, 16H01794) from the Japan Society for the
Promotion of Science.

Fig. 5 Expected study framework.

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Katsuhiko YOSHIDA
Katsuhiko Yoshida, Ph. D., is a senior researcher
at the National Institute for Environmental
Studies (NIES). His research field is mathematical
ecology. He is developing original models forvarious types of ecosystem including those of the
Ogasawara Islands. By means of computer
simulations, he is trying to reveal ecosystemchanges after various kinds of disturbance. He currently manages a research
project for NIES on the sustainability of ecosystems of the Ogasawara
Islands.
(Received 29 October 2019, Accepted 27 December 2019)