1 mitigation and adaptation strategies in the control of biological invasions charles perrings...

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Mitigation and Adaptation Strategies in the Control of Biological Invasions

Charles PerringsUniversity of York

4th BIOECON WorkshopVeniceAugust 2003

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The source of risks of biological invasions

• Biological sources of risk include species based factors (e.g. plasticity, dispersal ability) and system based factors (e.g. habitat fragmentation) in the invasiveness of species and the vulnerability of ecosystems.

• Abiotic sources of risk include, e.g., the impact of climate change on the distribution of species.

• Socio-economic sources of risk include, e.g., changes in trade transport and travel as a result of developments in the global trading system.

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Invasibility

• Ecosystems vary in their natural susceptibility to invasion. While pelagic marine systems appear to be least susceptible, mixed island systems, lake, river and near-shore marine systems are especially vulnerable (Heywood, 1995).

• The probability of establishment and spread also depends on way in which the environment is altered by human behaviour, and the way that potentially invasive species are introduced (Mack et al, 2000).

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Invasiveness

• Invasiveness depends partly in the characteristics of species, such as their plasticity, their dispersal ability, competitive ability, tolerance to temperature, salinity, oxygen concentration etc.

• The probability of establishment of intentionally introduced species is higher than that of unintentionally introduced species simply because intentionally introduced species have been selected for their ability to survive in the environment where they are introduced (Smith et al, 1999) and may be introduced repeatedly (Enserink, 1999).

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The response options

• There are two ways decision-makers can respond to the prospect of biological invasions: through mitigation and adaptation (Shogren, 2000; Shogren and Crocker, 1999).

• Mitigation involves actions that reduce the likelihood of introduction, establishment or spread of an invasives species. Mitigation implies action before the event or process.

• Adaptation involves actions that reduce the impact of introduction, establishment or spread without changing the likelihood that it will occur. Adaptation may involve actions taken before, during or after the process.

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Mitigation

Mitigation includes actions designed to reduce the likelihood of new introductions (invasiveness) or the vulnerability of potentially invaded systems (invasibility), Examples include:

• red, green (black, white) and amber lists, • quarantine restrictions,• Biosecurity in invasion pathways,• trade measures permitted under the Sanitary and

Phytosanitary Agreement, • actions to strengthen the resilience of existing systems to

invasion.

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Adaptation

Adaptation includes actions to reduce the impact of the introduction, establishment and spread of invasive species without reducing the likelihood of any one of these. It includes:

• Actions that reduce the impact of introductions,

• Actions that pool or transfer the risk of introductions,

• Actions that facilitate either of the above.

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Adaptation

Actions that reduce the impact of introductions, e.g.:• pest and pathogen reporting requirements• eradication• control or containment• measures to enable coexistence, defensive expenditures

Actions that pool or transfer the risk of introductions: • insurance

Actions that facilitate adaptation• establishment of markets in the effects of invasions • establishment of institutions/policies to support adaptation

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Predicting invasion risks

• Williamson (1999) many if not most new impacts by invasives are not predictable (see also Lawton 1999; Law et al., 1999; Kareiva et al., 1996). But….

• It is possible to understand both the invasiveness of different species, and the invasibility of different habitats (Rejmanek, 1989; Ross, 1991).

• Ecological models can i) predict numbers of weeds and the yield losses; ii) test the sensitivity of population models to find points at which control will be most effective; and iii) explore the general determinants of invasions. Watkinson, Freckleton and Dowling (2000).

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Framing the problem

• Suppose that the uninvaded system, S(0), can exist in m possible states: S1(0),…,Sm(0) and the conditional probability that the system is in state j at time t given that it was in state i at time s is given by pij(s,t) with jpij, (i,j = 1,2,...,m). The pij(s,t) are the set of transition probabilities.

• Suppose the introduction of an invasive species between time 0 and time t changes the set of states from S1(0),…,Sm(0) to S1(t),…,Sn(t) where n > m. The dynamical implications of species introductions are then summarised in the associated probabilities transition matrix, P.

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The limiting transition probabilities

• From the definition of the conditional probabilities it follows that pij(s,t) with pij(t,t+1) = hpih(t)phj and hence

that P(t+1) = P(t)P.

• It also follows that P(t)= Pt, and hence that in the limit

limt P(t)= P

• The elements of this define the limiting transition probabilities of the system.

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The limiting transition probabilities

• The chain is 'proper' if P has no eigenvalues ( 1) of absolute value 1.

• It is 'regular' if it is both proper and 1 is a simple root of the characteristic equation of P.

• All proper Markov chains have limiting transition probabilities. We are interested in Markov chains that are proper (and so have limiting transition probabilities) but that are not necessarily regular.

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The limiting transition probabilities: irregular chains

If P is proper but not

regular, it can be written

in the normal form:

This implies that in

the limit it takes the

form:

nnnmnmn

mmmmm

mm

PPPP

PPP

P

P

P

11

11111

11

0

000

000

0

00

00

Q

P

P

Pmm

mm

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Cases to be considered

a) An introduced species fails to establish, naturalise and spread

b) The probability that an introduced species succeeds in establishing naturalising and spreading is positive.

c) The probability that an introduced species succeeds in establishing naturalising and spreading is positive, but has different effects in different states of nature.

d) The probability that an introduced species succeeds in establishing naturalising and spreading is positive, but it does not converge to a stable population size.

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Case (a)

a) An introduced species fails to establish, naturalise and spread

0

00

00

Q

P

P

Pmm

mm

The invaded states fall within the last n-m rows and columns, ie, they vanish in the limit

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Case (b)

b) The probability that an introduced species succeeds in establishing naturalising and spreading is positive.

P is both proper and regular, and so is irreducible. This has a number of implications: – there are not multiple limiting states

(equilibria).

– the limiting transition probabilities are positive – the limiting transition probabilities are

independent of the initial state.

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Case (c)

c) The probability that an introduced species succeeds in establishing naturalising and spreading is positive, but has different effects in different states of nature.

• The probability transition matrix is reducible, each isolated stochastic matrices on the principal diagonal represents a separate attractor – an essential state of the system.

• Transitions are only possible between non-essential and essential states, between non-essential states in the same group, and between essential states in the same group.

• The limiting absolute probabilities of essential states are positive. • The limiting absolute probabilities of all other states are zero.

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Case (d)

d) The probability that an introduced species succeeds in establishing naturalising and spreading is positive, but it does not converge to a stable population size.

• The matrix Ph may be permuted to block diagonal form, in which the number of blocks is h and each block has the same dominant eigenvalue.

• The chain has a period of h:

hhh

h

h

h

P

P

P

P

00

00

00

22

11

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Limiting absolute transition probabilities and resilience• The probability that the system will be in state i at time t is

given by the absolute probability, pi(t), and the probability that it is in any one of n possible states by the vector p(t).

• Since the transition probabilities conditional on the state of the system at time t are given by Pt, p(t) evolves according to the recursive relation, p(t) = p(0)Pt, and the absolute limiting probabilities are defined by limt p(t) = p(0) Pt .

• These limiting transition probabilities of the system are indirect measures of the Holling-resilience of the limiting states.

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The control strategies: adaptation

• Adaptation changes the value of uncertain outcomes without changing the likelihood that they will occur, defensive expenditures being good examples.

• I take this to be action that directly changes the abundance of the invasive species (through, eg, pest control).

• A control, ui(t), changes the abundance of an invasive

species, xi(t), at time t.

tt uPxx

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The control strategies: adaptation

• Since the choice of u(t) has no implications for P it does not change the transition probabilities.

• If P is regular then the limiting absolute probabilities are independent of the initial probabilities. In this case the control has no implications for the eventual state of the system.

• If P is not regular then the limiting absolute probabilities are do depend on the initial probabilities. In this case the control does have implications for the eventual state of the system.

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The control strategies: mitigation

• Mitigation. This changes to the probability law itself through, for example, management of the 'invasibility' of systems or the regulation of invasion pathways associated with trade, transport and travel.

• The control implies actions that change the transition probabilities through selection of a feedback matrix, F(t), that works on the set of state variables over which the decision-maker has control, defined by Cx(t).

• u(t) takes the form F(t)y(t), where y(t) = Cx(t):

ttt CxFPxx

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The control problem

• The value function may be written in one of two forms:

which is maximised over the interval [0,T], subject to the dynamics of the system given by the relevant eq of motion.

• I consider the conditions (a) for the efficiency of the control policy, and (b) for the effectiveness of the control policy (the controllability of the system).

T

t

tT

T dtt,tYeWeEt,t,tV0

uxxux

T

t

tT

T dtt,tYeWeEt,t,tV0

FxxFx

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The efficiency of the control

• The first order necessary conditions on the vector of control variables, u(t), require that the controls be increased up to the point where the expected marginal benefits of control just offset the marginal social cost of control.

• In an adaptation strategy, the marginal social cost of control is simply the shadow price of the resource given the transition probability matrix P.

• In a mitigation strategy, the marginal social cost of control is the shadow value of the change in probabilities induced by the feedback matrix, F.

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The effectiveness of the control

• Controllability requires that the controls are able to reach the targeted state variables.

• The system is controllable if there exists a sequence {u(t)} or {F(t)}such that x(T) = xT given x(0) = x0 – i.e. a control sequence that will guide the system from x0 to xT.

• In adaptation strategies it requires that the rank of the controllability matrix U=(I,P,P2,...,Pn-1) is n.

• In mitigation strategies it requires that the rank of the controllability matrix Y=(F,PF,P2F,...,Pn-1F) is n.

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The effectiveness of the control: an illustration

Suppose that P has the form:

with limiting absolute transition probabilities p = (1,0), and that F is given by:

22212221

11 010

pppp

pP

2222

00

ffgF

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The effectiveness of the control: an illustration

Then P + F is:

with the same limiting absolute transition probabilities, i.e. p = (1,0).

• Because the system is not controllable, application of the control has no impact on the limiting absolute probabilities.

22222221

01

fpfpFP

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The effectiveness of the control: an illustration

But if F takes the form:

then P + F is:

and the limiting absolute transition probabilities, p , is a strictly positive vector.

2221

1211

ff

ffF

22222121

12111

fpfp

ffFP

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Western Flower Thripps: an example

• In 1986 the UK horticulture industry was invaded by the Western Flower Thripps, Frankliniella occidentalis.

• There were a number of separate introductions most due to the horticultural trade with the Netherlands.

• The species affected glasshouses only, and its introduction and subsequent spread between glasshouses was solely due to anthropogenic movements of plant material.

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Western Flower Thripps: an example

• It is unable to survive outside of glasshouses in UK conditions. Its spread within glasshouses is dependent on pest control regimes. In principle, therefore, the transition probabilities were controllable.

 • For two years the UK Plant Health Service sought to

eradicate the species, before admitting failure and advising producers to treat the organism as if it were endemic.

• The control method involved killing the organism wherever it was detected by destruction of all infected plant material, followed by application of pesticides.

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Western Flower Thripps: an example

• The focus of the control was the abundance of the organism itself, rather than the transition probabilities.

• It was believed that the system might converge on one of two states: with and without the organism.

• The controls were intended to increase the limiting absolute probability that the organism would be eradicated.

• However, because (a) the transition probabilities (the transmission mechanisms) were not addressed, and (b) the control was not efficient, the strategy failed.

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Propositions: Adaptation

i) Adaptation strategies will have no impact on the dynamics of the system if and only if the probabilities transition matrix/Markov chain is both proper and regular.

ii) Adaptation strategies may affect the limiting absolute transition probabilities of the system only if the probabilities transition matrix/Markov chain is proper but not regular.

iii)Adaptation strategies will be efficient only if the expected marginal net benefit of a control, ui(t), is equal to the user cost of the resource regulated by that control.

iv)Adaptation strategies will be effective only if the controllability matrix, (I,P,P2,...,Pn-1), is of full rank.

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Propositions: Mitigation

v) Mitigation strategies will affect the long run equilbrium properties of the system if the probabiltiies transition matrix/Markov chain is proper.

• Mitigation strategies will increase the resilience of the system in state i over some interval (s,t) only if fii(s,t) > 0 (that if fii(s,t) > 0, then fij(s,t) < 0 for at least one j).

• Mitigation strategies will be efficient only if the expected marginal net benefit of a control, fi(t), is equal to the user cost of all the processes affected by that control.

• Mitigation strategies will be effective only if the controllability matrix, (F,PF,P2F,...,Pn-1F) is of full rank

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The management of invasive species is a problem in the management of risk.

• Biological sources of risk include species and system based factors in the invasiveness of species and the vulnerability of ecosystems.

• Abiotic sources of risk include the impact of climate change on the distribution of species

• Socio-economic sources of risk include changes in trade transport and travel as a result of changes in the global economic system and enlargement of the EU.

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The management of invasive species is a problem in the management of risk.

• Private resource users already have an incentive to protect their own interests where these are threatened by invasive pests and pathogens.

• But they have little incentive to mitigate damage to others.

• Nor are such risks are commercially insurable for the reason that they are fundamentally uncertain and potentially very large. It is impossible to compute such risks actuarially.

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The environmental liability directive

• EC White Paper on Environmental Liability (COM(2000) 66 final) anticipates a Community framework directive on environmental liability that will provide resource users with a strong incentive to take account of their actions, and hence to seek to insure themselves against invasions losses.

• The proposed directive is expected to cover liability both for – damage due to the use, transport and release into the environment of

genetically modified organisms, micro-organisms, plant protection and biocidal products; and

– for damage to habitats or areas that subject to legal conservation/protection.

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MEAs and invasive species

• Environmental authorities have contractual commitments to address the problem of invasive species under – the Convention on Biological Diversity (CBD) , – the Convention on the Conservation of European Wildlife and

Natural Habitats (Bern Convention), and – the FAO International Plant Protection Convention (IPPC) .

• These commitments require an understanding of how invasion pathways have evolved with the expansion of trade, transport, travel and the greater coordination of activities in different locations.

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MEAs and invasive species

• A precondition for the rational evaluation of mitigation as an option to adaptation is an improvement in our understanding of the invasion outcomes associated with alternative actions.

• It must be possible to attach probability density functions to invasion outcomes in order to evaluate the invasion risks of different actions.

• If it is not possible to calculate invasion probabilities, then adaptation options will tend to dominate by default unless the potential risks warrant precautionary action.

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Precaution and scientific proof

• A precautionary policy is indicated where there exists no probability distribution of outcomes in which the decision-maker has confidence, but where possible outcomes include some with high and irreversible cost.

• This implies a weaker test than that required by standard scientific proof.

• Historic examples of such tests include ‘scientifically based suspicion’, ‘reasonable grounds for concern’ and the ‘balance of evidence’ (Harremoës et al, 2001). All involve ‘early warning signs’ rather than conclusive proof.

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Mitigation: a precautionary response

• The defining characteristic of a precautionary approach is that it enables learning without risking the most severe (but uncertain) consequences of an action.

• Since precautionary action is triggered by the potentially severe costs of novel policies, activities or events, learning should establish whether an action does or does not involve such costs (e.g. quarantine restrictions, field trials, research motivated moratoria).

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The public good element in mitigation and adaptation

• Mitigation generally offers benefits that cannot be captured by the individual undertaking the actions. It is, at best, an impure public good.

• Adaptation offers benefits that may be captured by the individual undertaking the actions - may be both rival and exclusive in consumption (e.g. defensive expenditures).

• Adaptation may also confer benefits or costs on others - may be non-rival and non-exclusive in consumption (e.g. eradication campaigns).

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The problem for equity

• In principle, adaptation strategies for the control of invasive species typically favour those with the resources to adapt after the fact.

• Mitigation strategies, on the other hand, typically favour those whose ability to adapt after the fact is strictly limited, or who are unable to pool the risks of invasions.

• But attitudes to risk depend on what decision-makers have to lose. The poor are generally willing to pay less to reduce risks than are the rich both because their ability to pay is less and because they have less to lose.

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The vulnerability of the poor

• The disproportionate impact of extreme events on low-income economies is due less to environmental factors than to the extreme vulnerability of the poorest sections of those communities.

• The poorest in society are often the most exposed to risk.

• The capacity both to avoid and to recover from disasters is quite limited, and the probability that people affected by disaster will lose their lives or livelihoods is often high.

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Implications for response options

• Mitigation is the more equitable response.

But…

• Given differences in adaptive capacity between poor and rich countries, there is an incentive for richer countries to bet on their capacity to respond to the threat posed by invasive species more effectively than poorer countries.

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Implications for Europe

• At a European scale there is a case for establishing an equivalent centre (to the ACDC) under the 6th Framework Programme, supported by resources to protect the community against the introduction of potentially invasive and harmful species.

• Internationally, there seems to be little alternative to the GEF sponsors, UNEP, UNDP and the World Bank.

• They should be urged to consider the establishment of a resource capable of protecting both global and regional interests from the threat of Biological Invasions by strengthening the weakest links in the chain.