Assessing the Relationship Between Propagule Pressure and Invasion Risk in Ballast Water (2011) / Chapter Skim
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4 Relationship between Propagule Pressureand Establishment Risk
4 Relationship between Propagule Pressureand Establishment Risk
Pages 72-113
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From page 72... ...
Managing invasion risk by setting a discharge standard assumes that, despite these powerful modifying factors, organism density alone is a reasonable predictor of establishment probability. Consequently, this chapter examines the relationship between organism density and invasion risk, and considers how this relationship might help inform an organism-based discharge standard.
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From page 73... ...
that is subject to a ballast water discharge standard. However, both the initial number of organisms NI (conventionally denoted N0 in population modeling)
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From page 74... ...
The Hypothetical Risk–Release Relationship In general, the relationship between invasion risk and propagule pressure is expected to be positive, although its shape is unknown. A priori, it might take any of a number of standard shapes including linear, exponential, hyperbolic, and sigmoid (Ruiz and Carlton, 2003)
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From page 75... ...
Relationship Between Propagule Pressure and Establishment Risk 75 A B FIGURE 4‐2 Conceptual application of a risk–release relationship to inform ballast water organism discharge standards. S is the observed risk of ballast‐mediated species inva‐ sion; N is the observed number of organisms released. (Axis units depend on whether the model represents a single species or multiple species.)
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From page 76... ...
Thus, it is expected that there should be at least one threshold in the risk–release relationship that could in principle prove useful in informing discharge standards. Despite understanding that the overall theoretical shape is hyperbolic or sigmoid for a single species, it is possible for a given set of risk–release data to be better characterized by a linear or even an altogether different model.
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From page 77... ...
Relationship Between Propagule Pressure and Establishment Risk 77 TABLE 4‐1 Approaches Taken to Modeling the Relationship Between Invasion Risk and Propagule Pressure Scale Sample structure1 Type Single species Multiple species examples examples Descriptive Statistical Memmott et al. Lonsdale (1999) Logistic regression: (2005)
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From page 78... ...
SINGLE-SPECIES MODELS It is informative to examine the risk–release relationship at the scale of a single species, for two main reasons. First, this approach allows examination of invasion scenarios for certain model species, such as fast growing, high impact, or commonly released invaders, which could be used to obtain upper bounds for discharge standards under best-case (for invasion)
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From page 79... ...
In a simple example, Drake and Jerde (2009) fit a spline, or a series of local regressions, to establishment probability as a function of propagule pressure in the scentless chamomile (Matricaria perforata)
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From page 80... ...
Whereas statistical models describe a relationship only over the range of data to which they are fit, mechanistic models are presumed to extrapolate well over the entire biologically realistic parameter space. Furthermore, descriptive models allow one to investigate the shape of a relationship, while mechanistic models force the user to specify the processes driving the relationship and to link causative variables explicitly.
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From page 81... ...
Relationship Between Propagule Pressure and Establishment Risk 81 A B C FIGURE 4‐3 Single‐species risk–release relationships obtained from descriptive models. (A) Spline fit to short‐term establishment probability of scentless chamomile (Matricaria perforata)
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From page 82... ...
To implement these probabilistic models, studies have examined population establishment over a range of initial population sizes either from directed experiments or from descriptive population data. Memmott et al.
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From page 83... ...
, an approach that has been applied more recently to the analysis of establishing invaders (Bartell and Nair, 2004; Neubert and Parker, 2004; Andersen, 2005) , and that has been proposed for use in comparing ballast water discharge standards (USCG, 2008)
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From page 84... ...
84 Propagule Pressure and Invasion Risk in Ballast Water BOX 4‐1 Probabilistic Model Framework This box illustrates the development of the simple probabilistic model in Leung et al. (2004) and shows how it provides insight into the overall shape of the risk–release relationship. It begins with a simple probability statement in which N is the number of propagules released and p is the individual establish‐ ment probability of each propagule. In this case, 1‐p is the probability of a sin‐ gle propagule failing to establish, and (1‐p)
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From page 85... ...
Relationship Between Propagule Pressure and Establishment Risk 85 These equations illustrate that simple probability statements combined with basic principles of population growth reveal two candidate shapes for the overall pE vs. N curve: hyperbolic or sigmoid. However, the shape of the curve for a given empirical dataset over a limited parameter space may appear linear, particularly for high (both curves) and low (sigmoid curve)
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From page 86... ...
86 Propagule Pressure and Invasion Risk in Ballast Water A B
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From page 87... ...
Relationship Between Propagule Pressure and Establishment Risk 87 1.0 0.8 Establishment probability 0.6 0.4 0.2 0.0 1 3 5 7 9 11 Initial number C D FIGURE 4‐5 Continued Single‐species risk–release relationships predicted by probabilistic models for the establishment probability of (A) the psyllid Arytai‐ nilla spartiophila (Memmott et al., 2005)
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From page 88... ...
However, ballast water discharge is a repeated event, which will tend to increase invasion risk, and the organisms may rapidly be redistributed in the physical environment, which may immediately alter the effective initial number of individuals with the
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From page 89... ...
Relationship Between Propagule Pressure and Establishment Risk 89 A B FIGURE 4‐6 Single‐species risk–release relationships obtained from dynamic demo‐ graphic simulation models. (A) Predicted proportion of populations exceeding 20 indi‐ viduals after 100 years from a population growth model of tree squirrels (Wood et al., 2007)
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From page 90... ...
90 Propagule Pressure and Invasion Risk in Ballast Water BOX 4‐2 Dynamic Demographic Model Framework This box illustrates the development of a dynamic demographic population model, following that formulated by Kramer and Drake (2010) . The model framework begins with the standard continuous time equation for a homoge‐ neous population of size N growing as a function of the difference between the birth rate ()
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From page 91... ...
. In a homogeneous environment, organisms will disperse and the effective initial population size will rapidly decrease; an advective environment and intraspecific behavior may either enhance
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From page 92... ...
For organism release from ballast water, there are snapshot surveys of particular size classes of organisms collected from a subset of tanks on a subset of ships arriving in selected locations over brief and recent time periods, identified to the lowest taxonomic level possible which nevertheless is often well
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From page 93... ...
Descriptive Models As for the single-species scale, statistical models of the multi-species risk– release relationship offer a phenomenological description of a pattern without requiring that the underlying mechanisms be specified. The majority of these studies, recognizing the difficulty of measuring propagule pressure directly, have measured a proxy variable of human activity ranging from population to transport to economic indices.
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From page 94... ...
94 Propagule Pressure and Invasion Risk in Ballast Water TABLE 4‐2 Spatial and Temporal Scale of Historical Invasion Records, and Spatial, Tem‐ poral, and Sampling Scale of Ballasted Organism Surveys in Inland and Coastal Waters of the U.S. and Canada Invasion Records Ballast Surveys Sample type Location Decades Sources Years (N) Sources (mesh size)
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From page 95... ...
. The density measures have been made with different methods and taxonomic foci, are recent and short-term relative to the accumulation of invaders over decades of ballast water release (Table 4-2)
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From page 96... ...
96 Propagule Pressure and Invasion Risk in Ballast Water A–C D–E FIGURE 4‐8 Descriptive models of multi‐species risk–release relationships. Comparison of log‐log (dotted) , log‐linear (dashed)
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From page 97... ...
Relationship Between Propagule Pressure and Establishment Risk 97 BOX 4‐3 Linear Statistical Multispecies Models Linear models have been used to estimate the multi‐species risk–release relationship for ballast water. To date, the most widely analyzed data at this scale are invasion trends in the Great Lakes. A variety of analyses have been conducted for this system using different data subsets, and different depen‐ dent and independent variables. In all the analyses, the data have been parsed into temporal intervals to provide multiple data points for model fitting. The results are not consistent among analyses. Depending on the data subset, there may or may not appear to be a signifi‐ cant risk–release relationship. Ricciardi (2001) used a linear regression to esti‐ mate the rate of all species invasion vs. shipping tonnage in net tons, by decade from 1900 to 1999 (y = 0.062x, r2 adj = 0.62, p<0.004)
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From page 98... ...
98 C A BOX 4‐3 Continued B D FIGURE 4‐9 Invasion patterns in the Great Lakes. (A) The number of invaders scales positively with net shipping tonnage by decade 1900–1999 (Ricciardi, 2006)
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From page 99... ...
Relationship Between Propagule Pressure and Establishment Risk 99 354 ships sampled in four U.S. ports, of which three are included in the 17 ana‐ lyzed; Minton et al., 2005) . Repeated random draws generated a bootstrapped estimate of the median and the first and third quantile invasion rates for each port. Together, these per‐capita invasion rates spanned four orders of magni‐ tude from 10‐11 to 10‐8, or one invasion for every 10 million to 10 billion organ‐ isms (Reusser, 2010)
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From page 100... ...
. The results from analyses to date are ambiguous and highlight that proxy variables may not always be reliable predictors of invasion risk, particularly across regions (see Box 4-3)
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From page 101... ...
, but not at the full scale of ballast water discharge. At present, therefore, there are not sufficient taxonomic information or empirical data to parameterize either a probabilistic or a demographic model for all the species in a ballast assemblage.
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From page 102... ...
Dynamic Demographic Models Like probabilistic models, dynamic demographic models could in principle be scaled up from the single-species scenario to model the combined risk of many species establishing. Again, such an exercise would require constructing and parameterizing a model with the identity, initial number, and invasion success of each population, and again, the resulting relationship would apply only to that suite of species.
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From page 103... ...
Relationship Between Propagule Pressure and Establishment Risk 103 BOX 4‐4 Outline of a Simple Multispecies Probabilistic Model The single‐species probabilistic model developed in Box 4‐1 is readily ex‐ tended to a multispecies probabilistic model. Equation 4‐3 in Box 4‐1 defines the establishment probability for a single species as pE = 1-e-N. This equation can be modified to accommodate S species, each with its own establishment probabilty ps.
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From page 104... ...
. The classical version of these models typically involves several restrictive assumptions including spatial homogeneity and random movement (at least at the population level)
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From page 105... ...
Obtaining a Discharge Standard from Multiple-Species Models Multi-species models represent an attempt to capture the complexity of wholesale ballast water release. Descriptive and mechanistic models can readily be formulated in conceptual and mathematical terms at this scale.
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From page 106... ...
The following conclusions and recommendations identify how models might be put to use at present, and in the future, to help inform a discharge standard. Ballast water discharge standards should be based on models, and be explicitly expressed in an adaptive framework to allow the models to be updated in the future with new information.
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From page 107... ...
In the case of ballast water, both invasion risk and organism density discharged from ballast water are characterized by considerable and largely unquantified, uncertainty. At the multi-species scale in particular, the existing data (historical invasion records vs.
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From page 108... ...
2009. Estimating establishment probabilities of Cladocera introduced at low density: an evaluation of the proposed ballast water discharge standards.
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From page 109... ...
2009. Factors influencing densities of non-indigenous species in the ballast water of ships arriving at ports in Puget Sound, Washington, United States.
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From page 110... ...
2010. Density Matters: Review of Ap proaches to Setting Organism-Based Ballast Water Discharge Standards.
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From page 111... ...
2004. Predicting invasions: propagule pressure and the gravity of Allee effects.
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From page 112... ...
2008. United States Coast Guard Ballast Water Discharge Standards Draft Pro grammatic Environmental Impact Statement.
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From page 113... ...
2005. Supply-side invasion ecology: charac terizing propagule pressure in coastal ecosystems.
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