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3  Sources of Variation Influencing the Probability of  Invasion and Establishment  An implicit assumption in the desire of the U.S. Environmental Protection Agency (EPA), the United States Coast Guard (USCG), and other organizations to develop and refine a numeric standard for discharged ballast water is that there is a quantifiable relationship between the number of individuals of a given species released in a ballast discharge and the probability of its eventual estab- lishment. These agencies have focused on inoculum density (ID, the number of organisms per unit volume of discharged ballast water), with the goal of setting the standard at a value(s) low enough to reduce or prevent the introduction of nonindigenous species. While a relationship between inoculum density and es- tablishment probability may exist, many other factors beyond the simple density of released organisms affect establishment success in aquatic (freshwater and marine) systems. These factors include the identity (taxonomic composition), sources, and history of the propagules, and their abundance (total number of organisms), quality, and frequency of delivery. Further influencing the outcome of propagule release is a host of factors that include both species traits and the recipient region’s environmental traits. The following equation reflects the complex and uncertain relationship be- tween propagule pressure, other variables, and the probability of establishment: PE = f (PP, ε) where PE = probability of establishment of a self-sustaining population of a spe- cies f = function PP = propagule pressure over a given temporal–spatial scale ε = a modifier that accounts for the many variables that can influence the survival, reproduction, and establishment of a species. The factors encompassed by ε (sources of variation) are discussed here to un- derscore the importance of both event-specific (the moment of the release of a   55 

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56    Propagule Pressure and Invasion Risk in Ballast Water    given inoculum from a single ship) and site-specific conditions when discussing invasion risk. Figure 3-1 summarizes these sources of variation. The figure commences at the release or discharge of ballast water. At this stage, critical variables include (1) inoculum abundance, density, and frequency, (2) the identity, diversity, source and history of the inoculating propagules, and (3) propagule quality. Post-discharge processes then strongly influence the fate of the released propa- gules. These variables include both species traits and environmental traits, cov- ering a very broad range of biological and ecological phenomena. These sources of variation shown in Figure 3-1 are reviewed below. This overview is not a comprehensive list of all factors that can influence invasion success, but is intended to illustrate significant sources of variation that are likely to influence the relationship between propagule supply and invasion outcome. PROPAGULE PRESSURE Inoculum Abundance, Density, and Frequency A long-standing presumption in invasion biology is that an increase in in- oculum abundance, density, and frequency will increase the probability of a species establishing a population in a new region. Thus, salmonid fish stocked at higher abundances and/or frequency are far more likely to colonize a new lake or reservoir than those that are not (Colautti, 2005). During World War II, the Korean War, and the Vietnam War, increased invasions occurred around the world correlated with increased shipping (and thus presumptive increase in spe- cies transportation and release) of those eras (Carlton and Norse, 2003). Nu- merous other such dose-response relationships are documented in the island biogeography, fisheries, and population biology literature (Cowx, 1997; Ricklefs and Miller, 1999; Losos and Ricklefs, 2009). Conversely, when inoculum ab- undance, density, and frequency decrease, a presumption is that the probability of species becoming established will also decrease. At its extreme, this is dem- onstrated by the history of vectors that cease to operate or are significantly re- duced. During the Atlantic commercial oyster industry that brought oysters (Crassostrea virginica) from the United States east coast to the west coast (an episode that flourished between the 1870s and 1920s), numerous Western Atlan- tic bay and estuarine species were introduced to the North Eastern Pacific Ocean (Cohen and Carlton, 1995). When the industry ceased, documented invasions by that vector ceased. When Japanese oysters (Crassostrea gigas) were intro- duced to France in the 1970s, numerous western Pacific species colonized Eu- rope (Goulletquer et al., 2002); when the industry ceased, documented invasions by that vector ceased. In terms of the focus of this report, inoculum density in ballast water can vary hugely (Chapter 1). ID is usually reported as the number of organisms

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Sources of Variation Influencing the Probability of Invasion and Establishment  57        FIGURE  3‐1   Examples  of  variables  altering  establishment  probability  (PE)  of  nonindigenous  species  released  in  ballast  water  and  sediments.   Processes  in  the  right  hand  column  impact  the  outcome  of survival, reproduction, and establishment. 

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58    Propagule Pressure and Invasion Risk in Ballast Water    (propagules) per cubic meter of water, representing the number of individuals that could be released upon discharge. Ballast systems can also have attached fouling organisms on tank walls that form more-or-less permanent (in ballast tanks) and transient (in flooded cargo holds) communities, as well as benthic assemblages. In the case of these fouling and benthic organisms, their densities would be reported as per square meter. Fouling and benthic communities could contribute propagules (larvae) to the water, such that ballast systems would then essentially be self-seeded. Fouling and benthic organisms, often not quantified or characterized in ballast communities, could conceivably be released as well during deballasting. As with inoculum density, inoculum frequency—the rate of propagule deli- very per a given cohort of vessels over a given time period—can vary widely (see Chapter 1). Thus, combining the concepts of ID with propagule source and frequency, an enormous range of scenarios can potentially strongly influence invasion outcomes. Patterns can range from one inoculum of ballast water being released from one source at one time into one location to multiple inoculations from multiple sources released at multiple times in multiple locations. If envi- ronmental conditions are suitable, a single large, albeit episodic, inoculum (a so- called “pulse” event) may result in a successful invasion, even when many smaller inocula (“press” events), even if constant and steady, may not (see Bender et al., 1984). As noted in Chapter 4, small releases spaced sufficiently close in time can effectively resemble a single large release, in the form of a “cumulative load.” Also noted in Chapter 4, and applicable here as well, is a “rescue” effect where multiple inocula act to sustain a nonindigenous population that might otherwise not have become established. Source and History of Propagules and Their Effect on Species Identity, Diversity, and Abundance Significant variation can exist in the characteristics of biota transported in ballast from different source regions. Even when controlling for total concentra- tion (as, for example, with a discharge standard), species composition of a cubic meter of ballast water loaded from different sources can exhibit strong spatial and temporal variation. Source regions can be separated into distinct biogeo- graphic zones (Ekman, 1953; Briggs, 1974; Udvardy, 1975) that are thought to experience differences in the capacity of their species to colonize a particular target location, assuming equal opportunity and similar habitat types (Mooney et al., 2005; Sax et al., 2005; Lockwood et al., 2007; Davis, 2009), such as the in- tertidal mudflat of a bay. The underlying mechanisms may include differences in physiological tolerance, competitive ability, and life history. For example, it has been suggested that biota from some geographic regions may be more suc- cessful in invading, compared to others, due to competitive superiority or partic- ular suites of life history characteristics that have evolved in those regions (Vermeij, 1991, 1996). Numerous studies demonstrate asymmetries in the im-

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Sources of Variation Influencing the Probability of Invasion and Establishment  59    portance of different donor regions as sources of invasions (e.g., Carlton, 1992; Galil and Zenetos, 2002), but the extent to which this is driven by specific traits versus differences in opportunity (transport) or biotic and abiotic characteristics of recipient regions remains largely unexplored. With respect to propagule history, there is considerable variation among ballast tanks and voyages in initial conditions (environmental and biotic), voyage durations/routes, and tank residence times that can affect the resident organisms. Past studies have shown that while some species can increase in abundance over time during the voyage (Carlton, 1985; Gollasch et al., 2000; Seiden et al., 2010), mortality rates (which can vary greatly among voyages) generally increase with residence time (Wonham et al., 2000; Verling et al., 2005). Propagule Quality Organisms are exposed to a variety of conditions during the transport process that can affect propagule quality. Propagules that arrive that are severe- ly physiologically compromised (damaged, starved, or otherwise stressed) are not as likely to survive as those that have enjoyed luxurious transport conditions. For example, ballasted communities are often closed systems that change over time, such that the organisms present experience changes in temperature, water chemistry, and food that affect both physiological condition and survivorship. Of those organisms that survive transit to a recipient port, physiological condi- tion upon arrival can affect the probability of establishment, in terms of both initial survival upon discharge and their eventual capacity to reproduce. Thus, the relationship between propagule supply and probability of establishment may differ greatly among individual discharge events, even when controlling for in- oculation density. While there are likely strong effects of season, duration, source and many other factors that affect the condition of organisms upon arriv- al, with likely consequences for establishment probabilities, few data are availa- ble that quantify the condition of organisms upon arrival or resulting variation in performance. SPECIES TRAITS Species traits that influence the density and quality of propagules upon dis- charge (discussed above) include a host of characteristics that describe the life history, genetics, biology, and eventual population abundance of a species should it survive initial release. The likelihood of colonization can differ dra- matically among species, reflecting a combination of both species-specific idio- syncratic characteristics as well as broader traits shared by related phylogenetic groups. It is easy to imagine how particular traits may confer advantages under certain circumstances, and there is a rich literature on this topic (Williamson,

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60    Propagule Pressure and Invasion Risk in Ballast Water    1996; Ehrlich, 1986; Sax et al., 2005, Lockwood et al., 2006; Cadotte et al., 2006). While there are numerous examples of “matches” of life history traits, trophic modes, or other characteristics with the new environment in which spe- cies have been introduced, there is still a great deal of uncertainty—and thus lack of predictability—in aquatic ecosystems about which particular traits confer greater advantage. Nonetheless, one should expect difference among species in probability of establishment (controlling for conditions and propagule supply) due to variation in a wide range of biological and ecological traits. Genetics: Bottlenecks, Quality, Variability, Enhancement, and Novelty Invasion success may be related to a complex array of genetic phenomena. A released inoculum may have only a small proportion of the total genetic ma- keup (called founder effect) of the species in question—a bottleneck which may seriously inhibit the ability of the population to adapt to the range of environ- mental conditions found in a new location. Potentially overcoming this lowered genetic diversity is that multiple inocula of the species may be continuously released into the same location, either from the same source or from multiple sources; both could work to enhance genetic heterozygosity. The genetic quality of founding individuals (the “breeding value” of individuals for total fitness; Hunt et al., 2004) can be altered by transportation conditions. Novel strains of already-present species could also be introduced. In North America, the distri- bution and abundance of the native common reed grass Phragmites australis has increased dramatically since the 1800s. Genetic analysis revealed that an intro- duced genetic strain of Phragmites was responsible for the observed spread (Sal- tonstall, 2002; Vasquez et al., 2005). When the European green crab Carcinus maenas, introduced to the United States east coast in the early 1800s, began spreading north into Canada in the 1980s, it was assumed that Carcinus was simply expanding its range; instead, new genetic lineages from northern Europe had been separately introduced and were responsible for the northern appearance of this species (Roman, 2006). In a similar fashion, species long thought to be incapable of being introduced could become established because of the introduc- tion of novel strains from new regions, due to altered trade routes. Life History Characteristics Invasion success can be profoundly influenced by life history characteris- tics. These include whether a species broods its young (direct development) versus releasing planktonic larvae, sexual versus asexual reproduction, and the ability to form resting stages. An example of direct development facilitating an invasion is the recent establishment of the North Atlantic rocky shore snail Lit- torina saxatilis in San Francisco Bay (Carlton and Cohen, 1998). This small periwinkle broods its young, which means that “miniature adults” can be re-

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Sources of Variation Influencing the Probability of Invasion and Establishment  61    leased directly from a parent onto the rock substrate, with potentially high juve- nile retention; the species can thus create dense populations of individuals that can easily locate and reproduce with each other. In contrast, newly released nonindigenous species that reproduce sexually and produce planktonic larvae are likely to have their larvae so widely dispersed that the likelihood of individ- uals surviving and settling out of the water adjacent to each other is low, unless inoculation and subsequent reproduction occur in a highly retentive environ- ment, as discussed below. Population Density and Abundance: Initial Post-Discharge Survival and the F1 population Propagules that have survived release may settle and grow in the new envi- ronment, and, if so, establish initial populations. At this point, this initial found- er population—although composed of individuals that have grown to adult- hood—faces extinction risk from many biological, ecological, physical, and chemical sources, prior to any of the individuals successfully reproducing. The founder population density is not the same as the inoculum density, which is the number of individuals released into the environment. Many of the individuals in the ID will perish upon release, leaving a proportion (which will vary across a vast spectrum of species and environmental regimes) to potentially survive, feed, and grow. If the founding population survives initial extinction and produces a first generation (F1), these new individuals, the first to be born in the new location, could, in turn, form dispersed metapopulations with a lowered probability of the newly colonizing species going extinct. The processes that influence the fates of both the initial founder population and F1 reflect the entire suite of species traits and environmental traits already discussed that influence the probability of colo- nization, including the variables of demographic stochasticity discussed in Chapter 4. Habitat, Trophic, and Physiological Breadth A broad combination of ecological traits can result in a complex repertoire of advantages or disadvantages in colonization success (Ehrlich, 1986; Sax et al., 2005; Cadotte et al., 2006; Lockwood et al., 2006; Davis, 2009). Species that are eurytopic (broad habitat and physiological breadth) and euryphagic (broad feeding range) may have a higher likelihood of initial survival than spe- cies that are stenotopic and stenophagic (of narrow habitat, physiological, and feeding range). Alternatively, given the almost inconceivable number of cir- cumstances that could greet released organisms, it is possible that particular functional groups, such as a certain trophic mode or a sedentary life-style, may be beneficial. Habitat, trophic, and physiological breadth of a colonizing species

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62    Propagule Pressure and Invasion Risk in Ballast Water    are closely linked to environmental compatibility and matching, discussed be- low. For example, species with more exacting food requirements may do well if their food is present, particularly those nonindigenous herbivores or carnivores that are introduced with, or at some point follow, their introduced plant and an- imal prey. Dispersal and Mobility A broad range of post-settlement dispersal mechanisms exist across thou- sands of species of protists, animals, and plants, ranging from passive means (such as entrainment on floating plants or anthropogenic debris—Thiel and Haye, 2006) to active means of locomotion (Levinton, 2008). This broad range of dispersal and mobility characteristics may influence initial colonization sce- narios and the differential importance of metapopulation extinction. Thus, spe- cies that disperse to new locations relatively quickly and form new populations may have a higher probability of permanent establishment (and conversely a lower risk of extinction) than those species with low dispersal capability. Close- ly linked to the importance of dispersal and mobility is the role of propagule retention in a habitable environment, discussed below. Environmental Matching Upon delivery to a recipient region, a suite of local environmental factors may affect the probability of establishment, such that delivery of identical inocu- la to multiple locations or at different times can result in very different estab- lishment outcomes. In other words, there is variation among sites in resistance or susceptibility to invasion (see Lonsdale, 1999, for detailed discussion of the components of invasion resistance). At its most extreme, the probability of es- tablishment can be low or zero, even when large numbers of propagules are re- leased, when the environment is inhospitable (for example due to severe mis- matches in temperature or salinity). There are often strong differences in species assemblages among different source habitats. The differences are perhaps most striking when comparing bi- ota from open-ocean, coastal marine bays and estuaries, and freshwater, which can differ in taxonomic groups, functional groups, species life histories, and species environmental tolerances. Such large inter-habitat differences are thought to result in major barriers to invasions. Thus, the probability for oceanic or freshwater species to become established in the variable salinity of coastal bays and estuaries is generally considered low. Indeed, this is the rationale for the use of mid-ocean ballast water exchange (Ruiz and Reid, 2007, Santagata et al., 2008). As with all biota, there are exceptions, where some species can oc- cupy a wide environmental range that extends across these disparate habitats.

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Sources of Variation Influencing the Probability of Invasion and Establishment  63    It is evident that each species has limits to its geographic distribution im- posed by environmental requirements and tolerances, defining its potential range; outside of this envelope, colonization cannot occur. While the specific environmental tolerances are not known for most marine and freshwater species, the likelihood of a successful invasion is expected to increase as environmental conditions approach those in its current range (i.e., when there is strong envi- ronmental matching). Thus, organisms transferred among biogeographic zones with similar environmental conditions (e.g., temperature regime) are more likely to find suitable conditions for colonization than those from dissimilar regions, controlling for other factors. On average, a decrease in the percentage of species that can colonize is expected as environmental similarity decreases. A mismatch in environmental conditions can range from permanent to tran- sient (controlling for the same inoculum). Transient mismatches can result from seasonal climatic variations, such as might occur for ballast being released in the winter versus summer, or daily weather variations, such as storms or unusual temperature conditions. More broadly, the environment can change over years, decades, or centuries, such that invasions previously excluded, despite long-term inoculation, can be successful at a later time. These changes encompass direc- tional climatic changes (such as warming temperatures), other long-term envi- ronmental shifts that may or may not be related to climate change (such as changes in regional hydrography that would alter propagule retention), or ma- crocyclic events (such as El Niño – Southern Oscillations or decadal oscilla- tions). While there is general consensus that environmental matching is a key vari- able in invasion outcome, and many different models exist to predict the poten- tial range of species (based on environmental matching) (Sax et al., 2005; Ca- dotte et al., 2006; Lockwood et al., 2006; Phillips and Dudik, 2008; Elith and Leathwick, 2009), many of the model outputs have not been rigorously tested, such that a precise understanding of variation in invasion probability as a func- tion of environmental dissimilarity is not yet available. ENVIRONMENTAL TRAITS A number of abiotic and biotic processes play a significant role in determin- ing the invasion success of organisms in discharged ballast water. These are discussed below, focusing first on abiotic characteristics of the recipient region, followed by biotic interactions between invaders and species in recipient re- gions, and finally the role of disturbance regimes.  Scale of Habitat Fragmentation or Connectivity Several characteristics of coastlines and bays/estuaries are likely to influ- ence the likelihood of establishment and spread of propagules introduced by

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64    Propagule Pressure and Invasion Risk in Ballast Water    ballast water discharge. These factors include the relative distance among bays/estuaries and appropriate recipient habitats along the outer coast, which can influence how connected these habitats are to each other. Increased continuity of invasible habitat, including artificial substrate (Glasby et al., 2007; Ruiz et al., 2009), will increase the connectivity of populations to the degree that propagules (e.g., larvae) can disperse with currents among other bays and invasible habitats. Increased connectivity can result in larger effective population sizes for invad- ers, and thus reduced likelihood of demographic stochasticity, inbreeding, or other problems associated with small populations. Conversely, highly frag- mented habitats can lead to population isolation and smaller population sizes, with increased demographic stochasticity and increased inbreeding. The diversi- ty of the habitats available with bays/estuaries will also be likely to increase the likelihood of establishment, due to increased likelihood of the presence of habi- tats with minimum requirements of food or shelter from predators. An example of the importance of habitat continuity and connectivity on risk of establishment is presented by the European green or shore crab (Carcinus maenas) and the Chinese mitten crab (Eriocheir sinensis). The European green crab successfully colonized nearly 1,500 km of shoreline along the North Amer- ican Pacific coast from Vancouver Island, British Columbia, to Monterey Bay, California, over an approximately ten year period after it was first discovered in San Francisco Bay around 1990 (Behrens Yamada et al., 2005). In contrast, since its discovery in the early 1990s, also in San Francisco Bay, the Chinese mitten crab has not expanded beyond the boundaries of the bay despite also hav- ing a planktonic dispersal stage. Unlike the European green crab, which is re- stricted to marine waters, mitten crabs require both marine and fresh water to complete their life cycle, returning to marine waters only for reproduction (Rud- nick et al., 2005). The differences in life history coupled with the spatial separa- tion of low salinity estuaries along the west coast may have provided an effec- tive obstacle to subsequent spread for mitten crabs but not for green crabs. Retention of Propagules in Habitable Environment: Diffusion vs. Retention The probability of invasive species establishment and spread can be influ- enced by aspects of the local and regional oceanography and geomorphology of the recipient habitat, typically a bay or estuary (Crisp, 1958; Cohen et al., 1995). Among the many factors that are likely to influence this probability are resi- dence time within the bay/estuary, magnitude and frequency of inputs from ad- jacent nearshore oceans, and inflow from local watersheds. These inputs will frequently dictate several physical properties of the bay/estuary that will influ- ence the likelihood that propagules introduced through ballast water will become established. One is the residence time of a given parcel of ballast water, which will strongly influence the degree to which planktonic stages (larvae, eggs, small juveniles) are retained in the bay/estuary vs. advected out to offshore waters. A second set of factors influenced by ocean and watershed inputs is water column

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Sources of Variation Influencing the Probability of Invasion and Establishment  65    properties such as temperature, salinity, turbidity, nutrient levels, and pelagic food web components including phytoplankton and zooplankton. Overall, the greater the residency time of a parcel of water and the greater the hydrographic restrictions that would lead to decreased larval export from a suitable environ- ment (Crisp, 1958), the greater the probability of the development and survival of initial and continuing populations. Biological Interactions with Resident Species The risk of establishment and subsequent spread can be influenced by a host of interactions between the invading propagules and organisms in the recipient habitat both native and nonindigenous. Decreasing the probability of establish- ment, for example, would be the presence of predators, competitors, pathogens, and parasites that might reduce the chances that newly introduced propagules from ballast discharge will result in an established population (Sakai et al., 2001). This Biotic Resistance Hypothesis (BRH), where invaders have no co- evolved defenses and competitive advantages and native consumers limit inva- sion, dates back to Elton (1958). The absence of species that would provide trophic support (for example, having no co-evolved prey capture strategies) or the absence of habitat created by other species (that might provide refugia) could also decrease the probability of establishment of ballast water invaders. Increasing the probability of establishment could be the absence of preda- tors and parasites that would normally curb an organism’s growth and survival in its native range. Increased success that is the result of “release from enemies” is referred to as the Enemy Release Hypothesis (ERH) (Torchin et al., 2003). The probability of establishment is also aided by the naïve prey hypothesis (NPH), which argues that naïve prey may be less defended against new invasive predators (Parker et al., 2006; Sorte et al., 2010). A related idea suggests that nonindigenous species may possess “novel weapons” (e.g., phytochemicals in plants, novel modes of consumption) that native species cannot overcome (Cal- laway and Rindenour, 2004). Similarly, the absence of co-evolved competitors (the Competitive Release Hypothesis, CRH, formerly called the Evolution of Increased Competitive Ability, Blossey and Notzhold, 1995) could facilitate invasion, particularly if the species involved represent novel trophic modes in the recipient system. Further facilitating establishment could be the presence of species that would provide food or refugia for invading propagules. Finally, it has also been shown that the success of invaders may be facilitated by other invasions, for example, where an introduced consumer selectively reduces na- tive prey, thus releasing an introduced competitor (Grosholz, 2005; Parker et al., 2006). This ability of one invader facilitating others could potentially result in a process referred to as invasional meltdown (Simberloff, 2006). The relative importance of these hypotheses is debated, and evidence for them in marine systems is often equivocal (Parker et al., 2006). An interesting example of a food web interaction that has affected invasion success involves

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66    Propagule Pressure and Invasion Risk in Ballast Water    the salt marsh cordgrass Spartina alterniflora, native to the Western North At- lantic Ocean, and hybrids. The expansion of hybrid Spartina in San Francisco Bay and Spartina alterniflora in Willapa Bay, Washington, has resulted in dra- matic shift towards a food web dominated by deposit feeders, many of them nonindigenous, at the expense of native surface-feeding worms and clams (Neira et al., 2005, 2007; Levin et al., 2006; Grosholz et al., 2009). Other invasive spe- cies in San Francisco Bay such as the North Atlantic mussel Geukensia demissa are strongly dependent in certain localities on the habitat created by Spartina. This facilitation appears strongest for invading species that have evolved in ha- bitats where Spartina was present historically (Grosholz, unpublished data). This is a good example of how a species can modify marine and estuarine habi- tats and dramatically change the food web, in some cases increasing abundances of other nonindigenous species at the expense of native species. Disturbance Regimes Another factor that may influence the probability of establishment of prop- agules from ballast water is the issue of human disturbance (habitat modifica- tion, water quality changes, and so forth) and how this disturbance could influ- ence the likelihood of both establishment and spread. Although this idea has a long history in invasion biology (Elton, 1958; Mack et al., 2000), studies of in- vasions in other systems have provided contradictory evidence that disturbance increases the likelihood of establishment (Simberloff, 1989; Case, 1996; Stohlgren et al., 1999; Mack et al., 2000). In marine systems, this idea has not been rigorously tested and remains an open question (see Ruiz et al., 2000). Studies have shown that reducing space competition and diversity can locally (at the small patch level) increase invasion success (Stachowicz et al., 1999). How- ever, this is only a small-scale effect, and the degree to which human distur- bance opens up free space in space-limited systems and whether this increases the likelihood of establishment and subsequent spread remains uncertain. THE BEST-CASE SCENARIO FOR AN INVASION The above sections suggest the conditions under which the probability of the invasion of a nonindigenous species would likely be maximized. High- quality propagules released in a retentive environment that closely matches that of the species’ origin are more likely to survive and develop initial populations. Inocula with high genetic variability may also be favored. Further favoring es- tablishment are biological characteristics such as being eurytopic and euryphag- ic, and life history characteristics such as direct development, asexual reproduc- tion, and/or the ability to form resting stages. Once initial reproducing popula- tions are formed, efficient dispersal capabilities combined with habitat connec- tivity may insure the development of large effective population sizes that would

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Sources of Variation Influencing the Probability of Invasion and Establishment  67    reduce inbreeding and the probability of extinction. Finally, significantly in- creasing the probability of establishment could be the absence of predators, pa- rasites, and competitors. While it is extremely difficult to quantitatively prioritize all of these va- riables that vary across species, space, and time, initial habitat compatibility and propagule retention are likely to be critical. The importance of the latter two variables underscore the relative role of inoculum density: very low inocula that match these two scenarios along with the other “best-case” criteria above could lead to highly successful invasions. Thus, one female crab with stored sperm introduced into a lagoon with highly restricted tidal exchange could produce an initial and even dense first-generation population of crabs that could then inter- breed, and eventually exit the site that had exacted as an incubator. Conversely, of course, any best-case situation can quickly turn into invasion failure, such that propagules of the very highest quality (in terms of potential for settlement and survival) could arrive at a location where there would be instant mortality from any number of variable physical, chemical, or biological processes. In conclu- sion, the thread of inherent stochasticity winds inextricably through invasion dynamics. CONCLUSIONS Although a general assumption is that a decrease in the delivery of propa- gules of nonindigenous species—in terms of both release abundance and fre- quency—to a new region will result in a decrease in invasions, the precise na- ture of the response can vary enormously over species, time, and environments. In short, while inoculum density is a key component, it alone is not sufficient to explain the entire invasion process, which involves a large number of variables. These variables arise from a complex, reticulate mesh that weaves together the broad concept of propagule pressure (which itself involves many inter-related and often difficult-to-quantify phenomena and processes) with species traits and the multifaceted biological, ecological, physical, and chemical nature of the re- cipient environment, which changes over time. Inoculum density, the basis of proposed discharge standards, is thus but one of scores of variables that can and do influence invasion outcome. Any method that attempts to predict inva- sion outcomes based upon only one factor in the multi-dimensional world of the invasion process is likely to suffer from a high level of uncertainty. REFERENCES Behrens Yamada, S., B. R. Dumbauld, A. Kalin, C. E. Hunt, R. Figlar-Barnes, and A. Randall. 2005. Growth and persistence of a recent invader Carcinus maenas in est- uaries of the northeastern Pacific. Biological Invasions 7:309–321. Bender, E. A., T. J. Case, and M. E. Gilpin. 1984. Perturbation Experiments in Commu-

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