A mechanistic model for understanding invasions: using the environment as a predictor of population success
2011; Wiley; Volume: 17; Issue: 6 Linguagem: Inglês
10.1111/j.1472-4642.2011.00791.x
ISSN1472-4642
AutoresCarly Strasser, Mark A. Lewis, Claudio DiBacco,
Tópico(s)Cephalopods and Marine Biology
ResumoDiversity and DistributionsVolume 17, Issue 6 p. 1210-1224 BIODIVERSITY RESEARCHOpen Access A mechanistic model for understanding invasions: using the environment as a predictor of population success Carly A. Strasser, Corresponding Author Carly A. Strasser Centre for Mathematical Biology, University of Alberta, Edmonton, AB T6G 2G1, Canada Department of Oceanography, Dalhousie University, Halifax, NS B3H 4J1, Canada Carly A. Strasser, National Center for Ecological Analysis and Synthesis, University of California Santa Barbara, 735 State Street, Santa Barbara, CA 93101, USA.E-mail: strasser@nceas.ucsb.eduSearch for more papers by this authorMark A. Lewis, Mark A. Lewis Centre for Mathematical Biology, University of Alberta, Edmonton, AB T6G 2G1, CanadaSearch for more papers by this authorClaudio DiBacco, Claudio DiBacco Department of Oceanography, Dalhousie University, Halifax, NS B3H 4J1, Canada Fisheries and Oceans Canada Bedford Institute of Oceanography, Dartmouth, NS B2Y 4A2, CanadaSearch for more papers by this author Carly A. Strasser, Corresponding Author Carly A. Strasser Centre for Mathematical Biology, University of Alberta, Edmonton, AB T6G 2G1, Canada Department of Oceanography, Dalhousie University, Halifax, NS B3H 4J1, Canada Carly A. Strasser, National Center for Ecological Analysis and Synthesis, University of California Santa Barbara, 735 State Street, Santa Barbara, CA 93101, USA.E-mail: strasser@nceas.ucsb.eduSearch for more papers by this authorMark A. Lewis, Mark A. Lewis Centre for Mathematical Biology, University of Alberta, Edmonton, AB T6G 2G1, CanadaSearch for more papers by this authorClaudio DiBacco, Claudio DiBacco Department of Oceanography, Dalhousie University, Halifax, NS B3H 4J1, Canada Fisheries and Oceans Canada Bedford Institute of Oceanography, Dartmouth, NS B2Y 4A2, CanadaSearch for more papers by this author First published: 07 June 2011 https://doi.org/10.1111/j.1472-4642.2011.00791.xCitations: 7AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract Aim We set out to develop a temperature- and salinity-dependent mechanistic population model for copepods that can be used to understand the role of environmental parameters in population growth or decline. Models are an important tool for understanding the dynamics of invasive species; our model can be used to determine an organism's niche and explore the potential for invasion of a new habitat. Location Strait of Georgia, British Columbia, Canada. Methods We developed a birth rate model to determine the environmental niche for an estuarine copepod. We conducted laboratory experiments to estimate demographic parameters over a range of temperatures and salinities for Eurytemora affinis collected from the Nanaimo Estuary, British Columbia (BC). The parameterized model was then used to explore what environmental conditions resulted in population growth vs. decline. We then re-parameterized our model using previously published data for E. affinis collected in the Seine Estuary, France (SE), and compared the dynamics of the two populations. Results We established regions in temperature–salinity space where E. affinis populations from BC would likely grow vs. decline. In general, the population from BC exhibited positive and higher intrinsic growth rates at higher temperatures and salinities. The population from SE exhibited positive and higher growth rates with increasing temperature and decreasing salinity. These different relationships with environmental parameters resulted in predictions of complex interactions among temperature, salinity and growth rates if the two subspecies inhabited the same estuary. Main conclusions We developed a new mechanistic model that describes population dynamics in terms of temperature and salinity. This model may prove especially useful in predicting the potential for invasion by copepods transported to Pacific north-west estuaries via ballast water, or in any system where an ecosystem is subject to invasion by a species that shares demographic characteristics with an established (sub)species. Introduction Estuarine ecosystems are susceptible to invasions by planktonic non-indigenous species, primarily via ballast water discharges of commercial ships. Estuaries in the north-east Pacific are particularly susceptible owing to high ship traffic from Asia and among ports along the North American coast (Carlton, 1987; Cordell & Morrison, 1996; Cordell et al., 2008). Copepods are among the most abundant taxa found in ballast tanks (Smith et al., 1999; Cordell et al., 2009), accounting for more than 56.3% (96 of 176 taxa) of the total number of organisms found in ballast samples entering Vancouver harbour (C. DiBacco unpublished data). Furthermore, ballast release has been implicated as the source for several successful cases of invasive copepod establishment (Hirakawa, 1988; Orsi & Ohtsuka, 1999; Seuront, 2005; Cordell et al., 2008). In some cases, these introductions may have contributed to displacement of native copepod species (Gubanova, 2000; Horvath et al., 2001; Riccardi & Giussani, 2007; Cordell et al., 2008), with potential consequences for higher levels of the food chain (e.g. Hobbs et al., 2006; Bryant & Arnold, 2007). A significant amount of research on invasive species has been devoted to risk assessment, or determining the potential for invasion of a particular habitat based on an array of factors, such as ecology, economics or physiology. Factors that have been considered include propagule pressure (Lockwood et al., 2005; Colautti et al., 2006), prior invasion success (Moyle & Marchetti, 2006), diversity of the invaded habitat (Borrvall & Ebenman, 2008) and similarity between native and introduced habitats (Carlton, 1996). Many of the published studies are correlative in nature, using statistical approaches to find patterns consistent across invasive species. This approach is contrasted with a mechanistic approach, wherein data on functional traits are used to infer potential ranges (Kearney & Porter, 2009). Correlative species distribution models are useful because they require minimal knowledge of the mechanistic links between the environment and the organism; this can be advantageous for species that are poorly studied. A disadvantage of such correlative studies is that their predictive power outside of the study environment is minimal (Davis et al., 1998). Many of the models used to predict invasion are ecological niche models (ENM) (reviewed in Guisan & Zimmermann, 2000; Peterson, 2003). ENM has gained attention recently as a potentially useful tool in the prediction of invasive species spread. Most uses of this type of model tend to rely on current species distributions combined with conditions in the invaded region to predict potential spread (e.g. Peterson & Vieglais, 2001; Peterson & Robins, 2003; Steiner et al., 2008), although more recently, there have been examples of combining ENM and physiological parameters to predict invasion (Kearney & Porter, 2004; Brown et al., 2008; Ebeling et al., 2008). A mechanistic approach to understanding species distributions, which includes understanding the limitations of distribution and abundance, provides more robust data that can be extrapolated to new environments (Kearney & Porter, 2009). In this study, we develop a mechanistic model for copepod population dynamics as a function of environmental parameters. Both correlative and mechanistic approaches are useful for understanding invasibility but require different types and amounts of data. It is useful to compare results from both approaches, and in the case of invasive species, such comparisons may better determine the potential for successful invasion of a given habitat (Drake, 2005). It is widely argued that propagule pressure is among the most important factors in determining invasion success (Kolar & Lodge, 2001; Lockwood et al., 2005). This includes number of individuals released and number of introduction attempts (both aspects of propagule pressure) (Kolar & Lodge, 2001). There are also characteristics that are common in groups of species that invade or spread and therefore are also important for determining success. For instance, in fish species, there is increased probability of invasion success if the species has a history of successful invasion in other areas, high physiological tolerance and a large number of propagules released (Moyle & Marchetti, 2006). Other biotic factors that are often significantly associated with invasion success are adult size, size of native range, trophic status and reduced biomass or diversity of native populations (Marchetti et al., 2004; Dzialowski et al., 2007). Along with propagule pressure and species characteristics, environmental characteristics are among the most important factors in determining invasion success. In fact, Moyle & Light (1996) found that abiotic factors were more important than biotic factors for establishments of invasive fishes. In a meta-analysis of 49 studies, Hayes & Barry (2008) found that the only characteristic that was consistently significantly associated with successful invasion was a close match between the native and introduced habitats. This is because invasive species must be able to survive and reproduce in the invaded habitat. Information on a species' demographic characteristics as a function of important environmental parameters would be useful in predicting its potential success as an invader (Ruesink et al., 1995). In most cases, there is no information available on intrinsic population growth rate as a function of environmental parameters for invasive species. Given a particular range of environmental parameters known to be important for population dynamics, a formula for calculating growth rate would allow researchers to estimate the risk of successful establishment for a given habitat. More interesting, perhaps, would be the comparison of population growth rates of native and invasive species, or among two or more invasive species. In this way, it may be possible to explore processes such as competition and niche differentiation that affect species distributions. Here, we develop a mechanistic model for calculating population growth rate and net reproductive rate as a function of temperature and salinity for an estuarine copepod. The model requires information about the proportion of individuals moving into the adult stage over time, mortality rates and fecundity. We parameterize the model using data collected on the calanoid copepod Eurytemora affinis, in a series of laboratory experiments. E. affinis is a species complex (Lee, 2000; Lee & Frost, 2002), occurring primarily in brackish environments. We found that over the range of temperatures and salinities tested, there is a zero-growth isocline in temperature–salinity space that demarcates where the population would be able to grow, and where it would decline to zero. We then reparameterized the model using previously published data on a separate clade of E. affinis from the Seine Estuary, France (Devreker et al., 2007, 2009). We were then able to compare mechanistic niches for the two clades of E. affinis. This serves to illustrate the utility of the model for predicting which (sub)species would likely dominate a given environmental niche based on the effects of abiotic factors on population growth rate. Model results for the single species case show that, given data on the relationship between environmental parameters and demographic parameters, regions of population growth or decline can be determined. Model results from comparing two (sub)species may provide insight into interactions between environmental (temperature and salinity) and biological (i.e. population growth rate) factors that influence species presence–absence. This may be an especially useful tool in studies where an invasive organism has the potential to displace a native species that occupies a similar niche. Eurytemora affinis is a dominant organism in many temperate estuaries. The species complex has the most eurytolerant members of its genus, occupying habitats with salinities that range from fresh to full-strength seawater (Heron, 1976). E. affinis is an important component of the estuarine food web (Koski et al., 1999; Tackx et al., 2003; Reaugh et al., 2007), including its role as a food source for higher trophic levels (Hardy, 1924; Meng & Orsi, 1991; Winkler & Greve, 2004). The ubiquity of E. affinis in the marine environment and its recent invasion to fresh water (Lee, 1999; Lee & Bell, 1999, and references therein) make it an ideal model organism to examine how temperature and salinity affect population dynamics in the laboratory. Eurytemora affinis is also an interesting organism for our study because of the extensive work that has been conducted on the species complex's ability to adapt to novel habitats and tolerate different salinity regimes. Although the species complex is capable of inhabiting a wide range of salinities, Lee et al. (2003) showed that there are trade-offs associated with a population evolving in high- vs. low-salinity environments. We can therefore assume that, in an estuary where an individual experiences a range of environmental conditions, that individual will maximize its time in the habitat for which it is most evolutionarily suited. Furthermore, using laboratory experiments where E. affinis was reared over multiple generations at a range of salinities, Lee et al. (2007) provided evidence that E. affinis populations adapted to a range of salinities have sufficient levels of genetic variation for fitness-related traits upon which selection could act, thereby affecting their ability to invade. Natural selection therefore plays an important role in determining E. affinis' ability to survive and reproduce in a particular salinity regime (Lee & Petersen, 2003). There have been several laboratory studies examining the effects of temperature and salinity on E. affinis-specific demographic parameters, including development time (Vuorinen, 1982; Nagaraj, 1988; Ban, 1994) and egg production (Hirche, 1992; Ban, 1994; Andersen & Nielsen, 1997; Devreker et al., 2009); however, none of these previous studies examine the effects of temperature and salinity on population growth rate explicitly. Here, we collected data on multiple population parameters for the purposes of determining the overall effects of temperature and salinity on the population via calculation of population growth rate. Methods Population model We used the Lotka integral equation to model the copepod birth rate; Lotka's model is a continuous-time equation that tracks birth rates over continuous time for an age (or stage)-structured population (Sharpe & Lotka, 1911; Lotka, 1939): (1) where B(t)dt is the number of female births in the time (t) interval t to t + dt, l(a) is the fraction of newborn females surviving to age a, and m(a) is the rate of production of females by females of age a. G(t) is the contribution of all females already present at t = 0; our model was structured such that G(t) = 0. To solve (1), we directly substitute B(t) = Qert, which gives the Euler–Lotka equation: (2) If we define the function ψ(r) to be (3) we can write the characteristic equation as ψ(r). There is exactly one real root r* that solves (2), giving the growth rate of the population. The net reproductive rate R0, which is the mean number of offspring per individual over its lifetime (Caswell, 2001), occurs where ψ(r) crosses the ordinate: (4) We can therefore obtain the population growth rate r* and net reproductive rate R0 by substituting appropriate equations for l(a) and m(a) into (2) and (4). The benefit of calculating the intrinsic rate of population increase, r, is that it integrates age at first reproduction, survivorship, brood size and frequency, and longevity into a single statistic. For E. affinis, (see Parameter estimation). Given that k is an integer, the gamma cumulative distribution function simplifies to (5) By substituting and simplifying, (2) becomes (6) The integral in (6) can be solved using integration by parts, such that (7) Substituting (7) into (6) yields (8) This can be numerically solved for the population growth rate, r. Experiments Laboratory set-up and algae culturing Experiments were conducted at the Centre for Aquaculture and Environmental Research, Fisheries and Oceans Canada, West Vancouver, British Columbia. Seawater (32 psu) and creek water (0 psu) were pumped from nearby sources to the laboratory facility and filtered to remove particles > 1 μm; brackish salinities used in the experiment were achieved by mixing seawater and creek water. We chose natural seawater and freshwater because they are more likely to mimic natural conditions. This does, however, introduce the possibility factors other than salinity differing among treatments, such as trace metals, pollutants or other dissolved chemicals. Two large incubators (5 and 10 °C) and one cold room (15 °C) were used to maintain experimental temperatures. Temperature loggers were used throughout the experiments to verify that environmental conditions were stable. Incubators and the cold room were kept on 12-h light/dark cycles. The marine green alga Tetraselmis suecia was cultured as food for all stages of E. affinis. T. suecia has a high lipid level and is mobile; therefore, it is easily grown in a laboratory setting. Preliminary experiments showed that T. suecia fluorescence was unaffected by transfer from higher to lower salinity waters and vice versa, without acclimation periods, suggesting that cells were not compromised by salinity changes. A high tolerance to salinity changes was important since the same algal stocks were used to feed copepods at salinities ranging from 4 to 12 psu. T. suecia was therefore cultured at 12 psu and added directly to copepod cultures irrespective of salinity conditions. The stock culture was kept at 15 °C. Broodstock collection and processing Eurytemora affinis adults were collected during high tide on two dates in September 2009 from the Nanaimo River Estuary on Vancouver Island, British Columbia (49°7′49.3′ N, 123°53′ 35.9′ W). Previous surveys showed E. affinis to be abundant in this location (Cordell & Morrison, 1996). Water temperature was approximately 16 °C, and salinity ranged from 3 to 8 psu over the course of the one-hour collection periods. A 250-μm plankton net with a 0.5-m-diameter opening was pulled horizontally by hand in 1–1.5 m deep water for approximately 10 m. Net contents were then rinsed into jars using estuary water and stored in a cooler for transport back to the laboratory. Field samples were stored at 15 °C until processed. Samples were first sieved to remove material > 2 mm. The remaining material was placed in a 500-ml beaker with 12 psu 15 °C seawater. Organic matter and non-copepod macroinvertebrates were removed via pipette from field samples after 2–3 h of settling time. Collections were stored overnight at 15 °C; the following day, any remaining organic matter and non-copepod macroinvertebrates were removed via pipette. Beaker contents were transferred to 500-ml plastic beakers with 200-μm mesh bottoms, nested inside solid-bottomed beakers, containing filtered 12 psu seawater and T. suecia at 8 × 104 cells ml−1. The mesh retained adult-sized copepods but allowed naupliar and early copepodite stages to pass through to the bottom beaker. Adult copepods from several beakers were collected and examined under a dissecting microscope to confirm the exclusive presence of E. affinis. In all cases, no species other than E. affinis were found. Species identification was made using Katona (1971). Photographs were taken of several E. affinis individuals and sent to J. Cordell (University of Washington) for further species confirmation. Lengths of individuals collected ranged from 400 to 800 μm with a 1:1 sex ratio. After 3 days in the laboratory setting, all beakers contained newly hatched nauplii, indicating that conditions were suitable for copepod viability. Adults were mixed and divided into one of the nine treatment combinations of three temperatures (5, 10 and 15°C) crossed with three salinities (4, 8 and 12 psu). Nauplii produced in the first week after transfer to new salinity and temperature conditions were not used for experiments; they were removed from beakers and cultured for use as future broodstock. Experimental setup After the initial week of broodstock acclimation, newly hatched nauplii were collected from broodstock beakers daily for experimental use. Nauplii from multiple beakers of the same treatment conditions were combined, and the number of nauplii was estimated by subsampling a small volume and counting the number of individuals present. Nauplii for each treatment were then divided into one of three 500-ml replicate beakers comprised of an internal beaker with a 50-μm mesh bottom nested in a solid-bottom beaker. Tetraselmis suecia was added at a concentration of approximately 8 × 104 cells ml−1. Copepods were reared from the first naupliar stage under treatment conditions. When all individuals were passed the copepodite IV stage, the interior beaker mesh was changed to 150 μm. This allowed late-stage copepodites and adults to be retained while facilitating removal of any newly hatched nauplii. Individuals in beakers were counted and their stages noted every 2 days for 60 days or until there were no live copepods remaining. Counting and staging involved estimating (1) the proportion of individuals in each developmental stage, (2) population size, and (3) the number of newly hatched nauplii. The proportion of individuals in each stage was estimated by subsampling beaker contents and examining five haphazardly chosen individuals under both a dissecting and a compound microscope. Stage identifications were made using Katona (1971). Subsampled individuals tended to be of the same stage, especially earlier in the experiment. Population size was estimated by averaging the number of copepods in five 1 ml samples to obtain the average number of individuals per millilitre. This average was then used to extrapolate back to the entire population by multiplying by the beaker volume. Once females began producing nauplii, the number produced was estimated in the same way. Nauplii were removed from experimental beakers after counting so that only the original population was assessed for population size and proportion in each stage. Parameter estimation We estimated the relationship between parameters associated with maturation rate, mortality rate, fecundity, and temperature and salinity. These rates were assumed to have a quadratic relationship with both temperature and salinity: There is an optimum value for both temperature and salinity above and below which rates should result in slower population growth. We therefore fit our data to a model with quadratic terms for each of the parameters estimated of the form (9) After fitting the model to the data, we then systematically removed terms and compared the resulting models using F-tests. All models included the τ1T and τ2T terms; of the remaining terms, only those that significantly affected the fit were kept. Maturation rate Previous studies have shown that a gamma distribution best describes the expected proportion of individuals in a given stage over time for copepods (Manly, 1988; Klein-Breteler et al., 1994; Souissi et al., 1997). The gamma distribution is traditionally used for 'waiting times', that is events (such as moving to a new stage) that occur with some probability following a binomial distribution. We therefore assumed stage duration followed a gamma distribution with a scale parameter b and a shape parameter k. To calculate maturation rate for our model, we are only interested in the proportion of individuals that pass from the last copepodite stage (the copepodite V, hereafter CV, stage) into adulthood. We therefore only needed b and k parameters for the CV stage. The important parameters for the Lotka integral equation model are the probability of surviving to reproduce, and given that you do, the fecundity. Therefore, we are mapping directly to the adult stage, rather than describing the intervening stages. This means that effects of mortality rate are not included in maturate rate estimates. We used the additive property of probability distributions to estimate b and k from our measurements. The additive property states that if the time to develop to the first stage follows a gamma distribution, and the duration of each stage is independently gamma distributed, then the time of development to each stage will also follow a gamma distribution (Kempton, 1979). The data we collected in the laboratory were the proportion of the population that has yet to pass through the CV stage, which implies that over the course of the experiment, our data set begins at 1 and declines to 0. Since the gamma distribution over stages is additive and stage development is unidirectional, our data are cumulative and follow one minus the cumulative gamma distribution function. We used maximum likelihood to estimate b and k based on the proportion of individuals that had reached the adult stage over time (xi). The cumulative gamma distribution function can be simplified if k is a positive integer, as it is here, to To estimate b and k, we are interested in one minus the cumulative gamma distribution function, which we denote as π: (10) The log-likelihood equation used to estimate b and k is therefore (11) We estimated b and k for each replicate beaker and used the resulting outputs to estimate coefficients for equations expressing the relationship between b and k and temperature and salinity via nonlinear least squares (nls in the R programming language): (12) (13) The exponential form of these equations forces estimates of b and k to be > 0. Maturation rates can be calculated from b and k since duration time . Maturation rate into adulthood is then (14) Time constraints prevented us from assessing sex and stage for all experimental individuals at each time step. We therefore assumed that mortality rate is constant across stages and were not able to ascertain its effects on maturation rate. Mortality rate Mortality rates were estimated from population size estimates over time. Nauplii produced by females in experimental treatments were removed within 48 h of production. As a result, copepod populations in each beaker underwent a pure death process (i.e. no individuals joined the population during the experiment). Population decline over time can therefore be used directly to estimate mortality rates. Time constraints limited our ability to obtain stage-specific population size estimates; therefore, mortality rate was estimated for the entire population regardless of stage. Population size estimates for each beaker over time (N(t)) were first normalized to the largest size estimated in that beaker over the course of the experiments to give . This value was always the size estimated at t = 1. This was necessary since starting population sizes were not equal among beakers (although densities were consistently below those reported in other experiments on E. affinis; see Ban (1994) and Devreker et al. (2007)). Normalized size data were then log transformed, and a linear decline over time was assumed. We used a linear model (implemented in R using the lm command) to estimate coefficients for the relationship between population size, time, temperature and salinity: (15) Each population declined over time from their normalized value of ; therefore, the y-intercept was assumed to be zero since . From this equation, it follows that mortality rate μ is (16) Fecundity Fecundity (β) was estimated for adult females using population size estimates, the proportion of adults at a given time step, the assumption of a 1:1 sex ratio and the number of nauplii produced per time step. The equation used to calculate fecundity was (17) where nn is the estimated number of newly produced nauplii, nT is estimated population size (excluding newly produced nauplii), and a is the proportion of adults in the population (estimated number of adults divided by estimated population size). β was calculated for each time step in each replicate beaker where adult females successfully produced nauplii. We assumed no Allee effects (no mate limitation) and no senescence (all adult females were capable of reproduction). These are valid assumptions since there were always adult males present and culture volume was not prohibitively large, and because there is no evidence of senescence in copepods. We used nonlinear least squares to estimate coefficients for an equation expressing β as a function of temperature and salinity: (18) The exponential form forces estimates of β to be > 0. Comparing two populations One potential use for our model is for comparing population growth rates across environmental parameters for two or more species or subspecies. To illustrate this, we calculated parameters for the population model (8) using previ
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