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Oecologia

, Volume 175, Issue 1, pp 417–428 | Cite as

A population model for predicting the successful establishment of introduced bird species

  • Phillip Cassey
  • Thomas A. A. Prowse
  • Tim M. Blackburn
Global change ecology - Original research

Abstract

One of the strongest generalities in invasion biology is the positive relationship between probability of establishment and the numbers of individuals introduced. Nevertheless, a number of significant questions remain regarding: (1) the relative importance of different processes during introduction (e.g., demographic, environmental, and genetic stochasticity, and Allee effects); (2) the relative effects of propagule pressure (e.g., number of introductions, size of introductions, and lag between introductions); and (3) different life history characteristics of the species themselves. Here, we adopt an individual-based simulation modeling approach to explore a range of such details in the relationship between establishment success and numbers of individuals introduced. Our models are developed for typical exotic bird introductions, for which the relationship between probability of establishment and the numbers of individuals introduced has been particularly well documented. For both short-lived and long-lived species, probability of establishment decreased across multiple introductions (compared with a single introduction of the same total size), and this decrease was greater when inbreeding depression was included. Sensitivity analyses revealed four predictors that together accounted for >95 % of model performance. Of these, R 0 (the average number of daughters produced per female over her lifetime) and propagule pressure were of primary importance, while random environmental effects and inbreeding depression exerted lesser influence. Initial founder size is undoubtedly going to be important for ensuring the persistence of introduced populations. However, we found the demographic traits, which influence how introduced individuals behave, to have the greatest effect on establishment success.

Keywords

Allee effect Demographic models Environmental stochasticity Exotic birds Invasion ecology Propagule pressure VORTEX 

Introduction

The number of individuals introduced into a new environment is consistently found to be one of the best predictors for the establishment success of exotic populations: larger and/or more frequent introductions are more likely to establish (see reviews in Lockwood et al. 2005; Colautti et al. 2006; Hayes and Barry 2008; Simberloff 2009; Blackburn et al. 2011). This relationship has been reported in a range of systems including insects released for the purposes of biocontrol (Hopper and Roush 1993), field experiments on forest understory plants (Von Holle and Simberloff 2005), birds introduced to New Zealand by acclimatization societies (Cassey 2001; Duncan 1997; Green 1997; Veltman et al. 1996), and experimental, as well as theoretical, frameworks (Drake et al. 2005; Drake and Lodge 2006). It is consistent with the fundamental paradigm in conservation biology that, all else being equal, smaller populations are more likely to go extinct than larger populations because of the impacts of demographic, environmental, and genetic stochasticity, and Allee effects (Soulé 1987).

The positive relationship between establishment success and the total number of individuals introduced (termed propagule pressure sensu Lockwood et al. 2005, 2009) is well established (Williamson 1996; Simberloff 2009), although it has been noted that estimates of propagule pressure for many arrivals of non-indigenous species are rarely reliable (Haydar and Wolff 2011) or even available (Jerde and Lewis 2007). In addition, this total number may be spread across several separate releases or escapes, and hence, propagule pressure can be viewed as having two components (Pimm 1991): the number of introduction events (propagule number) and the number of individuals per introduction event (propagule size) (Lockwood et al. 2005, 2009). Based on the generality of the relationship between establishment success and propagule pressure, it has been proposed that propagule pressure should form the basis of a null model for all invasion studies (Colautti et al. 2006), and as a foundational element of all risk analyses for introductions of non-indigenous species (Drake and Lodge 2006). Nevertheless, exceptions to the relationship have been reported (e.g., Haydar and Wolff 2011; Nuñez et al. 2011; Yeates et al. 2012), and a number of significant questions of detail remain to be addressed (see also Drake and Jerde 2009; Johnston et al. 2009). First, while small populations are more susceptible to demographic, environmental, and genetic stochasticity, and to Allee effects, the relative importance of these different processes in the success or failure of establishment by exotic species has received little attention. One notable exception is a classic study by Grevstad (1999), who used simulation models to explore establishment success in insect biocontrol agents as a function of demographic stochasticity, environmental stochasticity, and Allee effects. Her models showed that demographic stochasticity poses a significant risk of extinction only for very small populations, and that environmental stochasticity becomes a more important cause of extinction once the population is sufficiently large to escape demographic effects (see also Lande 1993). Incorporating Allee effects provided evidence that a threshold population density existed below which establishment success was greatly reduced (Dennis 2002; Taylor and Hastings 2005; Tobin et al. 2011). However, the influence of this threshold also depends on the role of environmental stochasticity on population growth rates: a run of good years can boost the density of a population that would otherwise succumb to Allee effects (Taylor and Hastings 2005). Thus, Liebhold and Bascompte (2003) found that when the initial introduction was below the Allee threshold, environmental stochasticity functioned to increase the probability of establishment; yet, when the introduction was above the Allee threshold, stochasticity served to decrease the probability of establishment. Furthermore, the majority of experimental tests and population models of the probability of establishment and Allee effects (including propagule pressure) have not incorporated genetic stochasticity (e.g., see Liebhold and Bascompte 2003; Jerde et al. 2009; Kramer and Drake 2010; Gertzen et al. 2011). Yet, population bottlenecks, genetic drift, and inbreeding can all cause declines in mean fitness, and hence, increase the likelihood that a small introduced population will go extinct (Frankham et al. 2004). The impact of these effects on populations experiencing environmental stochasticity and/or Allee effects is unclear.

Second, the relative effects of single versus multiple releases on establishment success also remain relatively unexplored (Drake et al. 2005; Lockwood et al. 2005). The total number of individuals introduced (propagule pressure) can all be released at once or introduced in smaller batches over a longer period of time. In the latter case, the number of releases (propagule number), the number of individuals involved (propagule size), and the time between releases (lag) can all vary. Hopper and Roush (1993) argued that number of individuals per introduction should be the best predictor of success if Allee effects apply, but that number of introductions would be the best predictor if environmental stochasticity is the most important determinant of success (see also Haccou and Iwasa 1995; Haccou and Vatutin 2003). Grevstad’s (1999) models also suggest that Allee effects favour fewer introductions of more individuals, but that success is higher for many separate introductions of few individuals if environmental stochasticity is high. Again, however, these models ignore genetic effects. Thus, while Brook (2004) argues that multiple introductions may promote establishment by supplementing genetic diversity in introduced populations, it is unclear whether a series of small bottlenecks is a better strategy for maintaining mean fitness in a population than one large (i.e., less stringent) bottleneck.

Third, few studies have considered the effects of different life history syndromes on the relationship between establishment success and numbers introduced. Propagule pressure is believed to influence establishment because of Allee effects, demographic and environmental stochasticity, and genetic effects; yet theory, models, and data suggest that a species’ susceptibility to these effects should depend on its life history characteristics (e.g., Grevstad 1999; Sæther et al. 2004; Taylor and Hastings 2005; Blackburn et al. 2009a; Jeppsson and Forslund 2012; Sol et al. 2012). For plant invaders, Seastedt and Pyšek (2011) observed that the possession of growth traits (i.e., high production and fertility) which allow for the exploitation of resource opportunities in their introduced range may be of "some importance" for plant invaders. However, the majority of studies have failed to uncover consistent demographic predictors of establishment success among invasive species. Life history traits do not predict establishment success in amphibian introductions (Tingley et al. 2011) and are inconsistent predictors of success in birds (Blackburn et al. 2009a, b; Sol et al. 2012). They are not identified as consistently associated with success in a qualitative meta-analysis of birds, finfish, insects, mammals, plants, reptiles/amphibians, and shellfish (Hayes and Barry 2008; see also Kolar and Lodge 2001). These inconsistencies may arise from associations between traits and the mean number of individuals released, or because of the high intra-species variation in the numbers of individuals released in different introduction events (Cassey et al. 2004). They may also be indicative of more complex relationships between life history, propagule pressure, and establishment success than assumed by the statistical modeling approaches employed (Sol et al. 2012). Grevstad’s (1999) models suggest that the negative effects of Allee effects and environmental stochasticity are exacerbated when population growth rates are reduced, but she did not explore these associations in detail. Moreover, her models addressed parameter ranges typical of insect biocontrol agents, which may therefore not be representative of life history associations for the smaller introductions of larger-bodied animal species.

Here, we adopt a simulation modeling approach to explore a range of details in the relationship between establishment success and numbers of individuals introduced. Our models are intended to replicate, as far as possible, the characteristics of historical bird introductions (Duncan et al. 2003), with which we are particularly familiar (Cassey et al. 2004; Blackburn et al. 2009b). Birds, like most other taxa, have frequently been moved well outside their native ranges via human actions and established themselves as exotic species (Blackburn et al. 2009b). In their native ranges, small and declining populations of birds are also of global conservation concern (Şekercioğlu et al. 2004; Brook et al. 2008), and knowledge of the causes of success and failure of exotic introductions may help to improve the chances that threatened species re-introductions also succeed (Blackburn and Cassey 2004; Cassey et al. 2008). Here, we assess how the probability of establishment varies for different propagule pressures under a range of different release strategies, from all individuals introduced in one attempt to five smaller releases with different lag times between releases. We assess the outcome of these different release strategies under different levels of environmental stochasticity and inbreeding depression, and in the presence or absence of a demographic Allee effect.

Our approach is twofold. First, we demonstrate how the combined effects of introduction efforts and small population stochasticity differ between species with three different hypothetical life history syndromes; one typical of a short-lived passerine and two typical of larger, longer-lived species. Second, we employ a full-model sensitivity analysis to explore the relative influence of the different parameters modeled on the probability of establishment in our system. The full-model sensitivity analysis explores a wide range of model parameter values, and is inclusive of the parameter space within which bird life histories, small population stochasticity, and introduction events fall.

Methods

VORTEX simulations

Introductions were simulated using VORTEX (version 10.0) software for population viability analysis (Lacy 2000). Individual-based VORTEX models employ a discrete time, pre-breeding census design (Caswell 2001) and account for random demographic, environmental, and genetic factors, making them perfect for simulating the fate of the small numbers of animals typically released during an introduction attempt. VORTEX models individual animals as they transition through a number of steps each year including (but not limited to) reproduction, dispersal, mortality, harvesting, translocation, and supplementation. Demographic stochasticity (i.e., variation in the population growth rate that occurs even if the mean demographic rates remain constant) is automatically included. For example, whether an animal survives in a given year is determined by sampling from a Bernoulli distribution with probability p equal to the mean survival rate for animals of that age class. Further, environmental stochasticity (i.e., inter-annual variation in demographic rates) can also be included, most simply by sampling the survival or fertility rates applied each year from a normal distribution. Finally, VORTEX also permits consideration of genetic stochasticity, by simulating allele transmission from parents to offspring at a number of loci. Mating pairs are formed randomly and inbreeding depression (i.e., the reduced fitness of offspring produced by closely related individuals) can then be flexibly incorporated (see details below).

Scenario testing

Among birds, species can be placed along a ‘slow-fast continuum’, where species with a high fecundity rate, but low survival, are found at one end and species that mature late, produce few (often a single) offspring, and have a long life expectancy, at the other (Sæther and Bakke 2000). The majority (>50 %) of exotic bird introductions (see Blackburn et al. 2009b) have been in the order Passeriformes (small-bodied, highly fecund, fast-living songbirds) with large numbers also in the orders Psittaciformes (medium-bodied, slow reproducing, long-lived parrots), and Galliformes (large-bodied, highly fecund, moderately-lived gamebirds). Using VORTEX, we developed three different avian life histories that broadly capture this variation (Table 1) with which to demonstrate the expected probability of establishment for different introduction scenarios:
Table 1

Demographic details of the three different hypothetical life history syndromes tested: one typical of a short-lived passerine and two typical of larger, longer-lived species

Rate

Passerine

Long-lived 1 (same R 0)

Long-lived 2 (same r)

Juvenile survival, s 0

0.20

0.30

0.30

Subadult survival, s 1

0.35

0.53

0.53

Adult survival, s 2+

0.50

0.75

0.75

Annual offspring, m

7.00

2.56

2.97

Net reproductive rate, R 0

1.19

1.19

1.38

Population growth rate, r

0.10

0.05

0.10

Generation time, G

1.74

3.45

3.24

  1. 1.

    Following Legendre et al. (1999), we set parameters on a demographic model for a generic passerine, using average demographic characteristics common to passerines (see Legendre et al. 1999; Table 1): survival rates for juveniles (<1 year), subadults (1 year), and adults (≥2 years) of 0.2, 0.35, 0.5, respectively. Females (≥1 year) produced seven offspring annually, resulting in a deterministic annual population growth rate (r) of 0.10, a net reproductive rate (R 0 the average number of daughters produced per female per generation) of 1.19, and a generation time [G calculated as ln(R 0)/r] of 1.74 years.

     
  2. 2.

    We developed a model for a hypothetical, long-lived species with the same net reproductive rate as the passerine that was realized by increasing the previous age-structured survival rates by 50 % and reducing fertility accordingly. Although R 0 remained constant, this decreased the population growth rate (r = 0.05) and increased the generation time (G = 3.45) relative to the passerine life history.

     
  3. 3.

    We set parameters on a final hypothetical model for another long-lived species using the higher survival rates as above, but with fertility adjusted to produce the same population growth rate as the passerine life history (r = 0.10). This increased both the net reproductive rate and the generation time relative to the passerine demography (R 0 = 1.38 and G = 3.24, respectively).

     

For these three hypothetical life histories, we explored the effects of propagule pressure, environmental stochasticity, inbreeding depression, and introduction strategy on the probability of a successful introduction. We tested propagule pressures between 10 and 300 individuals. We modeled the fate of single releases (i.e., all individuals introduced in the first simulation year), as well as introduction strategies for which total propagule pressure was split across two or five release events. For the latter, we also tested lag times between introductions from 1 to 5 years. Following the initial founder event, subsequent introductions were implemented using the ‘Supplementation’ option in VORTEX and consisted of unrelated individuals released at the same location, where they can interbreed with individuals from previous introduction events. The propagule pressures, numbers of release events and lag times are all based on typical values for bird introductions reported by acclimatization societies from Australia and New Zealand (Duncan et al. 2001; Legendre et al. 1999).

We modeled the effects of inbreeding depression as a reduction in juvenile survival rates due to two genetic mechanisms, requiring specification of the total inbreeding depression (‘lethal equivalents’) due to lethal alleles relative to other genetic mechanisms. All founder individuals were assigned lethal alleles at each of a number of modeled loci. If inbred descendants received two copies of the same lethal allele, they were killed. Second, juvenile survival rates (s j) were reduced exponentially as inbreeding increased according to the formula:
$$s_{\text{j}} = s_{0} {\text{e}}^{ - bF}$$
where s 0 is the survival rate of non-inbred juveniles. F is the inbreeding coefficient (i.e., the probability that two alleles at any locus of an individual are identical by descent), and b is the lethal equivalents component attributed to mechanisms other than lethal alleles. For simulations that included inbreeding effects, we assumed a genetic load of 3.14 lethal equivalents per individual based on the median reported for 40 mammalian populations (Ralls et al. 1988), of which 50 % was due to recessive lethal alleles (Miller and Lacy 2005).

We tested models for which demographic stochasticity (inherent within the VORTEX structure) was the only source of variability, as well as scenarios that included environmental stochasticity by sampling the annual demographic rates (age-structured survival rates and % females reproducing) from a normal distribution with a 5 or 10 % standard deviation. All simulated introductions consisted solely of adult birds at an equal sex ratio. We assumed a short-term, monogamous breeding system, thereby allowing the number of males to limit the number of matings annually. We defined successful introductions as those which attained a population size of 1,000 individuals or persisted for at least 100 years.

Full-model sensitivity analysis

To explore the expected probability of establishment for a substantially wider range of life histories, than focused on in the scenario testing, we conducted a thorough sensitivity analysis on 14 simulation parameters (Table 2). To ensure adequate coverage of the multi-dimensional parameter space, we used latin hypercube sampling to generate 100,000 distinct parameter sets whilst ensuring equal coverage of every individual parameter (Fang et al. 2006). In addition to testing different propagule pressures and introduction strategies as detailed above, we included the following in the sensitivity analysis (Table 2):
Table 2

Parameters, and their ranges tested, in the full model sensitivity analysis using uniform distributions and Latin hypercube sampling

Parameter

Range

Introduction scenarios

 Propagule pressure

10–300

 Propagule number

1, 2, 5

 Lag time between multiple introductions (years)

1–5

Demographic ratesa

 Juvenile survival (0–1 year), s j

0.1–1

 Adult survival (>1 year), s a

s j–1

 Fertility, m

1–12

Environmental variation

 Benevolence/hardship frequency

0–0.2

 Benevolence/hardship multiplier on vital ratesb

0.5–1.5

 Standard deviation (%) in survival

0–10

 Standard deviation (%) in females reproducing

0–10

Allee effect

 Minimum % females breeding

0–50

 Threshold population size for allee effect

20–100

Inbreeding depression

 Lethal equivalentsc

1–30

 Percent due to recessive alleles

10–90

aWe only tested combinations of demographic rates that produced population growth rates (r) ranging from 0 to 0.3

bValues above 1 represent benevolent events whereas values below 1 represent hardships

cThe number of lethal equivalents per diploid organism can exceed 30 but is most typically in the range 1–5 (Ralls et al. 1988)

  1. 1.

    Demographic rates—For simplicity, we assumed age-structured survival rates for two age classes, juveniles (<1 year) and adults (≥1 year), and constrained adult survival (s a) to exceed juvenile survival (s j). Annual fertility rates (m) were restricted to a maximum of 12 offspring per female. We only tested positive population growth rates ranging up to 0.3 because pilot testing demonstrated that the probability of establishment was very close to 1 for all r above this threshold.

     
  2. 2.

    Allee effect—We tested different parameterisations of a simple demographic Allee effect that, once population size fell below some threshold, linearly reduced the mean percentage of females breeding to a minimum of zero at a population size of zero (Stephens et al. 1999).

     
  3. 3.

    Environmental stochasticity—Environmental variation was incorporated in two ways. First, we simulated the effects of unusual environmental conditions: in each simulation it was assumed that either negative ‘hardships’ or positive ‘benevolences’ could affect vital rates and we established the probability that such events would occur each year (see Table 2 for details). The amplitude of these effects was specified using a vital rate multiplier with values less than one (hardship) or greater than one (benevolence). For example, a multiplier of 0.5 represented a hardship that reduced survival and reproduction rates by 50 %. Second, annual vital rates were sampled from normal distributions with mean equal to the deterministic rates and standard deviations ranging between 0 and 10 %.

     
  4. 4.

    Inbreeding depression—We altered the strength of inbreeding depression by varying the total lethal equivalents per individual introduced and the percentage of this genetic load due to recessive lethal alleles.

     

To investigate the important predictors of simulated establishment success we analysed data with boosted regression trees (BRT) using functions in the R package dismo (Hijmans et al. 2011). BRT that combine regression trees (models that relate a response to their predictors by recursive binary splits) and boosting (a method for combining simple models to improve predictive performance) are increasingly used as tools for prediction (Elith et al. 2008). BRT can fit complex, non-linear relationships and automatically handle interactions between predictors (Elith et al. 2008) so this technique is particularly useful for exploring and summarising the output from simulation studies (Prowse et al. 2013). Since introduction strategies involving multiple introduction events required specification of additional parameters (i.e., propagule number and the lag time between introductions), we first split the sensitivity analysis output into two datasets based on whether single or multiple introduction events were simulated. For each dataset, we evaluated BRT models that included different sets of predictors and tree complexities (i.e., different numbers of tree splits). Statistical models that included r, R 0 or G excluded the vital rates (s j, s a, m) from which they were calculated. All BRT models were performed with the routine gbm.step, using a binomial error and logit link function, a learning rate of 0.01, and a bag fraction of 0.75 (Elith et al. 2008). Model performance was compared using five runs of fivefold cross-validation (CV) fits, by examining the out-of-sample CV deviance and misclassification rate (De’ath 2007). We calculated relative influence metrics, as the sum of squared improvements at all splits determined by a predictor, after averaging over the collection of trees (Friedman and Meulman 2003). Although predictions can be improved by averaging over a collection of trees by boosting, there is no single tree produced to facilitate model interpretation (De’ath 2007). We therefore used partial dependency plots to examine relationships between the key predictors and the probability of simulating a successful introduction event.

Results

Scenario testing

For single introductions with demographic stochasticity only (i.e., without environmental or genetic effects), simulated probabilities of establishment (probability of establishment) rose to 100 % for all propagule pressures ≥80 individuals across all three demographic scenarios tested (Fig. 1a, d, h). For all life histories, the introduction strategy employed did not strongly affect simulation outcomes. Probability of establishment was reduced for strategies involving multiple introductions and this effect strengthened when inbreeding depression was included. The longer the lag time between introductions, the greater the negative effect on probability of establishment (Fig. 1a, d, h). Whereas the passerine life history was vulnerable to environmental stochasticity (Fig. 1b, c), probability of establishment curves for the hypothetical long-lived species were less susceptible to environmental variability (Fig. 1e, f, i, j). Notably, however, the long-lived life history for which R 0 was increased was most robust to environmental stochasticity (Fig. 1i, j), despite exhibiting the same deterministic population growth rate as the passerine demography.
Fig. 1

Simulated probability of establishment as a function of propagule pressure for different life histories, introduction scenarios and levels of environmental stochasticity. Probability of establishment is shown for the passerine life history (ac) and two hypothetical long-lived life histories with the same net reproductive rate (R 0; df) or population growth rate (r; gi) as the passerine. Each panel shows simulations excluding (black lines) and including inbreeding depression (grey lines) for three different introduction strategies: single introductions (solid lines) and introductions for which total propagule pressure is split across five separate release events with lag times of 1 year (dotted lines) or 5 years (dashed lines). Environmental stochasticity (i.e., annual variation in survival and fertility rates) was included by means of a 0, 5 or 10 % standard deviation on the annual demographic rates. All curves plot means derived from 1,000 stochastic replicates

Full-model sensitivity analysis

Sensitivity analysis (using the Latin hypercube approach) revealed species demographic rates to be the primary determinant of simulation outcomes. BRT models that included R 0 in place of the vital rates (s j, s a, m), the population growth rate (r), or generation time (G), produced the lowest CV misclassification rates (Table 3). Using a tree complexity of 5, BRT models that included R 0 and all other (non-demographic) predictors produced misclassification rates of 6.4 and 5.8 %, for datasets derived from single and multiple introduction strategies, respectively. Reducing to trees with only single splits did not compromise these misclassification rates (increases of 1.0/1.3 % only), so we used these simpler models to summarise the results of the sensitivity analysis (Fig. 2).
Table 3

Comparisons between boosted regression tree (BRT) models for simulations involving single or multiple introductions

Model

# Splits

Single introductions

Multiple introductions

Deviance

MC (%)

Deviance

MC (%)

Demography+all other parameters

R 0+all other parameters

5

0.308

6.4

0.276

5.8

s j + s a + m +all other parameters

5

0.332

7.1

0.267

5.5

R 0 +all other parameters

1

0.361

7.4

0.341

7.1

s j + s a + m +all other parameters

1

0.427

9.0

0.391

7.9

r + all other parameters

5

0.536

11.4

0.558

12.0

G + all other parameters

5

0.699

15.4

0.666

14.9

Demography+propagule pressure

R 0+propagule pressure

1

0.501

10.5

0.491

10.4

s a+propagule pressure

1

0.729

17.0

0.702

16.4

m+propagule pressure

1

0.893

19.8

0.893

20.4

s j+propagule pressure

1

0.896

21.5

0.908

22.1

Shown are the mean cross-validation deviance and misclassification rates (MC lower numbers indicate better-performing models) calculated from five fivefold cross-validation fits. BRT models including the net reproductive rate (R 0) achieved lower CV error rates than those including the deterministic population growth rate (r) or generation time (G). Bold text indicates the BRT model used to summarise the sensitivity analysis (as used in Fig. 2). BRT models that included the net reproductive rate (R 0), deterministic population growth rate (r), or generation time (G) excluded the vital rates (s j, s a , m) from which they were calculated

Fig. 2

Boosted regression tree (BRT) summary of the sensitivity analysis. a Relative influence of the top four predictors (i.e., simulation parameters) for selected BRT models, for simulated datasets with single (black bars) or multiple introductions (grey bars). b Predicted probabilities of establishment (PE) derived from the same BRT models for single introductions (black lines) or a different introduction strategy for which total propagule pressure is split across five separate release events (grey lines). (i) PE as a function of R 0, for propagule pressures of 10 (dashed lines), 50 (dotted lines), and 200 individuals (solid lines). (ii–iv) PE as a function of propagule pressure, the demographic effect of random benevolences or hardships (axis is the multiplier of vital rates; see Table 1), and the lethal equivalents per diploid genome, for R 0 values of 1 (dashed lines), 1.25 (dotted lines) and 2 (solid lines). These partial dependency plots assume unplotted parameters are set at their mean values

Relative influence metrics revealed four predictors that together accounted for >95 % of model performance. Of these, R 0 and propagule pressure were of primary importance, while random hardship or benevolences (modeled as negative or positive impacts on vital rates) and the lethal equivalents per individual exerted lesser influence (Fig. 2a). The relative importance of all other predictors, including Allee effects, was below 1 %. For simulations including multiple release events, neither propagule number nor the lag time between releases was an important determinant of simulation outcomes.

For propagule sizes of 50 individuals only, our BRT models predict probability of establishment to exceed 80 %, regardless of the number of propagules (assuming that other parameters are set to their mean values) (Fig. 2b). As before, the models predict lower probability of establishment when propagule pressure is split between multiple introduction events, even when high-impact environmental hardship/benevolences (vital rate adjustments of up to 50 %) and/or strong inbreeding depression were simulated.

Since species demography and propagule pressure were the primary drivers of probability of establishment in our simulations, using the sensitivity analysis datasets, we also fitted simple, single-split BRT models that used R 0 and propagule pressure as the sole predictors (Table 3). The performance of these models was impressive, with misclassification rates of approximately 10 % for both single and multiple introduction scenarios. In comparison, prediction error increased dramatically for models that included propagule pressure and a single demographic rate (s j, s a, or m) only (all misclassification rates >16 %; Table 3). For the latter BRT models, the relative influence of the demographic predictor always exceeded that of the propagule pressure covariate. For example, the relative influence of propagule pressure peaked at 46 and 48 % for BRT models where juvenile survival was the only additional covariate, for single and multiple introduction scenarios, respectively.

Discussion

The study of biological invasions has been hampered by a lack of general models for predicting the relative influence of demographic, environmental, and genetic factors on the establishment success of exotic populations. The notable exception is for models simulating the fate of colonizing populations for biological control (e.g., Fauvergue et al. 2012). Such models are motivated by the desire to optimize the release strategy for biocontrol insects, and had parameters set accordingly. For example, in her classic paper, Grevstad (1999) modeled establishment by a species assumed to be univoltine, with discrete generations, a mean fecundity of 200 eggs per female, and an expected survival rate to reproductive maturity of 0.02, resulting in R 0 (expected reproductive rate per female) of 2.0. She modeled releases of 1,000 individuals, as a single event, or as up to 250 independent releases (i.e., inter-breeding between introduced populations was not permitted). While the outcomes of these models and subsequent ones (e.g., Liebhold and Bascompte 2003, gypsy moth Lymantria dispar) are likely to be relevant for species with fast life histories (like biological control insects), or unusual reproductive strategies (e.g., cyclic parthenogenesis; Gertzen et al. 2011, spiny water fleas Bythotrephes longimanus), their wider generality (particularly for vertebrate introductions) has to date been unclear. Hence, we have extended this modeling approach to examine establishment success in species with life histories typical of a different class of highly mobile vertebrate organisms, birds. Our results reveal some similarities, but also unexpected differences to previous work in this area.

Increasing propagule pressure substantially improved the probability of population establishment in all our simulations, as has been observed in empirical studies of exotic birds (Cassey et al. 2004), and in invasive species more generally (Lockwood et al. 2005; Simberloff 2009). Interestingly, our models predicted lower probability of establishment when propagule pressure was split between multiple introduction events: on average, one introduction event always outperformed multiple introduction events that summed to the same size. A single introduction of a greater number of individuals minimizes the risk of extinction through demographic, genetic, and Allee effects in the introduced population. Even under simulated conditions of extreme environmental variability (modeled as inter-annual variation in vital rates), we found no evidence that spreading the risk across multiple introductions improved probability of establishment. Instead, a single, larger release grows more quickly and is more capable of riding out negative environmental conditions, because the population size is less likely to be reduced to a level where demographic, genetic, and Allee effects come into play. Further, a large release allows the introduced population to take full advantage of favourable conditions should they occur. In contrast, delaying the introduction of individuals delays their reproductive contribution to future generations. As a consequence, probability of establishment for our simulated multiple release strategies was negatively correlated with introduction number and the lag time between introduction events (Fig. 1). These results run contrary to the prediction by Brook (2004) that a strategy of multiple introductions is most likely to succeed because genetic variation is added each time an introduction occurs. Instead, our simulations suggest that it is better to have all one’s eggs in one basket, at least when total propagule pressure is realistically small (e.g., 10–300 individuals as tested here) which leaves introduced populations susceptible to the stochastic processes contributing to the ‘extinction vortex’ (Gilpin and Soulé 1986).

We assumed multiple releases were separated in time, but that all introductions occurred at the same location (e.g., a single acclimatisation region or exotic population). Therefore, sequential introduction events shared the same deterministic components to their vital rates. Multiple releases separated in space are, however, a different matter, because deterministic vital rates can vary spatially due to differences in habitat suitability (Haccou and Iwasa 1995; Haccou and Vatutin 2003). Multiple sequential introductions in space have been shown to improve probability of establishment by increasing the probability that at least one group of individuals encounters conditions that allow population growth and establishment. For example, Grevstad (1999) simulated multiple, independent introductions of an insect biocontrol agent which were assumed to be reproductively isolated and therefore could not affect the success of each other. Under conditions of environmental stochasticity, she found that a single release was not always optimal: rather, more releases of fewer individuals could slightly improve probability of establishment (quantified as the proportion of simulations for which at least one population established), although probability of establishment declined once more if total propagule pressure was split into many, very small releases.

While propagule pressure strongly influenced probability of establishment in all our simulations, our results revealed an even stronger effect of species demography. Indeed, demography was the primary determinant of simulation outcomes. Similar to Sol et al. (2012), we found that longer-lived species established better in the simulation. All else being equal, and assuming a constant population growth rate (r), probability of establishment was lower for simulations modeling a typical passerine life history than for simulated species with longer generation times and higher net reproductive rates (average number of offspring per female) (Fig. 1). Establishment was more or less assured for the latter species once propagule pressure reached 200 individuals under all modeled scenarios of demographic, environmental, genetic, and Allee effects. In contrast, probability of establishment for the typical passerine life history was substantially depressed by environmental stochasticity and genetic effects, and was only about 50 % under our highest levels of environmental stochasticity, even for single releases of 300 individuals (Fig. 1c). The depressing effect of inbreeding was relatively greatest at intermediate levels of environmental stochasticity. Species with high R 0 were less susceptible to inbreeding depression because the effects of the lethal equivalents were modeled as a reduction in juvenile survival rates, while long-lived species are more robust regarding variation in juvenile survival (Legendre et al. 1999). If inbreeding were to affect later stages of the life-history, such as fecundity, then species with high R 0 may, in consequence, be more susceptible. Although there is some evidence for this (O’Grady et al. 2006), empirical studies of inbreeding effects on birds have documented significant effects on juvenile survival, but not post-reproductive stages (Greenwood et al. 1978).

A robust understanding of the influence of species-level traits on establishment success in birds has been elusive. In a quantitative meta-analysis of studies of the establishment success of exotic birds, Blackburn et al. (2009a) found that mean effects for traits relating to population growth rates conflicted in sign: in general, successful establishment was greater for species with larger body mass, whereas clutch size was not consistently related to establishment success. More recently, Sol et al. (2012) identified a complex relationship between life history strategy and establishment success in birds. They found that species that either combine several broods per year with a relatively short life span or that lay a single clutch per year but have a very long life span were significantly more successful than other species which allocate all their reproductive effort into only a few reproductive events. However, they suggested that ‘fast’ population growth will only be advantageous in very particular cases, when the founder population is small and when the environmental pressures posed by the recipient location are favourable. They conclude that successful invaders are, in general, characterized by life history strategies that give priority to future rather than current reproduction. Our simulations based on bird life history parameters are in broad agreement with these results, as we found probability of establishment to be higher when the number of offspring per female per generation was higher, which is associated with longer generation times, higher survival rates, and lower annual fertility rates. However, unlike Sol et al. (2012), we found no situation in which ‘fast’ population growth was advantageous, although we only tested combinations of demographic rates that produced r in the range from 0.0 to 0.3.

In addition, sensitivity analysis revealed genetic effects and the influence of extreme environmental events on establishment probability in our simulations (Fig. 2). Extreme events were modeled as either a positive or negative multiplier on the population vital rates in a given year, occurring with a given probability (Table 3). Whereas benevolences could improve probability of establishment for simulated species with very low R 0, species with high R 0 were immune to all but the most severe hardships modeled [(Fig. 2b(iii)]. Populations that are quite likely to fail may get a relative boost from extreme events, because bad years do not make much difference to populations that would fail anyway, but good years can. The effect of extreme events was most pronounced for simulated species with intermediate R 0 and, therefore, intermediate chances of establishment. Similarly, genomes carrying higher lethal equivalent loads tip the balance towards failure for populations with intermediate chances of establishment, but have negligible effects for extreme values of R 0 [Fig. 2b(iv)], where either success or failure is more or less guaranteed.

Sensitivity analysis revealed that R 0 was the most influential parameter on probability of establishment in our simulations (Fig. 2), followed by propagule pressure. Probability of establishment was low for species with low R 0, and high for species with high R 0, controlling for propagule pressure. The strong effects of R 0 and propagule pressure on probability of establishment obviously arise because these characteristics help populations overcome stochastic effects, but the effects that make the most difference to probability of establishment for a given R 0 and propagule pressure here are extreme events and genetic factors. Demographic stochasticity has theoretically been shown several times to influence probability of establishment only at very low population sizes (Grevstad 1999). The lack of influence of Allee effects in our models is supported by empirical data for bird and insect introductions, which suggests that Allee effects are insufficient to induce critical thresholds in a population size below which extinction is inevitable (Duncan, Blackburn, Rossinelli & Bacher, unpublished manuscript). Environmental stochasticity appears to matter most in terms of the impact of extreme events; “normal” variation is obviously likely to affect population growth rates, but will only greatly influence the outcome of these simulated introduction events when R 0 is close to 1.0. Environmental stochasticity may matter much more in nature with spatially discrete populations in environments of marginal suitability, although our simulations do model populations with low positive mean growth rates, including r = 0.

Using individual-based demographic simulations of establishment processes and thorough sensitivity analysis permits predicted probabilities of establishment to be extracted for any typical life history. Such predictions could be compared to empirical data on deliberately introduced birds, provided demographic data for those species were available. The fact that our models identified species demography as the primary influence on establishment probability is convenient from a practical viewpoint, since the other processes we tested (environmental stochasticity, Allee effect, inbreeding depression) are notoriously difficult to quantify. It does, nevertheless, leave us with a quandary: why do simulation models suggest species demography is the most important determinant of establishment success, whereas empirical studies have consistently found propagule pressure to be most important? Possible explanations include uncertainty in estimating demographic rates, especially for species when introduced to a new environment, or that most empirical studies focus on limited numbers of life history correlates that are of variable utility as surrogates for demography. This latter suggestion fits with the recent study by Sol et al. (2012) which identified complex interactions between life history and establishment success in birds. While initial founder size is undoubtedly going to be important for ensuring the persistence of introduced populations, it seems that the demographic traits influencing how introduced individuals behave is slowly coming back to the fore.

Notes

Acknowledgments

PC, TAAP, and TMB formulated the idea for the study and designed the analyses. TAAP conducted the simulations, and TAAP and PC conducted the statistical analyses. PC, TAAP, and TMB wrote the manuscript. Communicated by Ola Olsson. We are grateful to BW Brook for insightful discussions that greatly improved this manuscript. Comments from Ola Olsson and two anonymous referees were gratefully received. PC is an ARC Future Fellow (FT0991420).

Supplementary material

442_2014_2902_MOESM1_ESM.jpg (3.8 mb)
Supplementary material 1 Fig. S1 Partial dependency plots (on the logit-scale) derived from boosted regression tree (BRT) analysis of the sensitivity analysis output for single introduction scenarios only (see the selected model in Table 3 of the main text). The BRT model was fitted with simulation outcome (establishment success or failure) as the response and used ten simulation parameters as predictors of the outcome: net reproductive rate (R 0, calculated from the survival and fertility rates specified) and all other non-demographic simulation parameters that were varied in the sensitivity analysis. Each of these individual partial dependency plots assumes unplotted parameters are set at their mean values. The relative influence of each predictor in the fitted BRT model is shown in brackets on the x-axis. (JPEG 3934 kb)
442_2014_2902_MOESM2_ESM.jpg (4.3 mb)
Supplementary material 2 Fig. S2 Partial dependency plots (on the logit-scale) derived from boosted regression tree (BRT) analysis of the sensitivity analysis output for multiple introduction scenarios only (see the selected model in Table 3 of the main text). The BRT model was fitted with simulation outcome (establishment success or failure) as the response and used twelve simulation parameters as predictors of the outcome: net reproductive rate (R 0, calculated from the survival and fertility rates specified) and all other non-demographic simulation parameters that were varied in the sensitivity analysis. Each of these individual partial dependency plots assumes unplotted parameters are set at their mean values. The relative influence of each predictor in the fitted BRT model is shown in brackets on the x-axis. (JPEG 4365 kb)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Phillip Cassey
    • 1
  • Thomas A. A. Prowse
    • 1
  • Tim M. Blackburn
    • 2
  1. 1.School of Earth and Environmental SciencesUniversity of AdelaideAdelaideAustralia
  2. 2.Institute of ZoologyZSLLondonUK

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