• clonal reproduction;
  • habitat–distribution model;
  • information–theoretic model comparison (ITMC);
  • Salix spp.;
  • woody weed


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  • 1
    Predicting geographical areas susceptible to weed invasion is a primary target for land managers. Willows (Salix spp.) invading riparian environments have recently been increasing in number in south-east Australia. In order to prioritize management decisions, a clear understanding of the factors affecting recruitment success for sexually and asexually generated Salix recruits is vital.
  • 2
    Multiple variables are hypothesized to determine the spatial distribution of Salix recruits. Therefore an information–theoretic model comparison (ITMC) approach was used to analyse factors determining the abundance and distribution of Salix recruits along four rivers in south-east Australia with differing flow regulation. Generalized linear modelling techniques were applied to multiparameter candidate models, developed from existing knowledge of the system and plausible hypotheses. Predictor variables included parameters describing river disturbance, availability of propagule sources and competition for recruitment space.
  • 3
    Models of sexually produced Salix recruits performed well, generating 95% confidence sets of candidate models that were small relative to the potential set of models analysed (18%), whereas models of asexual recruits performed less well, indicated by 95% confidence sets that were large relative to the potential set of models explored (67%).
  • 4
    A multimodel inference approach was required: model results indicated that availability of mating partners in the environment plays an important role in determining the abundance of sexually derived Salix recruits, whereas for asexual recruits river disturbance parameters better predicted abundance.
  • 5
    For the models of sexual reproduction, model plausibility was strengthened by corroborative results from an independent data set collected in the same geographical region. However, the validation data set was too small to assess the predictive capability of the model-averaged model.
  • 6
    Synthesis and applications. Information–theoretic model selection methods helped clarify the relative importance of different model parameters on the abundance of Salix recruits. Knowledge of the link between river regulation and willow recruitment enables a greater degree of management flexibility in response to risk forecasting under future scenarios for different water flows. Targeting control programmes to focus on removal of female and seeding willows in rivers with low levels of disturbance may eliminate Salix recruits altogether, whereas the same treatment applied to high-level disturbance rivers is likely to result in persistent problems with asexual recruits.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Strategic management of invasive plant populations is reliant on the ability to predict geographical areas where remedial action will have the greatest probability of successful control. Unfortunately, application of predictive models in a spatial context is frequently hampered by uncertainty in the underlying processes contributing to weed distribution and abundance. Competing hypotheses lead to development of multiple candidate models, resulting in a high degree of uncertainty regarding selection of the most appropriate model to inform management practices. Recent recommendations to combat this problem include adoption of the information–theoretic model comparison (ITMC) approach (Johnson & Omland 2004; Rushton, Omerod & Kerby 2004; Stephens et al. 2005). A particular advantage of ITMC is the ability to address model selection uncertainty through comparison of multiple biological hypotheses by simultaneous evaluation of a suite of candidate models (Burnham & Anderson 2002). In addition, the paradigm of multiple working hypotheses is a more realistic reflection of the way scientists work than the ‘null hypothesis’ paradigm and is easier to convey to the public, which enhances its value in communicating applied problems (Westphal et al. 2003). In this study we constructed a set of models that aimed to predict the abundance of invasive willow recruits in Australia. Data were used to both select a parsimonious model and estimate the model parameters and their precision, generating issues of concern regarding both model selection bias and model selection uncertainty (Burnham & Anderson 2002) that were addressed through our use of the ITMC approach.

Eurasian willows (Salicaceae: Salix spp.) have naturalized widely in the southern hemisphere, including South Africa (Henderson 1991), New Zealand (van Kraayenoord, Slui & Knowles 1995) and southern Australia (Cremer 1999, 2003; ARMCANZ 2000), where they are considered invasive colonizers of riparian environments. Originally introduced to southern Australia in the late 19th century to stabilize levees, protect reclaimed swamplands and provide shade for livestock (Erskine & Webb 2003), these woody plant invaders have had many detrimental impacts on the landscape. These impacts include reduced channel capacity, channel diversion and erosion, increased sediment loads and increased flooding, all of which can directly influence water quality and river health (ARMCANZ 2000). Displacement of native flora and fauna is also of major ecological concern (Ladson et al. 1997). In comparison with the native river red gum Eucalyptus camaldulensis, which shares a similar niche, Salix species shed leaves at different times and rates, provide different levels of river shade and experience different litter breakdown rates (Schulze & Walker 1997). This results in changes in abundance, diversity and composition of terrestrial and aquatic invertebrates (Pidgeon & Cairns 1981; Lester, Mitchell & Scott 1994; Read & Barmuta 1999; Greenwood, O'Dowd & Lake 2004), with potential consequences for associated riparian fauna.

Factors contributing to variation in success of invasive species have received much recent attention (reviewed in Kolar & Lodge 2001). The success of Salix species in southern Australia is largely attributable to the versatility of their reproductive systems. One of the striking features of the Salicaceae is their capacity to regenerate either sexually or asexually, under a wide range of environmental conditions (Karrenberg, Edwards & Kollmann 2002 and references therein). The ability to grow clonally in addition to producing seed enables a limited number of successful seedlings eventually to colonize a large area. Willows also have flexible pollination systems, being entomophilous and anemophilous to varying degrees (Argus 1974; Tamura & Kudo 2000; Karrenberg, Kollmann & Edwards 2002). Finally, the Salicaceae are among the most frequently hybridizing of all plant families (Ellstrand, Whitkus & Rieseberg 1996).

These factors combined predict that Salix species possess the capacity for success in new environments. Historically the spread of willows in Australia followed importation patterns, but in recent years natural spread has increased in significance (Cremer et al. 1995). Salix species are dioecious and the majority of willow introductions to Australia were single-sex, consisting largely of either weeping willow Salix babylonica or crack willow Salix fragilis. Introductions in the 1980s of the early flowering males of Salix alba, Salix matsudana × alba and other hybrids have resulted in S. babylonica producing hybrid offspring, which may produce either male flowers, female flowers or both and display considerable variation in flowering times (Cremer 2003). Salix fragilis is also able to pollinate females of these newer introductions, recently resulting in the production of viable seed (Cremer 1999). Therefore barriers to hybridization have been eroded as a result of altered flowering times and gaps in flowering bridged by species that flower at intermediate times. In addition, species that were separated geographically in the native range have been planted in close proximity in the new environment, facilitating hybridization.

Asexual and sexual propagules pose differing degrees of risk to riparian ecosystems. Extensive vegetative propagation results in rapid, but spatially restricted, spread of relatively few genotypes. However, the recent rapid spread of seeding willows (via long-distance dispersal of seed) enables the founding of new populations in previously unoccupied habitat; thus the magnitude of willow invasion is now much worse than in the period 1940–60 (Cremer et al. 1995).

The relative proportions of sexually and asexually derived individuals may vary along resource gradients, because of differences in fitness and physiological performance between regeneration strategies, resulting in profound influences on the genetic composition of populations (Silander 1985). Studies of invasive Salix species that have naturalized in the USA suggest that seedling recruitment into mature willow populations is uncommon because of high levels of first-year seedling mortality (Sacchi & Price 1992; Mahoney & Rood 1998; Johnson 2000; Dixon 2003). To ensure survival a seedling must germinate in an area that is sufficiently close to a river to provide adequate water but be protected from intense scouring in periods of high flows (Mahoney & Rood 1998). For clonal plants experiencing limited seedling recruitment and low disturbance, the number of genets in a population is hypothesized to decline over time because of density-dependent mortality (Watkinson & Powell 1993). Douhovnikoff, McBride & Dodd (2005) propose a model whereby prolific clonal growth in Salix exigua populations in the USA accounts for longer term colonization of riparian zones, and the balance between the relative importance of seedling regeneration and clonal growth varies based upon river flow disturbance regime.

An understanding of the factors controlling relative abundance and distribution of sexually and asexually derived individuals in invasive populations of clonal plant species improves management predictions of occurrence and spread. The application of a predictive model in a spatial context relies on the existence of landscape-scale variables that define suitable habitat for that species (Austin 2002). In our study we aimed to quantify habitat preferences for sexually and asexually derived Salix recruits, using survey data collected from rivers with differing disturbance regimes in New South Wales, Australia. We used generalized linear models, which implicitly incorporate biotic interactions and negative stochastic effects because they effectively model realized ecological niches (Guisan & Zimmerman 2000; Guisan et al. 2002). Our analysis had four aims, to: (i) provide insight into the ecological processes that produce the current distribution pattern of Salix recruits in south-eastern Australia; (ii) determine whether recruitment of asexual and sexual propagules responds to different phenomena; (iii) identify the most plausible and parsimonious model of recruitment; and (iv) test the predictive capacity of this model with an independent data set.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

study species

Salix fragilis has preformed breaking points at the twig base that make the branches particularly brittle (Beismann et al. 2000). Fragments shed at breaking points and transported downstream are able to regenerate to produce new individuals, genetically identical to the parent. Only male S. fragilis were planted in the study area. In contrast, S. babylonica has non-brittle twig bases and propagates primarily through seed production, producing few asexual recruits (Cremer et al. 1995). Only female S. babylonica were planted in the study area. Willow seeds have a light pappus facilitating dispersal by air, making them highly mobile. Seeds can also be transported by water and can survive and germinate under water (Cremer et al. 1995).

With the exception of S. cinerea, the establishment of willows from seed in Australia has been restricted mainly to riparian sites, where bare sediments are exposed and remain moist for weeks or months from the time of seed shed in October to November. Willow seed is extremely short lived (Niiyama 1990; Karrenberg & Suter 2003) and in Australia seed banks are non existent (Cremer et al. 1995). Soil moisture content is an important factor for germination (van Splunder et al. 1996). Seed that fails to reach a moist surface and germinate within approximately 2 weeks of dispersal will usually die (Cremer et al. 1995).

site selection

Four rivers in south-east Australia were selected to establish the extent of willow invasion. All rivers were at similar latitudes, extending from Canberra (35°30′ S), southwards towards the state of Victoria, to approximately 36°30′ S. Substrate types were mixtures, in each case composed of Palaeozoic sediments, granitic and igneous rocks. Two rivers, the Murrumbidgee River and the Snowy River, are heavily regulated, whereas the Numeralla River (a tributary of the Murrumbidgee) and the Bobundara River (a tributary of the Snowy) represent unregulated flow in this region. These rivers are of considerable economic importance. The major regulatory structures in the Snowy River support the Snowy Mountains Hydro-electric Scheme, completed in 1974. This scheme diverts 1 × 106 megalitres (ML) of water annually westward to the Murray-Darling basin, an interbasin transfer scheme that underwrites $1542 million worth of agricultural products (Pigram 2000). The Murrumbidgee River is also a major tributary of the Murray-Darling River system, regulated by 26 dams and weirs and more than 10 000 km of irrigation canals (Kingsford 2003).

relative river disturbance levels

To compare disturbance regimes between rivers, we used a relative disturbance index (RDI; Douhovnikoff, McBride & Dodd 2005), where:

  • image

F is the annual peak flow and f is the annual mean flow. This index measures the magnitude difference between a river's peak flows and its mean flow. The mean flow estimates the lower boundary of the ‘recruitment band’ for willow (Mahoney & Rood 1998). The RDI quantifies the magnitude of peak flow disturbances above this assumed lower boundary for willow recruitment and has been found to influence willow recruitment behaviour in the USA (Douhovnikoff, McBride & Dodd 2005). Flow data were obtained from archives provided by the NSW Department of Infrastructure Planning and Natural Resources database (PINEENA V8.0; DIPNR 2004). For each river the maximum time span of the archive was used, post-dam construction for regulated rivers. This provided 35, 29, 55 and 16 years of historical flow data for the Murrumbidgee, Snowy, Numeralla and Bobundara rivers, respectively. On a scale of disturbance from low to high, the Murrumbidgee River was the least disturbed (Table 1), followed by the Numeralla and Snowy rivers. The Bobundara River was the most disturbed, with an RDI an order of magnitude greater than the Murrumbidgee River.

Table 1.  Survey information, including summary of river disturbance variables for each river
RiverDate surveyedNo. of 1-km sectorsRDIMean sinuosity (± SE)Maximum sinuosity
Murrumbidgee19953035·251·11 ± 0·0221·41
Numeralla19954668·681·14 ± 0·0181·43
Snowy (Jindabayne to Dalgety)19962383·831·14 ± 0·0231·38
Snowy (downstream from Dalgety)19975483·831·16 ± 0·0211·69
Bobundara199711304·661·20 ± 0·1011·92

Sinuosity, the ratio of channel length to straight-line valley distance (Leopold, Wolman & Miller 1964), was measured from 1:10 000 scale maps for each 1 km of river reach. Meandering dissipates energy in flowing water and regulates the movement of sediment through river systems, thus increasing the availability of bare sediment, which is essential for willow recruitment (Cremer et al. 1995; Mahoney & Rood 1998; Cremer 1999; Amlin & Rood 2002). The relative predictability of meandering means that a lengthy period is likely to elapse before newly deposited sediments are again eroded away, thus fresh sediments offer a relatively stable habitat to establishing plants (Karrenberg, Edwards & Kollmann 2002). In the context of this study, high disturbance equates to high RDI, and rivers possessing a high RDI value have higher sinuosity values, showing an increasing degree of meandering (Table 1).

survey methods

Surveys were conducted over a 2-year period from 1995 to 1997 during September and October (the southern spring), when the majority of the willows were in flower. At each site, rivers were divided into 1-km section lengths and surveyors walked along the river banks recording the species and gender of individual willow trees within 50 m of the river. The number of willow seedlings occurring in each 1-km section was also recorded. The origin of individuals was determined as arising either from intentional introduction (planting), sexual reproduction (spread via seed) or asexual reproduction (spread via detached or attached branches taking root). Intentional introductions were identified by their uniform spatial planting arrangements and advice from landholders. Willows propagated via sexual reproduction can be distinguished by the presence of a large tap root when isolated individuals are uprooted. Large numbers of similarly sized recruits were assumed to have originated from wind-blown seed.

The majority of planted trees were either S. babylonica or S. fragilis, but in some cases other Salix species and hybrid varieties were also planted. The latter are referred to as Salix‘bisexuals’ for the purposes of this study. Their presence potentially creates a trioecious population because individual plants in the bisexual category may produce either all male flowers, all female flowers or both male and female flowers.

In total approximately 110 km of riparian corridor were surveyed (Table 1). Two separate surveys were conducted on different reaches of the Snowy River, the first in 1996, extending from below Jindabayne Dam, 23 km downstream to Dalgety, and the second in 1997, from Dalgety, approximately 54 km south downstream towards Victoria.

statistical modelling

Information on the factors determining abundance of Salix recruits was obtained by fitting general linear regression models (GLM) to the data that combined multiple biological hypotheses. Three response variables could be gleaned from the survey data: (i) the number of Salix recruits; (ii) the number of recruits produced via asexual modes of reproduction and (iii) the number of recruits produced via sexual reproduction. For each response variable, multiparameter candidate models were developed using different combinations of explanatory variables, based on existing knowledge of the system and on plausible hypotheses. Asexual recruits do not require mating partners, therefore a propagule source can be defined as the presence of intentionally planted Salix species. The abundance of second-generation trees was assumed to be determined by initial plantings. Sexual recruits require a source of male and female gametes, so the presence of only females of S. babylonica or males of S. fragilis is insufficient to meet these requirements. However, a single hybrid tree may be capable of independent seed production because some hybrids produce both male and female flowers on a single tree (e.g. S. matsudana × alba). Hybrid willows are also capable of producing seed from either S. babylonica or S. fragilis. Combinations of explanatory variables were used in model construction that enabled mating opportunities to arise (Fig. 1). Each sampling unit recorded densities of both sexual and asexual recruits, enabling competition between the two types of recruits to be explored. We considered competition for recruitment space a likely predictor of recruitment. Prior to model construction Pearson correlations between explanatory variables were explored to test for collinearity (r < 0·4, P > 0·05 for all combinations).


Figure 1. Conceptual flow diagram used to formulate GLM to predict abundance of sexually generated Salix recruits in riparian environments of south-east Australia.

Download figure to PowerPoint

Data were collected from contiguous 1-km river sections and therefore spatial autocorrelation in the data had to be considered. Spatial autocorrelation is a scale-dependent measure reflecting the dispersal efficiency of invading species, and is expected to be more evident at finer spatial scales (Collingham et al. 2000). In this study one would expect spatial autocorrelation to be greater among asexual recruits than sexual recruits, because dispersal of plant fragments usually occurs over shorter distances than sexually produced seed, which being wind blown can travel long distances (Lascoux, Thorsen & Gullberg 1996). However, molecular genetic analysis of European populations has shown that even asexual fragments of S. fragilis can travel distances of > 10 km before establishment (Beismann et al. 1997), reducing the potential spatial autocorrelation at the 1-km scale of this survey. Spatial autocorrelation is problematic in statistical tests that assume independently distributed errors. To evaluate the degree of non-independence in error terms, plots of autocorrelation and partial autocorrelation functions for the residuals were examined, prior to computing Durbin–Watson statistics with bootstrapped P-values, which indicate the likelihood that error values have a first-order autoregressive component.

All explanatory variables were entered into the model as random effects, which are those effects associated with individual experimental units drawn at random from a population. As the number of recruits was a count, which could also be scaled as proportional data, we considered using either Poisson or binomial errors in the analysis. However, the data were highly overdispersed, especially the counts of sexual recruits and quasi-likelihood methods failed to correct for overdispersion. Therefore absences were excluded from both data sets (sexual and asexual recruits), resulting in a quantitative presence-only response variable. The data set of sexual recruits was further reduced to 30% of its original size by exclusion of low-density samples (< 100 recruits km−1). This approach is logical when considering the distribution of an invasive species because absence may result from dispersal failure rather than a lack of suitable habitat. In addition, the aim was to produce a model capable of predicting high-density occurrences requiring targeted management. The mean numbers of recruits per survey unit (± SE) were 947 ± 66·2, 3381 ± 39·0 and 22 ± 6·2 for the total, sexual and asexual categories, respectively. Data were linearized by log-transforming the number of recruits and GLM were constructed using the identity link function with normal errors. Inspection of plots of the residuals and fitted values were satisfactory. The statistics program R (R Development Core Team 2005) was used for all analyses.

Following methods described by Burnham & Anderson (2002), the fits of a suite of biologically plausible models were compared using Akaike's information criterion (AIC), allowing models with different numbers of parameters to be directly compared with each other. In this study, the ratio of the number of observations (1-km river survey units) to the number of parameters was less than 40, requiring a bias correction term for small sample size (Hurvich & Tsai 1989; Burnham & Anderson 2002). The best fitting model has the smallest AIC (termed AICmin) and the relative support for each model can be determined by evaluating the difference between model AIC and the minimum AIC:

  • ΔAICi = AICi − AICmin

Models with ΔAICi within 0–2 of the best model are considered to have substantial support as candidate models (Burnham & Anderson 2002). Akaike weights (wi) were used as indicators of the strength of evidence for a particular model being the best out of the set of candidate models considered. Akaike weights have a probabilistic interpretation and can be considered as the relative model likelihoods normalized to sum to 1. Construction of a 95% confidence set of models was achieved by establishing the smallest subset of candidate models for which the wi summed to 0·95, generating a 95% confidence that this set contained the best approximating model to the true model (Whittingham et al. 2005). The likelihood that a predictor variable was contained in the best approximating model was obtained by calculating the sum of the Akaike weights for each model containing that particular variable.

If no single model is clearly superior to others in the set (as was the case in this study), a model averaging approach is recommended, which bases inference on the entire set of models (Burnham & Anderson 2002). Model averaging uses the average of parameter estimates or model predictions from each candidate model weighted by its Akaike weight (Burnham & Anderson 2002; Gibson et al. 2004; Whittingham et al. 2005). Unconditional standard errors (not conditional on any particular model) provide a better reflection of the precision of a given model coefficient (Burnham & Anderson 2002), and were calculated using the conditional sampling variances from each model and their Akaike weights, prior to generating an unconditional 95% confidence interval for each variable in the model. Finally, model-averaged estimates were compared with a GLM including all variables to assess the potential impact of model selection bias on parameter estimates (Whittingham et al. 2005).

To examine interaction effects, a fitted response surface was generated from the AICmin model. Fitted values were calculated for each term in the model. An interaction term between two factors should be combined with the main effects marginal to the interaction. Therefore lower order ‘relatives’ of a high-order term were absorbed into the term, allowing the predictors appearing in the high-order term to range over their values (Fox 2003). The values of other predictors were fixed at their mean. This was implemented in the R effects package (Fox 2005), available on the Comprehensive R Archive Network (

The applicability of the model to other locations was assessed using presence-only data from the 1997 survey of the southern region of the Snowy River (i.e. outside the survey area used in the original model). Predictive variables contained in the AICmin model of the training data set were included in the construction of a GLM using the Snowy River 1997 data. The performance of this model was compared with that derived from the logistic regression equation of the model-averaged model applied to the Snowy River 1997 data.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

model selection

Models to explain the number of sexual recruits produced 95% confidence sets that were small relative to the potential set of models: 21 models were considered plausible, a figure that represents 18% of the total set of models analysed, indicating that the modelling process had successfully captured a large proportion of the variation in the data. These models consistently included the number of S. babylonica, S. fragilis and Salix bisexuals planted, plus an interaction term between the abundance of S. babylonica and S. fragilis. Selection probabilities for these variables were all > 0·98. Other variables received weaker support, in particular RDI, sinuosity and the density of asexual recruits, which all had selection probabilities < 0·21 (Table 2c).

Table 2.  Results of ITMC-based model selection for the abundance of (a) Salix recruits, (b) asexually produced recruits and (c) sexually produced recruits. Models shown represent the 95% confidence set for each data set. The table includes the variables included in each model, AICc, AICc differences (Δi), Akaike weights based on the entire set of models (wi) and Akaike weights based on models in the 95% confidence set (95%wi). The selection probability for each parameter was determined by summing all wi scores for all possible models in which the predictor was included. Parameter estimates (β) presented were generated by averaging across all models (weighted by the Akaike weights, 95%wi), along with unconditional standard errors and 95% confidence intervals (CI) for each parameter. Model variables: RDI, river disturbance index; CS, channel sinuosity; Sbab, number of S. babylonica; Sfg, number of S. fragilis; Sbx, number of Salix bisexuals; loga, log(10) number of asexually produced recruits; logsx, log(10) number of sexually produced recruits
ResponseConstantRDICSSbabSfgSbxSbab:SbxSfg:SbxSfg:SbabLogaLogsxAICcΔi w i 95%wi
(a) All recruits
AICmin model + ++++    281·790·000·1590·164
2 + + +     282·610·820·1060·109
3 + +++++   283·581·790·0650·067
4 ++++++    283·641·850·0630·065
5 + ++++ +  283·932·140·0550·056
6 +  ++ +   283·932·140·0550·056
7 +++ ++    284·192·400·0480·049
8 + +++  +  284·592·800·0390·040
9   ++++    285·023·230·0320·033
10 +  ++     285·063·270·0310·032
11 +++++++   285·443·650·0260·026
12 + +++ +   285·673·880·0230·024
13 + ++++++  285·723·930·0220·023
14 ++ ++ +   285·763·970·0220·023
15 ++++++ +  285·824·030·0210·022
16 + + +     286·164·370·0180·018
17 + +++ ++  286·334·540·0160·017
18 +++++  +  286·404·610·0160·016
19   +++  +  286·434·640·0160·016
20   ++++ +  286·584·790·0150·015
21 ++ ++     286·764·970·0130·014
22   +++++   286·835·040·0130·013
23 + +++     287·045·250·0120·012
24  + ++     287·215·420·0110·011
25 +++++ +   287·545·750·0090·009
26 (global model) ++++++++  287·625·830·0090·009
27 +++ +     287·715·920·0080·008
28    ++ +   287·886·090·0080·008
29 +++++ ++  288·216·420·0060·007
30   +++ ++  288·356·560·0060·006
31   ++++++  288·356·560·0060·006
32  +++++    288·566·770·0050·006
33  ++++  +  288·566·770·0050·006
34 +++++     288·776·980·0050·005
35  +++++ +  288·797·000·0050·005
36   +++ +   288·827·030·0050·005
Selection probability 0·8470·2820·8650·8051·00·6710·3040·241      
Unconditional SE0·26270·00100·15280·00540·00390·01030·00030·00010·0001      
Unconditional 95% CI1·8514−0·000340·39650·01960·01410·0653−0·00010·00010·0001      
Bias −0·1480−2·660−0·6200·100−0·206−1·2104·560−0·070      
(b) Asexual recruits
AICmin model ++ +     +174·490·000·2810·296
2 ++       +175·671·180·1560·164
3 ++ +      175·701·210·1530·162
4 ++        175·831·340·1440·151
5 +  +     +177·142·650·0750·079
6  + +      178·744·250·0340·035
7 +        +178·894·400·0310·033
8 +  +      179·084·590·0280·030
9  + +      179·144·650·0270·029
10    +     +179·725·230·0210·022
Selection probability 0·8900·810 0·631     0·607    
β0·3740−0·00160·6306 0·0025     −0·0408    
Unconditional SE0·33510·00060·2788 0·0014     0·0234    
Unconditional 95% CI1·0308−0·00040·6870 0·0052     0·0051    
−0·2828−0·00280·5760 −0·0002     −0·0867    
Bias −0·0944−0·1450 −0·5520     −0·7525    
(c) Sexual recruits
AICmin model   +++ ++   41·330·000·1930·204
2   +++  +   41·370·040·1900·200
3   ++++ +   42·611·280·1020·108
4 + +++  +   43·412·080·0680·072
5  ++++  +   43·982·650·0510·054
6  ++++ ++   44·162·830·0470·050
7 + +++ ++   44·443·110·0410·043
8   +++  ++  44·483·150·0400·042
9   ++++++   44·683·350·0360·038
10   +++ +++  44·763·430·0350·037
11  +++++ +   45·354·020·0260·027
12 + ++++ +   45·494·160·0240·025
13   ++++ ++  45·894·560·0200·021
14 +++++  +   46·244·910·0170·018
15 + +++  ++  46·775·440·0130·013
16  ++++  ++  47·396·060·0090·010
17 +++++ ++   47·576·240·0090·009
18  +++++++   47·876·540·0070·008
19  ++++ +++  47·926·590·0070·008
20 + ++++++   48·126·790·0060·007
21 + +++ +++  48·186·850·0060·007
Selection probability 0·2010·1920·9920·9920·9870·2520·3390·9800·155     
Unconditional SE0·36770·00130·14810·00980·00890·00660·00010·00010·00030·0278     
Unconditional 95% CI2·92970·00150·482−0·00560·05910·03110·00030−0·00050·0593     
Bias −2·59−4·2820·1360·1250·0332·8−1·36−0·0470·583     

In contrast, the 95% confidence sets for models explaining the total number of recruits and the number of asexual recruits were large relative to the potential set of models (61% and 67%, respectively); this implied that the models for these response variables were poor. However, RDI performed well in these cases. For the asexual models the selection probabilities for relative river disturbance index (RDI) and sinuosity were high (> 0·8), indicating strong support (Table 2b). The RDI also had the second highest selection probability (0·847) in models designating the total number of recruits as the response variable (Table 2a).

For all models, those parameters with low selection probabilities showed high model selection bias. This indicated that simplifying the full model could increase the risk of producing biased parameter estimates. This is a problem that may not have been recognized if we had failed to use the ITMC approach.

Table 2 ranks the models according to their AIC differences, from highest to lowest. The highest Akaike weight for the sexual models was 0·204, suggesting high model selection uncertainty. In addition, the difference in Akaike weights between model 1 and model 2 was only 0·004, which provided further substantial support for the second model. These results clearly indicated the suitability of employing a model-averaging approach.

For all models, model-averaged coefficients revealed negative associations between the abundance of Salix recruits and RDI. However, there were four pieces of evidence suggesting that this relationship was stronger for asexual than sexual recruits: first, the selection probabilities described above; secondly, the coefficient was larger for models estimating the abundance of asexual recruits (−0·0016) than sexual recruits (−0·0010); thirdly, the high unconditional standard error associated with this variable in the sexual models; finally, graphical analysis of the data (results not shown) revealed that higher densities of sexual recruits (> 100 km−1) occurred exclusively in rivers possessing an RDI of < 70 (the Murrumbidgee and Numeralla rivers) whereas asexual recruits were present at high densities only when RDI ranged between approximately 70 and 85 (the Numeralla and Snowy rivers) and occurred only at low density in the Bobundara River (RDI 304·7). The overall proportion of sexual to asexual recruits was greater in lower disturbance rivers (Fig. 2).


Figure 2. The total number of S. babylonica (black), S. fragilis (white) and Salix bisexuals (grey) planted along the surveyed section (Table 1) of each riverbank. Pie charts display the proportion of sexually produced (white) and asexually produced (black) recruits. Salix bisexuals comprise S. alba, S. alba var. vitellina, S. × chrysocoma, S. cinerea, S. nigra, S. matsudana, S. matsudana × alba, S. × rubens, S. viminalis, S. pendula, S. purpurea and S. × reichardtii.

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A positive association was observed between river sinuosity and abundance in all models. Similar to RDI, the relationship was stronger for asexual recruits, as evidenced by selection probabilities and unconditional standard errors. Positive associations may reflect an unknown relationship between flow speed and establishment probability of recruits. In early stages of establishment, asexual recruits are likely to have a larger mass and less root material than sexual recruits, with possible implications for secure anchorage.

For the asexual models, a negative association existed between the model-averaged coefficient for density of sexually produced Salix recruits and the abundance of asexual recruits, implying asexual recruits suffer competition for recruitment space. In the models of sexual reproduction this relationship was reversed, and a positive association was observed with the density of asexual recruits. However, the high unconditional standard errors associated with both variables suggested considerable uncertainty regarding the true effect of each variable on the response.

In the models of sexual reproduction, the number of planted S. fragilis, S. babylonica and Salix bisexuals displayed positive associations with the abundance of sexually generated Salix recruits, indicating that the majority of Salix seed was dispersed locally. The 95% unconditional confidence intervals for these variables all excluded zero, indicating that each variable influenced the abundance of sexually generated recruits.

The interaction term between planted S. fragilis and planted S. babylonica was analogous to considering the interaction between males and females. A fitted response surface revealed that the abundance of sexually propagated recruits was highest when the density of male clones of S. fragilis was high and the density of female S. babylonica clones was low (Fig. 3a). A decrease in the number of recruits was observed when both male and female clones were present at high density, indicating potential competition for recruitment space between adults and juveniles. A similar pattern was shown for the fitted response surface of sexually produced Salix recruits, as affected by the density of Salix bisexuals and S. fragilis (Fig. 3b). However, in this case, lower densities of Salix recruits were also observed when both S. fragilis and Salix bisexuals were present at low densities, implying potential pollen limitation.


Figure 3. The interactive effects of (a) the density of S. fragilis and the density of S. babylonica, and (b) the density of S. fragilis and the density of Salix bisexuals, as predicted by the GLM for sexually produced Salix recruits. Factors that were not included in the axes were held constant at their mean.

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Significant (P < 0·05) positive spatial autocorrelation was observed in the residuals of the AICmin model of asexual recruits for the first six lag distances (lag interval 5 km), suggesting that model performance could be improved by incorporating an additional spatial parameter or independent variable correlated with space. In contrast, no positive spatial autocorrelation was observed in the AICmin model for sexual recruits. This may be a consequence of the greater mobility of seed within the landscape, or may alternatively arise as an artefact of data processing because low-density samples were excluded from the data set for sexual recruits. By deleting these samples we reduced the number of adjacent survey sectors, thereby reducing the likelihood that small-scale spatial autocorrelation would be significant in this data. The only evidence of spatial autocorrelation in the data set of sexual recruits was a significant negative autocorrelation at lag distance 2 (4 km), suggesting that the distribution of sexual recruits in the landscape was highly patchy. Spatial autocorrelation among adjacent river sectors could slightly inflate sample size or model power. However, the ITMC method uses a relative value to evaluate model success that is not dependent on sample size. In addition, the relative influence of the explanatory variables, which is a major factor of interest in this study, will not be affected by slight alterations in model power (Westphal et al. 2003).

model application

We chose to focus on the applicability of the models of sexual reproduction because sexually generated Salix recruits occur at the highest densities and create the most serious environmental problems in south-east Australia. A plot of fitted values against observed values for the AICmin model using the training data set is given in Fig. 4a (R2 = 0·61). The model selection process identified predictors of importance. These predictors could be used in a GLM to predict abundance of Salix recruits in areas not included in the training data set. The AICmin model contained an interaction term between S. fragilis and Salix bisexuals. However, this term had a lower selection probability than other variables and for this reason we chose to exclude it and include only those predictors contained in model 2 of the sexual models (Table 2). When applied to an independent data set (Fig. 4b), this model had moderate explanatory power in predicting the presence of sexually produced Salix recruits (R2 = 0·35). An attempt was made to apply the logistic regression equation of the model-averaged model to the Snowy River 1997 data set. However, in order to match the conditions under which the training data were modelled, only sampling units with > 100 recruits could be considered in the analysis, reducing the validation data set to only 12 data points, which was considered insufficient.


Figure 4. Plots showing fitted values on the x-axis and the observed response variable on the y-axis, along with a line showing the expected 1:1 relationship. (a) The AICmin model fitted to the training data set (R2 = 0·61, n= 30, P < 0·001). (b) Model 2 of the sexual models fitted to the Snowy River 1997 data (R2 = 0·35, n= 38, P < 0·001). Plot (a) is derived from data with a response variable > 100 recruits km−1.

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  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

The methods employed in this approach are broadly applicable to a variety of ecological situations that aim to derive models of general predictive utility when multivariate patterns of causality are suspected (Stephens et al. 2005). In this study ITMC model selection methods help clarify the relative importance of different model parameters on the abundance of Salix recruits, which could lead to improved targeting of management strategies.

Model results indicate that the frequency of mating partners within the environment is of greater importance than river disturbance indicators in determining abundance of sexually derived Salix recruits, whereas, for asexual recruits, the RDI and sinuosity are the most useful predictors of abundance, the latter being more easily measurable at a small scale. Planting ratios differed slightly between different rivers: a slight predominance of S. fragilis trees in comparison with S. babylonica were planted in the Murrumbidgee and Numeralla rivers, whereas this pattern was reversed in the Snowy River (Fig. 2). Planting ratios for the Snowy, Murrumbidgee and Numeralla rivers were not highly dissimilar, yet subsequent proportions of sexually and asexually derived recruits differed considerably when comparing the Snowy River with the latter two. This indicates that the physical conditions of the river do play a role in determining the relative abundance of sexual vs. asexual willow recruits in south-east Australia. This is consistent with studies of Salicaceae in their native habitats, where differences in the relative contributions of sexual and asexual regeneration strategies between different environments have been observed (Krasny, Vogt & Zasada 1988; Legionnet et al. 1997; Arens et al. 1998; Barsoum 2002; Douhovnikoff, McBride & Dodd 2005).

Modelling results identified RDI and channel sinuosity as the best predictors of the abundance of asexual recruits. Channel sinuosity is measured on a scale to match the survey data, whereas the RDI value is calculated at the scale of the whole river and is therefore confounded with other ‘river-level’ effects (Table 1). Therefore, one would expect channel sinuosity to have a higher model selection probability than RDI. However, this was not the case (Table 2b) and the RDI value was marginally more likely to influence variation in the dependent variable. Improvement in the performance of channel sinuosity as a predictive variable for asexually generated recruits may be observed if the reach scale is adjusted to a greater distance (e.g. sinuosity over 10 km). The lack of correlation between RDI and channel sinuosity implies that they are measuring different attributes of the river. In terms of data availability, RDI is reliant on time series gauging data whereas channel sinuosity is more readily obtainable from topological maps and likely to be of more practical use to river managers.

Other environmental variables may also be important for determining the abundance of asexually generated recruits. Planting of S. fragilis was ubiquitous throughout the Murrumbidgee, Numeralla and Snowy rivers, but asexual recruits were present at higher proportions only in the Snowy River (Fig. 2). The presence of Salix bisexuals in the Bobundara River provides a potential propagule source for the asexual recruits observed there, but asexual recruits only comprise 36% of the total recruit population (Fig. 2). This may occur because willows are still expanding their range in the study area, which contradicts the assumption of environmental equilibrium (Guisan & Theurillat 2000; Austin 2002) and can lead to biased results like truncated ecological response curves (Hirzel, Helfer & Métral 2001; Guisan, Edwards & Hastie 2002). The closer a species is to its maximum potential range, the better the observed goodness-of-fit for species distribution models (Collingham et al. 2000). In other words, absences may be because of historical causes rather than unsuitable habitat, and we have reflected this constraint through our use of quantitative presence-only data. However, despite this precaution, our analysis provides insufficient information to distinguish ideal habitat conditions for asexual recruits, indicated by the poorer model performance in comparison with the models of sexual recruitment. Whether the mode of reproduction is facilitated entirely through differences in river disturbance regimes, or as a result of other physical and environmental variables, cannot be determined solely from this study, or indeed from other published works. The inclusion of additional environmental variables, or measurement of variables at finer scales, in combination with surveying a greater diversity of riparian environments, is required to clarify habitat preferences for asexual recruits.

In the context of river management, studies in the USA have shown a reduction in river disturbance may eventually result in stand replacement of Salix populations by taller stemmed and more shade-tolerant species (Douhovnikoff, McBride & Dodd 2005). However, in south-east Australia a reduction in RDI does not equate to a reduction in the degree of anthropogenic activity in the river system. The Snowy River, which is subject to flow regulation, has a lower RDI than the unregulated Bobundara River. Flow regulation in Australian rivers is a highly contentious issue (Arthington & Pusey 2003; Kingsford 2003), with major consequences for biodiversity management and agricultural practice. A ‘set-aside’ policy implemented through reduced river disturbance or alteration of flow regimes to discourage willow recruitment is unfeasible because flow management cannot be determined by a single environmental problem. Management attention needs to focus on more direct measures of eliminating clonal Salix species, such as mechanical and chemical control.

The effective treatment of seeding willows in south-east Australia is an even more urgent priority (Cremer 2003). Wind-dispersed seed is capable of travelling large distances, and because this mode of dispersal is not bound to unidirectional river flow, as asexually dispersed recruits are, seed has the capacity to colonize unexpected or unsurveyed locations. Our model results demonstrate that interactions between mating partners largely determines the abundance of sexual recruits, emphasizing the importance of considering sex ratios within populations of invasive willows when addressing this urgent threat.

The unexpected consequences of altered flowering phenologies and hybridization have increased the problems caused by invasive willows in Australia. Planting only one sex of each species was designed to prevent potential hybridization between willows yet, despite this precaution, a high degree of hybridization has arisen in the new environment. It is inadvisable to introduce species such as willows, which already hybridize extensively in their native range (Meikle 1975), into new environments. Currently S. babylonica and S. × reichardtii are still regarded as non-weed species acceptable for sale (ARMCANZ 2000). We consider the model results to show S. babylonica is capable of hybridization with other Salix species currently present in south-east Australia, and recommend that it is removed from the safety list. The removal of invasive willow species already widespread in the environment is a contentious issue in southern Australia, because of conflicting stakeholder perceptions of the costs and benefits to industry and the environment. In situations where replanting is desirable to increase river bank stability, we suggest using native trees, such as river red gum Eucalyptus camaldulensis or river she oak Casuarina cunninghamiana.

The predictive capability of the model-averaged model was poor, possibly because of a small validation data set. However, this study was successful in identifying factors contributing to the abundance of sexually produced willow recruits. In addition, model plausibility was strengthened by similar model results using two independent data sets. Knowledge of the link between river regulation and willow recruitment enables a greater degree of management flexibility in response to risk forecasting under future scenarios. Altered flow regimes are a distinct possibility in this area of Australia, either as a consequence of a changing social or political environment or changing climatic conditions (Arthington & Pusey 2003). In view of our results, prioritization of investment in different forms of willow control can now be achieved. For example, removal of all female and seeding willows from riverbanks subject to increasing disturbance will result in persistent problems with high densities of asexual recruits, whereas the same treatment applied to river sectors with lower relative disturbance index or sinuosity may eliminate willow problems altogether. Finally, catchment management authorities will need to co-ordinate control programmes at the landscape scale to reduce pollen sources in the vicinity of females if any degree of success is to be achieved in reducing the density of Salix recruits in riparian zones.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

We thank Kurt Cremer (CSIRO Forestry) for granting access to the survey data and providing supportive enthusiasm, and Peter Caley for advice on using R. Surveys were conducted by Ruth Aveyard, Leon and Andrew Miners, Brian Lewin and Kurt Cremer. Funding was provided by the NSW Department of Land and Water Conservation, NSW Rivercare, NSW Total Catchment Management and the Natural Heritage Trust.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  • Agriculture and Resource Management Council of Australia & New Zealand, Australia & New Zealand Environment & Conservation Council and Forestry Ministers (ARMCANZ) (2000) Weeds of National Significance: Willow (Salix taxa, excluding S. babylonica, S. × calodendron and S. × reichardtii) Strategic Plan. National Weeds Strategy Executive Committee, Launceston, Tasmania, Australia.
  • Amlin, N.M. & Rood, S.B. (2002) Comparative tolerances of riparian willows and cottonwoods to water-table decline. Wetlands, 22, 338346.
  • Arens, P., Coops, H., Jansen, J. & Vosman, B. (1998) Molecular genetic analysis of black poplar (Populus nigra L.) along Dutch rivers. Molecular Ecology, 7, 1118.
  • Argus, G.W. (1974) An experimental study of hybridization and pollination in Salix (willow). Canadian Journal of Botany, 52, 16131619.
  • Arthington, A.H. & Pusey, B.J. (2003) Flow restoration and protection in Australian rivers. River Research and Applications, 19, 377395.
  • Austin, M.P. (2002) Spatial prediction of species distribution: an interface between ecological theory and statistical modelling. Ecological Modelling, 157, 101118.
  • Barsoum, N. (2002) Relative contributions of sexual and asexual regeneration strategies in Populus nigra and Salix alba during the first years of establishment on a braided gravel river bed. Evolutionary Ecology, 15, 255279.
  • Beismann, H., Barker, J.H.A., Karp, A. & Speck, T. (1997) AFLP analysis sheds light on the distribution of two Salix species and their hybrid along a natural gradient. Molecular Ecology, 6, 989993.
  • Beismann, H., Wilhelmi, H., Bailleres, H., Spatz, H.C., Bogenrieder, A. & Speck, T. (2000) Brittleness of twig bases in the genus Salix: fracture mechanics and ecological relevance. Journal of Experimental Botany, 51, 617633.
  • Burnham, K.P. & Anderson, D.R. (2002) Model Selection and Multimodel Inference: A Practical Information Theoretic Approach, 2nd edn. Springer-Verlag, New York, NY.
  • Collingham, Y.C., Wadsworth, R.A., Huntley, B. & Hulme, P.E. (2000) Predicting the spatial distribution of non-indigenous riparian weeds: issues of spatial scale and extent. Journal of Applied Ecology, 37, 1327.
  • Cremer, K.W. (1999) Willow management for Australian rivers. Natural Resources Management, Special Issue, December 1999, 122.
  • Cremer, K.W. (2003) Introduced willows can become invasive pests in Australia. Biodiversity, 4, 1724.
  • Cremer, K.W., Van Kraayenoord, C., Parker, N. & Streatfield, S. (1995) Willows spreading by seed: implications for Australian river management. Australian Journal of Soil and Water Conservation, 8, 1827.
  • DIPNR (2004) PINEENA, Version 8·0. New South Wales National Surface Water Archive, Department of Infrastructure, Planning and Natural Resources, NSW Government, Sydney, Australia. Available on DVD, using HYDSYS Time Series Management software.
  • Dixon, M.D. (2003) Effects of flow pattern on riparian seedling recruitment on sandbars in the Wisconsin River, Wisconsin, USA. Wetlands, 23, 125139.
  • Douhovnikoff, V., McBride, J.R. & Dodd, R.S. (2005) Salix exigua growth and population dynamics in relation to disturbance regime variation. Ecology, 86, 446452.
  • Ellstrand, N.C., Whitkus, R. & Rieseberg, L.H. (1996) Distribution of spontaneous plant hybrids. Proceedings of the National Academy of Sciences of the United States of America, 93, 50905093.
  • Erskine, W.D. & Webb, A.A. (2003) Desnagging to resnagging: new directions in river rehabilitation in southeastern Australia. River Research and Applications, 19, 233249.
  • Fox, J. (2003) Effect displays in R for generalized linear models. Journal of Statistical Software, 8, 115.
  • Fox, J. (2005) Effect displays for linear and generalized linear models. Version 1·0–8. (accessed 15/09/05).
  • Gibson, I.A., Wilson, B.A., Cahill, D.M. & Hill, J. (2004) Spatial prediction of rufous bristlebird habitat in a coastal heathland: a GIS-based approach. Journal of Applied Ecology, 41, 213223.
  • Greenwood, H., O'Dowd, D.J. & Lake, P.S. (2004) Willow (Salix×rubens) invasion of the riparian zone in south-eastern Australia: reduced abundance and altered composition of terrestrial arthropods. Diversity and Distributions, 10, 485492.
  • Guisan, A. & Theurillat, J.P. (2000) Equilibrium modelling of alpine plant distribution: how far can we go? Phytocoenologia, 30, 353384.
  • Guisan, A. & Zimmerman, N.E. (2000) Predictive habitat distribution models in ecology. Ecological Modelling, 135, 147186.
  • Guisan, A., Edwards, T.C., Thomas, C. & Hastie, T. (2002) Generalized linear and generalized additive models in studies of species distributions: setting the scene. Ecological Modelling, 157, 89100.
  • Henderson, L. (1991) Alien invasive Salix spp. (willows) in the grassland biome of South Africa. South African Forestry Journal, 157, 9195).
  • Hirzel, A., Helfer, V. & Métral, F. (2001) Assessing habitat suitability models with a virtual species. Ecological Modelling, 145, 111121.
  • Hurvich, C.M. & Tsai, C.L. (1989) Regression and time-series model selection in small samples. Biometrika, 76, 297307.
  • Johnson, W.C. (2000) Tree recruitment and survival in rivers: influence of hydrological processes. Hydrological Processes, 14, 30513074.
  • Johnson, J.B. & Omland, K.S. (2004) Model selection in ecology and evolution. Trends in Ecology and Evolution, 19, 101108.
  • Karrenberg, S. & Suter, M. (2003) Phenotypic trade-offs in the sexual reproduction of Salicaceae from floodplains. American Journal of Botany, 90, 749754,.
  • Karrenberg, S., Edwards, P.J. & Kollmann, J. (2002) The life history of Salicaceae living in the active zone of floodplains. Freshwater Biology, 47, 733748.
  • Karrenberg, S., Kollmann, J. & Edwards, P.J. (2002) Pollen vectors and inflorescence morphology in four species of Salix. Plant Systematics and Evolution, 235, 181188.
  • Kingsford, R.T. (2003) Ecological impacts and institutional and economic drivers for water resource development: a case study of the Murrumbidgee River, Australia. Aquatic Ecosystem Health and Management, 6, 6979.
  • Kolar, C.S. & Lodge, D.M. (2001) Progress in invasion biology: predicting invaders. Trends in Ecology and Evolution, 16, 199204.
  • Van Kraayenoord, C.W.S., Slui, B. & Knowles, F.B. (1995) Introduced Forest Trees in New Zealand. 15. The Willows. Bulletin 124. New Zealand Forest Research Institute, Rotorua, New Zealand.
  • Krasny, M.E., Vogt, K.A. & Zasada, J.C. (1988) Establishment of four Salicaceae species in response to a flooding event. Canadian Journal of Botany, 66, 25972598.
  • Ladson, A., Gerrish, G., Carr, G. & Thexton, E. (1997) Willows Along Victorian Waterways. Department of Natural Resources and Environment, Victoria, Australia.
  • Lascoux, M., Thorsen, J. & Gullberg, U. (1996) Population structure of a riparian willow species, Salix viminalis L. Genetical Research, 68, 4554.
  • Legionnet, A., Faivre-Rampant, P., Villar, M. & Lefèvre, F. (1997) Sexual and asexual reproduction in natural stands of Populus nigra. Botanica Acta, 110, 257263.
  • Leopold, L.B., Wolman, M.G. & Miller, J.P. (1964) Fluvial Processes in Geomorphology. W. H. Freeman, San Francisco, CA.
  • Lester, P.J., Mitchell, S.F. & Scott, D. (1994) Effects of riparian willow trees (Salix fragilis) on macroinvertebrate densities in two Central Otago, New Zealand streams. New Zealand Journal of Marine and Freshwater Research, 28, 267276.
  • Mahoney, J.M. & Rood, S.B. (1998) Streamflow requirements for cottonwood seedling recruitment: an integrative model. Wetlands, 18, 634645.
  • Meikle, R.D. (1975) Salix L. Hybridization and the Flora of the British Isles (ed. C.D. Stace), pp. 304338. Academic Press, London, UK.
  • Niiyama, K. (1990) The role of seed dispersal and seedling traits in colonization and coexistence of Salix species in seasonally flooded habitat. Ecological Research, 5, 317331.
  • Pidgeon, R.W.J. & Cairns, S.C. (1981) Decomposition and colonization by invertebrates of native and exotic leaf material in a small stream in New England (Australia). Hydrobiologia, 77, 113127.
  • Pigram, J.J. (2000) Options for rehabilitation of Australia's Snowy River: an economic perspective. Regulated Rivers: Research and Management, 16, 363373.
  • R Development Core Team (2005) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. (accessed 15/09/05).
  • Read, M.G. & Barmuta, L.A. (1999) Comparisons of benthic communities adjacent to riparian native eucalypt and introduced willow vegetation. Freshwater Biology, 42, 359374.
  • Rushton, S.P., Ormerod, S.J. & Kerby, G. (2004) New paradigms for modelling species distribution? Journal of Applied Ecology, 41, 193200.
  • Sacchi, C.F. & Price, P.W. (1992) The relative roles of abiotic and biotic factors in seedling demography of arroyo willow (Salix lasiolepis: Salicaceae). American Journal of Botany, 79, 395405.
  • Schulze, D.J. & Walker, K.F. (1997) Riparian eucalypts and willows and their significance for aquatic invertebrates in the River Murray, South Australia. Regulated Rivers: Research and Management, 13, 557577.
  • Silander, J.A. (1985) Microevolution in clonal plants. Population Biology and Evolution of Clonal Organisms (eds J.B.C. Jackson, L.W. Buss & R.E. Cook), pp. 107152. Yale University Press, New Haven, CT.
  • Van Splunder, I., Voesenek, L.A.C.J., Coops, H., De Vries, X.J.A. & Blom, C.W.P.M. (1996) Morphological responses of seedlings of four species of Salicaceae to drought. Canadian Journal of Botany, 74, 19881995.
  • Stephens, P.A., Bushkirk, S.W., Hayward, G.D. & Martinez del Rio, C. (2005) Information theory and hypothesis testing: a call for pluralism. Journal of Applied Ecology, 42, 412.
  • Tamura, S. & Kudo, G. (2000) Wind pollination and insect pollination of two temperate willow species, Salix miyabeana and Salix sachalinensis. Plant Ecology, 147, 185192.
  • Watkinson, A.R. & Powell, J.C. (1993) Seedling recruitment and the maintenance of clonal diversity in plant populations: a computer simulation of Ranunculus repens. Journal of Ecology, 81, 707717.
  • Westphal, M.I., Field, S.A., Tyre, A.J., Paton, D. & Possingham, H.P. (2003) Effects of landscape pattern on bird species distribution in the Mt Lofty ranges, south Australia. Landscape Ecology, 18, 413426.
  • Whittingham, M.J., Swetnam, R.D., Wilson, J.D., Chamberlain, D.E. & Freckleton, R.P. (2005) Habitat selection by yellowhammers Emberiza citronella on lowland farmland at two spatial scales: implications for conservation management. Journal of Applied Ecology, 42, 270280.