=Paper=
{{Paper
|id=None
|storemode=property
|title=A State-Transition DBN for Management of Willows in an American Heritage River Catchment
|pdfUrl=https://ceur-ws.org/Vol-962/paper07.pdf
|volume=Vol-962
|dblpUrl=https://dblp.org/rec/conf/uai/NicholsonCQ12
}}
==A State-Transition DBN for Management of Willows in an American Heritage River Catchment==
https://ceur-ws.org/Vol-962/paper07.pdf
A State-Transition DBN for Management of Willows in an
American Heritage River Catchment
Ann E. Nicholson Yung En Chee Pedro Quintana-Ascencio
Clayton School of IT, Australian Centre of Excellence Department of Biology,
Monash Univ., Australia for Risk Analysis, Univ. of Central Florida, USA
ann.nicholson@monash.edu Univ. of Melbourne, Australia Pedro.Quintana-Ascencio@ucf.edu
yechee@unimelb.edu.au
Abstract
Expansion of willows in the naturally mixed
landscape of vegetation types in the Upper
St. Johns River Basin in Florida, USA, im-
pacts upon biodiversity, aesthetic and recre-
ational values. Managers need an inte-
grated knowledge base to support decisions
on where, when and how to control willows.
Modelling the spread of willows over space
and time requires spatially explicit data on
willow occupancy, an understanding of dis-
persal mechanisms and how the various life-
history stages of willows respond to envi-
ronmental factors and management actions.
We describe an architecture for a manage-
ment tool that integrates environmental spa- Figure 1: Location of the St. Johns River Water Man-
tial data from GIS, dispersal dynamics from a agement District (SJRWMD) and Upper St. Johns
process model and Bayesian Networks (BNs) River basin in east-central Florida, USA.
for modelling the influence of environmen-
tal and management actions on the key life-
history stages of willows. In this paper we fo- historical marshlands had been drained for agriculture
cus on modelling temporal changes in willow and other purposes. The natural hydrological regime
stages using a form of Dynamic Bayesian Net- was severely altered by the loss of marshlands, and
work (DBN). Starting from a state-transition networks of canals, ditches and levees. This led to loss
(ST) model of the willow’s lifecyle, from ger- of floodplain storage capacity, increased flood suscep-
mination to seed-producing adult, we de- tibility and severity, degraded water quality, extensive
scribe the expert elicitation process used to habitat loss and declines in fish, wading birds, water-
develop a ST-DBN structure, that follows the fowl and other wildlife. In 1988, the St. Johns River
template described by Nicholson and Flores Water Management District (SJRWMD) and the US
(2011). We present a scenario-based evalua- Army Corps of Engineers began restoration of 607 km2
tion of the prototype ST-DBN model. of the USJR basin by acquiring land, building storages
and plugging drainage canals. The St. Johns River
was designated an American Heritage River in 1998.
1 INTRODUCTION In the last 50 years, woody shrubs, primarily, Car-
olina willow (Salix caroliniana Michx.), have invaded
The Upper St. Johns River (USJR) basin in east- areas that were historically herbaceous marsh (Kinser
central Florida (Figure 1) covers an area of 4890km2 of et al., 1997). In some management compartments, the
which 1620km2 was originally floodplain marsh domi- area of willows has more than doubled between 1989
nated by forested wetlands, shrub swamps and herba- and 2001 (Quintana-Ascencio and Fauth, 2010). This
ceous wetlands. By the 1970s, about two-thirds of the change to the historical composition of mixed vegeta-
tion types is considered undesirable, as extensive wil- Early seedling establishment and survival is governed
low thickets detract from biodiversity, aesthetic and by the soil moisture regime and degree of competition
recreational values. Overabundance of willows reduces from other plants. Soil moisture in turn, depends on
local vegetation heterogeneity and habitat diversity. water-table elevation and soil characteristics such as
People also prefer open wetlands that offer a view- texture and organic matter content (Pezeshki et al.,
shed, navigable access and scope for recreation activi- 1998). However, even under favourable conditions es-
ties such as wildlife viewing, fishing and hunting. tablishment and survival rates are very low. Experi-
mental data for seedling establishment in mucky (high
Managing the spread of willows over space and time re-
organic matter) soil resulted in survival rates of 7%,
quires spatially explicit data on willow occupancy, an
whilst seedlings in mixed and sandy soil had negligible
understanding of dispersal mechanisms and how the
survival rates (Quintana-Ascencio and Fauth, 2010).
various life-history stages of willows respond to envi-
ronmental factors and management actions. We de- Once germinants become a yearling or sapling, sur-
scribe an architecture for a management tool that inte- vival rates are much higher (in the region of 50-100%)
grates environmental spatial data from a Geographical and varies depending on the hydrological regime, with
Information System (GIS), dispersal dynamics from a prolonged inundation having an adverse impact on sur-
process model and state-transition Dynamic Bayesian vival rates (Quintana-Ascencio and Fauth, 2010).
Networks (ST-DBNs) (Nicholson and Flores, 2011) for
Like other willow species, S.caroliana is thin-barked
modelling the influence of environmental and manage-
and fire-sensitive. However, its response to fire can
ment actions on the key life-history stages of willows.
be complex and is mediated by factors such as burn
State-transition (ST) models are a convenient means of intensity and conditions during and after burning. For
organising information and synthesising understand- instance, if water levels during a burn are sufficient to
ing to represent system states and transitions that are protect a portion of the willow stem, resprouting may
of management interest. We build on recent stud- follow after the burn. On the other hand, intense fires
ies that combine ST models with BNs to incorpo- in unflooded marshlands can result in willow mortality
rate uncertainty in hypothesised states and transitions, (Kinser et al., 1997).
and enable sensitivity, diagnostic and scenario analy-
Managers seek to control the overall extent of wil-
sis for decision support in ecosystem management (e.g.
lows, their rate of expansion into other extant wet-
Bashari et al., 2009; Rumpff et al., 2011). Our ap-
land types and encroachment into recently restored
proach uses the template described by Nicholson and
floodplain habitats. They recognise that different ar-
Flores (2011) to explicitly model temporal changes in
eas differ in terms of their ”invasibility” as well as
willow stages.
biodiversity, aesthetic and recreational value. Fur-
thermore, different management interventions are sub-
2 BACKGROUND ject to different spatial, environmental and operational
constraints, and induce different effects on willows, de-
2.1 WILLOWS IN UPPER ST. JOHNS pending on willow life-history stage and level of cover
RIVER CATCHMENT at the time of treatment. The application of prescribed
fire depends on water levels and the quantity of burn-
S.caroliana is one of four willow species native to the able understorey vegetation; mechanical treatment re-
SJRWMD. It occurs over a wide range of saturated quires dry/drought conditions and suitable substrate
soil types along lakeshores and stream banks, and in that can support the weight of heavy equipment. Fire
swamps and marshes. S.caroliana produces a very can produce a range of subtle and complex responses,
large number of small seeds that disperse by wind and whereas mechanical clearing obliterates extant vege-
water. Fecundity increases with size, but an average tation, returning an area to an unoccupied state, re-
adult can produce 165,000 seeds annually (Quintana- gardless of the willow stage at time of treatment. The
Ascencio et al., unpublished data). architecture of our management tool aims to explicitly
Seeds do not exhibit dormancy and have only a short accommodate these spatial characteristics and man-
period of viability. For good germination and estab- agement considerations in modelling the temporal dy-
lishment to occur, the seedbed must be unshaded and namics of willow population structure and cover.
free of competition (i.e. bare) and consistently moist
but not inundated (Kinser et al., 1997; Pezeshi et al., 2.2 BAYESIAN NETWORKS FOR
1998; Lee, Ponzio et al., 2005). Such conditions can ENVIRONMENTAL MODELLING
result from natural and human disturbances such as
extended spring drawdown of slough areas, natural Bayesian networks (Pearl, 1988) are becoming increas-
and controlled burns, grazing and mechanical clearing. ingly popular for environmental and ecological mod-
elling and risk assessment. There have been several re- (e.g., in rangelands, grasslands and woodlands, see
cent surveys: Uusitalo (2007); Hart and Pollino (2009); Bestelmeyer et al., 2003; Sadler et al., 2010; Rumpff
Korb and Nicholson (2010); Aguilera et al. (2011), and et al., 2011). In this paper, we apply the template
guidelines for building BNs for environmental appli- proposed in Nicholson and Flores (2011), shown in Fig-
cations (e.g. Varis and Kuikka, 1999; Marcot et al., ure 2, which formalised and extended Bashari et al.’s
2006; Kuhnert et al., 2010). A typical early applica- model, combining BNs with the qualitative STMs. S T
tion involved building a model of the response of a represents the state of the system, has n possible values
particular species or landscape, to environmental con- s1 . . . sn , and may directly influence any of the envi-
ditions and/or management actions, in a limited area; ronmental and management factors, which are divided
e.g. modeling the effects of eutrophication (excessive into m main factors, F1 , . . ., Fm (which directly influ-
nutrients) in the Neuse River watershed (Borsuk et al., ence transitions) and other sub-factors, X1 , . . ., Xr
2004), or predicting future abundance and diversity of (which influence the main factors).
native fish in the Goulburn River in south-eastern Aus-
tralia (Pollino et al., 2007). Such models often had no
explicit representation of time, other than that implicit
in the causal process; or a single time-scale node was
used to ”flip” the BN’s prediction from one time-scale
to another (e.g. in Pollino et al. (2007), from 1-year to
5-years). However, some environmental applications
concerned with system behaviour over time and/or
space have used DBNs and Object-oriented Bayesian
Networks (OOBNs) to support this explicitly.
BNs are increasingly being coupled with Geographic
Information Systems (GIS) (e.g., Stassopoulou et al.,
1998; Smith et al., 2007; Johnson et al., 2012). In
such applications, there is typically one copy of the
BN associated with each cell in the GIS. Data layers
in the GIS may be used as inputs to the BN, and
outputs from one or more BN nodes may be fed back to
the GIS. Our tool architecture, presented in Section 3,
follows this basic structure. Figure 2: The generic ST-DBN combining STMs with
DBNs (Nicholson & Flores, 2011, Fig.10).
Dynamic Bayesian Networks (DBNs) are a variant
of ordinary BNs (Dean and Kanazawa, 1989; Kjærulff, The transition nodes, ST1 , . . . STi , . . ., STn repre-
1992; Nicholson, 1992) that allow explicit modelling of sent the transitions from each state si , each with at
changes over time. A typical DBN has nodes for N most n + 1 values (though usually with fewer), one
variables of interest, with copies of each node for each for each “next” state plus “impossible”, giving explicit
time slice. Links in a DBN can be divided into those modelling of impossible transitions. As with ordinary
between nodes in the same time slice, and those in the DBNs, there is an implied δT , which can be included
next time slice. While DBNs have been used in some explicitly as a parent of all the ST nodes, if the time
enviromental applications (e.g. Shihab and Chalabi, step varies. Each transition node ST has only some
2007; Dawsey et al., 2007; Shihab, 2008), their uptake of the causal factors as parents. The CPT for the ST
has been limited. This is perhaps because they are node is just a partition of the corresponding CPT if the
perceived to be ”very tedious” (Uusitalo, 2007), or be- problem was represented as an ordinary DBN, without
cause DBN algorithms are available only in software the transition nodes. The next state node, S T +1 , has
resulting from research projects,1 with DBN function- to combine the results of all the different transition
ality less well supported in the more widely used com- nodes, given the starting state S, and thus has n + 1
mercial products.2 parents. However, the relationship between the transi-
State-and-transition models (STMs) have been tion nodes and S T +1 is deterministic, so the CPT can
used to model changes over time in ecological sys- be generated from a straightforward equation.
tems that have clear transitions between distinct states Nicholson and Flores (2011) presented a complexity
1 analysis of the ST-DBN, compared to an ordinary
e.g. BNT, code.google.com/p/bnt
2
For example, the Netica Application DBN (without transition nodes). This showed that
(www.norsys.com) GUI interface has some DBN function- any models that explicitly represent all the transitions
ality, but this is not included in its API. (i.e. that have ST nodes), only remain tractable when
there are natural constraints in the domain; that is, if
the underlying state transition matrix for S is sparse,
and if different factors influence different transitions.
Such constraints were identified for the willow man-
agement problem in the USJR basin.
Figure 5: The four willow stages of management inter-
3 ARCHITECTURE est and the possible transitions of each stage. Arrows
indicate the direction of possible transitions.
Figure 3 shows the system architecture for the inte-
grated management tool. It includes a GIS database,
a dispersal process model, a ST-DBN model of willow 2005; Ponzio et al., 2006; Quintana-Ascencio & Fauth,
response to environment and management and a man- 2010). The knowledge engineering process was itera-
agement framework. For each cell (modelling unit), tive and incremental, following Boneh (2010), using a
the GIS database supplies data on environmental at- series of workshops (2 full-day, 4 half-day) between the
tributes such as soil and vegetation type and informa- knowledge engineers with BN modelling expertise (the
tion about landscape position and context (e.g. prox- first two authors) and the domain expert (the third au-
imity to canal structures or type of surrounding land thor), over a six week period. Between each workshop,
cover). This data provides inputs to parameterise the the models were updated in the BN software, reviewed
dispersal process model, which then makes predictions and revised.
on seed production that can be mapped and linked
to the ST-DBN. The data on spatial context also in-
forms the construction of management strategies (de- 4.1 NODES
fined here as a set of spatially explicit management
actions) and assists in decisions about feasible loca- The key points of interest are whether willow is present
tions for applying particular management actions. We in a cell or not, and if present, its lifecycle stage and
chose a cell size of 100x100 m (1 ha) to represent a its level of cover.
modelling unit. This reflects the resolution of available The stages of management interest modelled in the
data for environmental attributes, makes the compu- Stage node are: unoccupied, yearling, sapling (non-
tational demand associated with dispersal modelling reproductive juvenile) and adult.
feasible, and is a reasonable scale with respect to can-
didate management actions. The possible transitions amongst these four stages are
shown in Figure 5. Some stage transitions are not
The ST-DBN synthesises current understanding about possible (e.g. adults and saplings cannot become year-
how environmental conditions and management ac- lings and yearlings cannot remain as yearlings at the
tions, acting separately and in various combinations, next time step). The time step across the ST-DBN
influence transitions between the key stages of man- was chosen to be one year. An annual time step was
agement interest. For each cell, the underlying ST- considered appropriate given the willow’s growth and
DBN takes input from the GIS database and man- seed production cycle. Our domain expert did not see
agement decisions, and predicts willow response for any benefit in modelling at a finer temporal scale. In
the next timestep. These predictions can then be particular, seedlings were only of interest from a man-
mapped and aggregated across the target management agement point of view if they survived to the yearling
area to produce evaluation metrics for managers. In stage.
this way, managers can “implement”, visually compare
and quantitatively evaluate different candidate man- For these four stages or states, the BN has
agement strategies (or scenarios). The remainder of four corresponding transition nodes (shown in
this paper focuses on the development of the ST-DBN Fig. 4): UnOcc Transition represents the pos-
structure. sible transitions from Stage(T)=Unoccupied,
Yearling Transition represents the possible tran-
4 A ST-DBN FOR WILLOWS sitions from Stage(T)=Yearling, etc. Note that each
S Transition node has an additional state, NA (Not
Applicable), for when Stage(T) was other than S.
The development of the ST-DBN (Figure 4), drew
upon a range of sources and used a combination of Level of Cover refers to the proportion of area within a
knowledge derived from ecological and physiological cell that is occupied by willows of any lifecycle stage.
theory, field observations, field and glasshouse experi- When the willows reach the Adult (seed-producing)
ments and experts (e.g. Kinser et al., 1997; Pezeshi et stage, Size and Level of Cover are factors that influ-
al., 1998; Lee, Ponzio et al., 2005; Lee, Synder et al., ence Seed Production.
Figure 3: System architecture of the integrated management tool comprising a GIS database, a dispersal process
model, a ST-DBN model of willow response to environment and management and a management framework.
GIS excerpt shows a portion of the Blue Cypress Marsh Conservatioin Area within the USJR basin.
Figure 4: Willows ST-DBN, showing posteriors for Stage and transition nodes for the scenario starting with the
cell Unoccupied by willows, with favourable conditions for the transition to Yearling: high seed availability, just
right spring (germination) and summer (survival) precipitation, ”mucky” (organic, water holding) soil, enough
bare ground, no mechanical clearing or prescribed burn.
Stage transitions are governed by environmental and and convert areas occupied by adults back to an unoc-
management factors, acting alone or in some combina- cupied stage, or it might kill off large stems and reduce
tion. Environmental factors include soil type, amount canopy cover (Lee, Ponzio et al., 2005; Lee, Synder et
of bare ground, spring and summer precipitation and al., 2005). When adults are damaged in this way, they
local vegetation type. Candidate management actions become non-reproductive for a period as they attempt
include mechanical clearing (roller-chopping), burning, to recover by resprouting post-fire. For this period,
grazing, herbicide application and hydrological manip- they functionally resemble saplings and we represent
ulation. Each are subject to different spatial, environ- this in our ST-DBN by a transition from adult back
mental and operational constraints, and induce differ- to the sapling stage.
ent effects on willows, depending on willow life-history
The initial Level of Cover is determined by the num-
stage and level of cover at the time of treatment. For
ber of seedlings that survive when the Stage transi-
this prototype model, we concentrate on mechanical
tions from unoccupied to yearling. Stages from year-
clearing and burning. Table 1 gives a full listing of the
ling onwards are robust to environmental variability
Willow ST-DBN nodes, grouped into (colour-coded)
(e.g. fluctuations in precipitation and inundation), but
categories. Continuous variables were discretised for
they are affected by mechanical clearing (which always
implementation in Netica, with discretisation break-
returns the cell to Unoccupied) or burning (depending
points determined by a combination of empirical data
on the burn effectiveness).
and expert judgement.
Again, following the Nicholson and Flores ST-DBN
4.2 ARCS template, the four transition nodes are all parents of
the subsequent Stage(T+1) node.
Next, we describe the nature and influences on the pos-
sible transitions, represented by the arcs in the Willow 4.3 PARAMETERISATION
ST-DBN (shown in Fig. 4).
Unoccupied areas can become occupied by yearlings We have two stages to our model parameterisation.
if they are successfully colonised within a time step. In the parameterisation for this first prototype, our
Successful colonisation depends upon seed availabil- aim was to represent high-level behaviour, thus the
ity (which is determined by seed production in and CPTs were constructed using a combination of ex-
influx from neighbouring cells) and environmentally pert elicitation of process knowledge, expert interpre-
favourable conditions for seed germination and subse- tation of empirical data from field and glasshouse ex-
quent seedling survival. Otherwise, unoccupied areas periments, deterministic and probabilistic functions,
remain unoccupied. Figure 4 shows the Willow ST- statistical models and expert judgement. We do not
DBN starting as Unoccupied, under favourable condi- report details of these here, for reasons of space; they
tions. Note that the UnOcc Transition is split between will be reported elsewhere.
staying Unoccupied (61.3%) and transitioning to Year- The second phase will involve more detailed parame-
ling (38.7%), while all the other Transition nodes show terisation using judgements elicited from a larger pool
are 100% NA (Not Applicable). of domain experts. We will also use specific results
Early survival is low, but yearlings can become from experiments already completed (see Quintana-
saplings when environmental conditions are favourable Ascencio and Fauth, 2010) to calibrate CPTs for some
for growth and they are not impacted by mechanical nodes. The field and greenhouse experiments do not
clearing or burning. Otherwise, mortality will cause provide enough cases to learn the CPTs, nor do they
areas occupied by yearlings to revert to the unoccu- cover an exhaustive range of scenarios. However, they
pied stage. will provide guidance for the parameterisation.
As saplings grow, they can become reproductive 5 SCENARIO-BASED
adults, provided they are not impacted by mechani- EVALUATION
cal clearing or burning. Otherwise, they may remain
in the non-reproductive sapling stage, if burn impact
For this first prototype of the Willow ST-DBN, we
is minor, or revert to the unoccupied stage if burn im-
conducted scenario-based evaluation with our domain
pact is major or if mechanical clearing occurs.
expert throughout the knowledge engineering process.
In the absence of mechanical clearing or burning, We examined multiple scenarios designed to probe the
adults stay in the adult stage. Clearing results in al- encoded relationships for key environmentally-driven
most complete mortality and reversion to an unoccu- processes, such as seedling survival and expected re-
pied stage. The effect of fire depends upon its burn sponses to management actions, such as the effect of
intensity. If sufficiently severe, it can cause mortality burning. By inputting different combinations of values
Table 1: The nodes of the Willow ST-DBN, grouped into categories with colour-coding (see Figure 4).
Category (node colour) Nodes
Aspects of willow state (tan) Stage, Level of Cover, Size and Seed Production
Germination & seedling Seed Availability, Proportion Germinating, NumberGerminating
survival processes (orange) Seedling Survival Proportion and NumberSurviving
Environmental conditions (green) Soil Type, Vegetation, Enough Bare Ground,
spring and summer precipitation (Spring PPT, Summer PPT)
seasonal water availability for germination, survival and growth
(Available Water Spring, Available Water Germination,
Available Water Survival, Available Water GrowingSeas
Canal or Centre (i.e. accessibility)
Management options (red) Mech Clearing, Burn Decision (and associated with this option,
Burn Intensity and BurnEffect on Willow)
State-transitions (purple) UnOcc Transition, NonInterv YearlingTransition† ,
Yearling Transition, Sapling Transition and Adult Transition
† Representing expected yearling transition without overlay of management actions.
Table 2: Subset of scenario evaluation results, used to evaluate high-level behaviour of the Willow ST-DBN. For
each scenario, columns on the left show the evidence entered; the 4 columns on the right show the distribution
for Stage(T+1). For the Yearling, Sapling and Adult scenarios, the Level of Cover is High; the probabilities of
transitions to UnOccupied are greater for lower levels of cover.
No. Stage(T) Soil Avail Avail Enough Stage(T+1)
(Seed Avail= Water Water Bare UnOcc Yearling Sapling Adult
High) Spring. Survival Ground
1. UnOcc Sandy JustRight JustRight Yes 88.4 11.6 0 0
2. UnOcc Mucky JustRight JustRight Yes 61.3 38.7 0 0
3. UnOcc Mucky JustRight TooMuch Yes 94.6 5.4 0 0
4. UnOcc Mucky TooLittle JustRight Yes 100 0 0 0
Stage(T) Soil Avail Mech. Burn Stage(T+1)
Water Clearing Decision UnOcc Yearling Sapling Adult
Growing (Vegetation=
Season Grassland)
5. Yearling Mucky JustRight No No 1 0 99.0 0
6. Yearling Sandy JustRight No No 20.0 0 80.0 0
7. Yearling Sandy TooLittle No No 40.0 0 60.0 0
8. Yearling Sandy TooMuch No No 98.5 0 1.5 0
9. Yearling Mucky JustRight Yes No 99.0 0 1.0 0
10. Yearling Mucky TooLittle No Yes 81.9 0 18.1 0
Stage(T) Vegetation Mech. Burn Stage(T+1)
Clearing Decision UnOcc Yearling Sapling Adult
11. Sapling [Any] No No 10.0 0 67.0 23.0
12. Sapling [Any] Yes No 99.5 0 0.5 0
13. Sapling HerbWet No Yes 20.0 0 71.1 8.9
14. Sapling Woodland No Yes 15.0 0 69.1 15.9
15. Sapling Grassland No Yes 22.7 0 70.9 6.4
16. Adult [Any] No No 1.0 0 0 99.0
17. Adult [Any] Yes No 99.0 0 0 1.0
18. Adult HerbWet No Yes 0.92 0 1.6 97.5
19. Adult Woodland No Yes 0.96 0 0.8 98.2
20. Adult Grassland No Yes 0.8 0 4.0 95.2
for the relevant environment and management vari- Acknowledgements
ables, and examining the results in key intermediate
and final output nodes, we were able to identify er- AEN and YEC acknowledge the support of ARC Link-
rors in CPTs, logical inconsistencies, and nodes that age LP110100304. This project benefited from contri-
needed splitting, combining or redefining. butions by many thoughtful and hard-working indi-
viduals. D.Hall, K.Ponzio and K.Snyder (SJRWMD)
Table 2 presents a small subset of these scenarios to- provided access to sites, knowledge about willow inva-
gether with the distributions obtained for Stage(T+1), sion and advice on experiments. S.Green, J.Navarra,
while Figure 6 shows fragments of the BN with pos- H.Smith and E.Stephens assisted with field and green-
terior distributions for some of the variables of inter- house work. We thank J.Fauth (UCF) and the gradu-
est.3 The evaluation results in Table 2 and Figure 6 ate students of PQ-A’s Restoration Ecology classes for
are consistent with our understanding of the influence their efforts.
of environment and management actions on key life-
history stages of willows, as described in Sections 2.1
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