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The Dynamic Spatial Simulation Modelling of the Effects of
Land Use Change on Avian Species
Burak Gtneralp
University of Illinois at Urbana-Champaign
Department of Natural Resources and Environmental Sciences
S. Goodwin Ave. Urbana IL 61801 USA
Telephone:++1 217 333 93 49
Fax:++1 (217) 244-3219
guneralp@ uiuc.edu
Abstract
A spatial dynamic simulation model for two bird species was constructed. It is developed
as a part of a greater project being carried out in University of Illinois at Urbana-
Champaign. The project LEAM is about analysing urban sprawl in the United States and
developing policies to prevent it. Under LEAM project, a comprehensive urban
development model of Kane County in the state of Illinois was constructed. The model
presented in this paper is an integral part of the LEAM model and serves as a means to
evaluate the effects of urban sprawl on two bird species selected as indicators for their
ecosystems: Eastern meadowlark (Sturnella magna) for the grassland, and ovenbird
(Seiurus aurocapillus) for forest ecosystems. The model is capable of running for both
species with the help of a ‘switch’ variable. The model was integrated with a hypothetical
land use map through a spatial analysis software, Spatial Modelling Environment (SME)
and tested for behavioural validity. Non-spatial results were used for verification and
calibration; spatial results revealed the extent of effects of urban sprawl on avian species
in particular and wildlife in general. Lack of sufficient data was a significant problem
during the study and it is believed that the model could be improved with the availability
of more data on population dynamics and habitat requirements of grassland and forest
bird species. The spatial modelling studies are still novel approaches and their success
partly depends on availability of relevant and sufficient data. There is still much to
improve in this field and it is realistic to expect great contributions to the scientific and
practical theory from spatial dynamic modelling in the future.
Keywords: Urban sprawl, land use, habitat loss, habitat degradation, avian species,
system dynamics, spatial modelling.
I. Background
Ecological models need to represent spatial characteristics of species’ habitat adequately
to be accurate representations of the reality. Until recently, ecological models have been
constructed without explicit consideration of the spatial nature of the problem at hand.
This requires assuming that the habitat modelled is more or less homogeneous which is
not the case most often in real life. Habitats are often heterogeneous and there are spatial
interactions going on between various elements of the system. Moreover not only the area
sum but also the spatial arrangement of habitats plays a vital role on the population
dynamics of species. With the advance of computer technology and geographic
information systems, it is possible to construct spatially explicit models. This gave way to
come up with ecological models capable of simulating both on spatio-temporal domain.
What this means for land use managers and decision makers is more realistic models that
can be used more effectively by them.
Land-use changes in the United States lead to enormous uncontrolled habitat alterations
that influence plants and animals (Tumer et al.). Poorly planned urban development also
causes unnecessarily high infrastructure costs to the society that could otherwise be
avoided. This paper deals with the analysis of urban sprawl effects on wildlife bird
species. It is part of a greater research project being carried out in University of Illinois at
Urbana Champaign. The research project is also supported by the CERL and aims to
evaluate and analyse urban sprawl in United States. The study area of the research project
is Kane County near the Greater Chicago Area in the State of Illinois. Urban
development patterns in Kane County are studied to uncover its causes and to determine
its probable effects on wildlife, economy, and social structure of the county through
dynamic simulation modeling. Potential policy options to prevent the adverse effects of
urban development can be developed using the LEAM model platform.
The bird model presented in this paper was integrated with the LEAM model platform.
The platform, apart from the bird model, consists of models developed for other indicator
species such as raccoons and frogs, and models related to hydrological and socio-
economic dynamics of the county. An interactive version of the large-scale regional
model with its social, economic, and ecological components can be reached from the
website http://www.rehearsal.uiuc.edu/leam/. The regional model serves as an
experimental simulation platform where different aspects of urban sprawl can be
analysed from a holistic point of view where the social, economic, and ecological
esented in this paper, a hypothetical dynamic landscape
was used. The hypothetical land use map has a number of land uses ranging from
grassland to high intensity residential in accordance with the national land cover data
(NLCD) definitions (http://landcover.usgs.gov/classes.html). The resulting model has a
fairly generic structure and it is possible to employ for other species by only changing the
relevant parameters with no or little structural modification.
II. Selection of Indicator Species
An indicator bird species for grasslands was used in the model since grasslands are the
characteristic wildlife habitat in and around Kane County. An indicator bird species for
forests was modelled also to be used in another project for a mostly forested region in the
State of Georgia. The model runs for only one species at a time. The indicator species to
be simulated is selected with the help of a boolean variable in the model.
The indicator species for grasslands is Eastern Meadowlark (Sturnella magna). It is a
typical grassland bird species. It is used in the Kane County urban sprawl project. The
indicator species for forests is Ovenbird (Seiurus aurocapillus). It is already a threatened
species and therefore serves as a good ‘conservative’ indicator species. According to
Simons et al. (1999), the species is listed as one of the High Priority Southem
Appalachian Bird Species. It will be used in another urban sprawl project in the State of
Georgia. There is considerable amount of information on both species in the literature.
Conducting research on birds has its own challenges. First, due to the length of
observation time required and difficulties in observing large areas, research on birds
generally provide little information on their lifecycles. Moreover, studies on the same
species but from different locations may produce irrelevant even conflicting results.
Finally, there is little information on factors affecting neo-tropical birds in wintering
grounds and during migration periods and how they respond to them. The approach here
was to use information sources from studies conducted at locations close to the project
sites.
ILI. Eastern Meadowlark (Sturnella magna)
The range of Eastem Meadowlark is widespread in the eastem United States and
southeastern Canada extending as far west as Arizona. It is also resident in the Bahamas
and extends south to Mexico (Figure 1). These birds are chunky, ground-dwelling birds
and can be found in grasslands, pastures and prairies, but the population has been reduced
due to urban areas, and reservoirs.
Figure 1. Breeding distribution of the Eastern Meadowlark in the United States and
southern Canada, based on Breeding Bird Survey data, 1985-1991. Scale represents
average number of individuals detected per route per year. (Price et al.. 1995).
In spring, the male arrives first to the nesting grounds and establishes his territory. The
females arrive approximately 7-14 days after. The male's success depends on the territory
and his song. Males are polygamous and defend their territory, which is large enough for
two or three mates. Nesting begins late March to early May. The nest is built on the
ground in meadows, cornfields or weedy orchards. Throughout the months of April to
August, 4-5 eggs are laid. The female incubates the eggs which takes anywhere from 13-
14 days and broods the young. The first young will leave the nest within 11-12 days. Nest
on ground concealed by tall grasses (Bird Nature, 2001).
This bird's diet consists of about 70-75 percent insects such as grasshoppers, crickets,
beetles, ants, spiders, and wasps. In winter, they eat grains and weed seeds.
IL.II. Ovenbird (Seiurus aurocapillus)
Ovenbird is a neotropical bird species. It is a very vulnerable forest dwelling species is a
good indicator on the health of forests in Georgia in particular and within its habitat range
in general.
The range of this forest-interior dwelling bird extends from central and eastern Canada to
northeastern and north central United States (Figure 2). Its breeding habitat is large
mature deciduous forests and pine. The species nests are located in the open on the
ground. Adult females leave 4-5 eggs per nest. Incubation lasts 11 to 13 days fledging 8
to 10 days.
Ovenbirds may be more successful raising young in larger forests than in isolated forest
fragments. Donovan et al. (1995) suggested that long-term viability of Ovenbird
populations, as well as those of wood thrushes (Hylocichla mustelina) and red-eyed
vireos (Vireo olivaceus), depend on the maintenance of heavily-forested landscapes
throughout the breeding range (Conservation Commission of Missouri Report).
The ovenbird belongs to the warbler family of songbirds. It stays mainly on the forest
floor where it forages and builds its nest. Ovenbirds winter in Mexico, Central America
and northern parts of South A merica. Besides flying thousands of kilometres, these birds
must face habitat loss on two fronts. Large portions of the rainforest in South and Central
America are being cleared and bumed to make room for mines, settlements and ranches.
They return to Saskatchewan around the middle of May. Scientists call these birds neo-
tropical migrants. Like most songbirds, ovenbirds are territorial and return to the same
areas each year. While in North America, mature hardwood stands are their favorite
habitat.
Ovenbirds live in mature deciduous and mixed wood stands. They are most numerous
where the forest floor is shaded by a thick canopy of trees. Ovenbirds eat insect larvae
and worms.
Ovenbirds are vulnerable to predation along the forest's edge. To obtain food and avoid
predators, they live in the forest's interior. Furthermore, less forest edge helps to improve
the survival of all nesting songbirds (Saskatchewan Interactive). However, the width of
forest edge for ovenbird is not known with certainty (Dawson et al., 1998).
III. Modelling Description
The model is constructed using system dynamics methodology, an effective tool in
dealing with dynamic problems (such as deforestation in tropics, chronic high levels of
inflation, or in this study, habitat loss) (Forrester, 1968). It is essential in system
dynamics methodology that model structure should provide a valid description of the real
system (Forrester et al., 1980; Barlas, 1996). The purpose in a system dynamics modeling
study is, typically, to reveal how and why the problematic behavior is generated and to
find leverage points in the system, which are effective in eliminating the problematic
behavior. These leverage points is then used to generate ‘policies’ (such as tax
regulations) to improve the situation.
Figure 2. Breeding distribution of the ovenbird (Red areas on the map) (Nearctica, 2001).
The main building blocks of a formal system dynamics model are stocks, flows and
converters. Stocks (symbolized by rectangles) are also known as levels or state variables.
They represent major accumulations in the system. Flows (symbolized by valves), also
known as rates, change the value of stocks. In turn, stocks in a system determine the
values of flows. Flows represent activities that fill in or drain the stocks. Intermediate
concepts or calculations are known as converters. Converters are computed from stocks,
constants, data, and other converters unless they are constants (HPS, 1996). The focus
and the time frame of the study are crucial in deciding which elements of the system is to
be represented as stocks, flows or converters.
For example, populations of young and adult birds (young females, adult_females,
wintering young females, wintering_adult_females) are modelled as stocks in the stock-
flow structure of the model (Figure 3). The processes acting upon these populations
(reproduction, death, migration YF, migration AF, winter death) are represented as
flows. The variables that are used in the calculation of these flows such as
Carrying_capacity and maturation_adj_time are converters. The full model equations are
provided in the A ppendix at the end of the paper.
After extensive literature survey, two bird species are selected as indicator species for
two land classes: Eastern Meadowlark (Sturnella magna) for grassland habitats and
Ovenbird (Seiurus aurocapillus), an already threatened species, for forest habitats. A
systemic model was developed which is applicable for both species. However, it
considers only the population dynamics and related relationships with no spatial
emphasis. The model then integrated with a hypothetical land use data using spatial
modeling environment software, SME to add the spatial dimension to the analysis. This,
apart from being a rather novel approach, makes possible to carry out analysis that is
more realistic and reach results that are more reliable.
For the model presented in this paper, a hypothetical landscape consisting of 100 x 100
cells was used. Each cell is 30 m X30 m. The hypothetical land use map has a number of
land uses ranging from grassland to high intensity residential in accordance with NLCD
land cover class definitions. The crucial point about the maps is that they should have
sufficiently fine resolution to be able to represent and analyse the study region
effectively. The quantitative system dynamics model, once completed and validated, was
integrated with land-use map of that is needed by the model during simulation. Each
model will run for each pixel sequentially. The model runs for each pixel sequentially. In
addition to the communication amongst the model sectors, there is interaction between
neighbouring pixels. The nature of this interaction is mostly physical due to spatial
continuity (i.e. migration). It is worth noting pixels are artificial structures and they are a
means of spatial derivation devised for ease of analysis. The pixel interaction within the
model is presented in Figure 4. It considers the effect of land use change on migration.
The land use change and habitat affects population dynamics. population dynamics in the
target pixel together with the corresponding variables of neighbouring pixels may cause
emigration or immigration from the pixel to its neighbours through population dynamics.
Evidently, the land use changes in neighboring pixels affect the population dynamics in
the target pixel.
IIL. Main Assumptions
There are twelve major assumptions of the model:
* The ratio between female and male birds was assumed 1:1.
* Only female birds are considered in the model.
¢ Maturation period was assumed 12 months for both species.
* Only mature (adult) birds migrate between neighboring cells.
+ Simulation starts on January 1".
* Minimum Habitat Size was assumed 10 ha for both eastern meadowlark and ovenbird
(Hull, 2000; Fitzgerald et al., 2000; Kobal et al., 1998). This was accomplished
roughly but satisfactorily by the use of edge habitat formulation.
¢ Deaths occurring during seasonal migrations are not taken into account due to lack of
information (Moore et al., 1995).
¢ Differences between agricultural lands are not considered such as conventionally
tilled or no-tilled fields, mowing etc.
¢ Spatial differences in vegetative species, vegetation height, moisture or different
management practices within the same land uses are not considered.
¢ Only land use map was used in the study.
¢ It was assumed that individual birds return to the same breeding ground every year
(Hull, 2000).
* Cowbird parasitism was included inclusively in the edge habitat and habitat
suitability index formulations (Hull, 2000; Podolsky, 2000; Sherry et al., 1995).
LandUseMap
Carrying Capacity
Edge Habitat
Habitat Suitability
\ eo
cami apacity Realized
+ Canying Capacity Realized of Neighboring Cells
Population Carrying Capacity Realized Ratio
sf
Reproduction -—__ ¢+
+
Population Dynamics of the Bird Species in Breeding Habitat
he +
Immigration
4
Month, Emigration from Neighboring Cells
Seasonal Emigration (444 Seasonal Immigration
Death in Breeding Habitat
=H,
Population Dynamics during 0 a ~
+
: 4—)
“2 > during Winter
Figure 3. Broad Causal Loop Diagram.
Land Use
Change
[> Edge Habita' Emigration
Proportions
v Emigratio
Population a |
———+ Dynamics <<
Reproductiora— Immigratio
Figure 4. Sectors Diagram of the Model.
IILII. Broad Causal Loop Diagram
In system dynamics modeling, causal loop diagrams give a straightforward representation
of the whole model and help to identify the major feedback mechanisms in the system
under study.
The core of the model is the population dynamics of the species. The population in
breeding habitat is the focal point of the study and hence, it is the part of the model where
everything boils down. The land use pattern at a particular cell and whether it is located
in edge habitat dictate the realized carrying capacity for that cell. The realized carrying
capacity may be lower than or equal to the maximum carrying capacity. Maximum
carrying capacity is the carrying capacity in grassland for eastern meadowlark or in forest
for ovenbird (i.e. the most suitable habitats for these species). Land use patterns in the
particular cell and in its neighbouring cells are used in finding out whether that cell is an
edge habitat or not.
The ratio between the population and realized carrying capacity affects both reproduction
and emigration rates. If the ratio is low then reproduction is encouraged, emigration is
discouraged and visa versa. Reproduction increases population while death decreases.
These variables form two negative (goal-seeking) feedback loops (Figure 3). There is
another negative feedback loop formed by population in breeding habitat with seasonal
emigration. The population in breeding habitat is also affected by the immigration from
neighbouring cells.
A similar structure holds for population in wintering habitat except the absence of
reproduction and the ratio between the population and realized carrying capacity. The
reason for the absence is obvious for the first one and lack of sufficient knowledge on the
wintering grounds of the species for the latter.
The negative feedback loops are coupled with a positive feedback loop formed by
populations in breeding and wintering habitat, seasonal emigration, and seasonal
immigration.
Emigration from the cell is dictated by the ratio between the population and realized
carrying capacity, the population in breeding habitat and realized carrying capacities of
the neighbouring eight cells. On the other hand, immigration is the total emigration from
eight neighbouring cells to this particular cell.
The model and its sectors are described in more detail in the following section.
IIL.III. Model Sectors
There are seven sectors in the model. The relationships between these sectors and also
neighbouring cells are shown in Figure 4. Each variable begins with capital letter B in the
model to signal that they belong to the bird sub-model of the larger project. However, in
this paper they are presented without the capital letter for simplicity.
In the model sectors, some variables values/equations are different for the two bird
species. These variables take on the value depending on the value of GrL_F_ Species,
which is a control variable to switch the model from one species to another. If it is 1 the
model simulates for the grassland species; if 2, for the forest species.
TILIILI. Land Use Change
This sector contains variables related to land use. Land use patterns and changes may be
due to both anthropogenic and non-anthropogenic sources. LandUseMap reads the land
class from the land use map. | u index is a boolean variable; it is 1 if the land class is
suitable and zero if it is totally unsuitable (i.e. carrying capacity for that land class is
zero). Habitat Suitability Index (HSI) takes on values from 0 to 1 depending on the land
class (Table 1). HSI values for land use classes that are not listed in the table are zero for
both species. The more suitable land class the higher the value for Habitat Suitability
Index. Though calculated in the Edge Habitat sector edge index is also used in this sector
since edge habitat hinges on land use change (Figure 5).
ins) Land Use Change 8
og ad
: 6 fi
al Habitat Suitability index
Grl F Species
{
edge index * .
LandUseMap +
tu index
Figure 5. Land Use Change Sector.
Table 1. Habitat Suitability Index Values (HSIV) for eastern meadowlark and ovenbird
for different land use classes (HSIV for land use classes that are not listed in the table are
zero for both species.) based on Hull, 2000.
habitat suitability index Indicator Bird Species
[Eastern .
[Land Use Class Meadowlark Ovenbind
21 Low Intensity Residential {0.2 0.0
41 Deciduous Forest (0.0 1.0
42 Evergreen Forest (0.0 1.0
43 Mixed Forest (0.0 1.0
51 Shrubland (0.2 0.0
61 Orchards/V ineyards/Other |0.2 0.0
71 Grasslands/Herbaceous _{1.0 0.0
81 Pasture/Hay 0.8 0.0
82 Row Crops 0.6 0.0
83 Small Grains 0.6 0.0
84 Fallow (0.3 0.0
TIL.IILII. Edge Habitat
Edge formulation in the model is a practical way to deal with edge habitat, minimum
habitat requirement and suitable habitat shape (i.e. a narrow rectangular habitat is less
suitable than a square one with the same area) notions (Faaborg et al., 1995).
Edge habitat is a simple sector used in examining whether the particular cell is in edge
habitat and if so where it is located within the edge habitat. Everywhere within an edge
habitat does not support the same number of species so it is important to know where that
particular cell is located. For a cell to be edge habitat, it should have a land class suitable
for the bird species (i.e. ] u index is 1). It was assumed that the edge habitat is 180 m (i.e.
6 cells) in width (Norment et al., 1999; Dawson et al., 1998) and the cell is marked from
0 to 6, the value of edge index. Edge index is zero if the cell is not in the edge habitat and
it takes values from 1 to 6 depending on the location of the cell within the edge habitat. If
at least one of the cell’s eight neighbours is in an unsuitable land class (i.e. the cell
borders with an unsuitable land class), the value of edge index is 1 and it increases up to 6
as one moves away from the border and toward the interior of the suitable habitat. To
determine the value of edge index, 1 u index and edge index values of the neighbouring
cells must also be known (Figure 6).
For most of the grassland bird species, the minimum habitat size is 10 ha and it is 5 ha for
eastem meadowlark (K obal et al., 1998; Hull, 2000). The edge and habitat structures are
modelled based on these observations. Also for ovenbird, Dawson et al. suggests that
forest area should be greater than 30 ha and edge index formulation is modified for
ovenbird according to this observation.
Dawson et al. states that the depth of forest edge habitat is greater than 100 m so it seems
180 m is a reasonable conservative estimate for the width of edge habitat for ovenbird in
the model.
IILIILI1I. Emigration and Emigration Proportions Sectors
total emigration from a cell is determined by the breeding adult population,
adult_females, emigration rate, which is between 0 and 1.
total emigration = emigration_rate*A dult_Females
Emigration rate is a graphical function of the ratio between population and realized
carrying capacity (Over_under_CC_realized) (Figure 7). Hence,
Over_under_CC_ realized is simply a measure of crowding pressure on the population.
However, how to distribute these emigrates to the neighboring cells depends on their
realized carrying capacities (CC_realized). The number of emigrates to each direction is
found by, for example for north direction,
to_N =proportion_N * total_emigration
om Sage Haber a8
lu index@sw
luindex@s | u index@SE
Figure 6. Edge Index Sector.
The proportion of emigrates that will go in each direction is, again for north direction,
proportion_N =CC_realized@N / total_CC_realized
where,
CC_realized@N is the realized carrying capacity of the neighbouring cell at north of the
target cell and,
total CC_realized is the sum of realized camying capacity values of the eight
neighbouring cells (Figure 8).
gasaeeRaaaely
8
RS re
fon
B con Al en Data Points: [11
Giver undet CC yeaized Edt Output —f
Figure 7. The graphical emigration rate function.
IIL.ILIV. Immigration Sector
The total number of immigrants is calculated in this sector. Simply, the immigrants from
each neighboring cell, e.g. to_ N@S are summed to find the total number of immigrants
arriving into the cell, total immigration (Figure 9). The mathematical expression for this
variable is,
total immigration=to. W@E+to_ S@N+to SW@NE+to SE@NW+to_N@S+o NW@S
E+to_ NE@SW-+to E@W
IILIILV. Reproduction Sector
In this sector, the number of young immature birds survived and recruited into the
population is calculated. This number depends on a number of factors. Primarily it
depends on the number of adult females. There is also a nesting success rate, which is a
graphical function of, again the ratio between population and realized carrying capacity
(Over_under_CC_realized). Its value changes between 0 and 1 (Figure 10). An adult
female eastem meadowlark attempts to nest up to four times until she nests and breeds
two times during a breeding season (McCoy et al., 1999). Ovenbird female attempts to
nest up to two times until she nests and breeds one time during a single breeding season
(Podolsky, 2000). total successful nesting attempts reflects this aspect and it is simply the
number of successful nests that produced youngsters in a breeding season and hence is a
function of adult female population and nesting success rate (McCoy, 1999; Podolsky,
2000; Lanyon 1957).
Figure 8. Emigration and Emigration Proportions Sectors.
WE) mmgnon A @
oO ©
to SE@KW ww ten to SWQNE
— —
to E@w seta Arion to W@E
ome) »
to NE@SW to N@S to nw@se
Figure 9. Immigration Sector.
Hence, the mathematical expression for this variable is,
total_successful_nesting attempts = if GrL_F Species=1 then (Adult_Females
*((nesting_success_rate)+(nesting_success_rate“2)+2*(nesting_success_rate“2*(1-
nesting_success_rate))+3*(nesting_success_rate“2*(1-nesting_success_rate) “2)
+(nesting_success_rate*(1-nesting_success_rate))+(nesting_success_rate*(1-
nesting_success_rate)“2)+(nesting_success_rate*(1-nesting success _rate)“3))) else if
GrL_F Species=2 then (Adult Females*nesting_success_rate*(2-nesting_success_rate))
else 0
total successful nesting attempts is multiplied by young females per nest (2 for eastem
meadowlark (McCoy et al., 1999), 1.84 for ovenbird (Podolsky, 2000; Lanyon, 1957)) to
get the total number of female youngsters hatched and survived in a breeding season.
This number then uniformly distributed throughout the entire breeding season. The
breeding season for eastern meadowlark is from third week of April to second week of
August (Norment et al., 1999; Lanyon, 1957); for ovenbird it is from the end of May
until August (Conservation Commission of Missouri Report). young females per nest
reflects the number of female youngsters that are hatched and survived, they are not the
number of eggs laid or hatched per nest per se (Figure 11):
recruited_young females = if GrL_F Species=1 then (if MOD(time,12)>=3.75 and
MOD(time,12)<=7.25 then (total_successful_nesting_attempts*young females per nest
/3.75) else 0) else if GrL_F Species=2 then (if MOD(time,12)>=5 and MOD (time, 12)<7
then (total_successful_nesting_attempts*young_females_per_nest/2) else 0) else 0
iret Dupe
Foo Too Tes
‘ 0143 0.840
Hs 0.286 0.835
i 0.423 0.820
t 0571 aio
i a7 0.800
n 0.857 0780
9 1.000 0725
1.143 0575
s 1.286 0.230
- 1.423 o.0s0
1.571 0.025
[o.c00 174 0.000
b a a Pe
Over_under_CC-reakzed Eaoune |
Figure 10. The graphical nesting success rate function.
ius) Reproduction Sector a 86
ra ' nesting sugcess rate
¥ *
yng fmis a
> |
5
le GL F Species >>
young females per nest 2
total successful nesting attempts
Figure 11. Reproduction Sector.
TILILLVI. Population Dynamics
This is the most important and most complicated sector of the model. The (maximum)
carrying capacity for ovenbird is 0.043 based on data from Smith et al., 1987. It is
assumed 0.025 for eastern meadowlark based on the available literature (Vickery et al.,
1999; Winter, 1999).
The simulation is assumed to start on January 1". Hence, the initial population levels,
Pop Initial are zero in breeding habitat stocks and 0.008 in wintering stocks for both
young and adult females for eastem meadowlark. They are zero in breeding habitat stocks
and 0.01 in wintering stocks for both young and adult females for ovenbird. The initial
wintering population levels are calibrated to obtain stable oscillations in population level.
The reproduction is simulated in the Reproduction sector and the death rates are
straightforward. The death rate of adult females is a graphical function of
Over_under_CC_realized. There are two graphical death rate functions in the model, one
for grassland species (eastern meadowlark) based on McCoy et al. (1999), one for forest
species (ovenbird) based on Podolsky (2000). They are similar and the graphical death
rate function for grassland species is presented in Figure 12 as an example. The death rate
of young females is twice that of adults (McCoy et al., 1999). CC_realized is the real
carrying capacity of the cell found by multiplying the (maximum) carrying capacity with
a fraction depending on the value of edge index:
B CC realized = if B GrL_F Species=1 then (B Carrying Capacity*(if
B_edge_index=0 then 1 else if B_edge_index=1 then .05 else if B_edge_index=2 then .1
else if B_edge_index=3 then .25 else if B_edge_index=4 then .5 else if B_edge_index=5
then .7 else if B_edge index=6 then .8 else 1)) else if B_GrL_F Species=2 then
(B_Carrying_Capacity*(if B_edge_index=0 then 1 else if B_edge_index=1 then 0.01 else
if B_edge_index=2 then 0.01 else if B_edge_index=3 then .01 else if B_edge_index=4
then .05 else if B_edge_index=5 then .25 else if B_edge_index=6 then .75 else 1)) else 0
Adult Females has an outflow named imm_emm, which is the net migration per month.
There is a flow from Young Females to Adult Females called maturation and maturation
period; maturation adj time is assumed 12 months for both species. However, this is a
highly generalized approach. It may be calibrated to suit better for the chosen species
(Figure 13).
There are seasonal migrations between wintering and breeding habitats. Although eastern
meadowlark is not a neo-tropical species, it also migrates to south of the United States to
winter. Therefore, there are bi-directional migration flows to represent this situation,
Migration YF for the young female stock, Migration AF for the adult female stock.
Migration periods for eastern meadowlark are from the end of February until the end of
May during spring and from the end of August until the end of November during fall
(Hull, 2000; Lanyon, 1957). Migration periods for ovenbird are from the end of February
until the end of April during spring and from the end of September until the end of
November during fall (BirdSource, 2001). The mathematical expressions for the seasonal
migrations are,
B_ Migration AF = if B _GrL_F Species=1 then (if MOD(time,12)>=2 and
MOD(time,12)<5 then (B_Wintering Adult_Females/1) else if MOD(time,12)>=8 and
MOD(time,12)<11 then (-B_Adult_Females/1) else 0) else if B_GrL_F_ Species=2 then
(if MOD(time,12)>=2 and MOD(time,12)<4 then (B_Wintering Adult _Females/1) else
if MOD(time,12)>=9 and MOD(time,12)<11 then (-B_Adult_Females/1) else 0) else 0
B_Migration YF = if B _GrL_F Species=1 then (if MOD(time,12)>=2 and
MOD(time,12)<5 then (B_Wintering_Y oung_Females/1) else if MOD(time,12)>=8 and
MOD(time,12)<11 then (-B_Y oung_Females/1) else 0) else if B_GrL_F_Species=2 then
(if MOD(time,12)>=2 and MOD(time,12)<4 then (B_Wintering_Y oung_Females/1) else
if MOD(time,12)>=9 and MOD(time,12)<11 then (-B_Y oung_Females/1) else 0) else 0
There are stocks for the wintering period (Wintering Young Females, Wintering Adult
Females) and they have only death flow. The death rate for the adult is 0.05 and it is 0.1
for the young. It is taken constant due to lack of knowledge about their wintering grounds
and hence winter population dynamics. The losses during the migration are also not taken
into account. The winter death rates are approximately the average death rates in the
breeding habitat. The total population at any time is stored in Population for the breeding
habitat or Wintering Population for the wintering grounds depending on the time of the
year. They reflect the whole population (i.e. the sum of young and adult female bird
numbers multiplied by two.), not only the sum of adult and young females. Note that
these variables are not used in any function regarding the population in the model. Those
functions are calibrated to work with the number of total females, namely with the half of
the total population.
YF Death AF winter
[yng tml oth rate th rate winter]
itso Fopeteien +
Figure 13. Population Dynamics Sector.
IV. Validation and Analysis of the M odel Results
System dynamics models deals with the underlying causes that creates the problematic
dynamics in a system. Proper investigation of how and why those problematic dynamics
arise depends on a valid structural representation of the system. For this reason, structural
validity has foremost importance in system dynamics studies. Unless the structure is
adequately represented, the generated behaviour, regardless of how well it fits to the real
data, is irrelevant. This is not to say that behavioural validation is ignored but to evaluate
the behavioural validity of the model first it has to be structurally valid. Hence, the
purpose of the model presented in this paper is not to predict the number of adult bird
population at some point in time but to assess the vulnerability of the bird species to
habitat loss in their breeding grounds. Furthermore, the model serves under the greater
LEAM model to explore what conditions produce severe habitat loss and examine
strategies to reduce and even stop it (Barlas 1996; Sterman, 2000).
The non-spatial model was tested to carry out validation tests before integrating with the
spatial database. Although the ‘behavior validation’ of the model with respect to real data
is important only the structural validation tests are presented in this section since there
exists no long-term population dynamics data compatible with the time horizon of the
model. Nor is it possible to collect such long-term field data within the scope of this
research. As an example, Figures 14-15 illustrate the ‘extreme’ behavior of the system
when land suitability is zero. In Figure 14, the behavior of the variables population in
breeding habitat (1), and wintering population (2); and in Figure 15 (b) the behavior of
the adult female (1), and young female populations (2) are demonstrated. According to
this ‘extreme condition’ run, population level drops down to zero as expected.
The indirect structure tests revealed that the model structure yields meaningful behavior
under extreme parameter values and model behavior exhibits meaningful sensitivity to
the parameters. These are consistent with the empirical and theoretical evidence, offered
in literature such as Price et al., 1995; Donovan et al., 1995; Moore et al., 1995; Kobal et
al., 1999. In the next section, the model base run behavior is analyzed.
[W® 1: Pop'n in Breeding Hab 2. B Wintering Population
4 88
rt 5.008 p88
ee
5 8g — —
00 300 00 900 Tabq
Nae Graph 1: Page 1 (Untied Graph) Months 7:01 PM 1/1610
Figure 14. Model behavior when land suitability is zero.
[@ 1 BAduR Females 2:B Young Females
4 SHRED
N
\
\
\
4 F053
i el ee _
00 300 600 300 tad
Nae* Graph 1: Page 2 (Untitled Graph) Months 7:01 PM 1/1600
Figure 15. Model behavior when land suitability is zero.
V. Analysis of Results
The non-spatial model was run for both species. Figures 16 and Figures 17 are sample
output from the non-spatial base runs for eastem meadowlark, grassland species and for
ovenbird, forest species, respectively. The time step (dt) for the simulation runs is quarter
of a month and time unit is a month.
Populations of both bird species exhibit stable oscillations around 0.03 and 0.04, for
eastem meadowlark and ovenbird respectively (Figures 16-17). These equilibrium values
are in agreement with figures given in several studies in the literature (Donovan et al.,
1995; Lanyon, 1957). The population diminishes and drops down to zero as the birds
leave their breeding grounds during fall months and gradually increases as they arrive
from their wintering grounds during spring. The shaper increase observed in the middle
of spring is due to breeding. Correspondingly, their wintering population increases during
fall and diminishes during spring. The gradual decrease in wintering population during
winter months is due to the mortality. Since breeding occurs only in summer net death
rate in wintering grounds is equal to mortality.
After the non-spatial analysis, the model is integrated with the hypothetical dynamic
landscape. The landscape data consists of 20 consecutive maps, each corresponding a
particular month. The landscape has several land classes initially. However, in
subsequent maps a typical urban sprawl case is imitated where agricultural and other
open lands are consumed by the urban expansion each month. These landscape maps
served as input for the system dynamics model. Since the landscape changes the carrying
capacity and breeding capability of the bird species changes accordingly. This determines
the fate of the species in a particular cell.
Figure 16. Eastem Meadowlark Population and Wintering Population dynamics for 48
months (4 years).
Figure 17. Ovenbird Population and Wintering Population dynamics for 48 months (4
years).
Figures 18-19 are sample snapshots from spatial simulation. Figure 18 shows the edge
habitat map of eastem meadowlark. The carrying capacity is very low in light green areas
and increases towards interior (i.e. towards red areas and blue areas surrounded by the
red).
Figure 18. Snapshot of edge habitat map for eastem meadowlark.
Figure 19. Snapshot of edge habitat map for ovenbird.
Figure 19 is the edge habitat map for ovenbird. There is some suitable habitat for the
species but they are all located in the edge. The species is highly negatively affected in
edge habitats; hence, their population is always zero throughout the sample study area.
It is obvious from the simulation runs that urban sprawl leads to habitat loss for both
species. They are unable to live and breed in residential and industrial areas. For eastern
meadowlark, agricultural fields and for ovenbird small forest patches offer little or no
protection. What is more, the spatial modelling enabled to represent the edge habitat
concept appropriately. This is important since the spatial arrangement of the suitable
habitats should be recognized in order to reach meaningful and realistic results. Hence, it
is crucial to conserve large areas of native habitat for these bird species to sustain in the
face of ever-growing urban areas.
Food sources are not included in the model since it was impossible to incorporate the
intimate relations between the bird species and their food sources in a meaningful way in
the confines of this study. In addition, there is almost no data on this subject. It is also the
same for the predators of these birds. Therefore in this version of the model the bird
species have no impact on the ecosystems they belong to. Horizontal and vertical species
interaction on the food chain may significantly alter the results.
The policy implication of this study is in accordance with the main concerns of LEAM
framework. That is urban sprawl is destructive to the natural environment and it must be
replaced by smart growth where the development is to the benefit of both the wildlife and
people simultaneously and the use of lands is made in a most efficient way.
VI. Final Remarks and Further R esearch
Spatial characteristics of species’ habitat must be adequately addressed in ecological
studies to reach more realistic results and to make efficient use of insights gained from
these studies in land use decision-making. It is now possible to construct spatially explicit
models with the advance of computer technology and geographic information systems.
These advances allow constructing ecological models that are capable of simulating both
on spatial and temporal domains. The integration of spatial dimension into the study
increases the descriptive power of the model and enhances the relevancy of the proposed
policies to the real life. This improvement is crucial for land use managers and decision
makers who need accurate information to develop efficient policy options.
In spite of lack of data and hence inadequate validation, the model performs quite
satisfactorily both in non-spatial and spatial environments. In fact, it can be regarded as a
prototype for more improved and complex models to be constructed in the future.
However there is still a need for more data on the ecology of these bird species and their
interaction with their habitat. In addition, it should be noted that interspecies relations are
not considered in this modelling study. Horizontal and vertical species interaction on the
food chain may significantly alter the results.
Brown-headed cowbird parasitism may be included exclusively in the future but it is
included indirectly in the edge habitat and habitat suitability index formulations (Hull,
2000; Podolsky, 2000; Sherry et al., 1995).
The bird model presented in this paper is an integral part of the LEAM model platform. It
performs within the regional model as an indicator of the effects of probable land-use
changes in the Kane County on the native bird species. An interactive version of the
large-scale regional model with its social, economic, and ecological components is
available on the web (http://www.rehearsal.uiuc.edu/leam/). The regional model is an
experimental simulation platform where different aspects of urban development and land-
use changes can be explored where the social, economic, and ecological components
interact simultaneously.
The spatial habitat modelling is still a novel approach and their success partly depends on
the availability of relevant and sufficient data. There is still much to improve in this field
and it Is realistic to expect great contributions to the scientific and practical theory from
spatial dynamic modelling in the future (Dunning et al., 1995; Turner et al., 1995; Holt et
al., 1995).
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Appendix: The Model Equations
The variables representing attributes in neighbouring cells are assigned default values.
B_edge_index = if time<99999 then (if B_l_u_index=1 then (if
(B_l_u_index@E=0 or B_l_u_index@N=0 or B | index@NW=0 or
B_l_u_index@Sw=0 or B ylu | index@S=0 or B_l_u index@SE=0 or
BT index 0 or B_l_u index@W=0) then 1 else if (B edge index@E=1
or B_ edge index@N=1 or B edge _index@NW=1 or B_edge_index@SW=1 or
B_edge_index@S=1 or B_edge _index@SE=1 or B_edge_index@NE=1 or
B_edge_index@W=1) then 2 else if (B_edge_index@E=2 or B_edge_index@N=2
or B_edge index@NW=2 or B_edge_index@SW=2 or B_edge_index@S=2 or
B_edge_index@SE=2 or B_edge_index@NE=2 or B_edge _index@W=2) then 3 else
if (B_edge_index@E=3 or B_edge_index@N=3 or B_edge_index@NW=3 or
B_edge_index@SW=3 or B_ edge _index@S=3 or B_edge_index@SE=3 or
B_edge_index@NE=3 or B_edge index@w=3) then 4 else if
(B_edge_index@E=4 or B_edge _index@N=4 or B_edge_index@Nw=4 or
B_edge_index@SW=4 or B edge index@S=4 or B_edge_index@SE=4 or
B_edge_index@NE=4 or B edge index@w=4) then 5 else if
(B_edge_index@E=5 or B_edge index@N=5 or B_edge_index@NW=5 or
B_edge_index@SW=5 or B_edge index@S=5 or B edge _index@SE=5 or
B_edge_index@NE=! - or B_ edge index@W=5) then 6 else 0) else 0) else 0
B_edge_index@E =
B_edge_index@N =
B_edge_index@NE *
B_edge_index@NW = 0
B_edge_index@S = 0
0
0
B_edge_index@SE
B_edge_index@sw
B_edge_index@W = 0
B_l_u_index@E = 1
Blu | index@N = 1
wu
B_l_u_index@NE = 1
B_l_u_index@Nw = 1
B_l_u_index@S = 1
B_l_u_index@SE = 1
B_l_u_index@sw = 1
B_l_u_index@W = 1
B_total_emigration = B_emigration_rate*B_Adult_Females
B_to_E = B proportion E*B total_emigration
B_to_N = B proportion N*B total_emigration
B_to_NE = B proportion NE*B_total_emigration
B_to_NW = B proportion NW*B total_emigration
B_ to S = B proportion S*B total_emigration
B_to SE = B proportion SE*B_total_emigration
B_to SW = B proportion SW*B total_emigration
B_to W = B proportion W*B_total_emigration
BCC _realized@E = .025
B CC realized@N = .025
B_CC_realized@NE -025
B_CC_realized@NW = .025
wu
B CC_realized@S = .025
B CC _realized@SE 025
B CC_realized@sw = .025
B_CC_realized@W = .025
B_proportion_E = B CC_realized@E/B_total_CC_realized
B_ proportion N = B CC realized@N/B total_CC_ realized
B_proportion_NE CC_realized@NE/B total _CC_realized
B_proportion_NW } CC_realized@Nw/B total_CC_ realized
B_ proportion S = B CC realized@S/B total_CC_ realized
B proportion SE = B CC_realized@SE/B total_CC_realized
B_ proportion SW = B CC realized@SW/B_ total_CC_ realized
B_ proportion W = B CC _realized@W/B total _CC_ realized
B_total_CC_realized =
BCC realized@E+B | CC_realized@N+B_CC_realized@NE+B CC_realized@Nw+B_CC_
realized@S+B | cc realized@SE+B | Ce realized@w+B | CC_realized@sw
B Habitat Suitability Index = if B GrL_F Species=1 then (If
B_LandUseMap=11 or B_LandUseMap=12 or B_LandUseMap=22 or
B_LandUseMap=23 or B_LandUseMap=31 or B_LandUseMap=32 or
B_LandUseMap=33 or B_LandUseMap=41 or B_LandUseMap=42 or
B_LandUseMap=43 then 0 else if B_LandUseMap=21 then 0.2 else If
B_LandUseMap=51 then 0.2 else if B_LandUseMap=61 then 0.2 else if
B_LandUseMap=71 then 1 else if B_LandUseMap=81 then 0.8 else if
B_LandUseMap=82 or B_LandUseMap=83 then 0.6 else if B_LandUseMap=84
then 0.3 else if B_LandUseMap=85 then 0.0 else 0) else if
B_GrL_F_Species=2 then (if B_LandUseMap=41 or B_LandUseMap=42 or
B_LandUseMap=43 then 1.0 else 0.0) else 0
B_LandUseMap = 71
B_l_u_index = if B_GrL_F_Species=1 then (if B_LandUseMap=21 or
B_LandUseMap=51 or B_LandUseMap=61 or B_LandUseMap=71 or
B_LandUseMap=81 or B_LandUseMap=82 or B_LandUseMap=83 or
B_LandUseMap=84 or B_LandUseMap=85 then 1 else 0) else if
B_GrL_F_Species=2 then (if B_LandUseMap=41 or B_LandUseMap=42 or
B_LandUseMap=43 then 1 else 0) else 0
B_total_immigration =
B_to_W@E+B_to_S@N+B_ to SW@NE+B to SE@NW+B_ to N@S+B_to_NW@SE+B_to_NE@SW+
B_ to E@W
B_to_E@W =
B to )N@S =
B_to_ NE@SW
B_to_NW@SE
B to S@N =
B_to_SE@NW
B_to_SW@NE
B to ) WEE =
B ; Adult _Females(t) = B Adult_Females(t - dt) + (B_maturation +
B_imm_emm + B Migration AF - B Death AF) * dt
niu
faba
er1r1reliee
22 22
INIT B_Adult_Females = 0
B_maturation = B_Young Females/B_maturation_adj_time
B imm_emm = (B_total_immigration-B_ total _emigration)
B "Migration , AF = if B GrL F Species= 1 then (if MOD(time,12)>=2 and
MOD(time,12)<5 then (B } Wintering | Adult_Females/1) else if
MOD(time,12)>=8 and MOD(time,12)<11 then (-B Adult _Females/1) else 0)
else if B_ GrL_F Species=2 then (if MOD(time, 12)>=2 and MOD(time,12)<4
then (B } Wintering | Adult_Females/1) else if MOD(time,12)>=9 and
MOD(time,12)<11 then (-B Adult _Females/1) else 0) else 0
B Death _AF = B Adult_Females*B adlt_fml_dth_rate
B_Wintering_Adult_Females(t) = B_Wintering Adult_Females(t - dt) +
(B_maturation_winter - B Migration_AF - B Death _AF_ winter) * dt
INIT B_Wintering Adult_Females = B Pop Initial
B_maturation_winter = B Wintering_Young_Females/B_maturation_adj_ time
B } Migration | AF = if B GrL F Species=1 then (if MOD(time,12)>=2 and
MOD(time,12)<5 then (B ; Wintering | Adult_Females/1) else if
MOD(time,12)>=8 and MOD(time,12)<11 then (- B_Adult_Females/1) else 0)
else if B_ GrL_F Species=2 then (if MOD(time,12)>=2 and MOD(time,12)<4
then (B } Wintering | Adult_Females/1) else if MOD(time,12)>=9 and
MOD(time,12)<11 then (-B_Adult_Females/1) else 0) else 0
B_Death_AF_winter =
B Wintering Adult_Females*B adlt_fml_dth_rate winter
B Wintering Young Females(t) = B Wintering Young Females(t - dt) + (-
B_maturation_winter - B_Death_YF_winter - B Migration_YF) * dt
INIT B_Wintering_Young Females = B Pop Initial
B_maturation_winter = B Wintering_Young_Females/B_maturation_adj_ time
B Death YF winter = B Wintering Young Females*B yng fml_dth rate winter
B } Migration YF = if B_GrL_F_Species=1 then (if MOD(time,12)>=2 and
MOD(time,12)<5 then (B } Wintering » Young _Females/1) else if
MOD(time,12)>=8 and MOD(time,12)<11 then (-B_Young Females/1) else 0)
else if B_GrL_F Species=2 then (if MOD(time,12)>=2 and MOD(time,12)<4
then (B_Wintering Young Females/1) else if MOD(time,12)>=9 and
MOD(time,12)<11 then (-B_ Young Females/1) else 0) else 0
B_ Young Females(t) = B_Young Females(t - dt) + (B_reproduction +
B Migration_YF - B_ maturation - B Death_YF) * dt
INIT B_Young Females = 0
B_reproduction = B_yng_fmls
B Migration_YF = if B GrlL_F Species=1 then (if MOD(time,12)>=2 and
MOD(time,12)<5 then (B } Wintering | Young Females/1) else if
MOD(time,12)>=8 and MOD(time,12)<11 then (-B_Young Females/1) else 0)
else if B_GrL_F Species=2 then (if MOD(time,12)>=2 and MOD(time,12)<4
then (B ; Wintering | Young _Females/1) else if MOD(time,12)>=9 and
MOD(time,12)<11 then (-B_Young Females/1) else 0) else 0
B_maturation = B_Young Females/B_maturation_adj_time
B_Death_YF = B Young Females*B_yng_fml_dth_rate
B_adlt_fml_dth_rate = if B GrL_F Species=1 then B adlt_fml_dth rate g
else if B GrL_F Species=2 then B adlt_fml_dth_rate f else 0
B_adlt_fml_dth_rate winter = 0.05
B Carrying Capacity = if B GrL_F Species=1 then
(0.025*B Habitat_Suitability_Index) else if B_GrL_F_Species=2 then
(0.043*B Habitat Suitability Index) else 0
B_CC_realized = if B_ GrL_F_Species=1 then (B Carrying Capacity* (if
B_edge_index=0 then 1 else if B edge _index=1 then .05 else if
B_edge_index=2 then 4 else if B edge index=3 then .25 else if
B_edge_index=4 then .5 else if B_ edge index=5 then .7 else if
B_edge_index=6 then .8 else 1)) else if B_ GrL_F_Species=2 then
(B_Carrying Capacity*(if B edge index=0 then 1 else if B edge index=1
then 0.01 else if B_ edge index=2 then 0.01 else if B_edge index=3 then
.01 else if B_edge_index=4 then .05 else if B_edge index=5 then .25
else if B_edge index=6 then .75 else 1)) else 0
B_maturation_adj_time = 12
B_Over_under CC_realized = if B_CC_realized=0 then 10 else
((B. Adult_ Females+B ; Young _| Females) /B | CC_realized)
B Pop Initial = if B_ GrL_F_Species=1 then 0.008 else if
B GrL_F Species=2 then 0.01 else 0.0
B Wintering Population =
2*(B_Wintering Adult_Females+B Wintering_Young Females)
B yng fml_dth rate = B adlt_fml_dth_rate*2
B_yng fml_dth rate winter = 2*B adlt_fml_dth_rate winter
Pop'n_in Breeding Hab = 2*(B Adult_Females+B Young Females)
B_adlt_fml_dth_rate_f = GRAPH(B Over under CC realized)
(0.00, 0.00), (0.2, 0.01), (0.4, 0.015), (0.6, 0.035), (0.8, 0.085),
(1.00, 0.18), (1.20, 0.4), (1.40, 0.815), (1.60, 0.955), (1.80, 0.99),
(2.00, 1.00)
B_adlt_fml_dth_rate_g = GRAPH(B Over_under_CC_realized)
(0.00, 0.00), (0.2, 0.01), (0.4, 0.035), (0.6, 0.07), (0.8, 0.11),
(1.00, 0.18), (1.20, 0.4), (1.40, 0.815), (1.60, 0.955), (1.80, 0.99),
(2.00, 1.00)
B_emigration_rate = GRAPH(B Over_under_CC_realized)
(1.00, 0.00), (1.05, 0.05), (1.10, 0.1), (1.15, 0.15), (1.20, 0.2),
(1.25, 0.25), (1.30, 0.3), (1.35, 0.35), (1.40, 0.4), (1.45, 0.45),
(1.50, 0.5)
B total successful _nesting_ attempts = if B_GrL_F_Species=1 then
(By Adult Females*((B_nesting success __ rate)+(B } nesting | success _rate*2)+2
*(B_nesting success _rate*2*(1-
B_nesting success _rate))+3*(B_nesting success rate*2*(1-
B_ nesting success _rate)*2)+(B nesting success rate*(1-
B_nesting success _rate))+(B_ nesting success _rate*(1-
B_nesting success rate)*2)+(B_ nesting success rate*(1-
B_nesting success rate)*3))) else if B GrL_F " Species=. 2 then
(B_Adult_Females*B nesting success rate*(2-B nesting success rate))
else 0
B_yng_fmls = if B_GrL_F_Species=1 then (if MOD(time,12)>=3.75 and
MOD(time,12)<=7.25 then
(B_total_successful_nesting_attempts*B young females _per_nest/3.75)
else 0) else if B_GrL_F_Species=2 then (if MOD(time,12)>=5 and
MOD(time,12)<7 then
(B_total_successful_nesting_attempts*B young females per_nest/2) else
0) else 0
B_young_females_per_nest = if B_ GrL_F_Species=1 then 2 else if
B_GrL_F_Species=2 then 1.84 else 0
B } nesting | success rate = GRAPH(B Over_under_CC_realized)
(0.00, 0.85), (0.143, 0.84), (0.286, 0.835), (0.429, 0.82), (0.571,
0.81), (0.714, 0.8), (0.857, 0.78), (1, 0.725), (1.14, 0.575), (1.29,
0.23), (1.43, 0.09), (1.57, 0.025), (1.71, 0.00), (1.86, 0.00), (2.00,
0.00), (2.14, 0.00), (2.29, 0.00), (2.43, 0.00), (2.57, 0.00), (2.71,
0.00), (2.86, 0.00), (3.00, 0.00)
B_GrL_F_Species = 1
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