Western Michigan University ScholarWorks at WMU
Master's Theses Graduate College
4-2008
Habitat Suitability Modeling for Lake Huron Tansy in Michigan
Cathryn Elizabeth Whately
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Recommended Citation Whately, Cathryn Elizabeth, "Habitat Suitability Modeling for Lake Huron Tansy in Michigan" (2008). Master's Theses. 4449. https://scholarworks.wmich.edu/masters_theses/4449
This Masters Thesis-Open Access is brought to you for free and open access by the Graduate College at ScholarWorks at WMU. It has been accepted for inclusion in Master's Theses by an authorized administrator of ScholarWorks at WMU. For more information, please contact [email protected]. HABITAT SUITABILITY MODELING FOR LAKE HURON TANSY IN MICHIGAN
by
Cathryn Elizabeth Whately
A Thesis Submitted to the Faculty of The Graduate College in partial fulfillmentof the requirements for the Degree of Master of Arts Department of Geography
Western Michigan University Kalamazoo, Michigan April 2008 Copyright by Cathryn Elizabeth Whately 2008 ACKNOWLEDGMENTS
This thesis would not have come to fruition without the help and support of many people. I thank my major advisor, Dr. Kathleen Baker, for her constant supporti and encouragement. She was ever available, wrestled through the models with me, and encouraged me to be true to myself and my interests. I also thank my other committee members, Dr. Jay Emerson and Dr. Chansheng He. Dr. Emerson's availability and willingness to answer questions as they came up and his counsel
"Don't fret" on a couple of occasions were truly appreciated. Dr. He's encouragement, especially in the initial stages of the project as I worked to organize my ideas, was very helpful. The critical review of the thesis by all three has been indispensible. Additionally, all three committeemembers have nurtured my courage to look to the future.
I am also grateful for the time, patience and statistical support provided by Dr;.
Michael Stoline and to Michigan Natural Features Inventory for Lake Huron tansy population data.
I also thank the friends I have made in the course of my graduate studies.
Your friendship has made even the most stressful days good. I appreciated your willingness to listen as I verbalized my way through ideas, your help over the inevitable classroom hurdles, and the sharing of yourselves.
ii Acknowledgments-continued
Finally, my love and thanks to my family, Mike, Bridget, Cassandra and
James. Thank you so much for your support, encouragement and patience througho1!l!t this entire process.
Cathryn Elizabeth Whately
iii HABITAT SUITABILITY MODELING FOR LAKE HURON TANSY IN MICHIGAN
Cathryn Elizabeth Whately, M.A.
Western Michigan University, 2008
Little scientificresearch has been published that addresses the habitat requirement of the Lake Huron tansy, a Michigan threatened species. Adequate protection of the tansy, location of new populations, and identificationof potential restoration sites all depend on defining suitable habitat. Mahalanobis distance and partitioned Mahalanobis distance were combined with geographic information systems (GIS) to spatially model habitat suitability for Lake H ron tansy in Michigan. Several models were created for shoreline areas within the 14 counties in northern Michigan where the tansy is found.
Results suggested elevation, distance to shore, slope, direction to shore and aspect were important variables for describing suitable tansy habitat. Percent sand, percent gravel, growing season temperature, and winter temperature were also important in model variations. Results indicated that Mahalanobis distance produced more useful results than partitioned Mahalanobis distance and that the models built fromfewer variables often yielded more specific habitat suitability maps than the models based on more variables. The results also indicated that modeling habitat for a shoreline/dune specialist species presents challenges to traditional GIS methods. TABLE OF CONTENTS
ACKNOWLEDGMENTS...... 11
LIST OF TABLES ...... vu
LIST OF FIGURES...... viii
CHAPTER
1. INTRODUCTION...... 1
Statement of Problem...... 1
Research Objectives...... 4
2. REVIEW OF RELATED LITERATURE...... 6
Species Biology ...... 8
Species Habitat ...... 9
Habitat Information...... 12
Statistical Methods...... 14
Justification of Habitat Variables...... 23
3. DATA AND METHODS...... 28
Habitat Variables ...... 28
Topography ...... 29
Study Area...... 29
Soil Parameters...... 30
Shoreline Data ...... 32
Bedrock...... 32
Climate ...... 32
IV Table of Contents-continued
CHAPTER
Population Data...... 35
Statistics and Habitat Modeling...... 36
Determination of Appropriate Habitat Variables ...... 36
Comparison of Means ...... 36
Principal Components Analysis...... 38
Habitat Models ...... 40
Eleven Variables Models ...... 40
Seven Variables Models...... 41
Model Testing ...... 43
Habitat Suitability Maps...... 44
4. RESULTS ...... 45
Determination of Appropriate Habitat Variables...... 46
Comparison of Means ...... 46
Ten Meter Data ...... 46
Fifteen Meter Data ...... 46
Principal Components Analysis ...... 50
Habitat Models...... 66
Eleven Variables...... 67
Partitioned Mahalanobis Distance (k = 7) (Model A)...... 68
Partitioned Mahalanobis Distance (k = 11) (Model B) ...... 69
V Table of Contents-continued
CHAPTER Seven Variables...... 72 Full Mahalanobis Distance (Model C) ...... 78
Partitioned Mahalanobis Distance (k = 7) (Model D) ...... 80 Partitioned Mahalanobis Distance (k = 4) (Model E) ...... 82 5. DISCUSSION AND CONCLUSIONS...... 86 Biological Factors...... 90 Non-spatial Biological Factors...... 91 Biological Factors with a Spatial Component...... 93 Limits to Model Sensitivity ...... 95 Limitations of Data...... 95
Included Variables ...... 95
Unavailable or Unused Data ...... 98 Limitations of Methods ...... 100 Choice of Included Components ...... 100 Assumptions...... 101 Model Choice...... 104 Conclusions...... 106 BIBLIOGRAPHY...... 111
vi LIST OFT ABLES
1. Variables and abbreviations used in this study...... 37
2. Hypothetical Principal Components Analysis results based on four variables ...... 41
3. Descriptive statistics of 42 variables measured at 10 meter scale forthe study area and test populations...... 47
4. Descriptive statistics forseven variables measured at 15 meter scale for the study area and test populations...... 49
5. Eigenvalues for42 variable model obtained from SAS...... 51
6. Eigenvector values obtained from Principal Components Analysis of 42 variables measured at 10 meter scale...... 53
7. Eigenvalues obtained for11 variable model in SAS...... 68
8. Eigenvector values obtained fromPrincipal Components Analysis of 11 variables measured at 10 meter scale ...... 70
9. Suitability data for the study area and the test populations...... 74
10. Eigenvalues forseven variable model obtained fromSAS ...... 77
11. Eigenvector values obtained fromPrincipal Components Analysis of seven variables measured at 15 meter scale...... 79
12. Comparison of means obtained fromMahalanobis distance extension (Jenness 2003) and means calculated within SAS for the seven variables measured at 15 meter resolution...... 105
Vll LIST OF FIGURES
1. Lake Huron tansy growing along Lake Michigan in Charlevoix County, MI...... 2
2. Michigan distribution of Lake Huron tansy by county...... 11
3. Locations of Michigan weather stations used to interpolate climate variables for Lake Huron tansy habitat suitability ...... 34
4. Methods used to determine appropriate habitat variables needed to model habitat suitability for Lake Huron tansy...... 39
5. Flow of processes used to obtain habitat suitability maps for Models A-E ...... 42
6. Scree plot of 42 variable Principal Components Analysis ...... 52
7. Scree plot of 11 variable Principal Components Analysis ...... 69
2 8. Cumulative frequencygraph for D (k:=7)for 10 meter, 11 variable model...... 72
9. Suitable habitat forLake Huron tansy based on D2(k=7) S 500,000 using the 10 meter, 11 variable model...... 73
10. Cumulative frequencygraph for D2(k=l 1) for 10 meter, 11 variable model...... 75
11. Suitable habitat for Lake Huron tansy based on D2ck=l 1) S 527, 880 using the 10 meter, 11 variable model...... 76
12. Scree plot of seven variable Principal Components Analysis...... 78
13. Cumulative frequencygraph for D2 of 15 meter, seven variable model...... 80
14. Suitable habitat forLake Huron tansy based on D2 S 7.3 using the 15 meter, seven variable model...... 81
2 15. Cumulative frequencygraph forD (k:=7) of 15 meter, seven variable model...... 82
vm List of Figures-continued
16. Suitable habitat forLake Huron tansy based on D2(k=7) S 11,921 using the 15 meter, seven variable model...... 83
17. Cumulative frequencygraph forD 2(k=4) of 15 meter, seven variable model...... 84
18. Suitable habitat for Lake Huron tansy based on D2(k=4) S 8.742 using the 15 meter, seven variable model...... 85
19. A portion of the habitat suitability map for Lake Huron tansy based on D2(k=4) S 8,742 using the 15 meter, seven variable model...... 87
20. A portion of the habitat suitability map forLake Huron tansy based on D2(k=7) S 11,921 using the 15 meter, seven variable model...... 88
21. A portion of the habitat suitability map for Lake Huron tansy based on D2(k=7) S 500,000 using the 10 meter, 11 variable model...... 89
22. A portion of the habitat suitability map for Lake Huron tansy based on D2(k=l 1) S 527,000 using the 10 meter, 11 variable model...... 90
23. A portion of the habitat suitability map forLake Huron tansy based on 2 D S 7. 3 using the 15 meter, seven variable model...... 91
24. Scatterplot of the test population values for July precipitation, growing season precipitation, and the presence of medium textured till, variables that were strongly correlated with Component 12 fromPrincipal Components Analysis of 42 variables...... 102
25. Scatterplot of the test population values for sine aspect, growing season precipitation, and the presence of exposed bedrock, variables that were strongly correlated with Component 15 fromPrincipal Components Analysis of 42 variables...... 102
26. Scatterplot of the test population values for elevation, distance to shore, and the presence of coarse textured till, variables that strongly correlated with Component 24 fromPrincipal Components Analysis of 42 variables...... 103
IX CHAPTER 1
INTRODUCTION
Statement of Problem
Michigan has 668 plant and animal species that are affordedprotection within the state by their designation as special concern,threatened or endangered (Michigan Natural
Features Inventory [MNFI] 2004). Many of the plant species are foundon the Great
Lakes shores, including Iris lacustris Nutt. (dwarf lake iris), Cirsium pitcheri (Torr . .)
T.&G. (Pitcher's thistle), Solidago houghtonii T.&G. (Houghton's goldenrod) and
Tanacetum huronense Nutt. (Lake Huron tansy) (MNFI 2004). Studies have been conducted to characterize the habitat of dwarf lake iris (Planisek 1983; Van Kley and
Wujek 1993) and Pitcher's thistle (Loveless 1971; Maun 1997; Hamze and Jolls 20©0;
Girdler and Radtke 2006), work is underway with Houghton's goldenrod (Pam Laureto, personal communication), but little research has been done to characterize the habitat of
Lake Huron tansy.
The Lake Huron tansy (Fig. 1) is listed as threatened in Michigan (Choberka et al.
2001), as endangered in Wisconsin (Wisconsin Department of Natural Resources
[WDNR] 2003) and as a species of special concernin Maine (Maine Department 0£
Conservation Natural Areas Program 2004). In all of the states where Lake Huron tansy is protected, the species is found on the shore of freshwaterrivers and lakes. The sh.ores tend to be low in organic material, and they are exposed to dynamic water levels, wind,
1 Figure 1. Lake Huron tansy growing along Lake Michigan in Charlevoix County, MI and ice scour (Choberka et al. 2001; WDNR 2003; Maine Department of Conservation,
Natural Areas Program 2004). Lake Huron tansy is associated with the Great Lakes shores in Michigan (Choberka et al. 2001). Human activities along the Great Lakes' shores have led to habitat destruction (Albert 2000; Peach 2006). Habitat destruction, in the forms of increased foot traffic, increased use of off-road vehicles and the introduction of exotic species in areas where T. huronense grows, is the primary threat to populations of Lake Huron tansy (Choberka et al. 2001; Environment Canada 2001; WDNR 2003;
Maine Department of Conservation Natural Areas Program 2004), and likely to the other protected dune species as well. Additionally, Lake Huron tansy is threatened because of the human induced changes in natural disturbance regimes (Choberka et al. 2001;
Environment Canada 2001; WDNR 2003; Maine Department of Conservation Natural
Areas Program 2004). Natural disturbance on the shoreline takes the form of wind-blown sand, changes in water level and scouring by ice (Ostlie 1991; Choberka et al. 2001;
WDNR 2003; Maine Department of Conservation Natural Areas Program 2004). 2 Humans have altered these natural disturbance regimes by installing stabilizing structures, such as retaining walls and piers, on lake shores and dunes (Ostlie 1991;
Choberka et al. 2001). Factors that minimize the normal dynamic water fluctuationsseen in the Great Lakes and along rivers, such as might be caused by the installation of dams along rivers or the selling of water fromthe Great Lakes, may also negatively impact the natural disturbance regime needed by the Lake Huron tansy (Ostlie 1991). In light of the threats to the Lake Huron tansy, it is imperative to learn more about the distribution of the species.
Knowledge of the distribution and spatial arrangement of a species is essential to the protection of that species (Gibson et al. 2004), as is understanding the factors that determine the distribution of the species (Rushton et al. 2004). As stated above, little is known about what habitat features are critical forthe success of T. huronense. Wiser et al. (1998) state that for rare plant species that have limited location data, statistical models can be useful forcharacterizing habitat. A statistical habitat suitability model would also be useful in locating previously unknown populations. Strauss and
Biedermann (2005) agree that formany species 'quantitative' data do not exist that would allow researchers to make spatially explicit predictions about the species; however, habitat models, because they quantify the relationship between the presence of the species of interest and the habitat, can be created and used to make predictions as to where the species of interest could be located. Gibson et al. (2004) also state that habitat suitability maps based on models help refinethe search for new populations. These habitat suitability methods include: Habitat Suitability Index (United States Fish and
Wildlife Service [USFWS] 1981; Breininger et al. 1998); generalized linear models
3 (Engler et al. 2004; Meggs et al. 2004); logistic regression (Erickson et al. 1998), discriminant function analysis (Lachenbruch 1975); Mahalanobis distance (Clark et al.
1993; Boetsch et al. 2003; van Manen et al. 2005) and partitioned Mahalanobis distance
(Rotenberry et al. 2002; Browning et al. 2005; Watrous et al. 2006). Additionally, as a protected plant species, T. huronense is a candidate forrestoration efforts. Maschinski and Wright (2006) argue that planning restorations forrare species based on predictions fromecological theory is advisable to allow a higher probability of success.
Without the knowledge obtained froma habitat model Lake Huron tansy might become extirpated within the state; the number of populations within the state appears to be declining. Of the 100+ populations listed for the state, only 60 have been verified as extant since 1980 (Choberka et al. 2001). Creating a habitat model helps identify gaps in our knowledge and in the data and, thereby, can guide future research (Wu and Smeins
2000). Knowledge of habitat needs also allows for informed experimentation (Wiser et al. 1998) in greenhouse or natural settings to better understand the biology of the species.
Finally, if suitable sites are not selected for restoration efforts, resources could be wasted.
Prior knowledge of suitable T. huronense habitat could also reduce landuse conflicts (Wu and Smeins 2000).
Research Objectives
The purpose of this research is to develop a habitat suitability model for the Lake
Huron tansy that will be usefulin delineating important habitat parameters for this species. This model will aid in locating new populations of T. huronense within the state of Michigan, and aid in locating suitable sites for restoration efforts. In order to achieve
4 the above stated purpose, the objectives of the study are: 1) determine what
environmental characteristics are important to describing "ideal" habitat for T. huronense
using principle components analysis and z-tests; 2) generate models using Mahalanobis
distance and partitioned Mahalanobis distance (test set: 75% of the populations); 3) verify
the models using the verificationset (25% of the populations) and a set of 100 random
locations within the study area; 4) generate a habitat suitability map based on each of the
models; and 5) compare outcomes based on Mahalanobis distance versus partitioned
Mahalanobis distance, and partitioned Mahalanobis distance based on a subset of the principal components versus the full set of principal components.
Chapter 2 of this document comprises a review of relevant literature on Lake
Huron tansy, dune environments along the Great Lakes, Mahalanobis distance and partitioned Mahalanobis distance. Chapter 3 describes the data and methods used to conduct the present study. Chapters 4 and 5 comprise the results of the present study and a discussion of, and conclusions drawn from, the results, respectively.
5 CHAPTER2
REVIEW OF RELATED LITERATURE
This chapter begins with background on Lake Huron tansy, including species
protection, taxonomy, biology and habitat. Species informationis followed by a
discussion of the Great Lakes' shoreline habitat, and the statistical methods used to model
habitat suitability, specificallyMahalanobis distance and partitioned Mahalanobis
distance. The last section addresses the rationale for the habitat variables used in the
present study.
The Lake Huron tansy is located in Maine, Nova Scotia, Newfoundland, along the
shores of the Hudson Bay and along the shores of Lake Athabaska, as well as on the
Great Lakes shores of Michigan and Wisconsin, and on the Lake Superior shores of
Ontario (Weatherbee2006). The species is listed as endangered in Wisconsin (WDNR
2003; USDA Natural Resources Conservation Service 2007), but is thought to actually be
extirpated in the state (WDNR2003). In Maine, Lake Huron tansy is of special concern,
because of restricted habitat (Maine Department of Conservation Natural Areas Program
2004; USDA Natural Resources Conservation Service 2007). T. huronense is listed as
threatened in Michigan (Choberka 2001; USDA Natural Resources Conservation Service
2007).
Tanacetum huronense has not been listed for federalprotection despite the fact
that it is protected in three of the four states where it occurs. This is due, in part, to its
confusing taxonomic status (Jolls and Sellars 1999; USDA Forest Service, Eastern
6 Region 2002). Synonyms (differentnames by which the species is known) for this species include: Tanacetum huronense Nutt., Tanacetum bipinnatum (L.) Schultz-Bip. ssp. huronense (Nutt.) Breitung, Chrysanthemum bipinnatum L. ssp. huronense (Nutt.)
Hulten, Tanacetum huronense Nutt. var. bifariumFem., Tanacetum huronense Nutt. var. floccosumRaup, Tanacetum huronense Nutt. var.johannense Fem., and Tanacetum huronense Nutt. var. terrae-novae Fem. (USDA Natural Resources Conservation Service
2007). The disagreement in taxonomy is seen as recently as 2006. In Volume 19 of the
Flora of North America, Tanacetum huronense Nutt., along with several other species, was subsumed into Tanacetum bipinnatum (Watson 2006). Weatherbee (2006) lists the
Lake Huron tansy as Tanacetum huronense, and states that it is the same or similar species that grows in Alaska and on the Pacificcoast. T. bipinnatum, the species into which T. huronense has been subsumed, is a polar species that is abundant in Alaska and
Canada, removing the species fromconsideration for federalprotection. For the sake of simplicity, the name Tanacetum huronense will be used throughout this paper. Because the type specimen (the specimen on which the Latin description of a newly described species is based) of T. huronense was collected near Mackinac Island, the name applies to at least the plants found in the Great Lakes region (Voss 1996), the focus of this study.
Tanacetum huronense belongs to the family Asteraceae. This large family is made up of 1,528 genera and more than 22,000 species and contains both herbs and shrubs. The family is divided into three subfamilies and 17 tribes thought to represent evolutionary lineages. T. huronense belongs in the subfamilyAsteroideae and the tribe
Anthemideae, a tribe comprising 109 genera and 1,740 species (Bremer and Humphries
1993). The genus Tanacetum is made up of at least fourspecies in North America (T.
7 balsamita, T. parthenium, T. vulgare, T. bipinnatum) (Watson 2006). The varieties of
Lake Huron tansy that have been described (Tanacetum huronense Nutt. var. bifarium
Fem., Tanacetum huronense Nutt. var.floccosumRaup, Tanacetum huronense Nutt. var. johannense Fem., and Tanacetum huronense Nutt. var. terrae-novae Fem.) have been determined on the basis of degree of pubescence, dissection of leaves, number of floweringheads and height of flowering stems.
Species Biology
Tanacetum huronense Nutt. is a rhizomatous (produces horizontal, above-ground stems), aromatic perennial that typically reaches a height of 10-80cm. The stems are erect and villous pubescent. The twice to thrice-pinnate leaves are more or less villous with narrow ultimate segments. Basal leaves are persistent and tend to be larger (23-36 x
3-9cm) than the cauline leaves (10-23 x 3-8cm), which become progressively smaller as one progresses up the stem. T. huronense flowers frommid-June to August. Flowering individuals generally have one to 30 yellow heads at the top of each flowering stem, rarely more. Flowering heads are 10-18mm wide. Disc flowersare perfect with five toothed corollas. Yellow ligulate flowers are commonly evident, ranging from inconspicuous to 4mm long. The achenes are 2-3.5mm long, five-angled and have membranaceous pappus lobes (Gleason and Cronquist 1991). T. huronense has a ploidy level of 2n=54 (Pringle 1976). The individuals foundin Michigan usually grow to 40-
80cm tall and have 6-30 heads. The plants tend to have 7-15 oblong leaves with oblong to oblanceolate pinnae (Choberka et al. 2001).
8 T. huronense flowers mid-June to August. The species appears to be self compatible; Jolls and Sellars (1999) found that seed set took place even when flower heads were enclosed in mesh bags. Various insect visitors were noted on uncovered heads including a member of the Anthocoridae, a member of the Tahinidae, and various members of the Syrphidae, Pompilidae, and Sphecidae (Jolls and Sellars 1999) and
Mordellidae (personal observation). No differencein seed set was noted between the bagged and the unbagged heads. Seed set appears to be robust. Germination of one-year old seed was greatest when seeds were exposed; burial of even 2 cm reduced germination
(Jolls and Sellars 1999). A period of winter dormancy appears to increase seed germination (Nichols 1934). Fruit forms shortly after flowering in July, August and
September (Choberka et al. 2001). Tanacetum huronense also reproduces asexually via rhizomes, horizontal above ground stems, allowing it to form clonal colonies (Choberka et al. 2001). It has been suggested that fragmentationof these clonal colonies may be means of dispersal and colonization (Weatherbee 2006), supported by the fact that ramets of T. huronense were successfully transplanted (Jolls and Sellars 1999). Marram grass
(Ammophila breviligulata), another dune species, has been shown to establish populations from rhizome fragments (Maun 1989). Jolls (personal communication) suggested that seedling germination and establishment might be critical points in the life history of T. huronense.
Species Habitat
Tanacetum huronense (sensu lato (in the broad sense)) inhabits a variety of habitats. In Canada, the species is found in open, dry places, coastal grasslands and
9 mountain valleys near snow (Argus et al. 1987), along calcareous river gravels (Scoggan
1979), along sandy terraces, and beaches of the coast (Blondeau 1986; as cited by Ostlie
1991) as well as coastal dunes (Pojar and MacKinnon 1994) and on steep clay banks
(Dutilly and LePage 1945; as cited by Ostlie 1991). In the United States, T. huronense is found along cobbly river beaches in Maine (Maine Department of Conservation Natural
Areas Program 2004), on sandy beaches, on the dunes, and in cracks in limestone pavement in Wisconsin (WDNR 2003) and Michigan (Choberka et al. 2001), and in coastal sand dunes in Alaska (Pojar and MacKinnon 1994 ).
Presently, the Lake Huron tansy is found in Leelanau, Grand Traverse, Kalkaska,
Antrim, Charlevoix, Emmet, Cheboygan, Presque Isle, Delta, Schoolcraft, Mackinac,
Chippewa, Luce and Alger counties in Michigan (Voss 1996)(Fig. 2). More than 100 occurrences are known fromthe state; 60+ have been verifiedextant since 1980
(Choberka et al. 2001). The populations are foundalong the Lake Huron, Lake Michigan and Lake Superior shores (Voss 1996; Choberka et al. 2001; Weatherbee 2006). The type specimen was collected from the Lake Huron shore at the Straits of Mackinac. All of the Michigan populations, Wisconsin populations and Ontario Lake Superior shoreline populations are considered to be typical (T. huronense var. huronense). While T. huronense appears to be a strict calciphile throughout its range (Ostlie 1991), it inhabits a variety of habitats in Michigan, mostly calcareous dune and beach systems (Choberka et al. 2001). These habitats are characterized by wind and wave action (Albert 2000), and scouring by ice (Albert 2000; Maine Department of Conservation 1999), which lead to natural disturbance. It has been suggested that plants found only on the beach or foredune, such as T. huronense and Cirsium pitcheri, actually depend on the extreme
10 ', I ;
Michigan Distribution of Lake Huron Tansy
- Present , ..... + [ Absent
0 48 500 97 000 194 000 Meters
� Data obtained from Michigan Center 4 T r for Geographic Information and '� � Michigan Natural Features Inventory r L T � f ,f l. �
Figure 2. Michigan distribution of Lake Huron tansy by county
11 conditions found in those locations for their survival (Albert 2000). The observation that
Lake Huron tansy is not as successful on the backdunes and at the treeline (Ostlie 1991) supports the idea that T. huronense needs the disturbance of the shore.
Habitat Information
Coastal shores, along with lakeplains and coastal marshes, support the greatest amount of biodiversity that is unique to, or dependent upon, the Great Lakes Ecosystem
(The Nature Conservancy [TNC] 1994; Albert 2000). Coastal shores contain 26% of
Great Lakes-dependent, globally significant elements (TNC 1994). Sand dune ecosystems represent a fragile component of the coastal shore because they are basically held together by beach grasses and other vegetation (Peach 2006). The complex of Great
Lakes sand dunes is one of the largest systems of freshwater dunes in the world with
Michigan containing more dunes than any other Great Lakes state (Albert 2000). The coastal shores of Michigan are extremely dynamic; in a relatively short amount of time the coastal dunes grow, change shape, and are destroyed (Albert 2000; Van Dijk 2004).
Dune formationrequires sand, wind, water-level fluctuations, and vegetation
(Albert 2000). The primary forcein the dune change is wind. There is a seasonal pattern to dune change seen along Lake Michigan (Van Dijk 2004). Wind appears to cause the greatest change to the shore's morphology in the fall and winter, when the winds are the strongest and there is the least amount of vegetation present to stabilize the shore. The prevailing winds are typically from the southwest. Dech and Maun (2005) found that zonation of plant communities in dune environments along Lake Huron was due to burial caused by moving sand.
12 Changes in lake levels make more or less sand available to the wind for transport
(Albert 2000). Vegetation reduces the velocity of the wind, causing the wind to deposit some of the sand that it is carrying. Additionally, some dune plants such as marram grass
(Amophila breviligualta) reproduce vegetatively by rhizomes; the rhizomes as well as roots stabilize the sand (Cheplick 2005). The strong winds that occur in the winter create large waves that break onto the shore. Along Lake Michigan, the accumulation of winter ice along the shoreline reduces the sand erosion due to the wave action and ground freezing reduces the amount of sand moved by the wind (Van Dijk 2004). The dune environment is also characterized by extremes in temperature; in the summer sand temperature can reach 120°F (Albert 2000).
While some of these changes can be part of the natural cycle, human induced changes can increase the impact of natural cycles. TNC (1994) has stated that human activity is changing the ecosystems of the Great Lakes region. The challenges that face the lakeshores include: alteration of lake levels; temperature changes, including those associated with global climate change; disruption of longshore transport; habitat destruction; and increased competition, which includes competition fromintroduced species (TNC 1994; Albert 2000; Weatherbee 2006). The alteration of lake levels, or interruptions of the natural fluctuations, reduces the flushingof nutrients and organic matter. Sand starvation results when jetties and other structures interrupt the movement of sediments by longshore transport (TNC 1994).
Habitat destruction is caused by recreational and residential development (TNC
1994; Peach 2006). The destruction of habitat causes fragmentationof populations, impairs sand transport, and reduces natural biodiversity (TNC 1994). Additionally,
13 because dunes are prone to accelerated erosion, large unvegetated blowouts develop when the sand on parabolic dunes becomes destabilized by pedestrian or vehicle traffic, or the removal of vegetation, causing the dune to be exposed to wind erosion (TNC 1994;
Albert 2000). Nordstrom and McCluskey (1985) found isolated buildings and sand fences substantially reduced wind velocity at Fire Island, New York. Bonanno et al.
(1998) found that recreational use was associated with plant community types, with high use being associated with decreased species richness, reduced density of colonizing species, and reduced ground cover of vegetation.
Exotic plant species increase the competition for nutrients and water experienced by native plants. Also, plants such as spotted knapweed (Centaurea maculosa Lam.) and baby's-breath (Gypsophila paniculata L.) stabilize the dunes, reducing the habitat available forLake Huron tansy (Albert 2000). The stresses having the greatest impact on the shore ecosystems are habitat destruction and alteration of physical processes, closely followed by competitive pressure fromexotic species (TNC 1994; Albert 2000).
Statistical Methods
A variety of methods have been used to generate habitat prediction models:
Habitat Suitability Index (HSI) (USFWS 1981; Breininger et al. 1998); generalized linear models (Engler et al. 2004; Meggs et al. 2004); logistic regression (Pereira and Itami
1991; Erickson et al. 1998), discriminant function analysis (Lachenbruch 1975); classification trees (Moore et al. 1991); Mahalanobis distance (Clark et al. 1993; Boetsch et al. 2003) and partitioned Mahalanobis distance (Rotenberry et al. 2002; Browning et al.
2005; Watrous et al. 2006). HSI is often used by researchers when quantitative data
14 documenting the locations of populations would be too difficult to collect or do not exist
(Johnson and Gillingham 2005). HSI requires an expert knowledge of the species of interest, because species-habitat relationships must be ranked (USFWS 1981), which can be a limitation of the method, depending on what is known of the species.
Logistic regression functions to determine whether there is a significant cause and effect relationship between the dependent variable (species presence in this case) and the independent variable(s) (habitat characteristics) (Rogerson 2001) and to predict a discrete outcome (suitable/ unsuitable) froma set of variables (habitat characteristics). An advantage of logistic regression is that no assumptions are made about the distribution of independent variables (Tabachnick and Fidell 2001).
Discriminant function analysis is used to determine which variables discriminate between two or more naturally occurring groups. Predicting the suitability of a location is based on knowing the values for the habitat characteristics at that location. Unlike logistic regression, there is an assumption that the predictor variables are continuous and normally distributed (Tabachnick and Fidell 2001).
Classification trees, often used for data mining, function to predict or explain responses on a categorical dependent variable (suitable/ unsuitable) based on their measurements on one or more predictor variables (habitat characteristics) (Moore et al.
1991). Classification trees are like dichotomous keys; decisions about the entity are made at each dichotomy. In the case of habitat suitability, an area may be designated suitable if it has a slope of 20 - 25%, the slope is south-facing, and soil moisture is between 15 - 20%, with a decision made at/for each variable. Classification trees are flexible, making them an attractive modeling option; however, classificationtrees should
15 not be used when more traditional statistical methods will work (StatSoft, Inc. 2007). A disadvantage of classification trees is that, like HSI, the habitat requirements of the species must be known in order to set up useful dichotomies.
The generalized linear model (GLM) is a generalization of least squares regression. It is used for analyzing linear and non-linear effects of continuous and categorical predictor variables on a discrete or continuous dependent variable. The generalization of GLM allows for the dependent variable to be discrete and allows the effectof the predictor variables to be non-linear on the dependent variable (StatSoft, Inc.
2007).
A disadvantage to using logistic regression, discriminant function analysis and generalized linear models is that all of these models require absence, as well as presence, data for the species of interest (Clark et al. 1993). An important assumption made about presence/absence data is that the two classes are mutually exclusive and that species absence indicates that habitat conditions are unsuitable (Boetsch et al. 2003). There are many reasons that the assumption of exclusivity may be violated. For example, the species may have not yet migrated to all suitable sites, or stochastic events may have removed the species fromsuitable sites where it had previously existed or beforeit could become established. Also, absence data are often chosen at random from locations not used by the species and assumed to be a suitable null model (Boetsch et al. 2003), but considering the previous examples, sites classifiedas unsuitable may actually be suitable, making the null model incorrect (Clark et al. 1993). Rare species add another layer of complexity. Generally, rare species collection is incomplete, making it difficult to generate a valid set of absence data (Boetsch et al. 2003). Mahalanobis distance does not
16 require absence data (Taguchi and Jugulum 2002), nor does partitioned Mahalanobis distance (Rotenberry et al. 2002), making them much better methods for rare species
(Boetsch et al. 2003).
2 Mahalanobis distance (D ) is a multivariate, generalized squared distance statistic that measures the amount of (dis)similarity between the center of two centroids. An advantage that D2 has over Euclidean distance, and other multidimensional distances, is that it takes into account the variance and covariance among the points, making the model very sensitive to intervariable changes in the referenceset (Taguchi and Jugulum
2002). Mahalanobis distance can be used to determine the similarity between a set of values from a collection of known samples (reference or training data) and the values from an unknown sample (Taguchi and Jugulum 2002). Assumptions of multivariate normality do not have to be met when using D2 (Knick and Rotenberry 1998).
Mahalanobis distance is a descriptive statistic and should not be used to make inferences;
2 however, if the data are multivariate normal, D followsa chi-square distribution and chi square probabilities may be used (Tabachnick and Fidell 2001).
The formula to calculate Mahalanobis distance is:
2 0 = (X - U) 1 L-1(X - U) where x is the vector of variables associated with the unknown location, u is the mean vector of variables associated with the referencedata, the apostrophe indicates the
1 transpose and L- is the inverse of the variance/covariance matrix associated with the reference data (Taguchi and Jugulum 2002). While D2 is a squared distance measure, it
2 is dimensionless (Knick and Rotenberry 1998). Small values of D indicate that the values of the unknown sample are very similar to the mean vector of known samples
17 (Taguchi and Jugulum 2002).
Mahalanobis distance can also be used in conjunction with geographic information system (GIS) to predict habitat suitability. Using GIS, Mahalanobis distance values can be mapped to show good, moderate, and poor habitats forthe species of interest. Clark et al. (1993) used D2 and GIS to predict habitat suitability and use by female black bears. Knick and Rotenberry (1998) used D2 and GIS to examine jack rabbit resource selection. Boetsch et al. (2003) used D2 and GIS to predict suitable habitat for a protected plant, mountain bittercress ( Cardamine clematis Shuttleworth ex
A. Gray). The Boetsch et al. (2003) study was conducted in order to determine whether the resulting model would be useful forlocating new occurrences and forthe conservation of the species. Thatcher et al. (2006) and Thompson et al. (2006) both used
Mahalanobis distance and GIS to predict suitable restoration sites for protected species;
Thatcher et al. (2006) to identify reintroduction sites for Florida panthers, and Thompson et al. (2006) to identify restoration sites for butternut, a tree species whose numbers have been greatly reduced by an invasive fungus. van Manen et al. (2005), Boetsch et al.
(2003), and Thompson et al. (2006) each studied protected plants species and chose to use D2 because the method does not require absence data and because the method works well with GIS data.
There are several assumptions associated with the use of Mahalanobis distance to predict optimal habitat and habitat use. One, the approach depends on the assumption that the study species is associated with optimal and measurable habitat conditions across the study region (Knick and Rotenberry 1998; Boetsch et al. 2003). Two, the method assumes that selection of habitats can be described by a multivariate mean and variance
18 and that the mean vector fullycharacterizes the optimal habitat (Knick and Rotenberry
1998). Because of these assumptions, species that are going to be more amenable to landscape-scale habitat modeling are those that are relatively common in their respective habitat, that respond to large-scale gradients that can be simulated using GIS predictors, and that are reliably associated with specific environmental conditions across the range of applications of the model (Boetsch et al. 2003).
Knick and Rotenberry (1998) tried to expand the usefulness of a Mahalanobis distance based model generated for black-tailed jackrabbits by using the model, which accurately predicted present use, to predict jackrabbit usage under a more biologically favorable environment (greater amounts of shrubland). They found that, while the simulated environment was biologically more favorable, the D2 scores forthe favorable land increased, indicating less favorable habitat. Knick and Rotenberry concluded that because D2 is determined using the multivariate mean vector of the GIS variables used to describe jackrabbit habitats that any change fromthe mean, biologically favorable or not, would be perceived by the model as unfavorable. The above described inherent problem with D2 suggested the need for a new model.
Before examining a new model, it is necessary to briefly review a couple of ecological concepts that are relevant to the new model. Species have a variety of habitat requirements. A species' fundamental niche is described by those habitat requirements.
For some habitat factors the species has narrow range of tolerance and it is these factors that tend to limit the species distribution. For other factors the species tolerance range is much broader, these tend not to be as limiting. Finally, there are habitat features that do not influencespecies presence at all (Krebs 2001). Part of the problem with D2 occurs
19 · because the model assumes that species are found only in optimal habitat and, therefore,
that the multivariate mean vector is the optimum forthe species (Rotenberry et al. 2002).
Species are in actuality found in less than optimal, as well as optimal, conditions. What
is given, however, is that the species locations must all meet, or exceed, the minimum
habitat requirements of the species. In response to optimal habitat problem, Rotenberry
et al. (2002) proposed that the identificationof a minimum set of basic habitat
requirements forthe species of interest might be more appropriate than the determination
of the multivariate mean vector, especially forspecies foundin a changing environment.
Additionally, GIS and remote sensing have made it much easier to include a variety of
habitat variables in models. It is possible that habitat variables that are not required by or
limiting to the species are collected or obtained and used to model habitat suitability. The
new model should reduce the impact of habitat variables that are measured, but that are
not relevant to describing suitable habitat.
Rotenberry et al. (2002) proposed partitioning D2 at a given location into p
differentcomponents (p = the number of habitat variables included in the model), where
each component represents the squared, standardized distance between the measurements
at the location of interest (y) and a plane of closest fit derived fromthe variable
measurements at species locations. The plane of closest fitrepresents a linear
approximation to the most basic combination of habitat variables required by the species
of interest. The equation forthe partitioning of Mahalanobis distance is:
2 D (y) = Lj=i df /Aj
where "Ajis the eigenvalue of the }th of p components and
dj = (y- µ)'aj
20 where y is the vector of habitat variable values at the location of interest, µ is the mean vector of the habitat variable values at known population locations, as before the apostrophe indicates the transpose of the difference, and aj is the vector of eigenvector values for the jth component.
Variation in the data collected at species locations can be partitioned into components that represent basic habitat requirements versus those components that do not represent requirements. The determination of components that represent basic requirements is done using Principal Components Analysis (PCA). When PCA of the data is run, the outcome is a series of principal components where the first component, the component with the largest eigenvalue, explains the greatest amount of variation, the second component, the component with the second largest eigenvalue, explains the next greatest amount of variation that was not explained by the first component, etc. Usually when a researchers works with PCA, (s)he is interested in findingwhat variables load onto the component that explains most of the variation in the data. However, in the case of partitioned Mahalanobis distance, the interest is in determining which variables correlate most strongly with the components having the lowest eigenvalues, because those components explain the least amount of variation. The variables associated with low eigenvalue components are the variables that have the least amount of variation and are most likely the minimum habitat requirements forthe species of interest, that is, the invariant aspects of occupied locations (Rotenberry et al. 2002). One major assumption
2 of partitioned D is that not all of the p components definelimiting combinations of habitat variables. Some of the components are present because the researcher decided to include p habitat variables in the model. Because the interest is only in the basic habitat
21 requirements, partitioned D2 is calculated froma subset of the components (k). Usually the k components are those that have an eigenvalue less than one and greater than zero.
The equation for partitioned Mahalanobis distance then becomes
D2 (k) = Lj=k dJ I Ai for components k through p where the p components are non-zero. Using D2(k), species requirements are defined in terms of combinations of variables, instead of in terms of individual variables. This method allows fortrade-offs among variables (Dunn and
Duncan 2000). The ability to account for trade-offs is important because it is more likely that predictor variables work in combination to define suitable habitat than that any one or more variables works singly (Clark et al. 1993).
2 2 Partitioned D , as full D , assumes that the species of interest preferred habitat can be described by a multivariate mean and variance, and, as with all classification techniques, D2(k) assumes that the species is distributed optimally across the landscape
(Knick and Rotenberry 1998) and that the variables chosen to describe the habitat are adequate and appropriate (Browning et al. 2005).
The use of D2(k) to determine and map habitat suitability is relatively new.
Browning et al. (2005) used GIS and D2(k) to predict the location of timber rattlesnake hibemacula. Habitat variables that were likely to be important to habitat selection for timber rattlesnakes were known a priori and a total of 15 habitat variables were used in the model. A subset of k = 4 components was used to calculate partitioned Mahalanobis distance. Using D2(k=4) model, 25% percent of the study area was deemed suitable and that 25% contained 82% of the known hibemacula. Watrous et al. (2006) used GIS and
D2(k) to predict not only habitat suitability but the minimum habitat characteristics for the
22 Indiana bat in the Champlain Valley, specifically of maternitycolonies. Wiser et al.
(1998) stated that habitat modeling can be usefulfor describing optimal habitat. Little was known about the general habitat requirements of Indiana bats in the Champlain
Valley area of New York and Vermont, so one of the goals of the Watrous et al. research was to use PCA to determine which habitat variables might describe the minimum habitat requirements of the Indiana bat in the Champlain Valley. Eighteen habitat variables were used, some of which were measured and tested at a variety of scales, to describe bat habitat. Four variables consistently appeared in the components with low eigenvalues.
The researchers calculated D2(k) using k = 3 and k = 8. They foundthe percentage of predicted suitable area decreased with the addition of components because adding components increased the number of habitat characteristics the unsampled locations had to match to the known locations in order to be considered suitable.
To date no published research has used partitioned Mahalanobis distance to model habitat suitability for a plant species. However, plants are excellent candidates forhabitat modeling because they are sessile, attached to the substrate and immobile, and more directly affectedby the microclimate, topography and other environmental factors
(Boetsch et al. 2003) than animals. Remotely sensed data and GIS can often be used to represent these factors.
Justification of Habitat Variables
In order to learnmore about the ecological requirements of Lake Huron tansy, a variety of habitat variables will be examined in the habitat suitability models. The choice of variables to use within the present study will be based on what is known about the
23 · species and based on what habitat variables have been used by other researchers.
Guisan and Zimmerman (2000) state that there are three types of ecological
gradients used in creating habitat distribution models: 1) resource gradients, those
variables that the organism consumes for growth (light, carbon, nutrients); 2) direct
gradients, those variables that are of physiological importance, but are not consumed (pH,
temperature); and 3) indirect gradients, those variables that do not themselves have physiological importance, but potentially affect resource and direct gradients (elevation,
slope, aspect). Indirect variables are the easiest to measure over a large area and can
often serve as surrogates for direct and resource variables. GIS layers often represent
indirect gradients.
A variety of variables could be used to describe Lake Huron tansy habitat. Lake
Huron tansy is found along the lake shores in the dunes, suggesting that distance to the
shore and bedrock layers are appropriate variables to include. The distance to the shore
variable may serve as a representative variable for natural disturbance, because wind
velocity is greater closer to the shore (Albert, 2000). Additionally, Jolls and Sellars
(1999) found that Lake Huron tansy presence was related to distance to the lake's edge.
The soil type is dictated in part by the bedrock. Engler et al. (2004) included a
substratum layer in their habitat suitability map of an endangered Swiss plant species in
order to provide information on geology and soil and van Manen et al. (2005) used a
geology layer in their habitat prediction models of protected plants in Shenandoah
National Park, as did Thompson et al. (2006) in their modeling of restoration sites for
butternuttrees in Mammoth Cave National Park.
The bedrock data are categorical. Both van Manen et al. (2005) and Watrous et
24 al. (2006) used categorical data in their habitat suitability models, despite violating the requirement of continuous data stated forMahalanobis distance. van Manen et al. (2005) included the categorical variables ecoregion and National Land Cover data. Whereas
Watrous et al. (2006) included the categorical variables canopy class, decay stage, amount of exfoliatingbark, and presence of cavities, loose bark, or splits in the tree.
Location on the dunes may be important forspecies success, so aspect of the dunes, slope and direction to the shore could be used in this study to address the location parameter. Aspect has been used as a habitat variable in predicting mountain bittercress occurrence in the Great Smoky Mountains National Park (Boetsch et al. 2003) and in predicting habitat suitability of protected plant species in Shenandoah National Park (van
Manen et al. 2005). Boetsch et al. (2003), van Manen et al. (2005), and Thompson et al.
(2006) included slope as a habitat variable, as did Engler et al. (2004) in their research of
Eryngiumalpinum, an endangered plant species in Switzerland.
Climate variables are useful in describing a species niche (Weatherbee 2006). As a plant, Lake Huron tansy requires moisture and the appropriate number of growing degree days. However, it is not known when during the year moisture and temperature play a role in plant success. Jarvis et al. (2005) used monthly averages for rainfall in their study for optimizing the collection of wild peppers in Paraguay using GIS. Engler et al. (2004) included cumulative April through August rainfall and cumulative April through September rainfall in the habitat suitability model of an endangered Swiss plant.
In order to determine which months or collection of months might be important to tansy success, monthly averages for the entire year could be used for precipitation, as could cumulative growing season (May- September) precipitation. Engler et al. (2004)
25 included July mean temperature in their habitat suitability model, whereas Jarvis et al.
(2005) used interpolated monthly averages forthe entire year. Interpolated monthly average growing degree days for April through September could be used as could cumulative growing degree days April through September and May through September in this research of Lake Huron tansy. Because the seeds of Lake Huron tansy are believed to be cold stratified (Nichols 1934), the inclusion of cumulative mean winter temperature
(December- February) as a habitat variable might be warranted.
The growing season formany herbaceous plants in temperate regions is bracketed by the last spring frost and the first fall frost. The Julian day in the spring when the chance of the last frost was 90% and the Julian day when the chance of the first fall frost was 90% could be usefulto include as habitat variables.
Lake Huron tansy is a calciphile (Ostlie 1991), indicating that pH would be a useful variable to include in the models. Wiser et al. (1998) included soil pH as one habitat variables in their research on predicting rare plant species occurrence in the
Appalachians. Lake Huron tansy is foundon sandy to rocky beaches, for this reason percent sand and percent gravel should be considered as habitat variables. Hill and
Keddy (1992) used percent sand plus percent gravel as a habitat variable in their work on predicting coastal plain plant rarities based on habitat variables. Many habitat suitability models have included elevation as a habitat variable (Hill and Keddy 1992; Boetsch et al.
2003; van Manen et al. 2005; Thompson et al. 2006); therefore, elevation could be included in this study as well.
It has been suggested that the grid cell size used when calculating a habitat prediction model should be comparable to the home range/dispersal range of the species
26 of interest (Erickson et al. 1998; Meggs et al. 2004; Carter et al. 2006). The home range of plants is small, and while the seed dispersal distance of Lake Huron tansy is unknown, seed dispersal formany herbaceous species declines with distance fromthe parent plant
(Krebs 2001). van Manen et al. (2005) used a 10m x 10m grid cell size, stating that high resolution GIS layers were adequate to depict plant responses, and they obtained useful models fortheir species of interest.
27 CHAPTER 3
DATA AND METHODS
The Data and Methods chapter is divided into two sections. The firstsection is a description of the habitat variables used in this study, where the data foreach variable were obtained, and how, if needed, the data were manipulated. The second section addresses the statistics used to determine which habitat variables were useful in describing "ideal" habitat for Tanacetum huronense, the methods used to create and verify habitat models, and finally, the methods used to obtain habitat suitability maps for the tansy in Michigan.
Habitat Variables
Because the habitat variables that are important for Lake Huron tansy success are relatively unknown, one of the objectives of this research was to determine which habitat variables best described "ideal" habitat for Lake Huron tansy. Wiser et al. (1998) stated that habitat modeling is useful for this task; therefore, several habitat variables were considered for modeling. All GIS conversions and analyses were performed in ArcGIS
9.2 (ESRI, Redlands, CA), unless otherwise stated. Habitat variable and population location layers were transformed to North American Datum (NAD) 83 Universal
Transverse Mercator (UTM) Zone 16N, as needed.
28 Topography
National Elevation Dataset (NED) shaded relief (1/3 arc second) grids were obtained fromthe United States Geological Survey (USGS) Seamless Data Distribution
System (USGS 2007). The downloaded NED grids were each projected into NAD 83
UTM Zone 16N and the cell size was set to 10 meters, using cubic convolution for resampling (USGS 2007). The projected grids were mosaiced to form a continuous elevation grid for northern Michigan. Slope, cosine of aspect, and sine of aspect were each calculated fromthe 10m NED using the Spatial Analyst extension in ArcGIS 9.1.
All other habitat variable grids used in the present study were set to the same scale as the
NED data.
Study Area
The study area comprised land within 1610 meters of Great Lakes shore in the counties where Lake Huron tansy is known to occur. The study area layer was based on the State Soil Geographic (STATSGO) data boundaries because the boundaries of the
STA TSGO layer were the most restrictive of all the habitat layers evaluated. The
ST A TSGO soil data for Michigan were obtained fromMichigan Center for Geographic
Information (MCGI) (MCGI 2002). The contiguous soil layer was dissolved based on the Dissolve field to create a simple polygon feature of the state, which was then used to create the "study area" layer. A 16 lOm buffer was created inland from the shore of the simple STA TSGO layer, resulting in the Study Area layer. "Extract by Mask" was used to reduce the size of each of the habitat layers to the size of the study area.
29 · Soil Parameters
The STATSGO data were used to obtain percent sand, percent gravel, and mean
pH of the top two layers of each soil type found within the study area. The state
STATSGO layer was clipped by the study area. Beforethe pH, percent sand and percent
gravel fromthe STATSGO data could be mapped, two layers of many to one database
relationships had to be summarized because the downloaded STA TSGO data are set up
such that map units are made up of components, and the cqmponents are comprised of
layers (USDA 1995). Data were summarized in Open Office Cale,a spreadsheet
program similar to MS Excel.
The weighted average pH for component was determined by the following
equation:
where laydeph is the ST A TSGO notation for depth to the lower boundary, laydepl is the
STA TSGO notation for depth to the upper boundary, phh is maximum pH in the layer,
and phi is the minimum pH in the layer. The weighted average pH for the top two layers
of each component was multiplied by the percentage of that component that was foundin
the map unit. Components fractions were summed, then divided by 100 in order to
obtain a value between zero and 14 for each map unit (USDA 1995).
The percent gravel foreach map unit was determined by calculating the mean
percent gravel foreach of the top two layers of each component using the following
equation:
(no4h+no41 M ean o/co G rave 1 = loo - ---) , 2
where 100 represents the percentage of soil material that passed through a 3-inch filter, 30 no4h is the ST A TSGO notation forthe maximum percentage of soil material that passed through a number 4 sieve, no41 is the STA TSGO notation for the minimum percentage of soil material that passed through a number 4 sieve, and overall the value to the right.of the minus sign is material that passed through a number 4 sieve, 1/16 inch(:::::1.6mm) or smaller. The amount remaining after subtracting the percentage of material 1/16 inch or smaller was considered gravel(Integrated Publishing 2007), weighting each value by the depth of the layer, and proceeding as described above for calculating the pH for each map unit.
The percent sand for each map unit was determined by calculating the mean percent sand foreach of the top two layers of each component and proceeding as described above for calculating pH for each map unit. The mean percent sand foreach layer was equal to the mean percentage of soil material that passes through a number 4 sieve minus the mean percentage of material that passes through a number 200 sieve, represented by the following equation:
S d (no4h+no41) - (no200h;no2001). M ean oo an = 2
Material that passes a number 4 sieve is smaller than gravel (1/16 in(::::: l.6mm)) and material that passes a number 200 sieve is smaller than sand(75µm); the percentage of material that is retained on the number 200 sieve is sand(Integrated Publishing 2007).
Once the average percentage of sand for each layer was determined the method followed that described forcalculating the pH of each map unit.
Once the data were summarized to map unit the tables were joined to the
STA TSGO polygon layer and each of the variables(pH, percent gravel and percent sand) was converted to a GRID layer using Spatial Analyst.
31 Shoreline Data
The ST A TSGO soil boundaries for Michigan were used to calculate distance and direction to the shore. In order to generate the straight-line distance inland fromthe
Great Lakes shoreline variable, the STA TSGO simple polygon was converted to a line file in ArcGIS 9.2. The line filewas then used to generate the straight-line distance file using the Spatial Analyst extension. The same line file was used to create a direction to shore layer, also using Spatial Analyst. Direction to the shore was represented in the model as the cosine and sine of the angular direction from the shore to the lake's edge. Bedrock
The bedrock data were obtained fromMCGI (MCGI 2002). The state bedrock layer was clipped to the study area. The bedrock study area layer was converted to a
GRID file, with a cell size of 1Om, based on bedrock type. The bedrock data were also reclassified into seven binary layers where "1" was equal to dune sand; lacustrine sand and gravel; end moraines of medium texture till; coarse textured glacial till; end moraines of coarse textured till; thin to discontinuous glacial till over bedrock; and, exposed bedrock, respectively, all bedrock types where tansies are found, and "0" was equal to all other bedrock types foreach layer. Climate
Climate data for the State of Michigan were obtained fromNational Climatic Data
Center (NCDC) (NCDC 2005). The obtained climate data were averaged over a 30 year period (1971-2000) (NCDC 2005). Climate layers were spatially interpolated using tension spline and the default values of weight= 0.1 and 12 points; the cell size was set to the same as the 10m elevation layer. The climate data were interpolated using tension
32 spline because this method produced the smoothest grid and the values at each of the weather stations were more faithfully represented. Over 50 weather stations are located in the northernLower Peninsula and the eastern Upper Peninsula of Michigan (Fig. 3); however, not every climate variable is collected at each weather station.
Mean monthly growing degree days for April through September were each interpolated based on 41 weather station sites where growing degree day data were collected. Cumulative growing degree days were determined for April through
September and May through September by summing the mean monthly growing degree days for the appropriate months. These data were also interpolated using tension spline.
Mean monthly temperatures for December, January and February were summed to represent winter temperature. Winter temperature for the study area was interpolated from50 climate station locations where temperature was recorded. The spring frost layer was based on the Julian day when there was a ten percent probability of having a temperature S 32° F later in the spring. The fall frost layer was based on the Julian day when there was a ten percent probability of having a temperature S 32° F earlier in the fall. Both of the frost layers were interpolated fromfrost/freeze data obtained from41 weather stations. Mean monthly precipitation for each month, January through
December, was interpolated from data collected at 56 weather stations that collect precipitation data. Growing season precipitation was interpolated fromthe sum of the mean monthly precipitation for May through September at the 56 weather stations.
33 1 .,. �l... //f----,• �-.,··•-r----· -, • i
,.._, _..-,e. .-- J,:;, r-' � . .�•trl,., ', ,..,...'l(,'J( �- .. ... \,\'. �,_• . ,' _J • • • ,\ t 0 ""-'·-,___i ---- ��------;• ', - 1__ /::· - ,�t�� '-,' ____ ',;/ - ��- ___,,-\ ----, � _,} Co)- /" = \ ,_ ? :� · ...... --\,�,.,_,,_ ·� i. . _,-..__ � -... l (.\ . 1 J > .. � !J ••\,,,,--,_-.,,. -~- \__ te/, /r-- ;,;-��I __/ . __J� h . n _ "i . .r iv,-' •,r. r'- , , ' ) • l ,; .• - \ , ._ .. � - L . ,' ,- - c'·, r- --,. • '--·-- I t I. _,.._ \I ·--- ...r . �J".,. ---c-·• r "-, I I '�/) _,,,, .. .
I • • I ' • I , 1•1;' . \._{ c·--1_:, ,,.,. ' • I I I Weather Station Locations --l ) �{/� ) ' '-1J '",,,- II ,~J, - '� , : �� I" ,L �- ... ·, Frst. Growing Degree Day, • I 'I0 __,//), -]- • ' Temperature, Precipration _,.,) ! I • • Temperature, Precination . • • • o Temperatur \ N (. ---I1 . • Prcipnatin . i . t�-i---t--r-• --t-- •. ! • • • • •/ ,J 0 12 5 25 +50 Miles • I i• __,,_r ------�
Figure 3. Locations of Michigan weather stations used to interpolate climate variables for Lake Huron tansy habitat suitability Population Data
Lake Huron tansy population locations were obtained fromMichigan Natural
Features Inventory (MNFI). The locations were collected by a number of individuals over time spanning from the late 1800s to the present. Element occurrence locations were obtained from voucher specimens and locations noted in the literature, locations noted by researchers conducting surveys, and locations noted by individuals who know the species of interest and reported the tansy's presence to MNFI. Because the data were collected over a long time frameand by a number of differentindividuals, the precision of the location data varies from the best guess on a township range map to exact global positioning system (GPS) locations. As the location information is privileged, exact locations were used only in model development and no maps of exact locations were included in the present study.
The given geographic coordinates for each population were entered into a database, converted to decimal degrees, and converted to a point shapefile. Population locations that had not been verifiedas extant since 1970 were removed from the dataset, resulting in 125 present day locations. A random number generator was used to randomly select 25% (n = 31) of the population, used as the verificationset. The remaining 75% (n = 94) of the population was used as the test set (van Manen et al.
2005).
35 Statistics and Habitat Modeling
The following section covers the methods used to determine the most appropriate habitat layers to use to describe "ideal" tansy habitat, the methods used to calculate partitioned Mahalanobis distance at both 10 meter and 15 meter resolution, to calculate full Mahalanobis distance for seven variables measured at 15 meter resolution, to test the habitat suitability models and the method used to generate the habitat suitability maps.
Determinationof Appropriate Habitat Variables
Comparison of Means
A total of 42 habitat variables were examined at the 10 meter resolution in this study (Table 1). The values for each habitat variable were assigned to each test population location using the "Extract Values to Points" tool. The population variable data were collated in MS Excel and imported into SAS (SAS Institute 2000). The range, mean and standard deviation of the test population data foreach habitat variable were calculated in SAS. The range, mean and standard deviation of the study area for each habitat variable were calculated in ArcGIS 9.2. A z-test, calculated in SAS, was used to compare the test population mean with the study area mean for each habitat variable. The same process was followedto compare the means of the seven variables collected at 15 meter resolution (elevation, slope, cosine aspect, sine aspect, distance to shore, cosine and sine direction to shore). The z-test was used to examine which variables in and of themselves differed at the population locations compared to the study area. Variables can work together in combination to create suitable habitat. Principal Components Analysis was used to examine which variables were strongly correlated with components having low variance (Watrous et al. 2006) (See Chapter 2 of this manuscript).
36 Table 1
Variables and abbreviations used in this study
Abbreviated Variable Variable Elevation NED Slope SLOPE Cosine Aspect COSASP Sine Aspect SINASP Distance to Shore DISTSH Cosine Direction COSDIR Sine Direction SINDIR Cumulative Growing Degree Days (April-September) CUMGDA Cumulative Growing Degree Days (May-September) CUMGDM April Growing Degree Days APRGDD May Growing Degree Days MAYGDD June Growing Degree Days JUNGDD July Growing Degree Days JULGDD August Growing Degree Days AUGGDD September Growing Degree Days SEPGDD Cumulative Winter Temperature (December-February) CUMWIN 90% Chance of First Fall Frost (Julian Day) FALFST 90% Chance of Last Spring Frost (Julian Day) SPRFST Growing Season Precipitation GROPPT January Precipitation JANPPT February Precipitation FEBPPT March Precipitation MARPPT April Precipitation APRPPT May Precipitation MAYPPT June Precipitation JUNPPT July Precipitation JULPPT August Precipitation AUGPPT September Precipitation SEPPPT October Precipitation OCTPPT November Precipitation NOVPPT December Precipitation DECPPT Quaternary QUAT Dune sand CODE_4 Lacustrine sand and gravel CODE_6 End moraines of medium textured till CODE12
37 Table 1 - Continued Abbreviated Variable Variable Coarse textured glacial till CODE13 End moraines of coarse textured till CODE14 Thin to discontinuous glacial till over bedrock CODE15 Exposed bedrock CODE17 Percent Gravel PCTGRA Percent Sand PCTSAN PH PH
Principal Components Analysis
In order to examine which habitat variables might best describe optimal tansy habitat, principal components analysis (PCA) of all 42 habitat variables was conducted using procedure PRINCOMP in SAS (Fig. 4). As is standard for the computation of partitioned Mahalanobis distance, the components with eigenvalues less than one were considered because these components describe the least amount of variation among test population locations. Within each component with an associated eigenvalue of less than one, the variable with the greatest eigenvector value and any variable(s) with an eigenvector value within 0.1 were considered, because these variables vary least across known locations, thereby potentially serving as niche limiting factors (Rotenberry et al.
2002), and important for tansy establishment. Scree plots were also created for each PCA and the location of the elbow was considered when determining which components to include in partitioned Mahalanobis distance. The z-test and PCA were used to inform the choice of variables used in the habitat suitability models.
38 Habitat Variables I \ 42 Variables 7 Variables lOmx 10m 15mx 15m ! ! Extract Habitat Variable Extract Habitat Variable Values to Points Values to Points l 2
Variables to include in habitat suitability models
Figure 4. Methods used to determine appropriate habitat variables needed to model habitat suitability for Lake Huron tansy
39 Habitat Models
Eleven Variables Models
Partitioned Mahalanobis distance scores were calculated forthe study area based on 11 variables (NED, SLOPE, COSASP, SINASP, DISTSH, GROPPT, CUMGDM,
CUMWIN, PCTSAN, PCTGRA, and PH) represented at 10m X 10m resolution.
Principal components analysis was calculated using the variable values associated with the test populations for the above 11 variables in order to obtain eigenvalues and eigenvectors. A scree plot was generated to note the location of the elbow. Components with an eigenvalue less than one were identified and used to calculate partitioned
Mahalanobis distance. Partitioned Mahalanobis distance was calculated for each unsampled location within the study area using raster calculator in ArcGIS 9.2. To do this, the principal component score for each unsampled location was determined foreach component of interest by subtracting the mean population location value of each variable fromthe pixel value of the layer of the corresponding variable at the unsampled locations, and multiplying that difference by the eigenvector value associated with that variable and summing for all variables. The scores for all components of interest were squared and then divided by their respective eigenvalues. The resulting values were summed to generate partitioned Mahalanobis distance scores.
Consider the following hypothetical example (Table 2) containing four variables, represented by GRID layers, with the population location means, eigenvector values, and eigenvalues seen below:
40 Table 2
Hypothetical Principal Components Analysis results based on four variables
Variable Location Mean Principal Component 3 Principal Component 4 Elevation 650ft 0.23 0.72 Percent sand 55% 0.54 0.37 Percent gravel 12% 0.49 0.26 pH 7.2 0.64 0.52 "A=0.82 "A=0.41
The raster calculator equations would look like the following:
PC3 = (([elev] - 650) x 0.23) + (([sand] - 55) x 0.54) + (([grav] - 12) x 0.49) + (([ph] - 7.2) x 0.64)
PC4 = (([elev] - 650) x 0.72) + (([sand] - 55) x 0.37) + (([grav] - 12) x 0.26) + (([ph] - 7.2) X 0.52) and
[PC3]x[PC3] [PC4]x[PC4] D2 (2) = ( ) + ( ) 0.82 0.41 where values in brackets referto the corresponding grid layers.
Two different sets of partitioned Mahalanobis distance scores were calculated for the study area based on the 11 variables represented at 10m resolution. One set
calculated using only those components whose eigenvalues were less than one (Model A)
(Fig. 5), and the second set calculated using all principal components (Model B), used to represent full Mahalanobis distance.
Seven Variables Models
Preliminary research on a subset of the data (results not shown) indicated that
NED, slope, aspect, annual heating degree days, growing season precipitation, and distance to shore were usefulhabitat variables to model tansy habitat suitability using full
Mahalanobis. Seven habitat variables (NED, SLOPE, COSASP, SINASP, DISTSH,
41 Values of chosen habitat Values of chosen habitat variables 1OmX 1 Om variables 15mX15m
Full MD using PMD based on PMD using all ArcView 3.3 subset components extension • • F • r 'I 'I r 'I Model A Model B Model C lOmXlOm lOmXlOm 15mX15m k=7 k= 11 '- ./ '- ,) '- ./
"' r "I ModelE Model D 15mX15m 15mX15m k=4 k=7 '- • ./ '- • ,) Distance values assigned to 100 random points, test points and validation points
Threshold distance value chosen based on cumulative frequencygraph
Maps created by reclassifying each distance grid based on its corresponding threshold value
Figure 5. Flow of processes used to obtain habitat suitability maps for Models A -E
42 COSDIR, SINDIR), represented at a 15m X 15m resolution, were chosen to compare results obtained using Mahalanobis distance (Model C) (Fig. 5) and partitioned
Mahalanobis distance calculated fromall principal components (Model D) and calculated using components with eigenvalues less than one (Model E). In order to determine
Mahalanobis distance, the mean vector, inverse variance covariance matrix and
Mahalanobis distance were calculated in Arc View 3.3 (ESRI, Redlands, CA) using the
Mahalanobis distance extension (Jenness 2003). The number of variables was limited to seven and cell size of 15m was chosen because of limitations of the extension.
Partitioned Mahalanobis distance was calculated as described previously. PCA was run using the habitat variable values associated with each test population for the seven
variables listed.
Model Testing
A set of 100 random locations within the study area was generated using "Create
Random Points" in ArcGIS 9 .2. The null referenceset represents the distribution of
D2(k) values if the Lake Huron tansy was randomly distributed within the study area (van
Manen et al. 2005). Mahalanobis distance values, both full and partitioned, were
assigned to the corresponding points of the test set locations, verificationset locations,
and the locations of the null referenceset using "Extract Values to Points".
The model was firsttested using cumulative frequencycurves. Cumulative
frequencygraphs of the D2 values for the three point sets were generated in MS Excel.
The frequencygraphs were firstcompared to determine whether the curve fromthe test
set differedfrom the curve for the verificationset; similarity indicates model consistency.
The graphs were then compared to determine whether the curve fromthe test set was
43 substantially differentfrom the null model curve; in this comparison, similarity in the curves indicates that the model is no better than random chance at choosing suitable Lake
2 Huron tansy locations (van Manen et al. 2005). Finally, the D value that maximized the difference between the test set cumulative frequencycurve and curve of the null reference set was chosen as the threshold value that distinguished suitable from unsuitable habitat (Fig. 5). This method of choosing a threshold value includes the greatest number of population locations within the smallest percentage of study area
(Pereira and Itami 1991; van Manen et al. 2005).
Habitat SuitabilityMaps
The Mahalanobis distance grid and the partitioned Mahalanobis distance grids were reclassified into two categories, suitable and unsuitable, based on the corresponding threshold value, selected as described previously, to generate the habitat suitability maps
(Fig. 5). The number of suitable and unsuitable pixels was used to determine the percentage of suitable habitat in the study area given each model.
44 CHAPTER4
RESULTS
This chapter is divided into two sections. The first section states the results obtained from the z-test comparing the mean of the test population for each habitat variable to the corresponding mean of each variable for the study area as a whole and the results obtained from PCA of 42 habitat variables at 10m resolution. These results informedwhich variables might be useful in defining suitable tansy habitat. The second section describes the results obtained fromhabitat modeling, covering models derived fromtwo differentsets of habitat variables. The firstset comprised 11 habitat variables represented at 1Om resolution. The 11 variable set was used to generate habitat suitability maps and to compare results obtained frompartitioned D2 calculated using a subset of principal components (k = 7) to the results obtained when partitioned D2 was calculated with the complete set of principal components (k = 11). The second set comprised seven variables represented at 15m resolution. The seven variable set was used to generate habitat suitability maps and to compare results obtained when partitioned D2 was calculated using a subset of principal components (k = 4) to results
2 obtained when partitioned D was calculated using the complete set of principal components (k = 7), and to compare partitioned D2 (k = 7) results to results obtained when D2 was calculated using the D2 extension available fromJenness (2003) in
ArcView 3.3.
45 Determination of Appropriate Habitat Variables
Comparison of Means
Ten Meter Data
Forty-two habitat variables were examined at 10 meter resolution (Table 1). The
test populations had significantly lower elevation (p < 0.0001) and significantly lower
distance to shore (p < 0.0001) than the study area as a whole (Table 3). The test
populations had significantlyhigher growing season precipitation (p = 0.0103) and April
precipitation (p = 0.0145) than the study area, but significantlylower June (p = 0.0068),
July (p < 0.0001) and November (p = 0.0484) precipitation. The Lake Huron tansy was found more often on dune sand bedrock than would be expected based on overall
presence of sand in the study area (CODE_4: p < 0.0001; QUAT: p = 0.0013). The tansy
was found in soils with a greater percentage of sand (p = 0.0115). None of the other 42
variables showed a significant difference between the study area as a whole and the test population locations.
Fifteen Meter Data
The same abbreviations were used for the seven variables measured at 15 meter resolution as were used forthe variables at 10 meter resolution. The elevation (p <
0.0001) and distance to shore (p < 0.0001) for Lake Huron tansy test population locations
were significantly lower than what was available in the study area (Table 4). None of the other five variables differed significantly between the study area as a whole and the test
population locations.
46 Table 3 Descriptive statistics of 42 variables measured at 10 meter scale forthe study area and test populations
Abbreviated Study Area Study Area Test Population Range Test Population Test Population Variable Stud� Area Range Mean SD (n=71) Mean (n=71) SD (n=71) NED 154.145 - 342.418 194.405 19.685 176.126- 272.858 181.833** 12.670 SLOPE 0-72.699 2.138 3.841 0-13.922 2.537 2.168 COSASP -1 - 1 0.047 0.693 -0.998 -1 0.105 0.653 SINASP -1 -1 -0.056 0.717 -0.999 -0.999 -0.055 0.757 DISTSH 0-1897.894 745.59 464.65 0-964.210 117.559** 152.754 COSDIR -1-1 0.009 0.704 -0.996 -1 -0.002 0.707 SINDIR -0.999 -0.999 0.051 0.708 -0.996- 0.999 0.059 0.714 CUMGDA 1883.435 -2977.005 2459.984 251.068 1884.54 - 2963.45 2463.373 230.780 CUMGDM 1872.614 - 2889.206 2413.683 231.112 1873.67- 2881.83 2418.358 215.114 APRGDD 10.820- 96.443 46.301 23.636 10.872 -83.200 45.015 18.315 MAYGDD 123.117 -344.074 241.916 43.808 123.764-340.466 239.456 41.442 JUNGDD 307.578 -595.500 477.501 56.351 308.536 -590.557 475.867 52.754 JULGDD 513.764 -771.992 665.513 53.826 514.309 - 770.872 664.375 52.457 AUGGDD 542.268 -729.052 639.527 43.473 546.235 - 719.453 642.375 40.521 SEPGDD 304.050 -475.174 389.226 44.01 310.506 - 460.483 396.285 39.859 CUMWIN 44.122- 75.152 60.131 7.056 49.670-69.546 61.56 4.576 FALFST 232.448- 277.505 259.613 9.046 234.858 -274.826 261.594 9.587 SPRFST 133.493 - 191.768 157.447 11.609 137.393- 189.848 155.322 11.119 GROPPT 3.542- 162.058 84.999 38.191 25.090-157.607 96.632* 39.268 JANPPT +:- 1.308- 3.467 2.099 0.51 1.353- 3.458 2.07 0.429 --..J Table 3 - Continued Abbreviated Study Area Study Area Test Population Range Test Population Test Population Variable Stud}'.Area Range Mean SD (n=71) Mean (n=71) SD (n=71) FEBPPT 0. 722 -2.036 1.298 0.292 0.772-1.867 1.237 0.200 MARPPT 1.435 -2.629 2.006 0.256 1.442- 2.397 1.994 0.216 APRPPT 1.320-2.702 2.242 0.239 1.425 -2.548 2.311 * 0.204 MAYPPT 2.228 -2.919 2.566 0.141 2.309 -2.784 2.582 0.122 JUNPPT 2.443- 3.521 2.875 0.264 2.465- 3 .480 2.79* 0.279 JULPPT 2.072- 3.420 2.978 0.217 2.095 -3.199 2.846** 0.280 AUGPPT 2.572- 3.883 3.243 0.267 2.610-3.651 3.232 0.232 SEPPPT 2.913 -4.322 3.556 0.307 3.006- 3.898 3.4907 0.231 OCTPPT 2.289 -3.739 2.962 0.298 2.565 -3.371 2.968 0.194 NOVPPT 1.978 -3.528 2.6 0.35 2.002- 2.991 2.518* 0.233 DECPPT 1.430-3.518 2.185 0.478 1.542-3.166 2.124 0.355 QUAT 1-17 8.22 4.239 4-17 6.606* 3.701 CODE_4 0-1 0.126 0.333 0-1 0.408** 0.495 CODE_6 0-1 0.412 0.492 0-1 0.422 0.497 CODE12 0-1 0.028 0.165 0-1 0.014 0.119 CODE13 0-1 0.09 0.287 0-1 0.028 0.167 CODE14 0-1 0.02 0.143 0-1 0.028 0.167 CODE15 0-1 0.169 0.374 0-1 0.084 0.280 CODE17 0-1 0.005 0.069 0-1 0.014 0.119 PCTGRA 0.150-73.475 16.46 18.904 2.255 -73.475 16.132 19.418 PCTSAN 16.940-90.521 57.646 20.649 22.882- 90.521 63.837* 20.322 PH 4.980-7.640 6.081 0.632 5.010-7.420 6.126 0.643 ** p <: 0.001
* p < 0.05 Table 4
Descriptive statistics forseven variables measured at 15 meter scale for the study area and test populations
Study Area Study Area Test Population · Test Population Test Population Variable Study Area Range Mean SD Range (n=90) Mean (n=90) SD (n=90) NED 154.386 -342.418 195.062 20.158 -176.13- 272.86 181.465** 11.656 SLOPE 0 - 64.168 2.138 3.714 0-16.29 2.598 2.392 COSASP -1 -1 0.036 0.697 -1 -1 0.063 0.715 SINASP -1 -1 -0.038 0.715 -1 -1 -0.055 0.704 DISTSH 0-1619.514 742.619 468.820 0-1009.02 68.291 ** 139.599 COSDIR -1 -1 0.004 0.700 -1 -1 0.098 0.720 SINDIR -0.999- 0.999 0.066 0.711 -1 -0.99 0.198 0.678 ** p < 0.01
'°+:> Principal Components Analysis
Principal Components Analysis (PCA) of all 42 variables resulted in 38 components that had non-zero eigenvalues (Table 5). Components 12 - 38 had eigenvalues (l) less than one, but greater than zero. The elbow of the scree plot occurred at Component 3, with an eigenvalue of 2.99 (Figure 6). Components 12- 38 explained
16.77% of the variation in the data, whereas components 3 - 38 explained 57.6% o:lithe variation in the data (Table 5). The variables that had the highest loading in Components
28 - 38 were all interpolated layers (Table 6). In general, the variables that together correlated with principal components 28 - 38 were growing degree days during the months of the growing season and late fall and winter precipitation.
The variables that had the greatest loading in Components 12 - 27 were: precipitation in July, growing season precipitation and end moraines of medium textured till (PC 12); direction to the shore (PC 13, 16); exposed bedrock and end moraines with coarse textured till (PC 14); exposed bedrock, aspect and growing season precipitation
(PC 15); aspect, slope, direction to the shore, growing season precipitation, precipitation in August, dune sand, lacustrine sand and gravel, and coarse textured glacial till (PC 17,
18); pH (PC 19); distance to shore, slope, aspect, growing season precipitation and lacustrine sand and gravel (PC 20); elevation and the bedrock types less commonly used by Lake Huron tansy ( coarse textured glacial till and thin to discontinuous glacial thll over bedrock) (PC 21); slope and May precipitation (PC 22); precipitation in June (PC 23); distance to the shore, elevation and end moraines with coarse textured till (PC 24); winter temperatures and spring or summer precipitation (PC 25, 26); and percent sand and percent gravel (PC 27) (Table 6). Four of the middle components (PC12- 27) pair
50 Table 5
Eigenvalues for 42 variable model obtained fromSAS
Component Eigenvalue Difference Proportion Cumulative 1 12.5125682 7.2188193 0.2979 0.2979 2 5.2937489 2.3035907 0.126 0.424 3 2.9901581 0.1537738 0.0712 0.4952 4 2.8363843 0.4230331 0.0675 0.5627 5 2.4133512 0.5735087 0.0575 0.6201 6 1.8398425 0.0897858 0.0438 0.664 7 1.7500567 0.1584425 0.0417 0.7056 8 1.5916142 0.2017171 0.0379 0.7435 9 1.3898971 0.1806044 0.0331 0.7766 10 1.2092927 0.0785419 0.0288 0.8054 11 1.1307508 0.1787404 0.0269 0.8323 12 0.9520104 0.0361195 0.0227 0.855 13 0.9158908 0.0490006 0.0218 0.8768 14 0.8668903 0.1090232 0.0206 0.8974 15 0.7578671 0.137625 0.018 0.9155 16 0.6202421 0.0842073 0.0148 0.9303 17 0.5360348 0.0136465 0.0128 0.943 18 0.5223883 0.1107776 0.0124 0.9555 19 0.4116108 0.0891537 0.0098 0.9653 20 0.3224571 0.0649262 0.0077 0.9729 21 0.2575309 0.0374235 0.0061 0.9791 22 0.2201075 0.0196604 0.0052 0.9843 23 0.200447 0.0413364 0.0048 0.9891 24 0.1591107 0.0639509 0.0038 0.9929 25 0.0951598 0.0202988 0.0023 0.9951 26 0.074861 0.0333174 0.0018 0.9969 27 0.0415436 0.0090616 0.001 0.9979 28 0.032482 0.0026001 0.0008 0.9987 29 0.0298819 0.0206345 0.0007 0.9994 30 0.0092474 0.00288 0.0002 0.9996 31 0.0063674 0.0021473 0.0002 0.9998 32 0.0042201 0.0011847 0.0001 0.9999 33 0.0030354 0.0007972 0.0001 0.9999 34 0.0022382 0.0018641 0.0001 1 35 0.000374 0.0002114 0 1 36 0.0001626 0.0000346 0 1
51 Table 5 - Continued Component Eigenvalue Difference Proportion Cumulative 37 0.0001281 0.0000824 0 1 38 0.0000456 0.0000456 0 1 39 0 0 0 1 40 0 0 0 1 41 0 0 0 1 42 0 0 1
14.00
12.00
10.00
� 8.00
� 6.00
4.00
2.00
0.00 0 10 20 30 40 50 Principal Component
Figure 6. Scree plot of 42 variable Principal Components Analysis
52 Table 6
Eigenvector values obtained fromPrincipal Components Analysis of 42 variables measured at 10 meter scale
Variable Prinl Prin2 Prin3 Prin4 Prin5 Prin6 Prin7 Prin8 NED -0.080506 -0.113918 0.310568 -0.259745 -0.088622 -0.074316 0.165083 0.138626 SLOPE -0.018173 -0.047926 0.208472 -0.141321 -0.039249 -0.147811 0.154095 -0.451117 COSASP -0.039445 -0.044299 -0.030352 -0.264675 -0.084161 0.002425 0.331365 -0.137343 SINASP -0.00186 0.078474 0.00652 0.233287 -0.089183 -0.241653 0.227006 -0.073456 COSDIR 0.101983 0.048272 0.055428 -0.15094 0.159647 0.005714 0.188565 -0.340976 SINDIR -0.011518 0.081139 0.124339 0.171511 -0.056239 -0.206424 -0.046914 0.008729 DISTSH -0.010148 -0.189883 0.203254 -0.220041 0.125961 0.170363 0.288714 -0.063228 GROPPT -0.134429 0.050129 0.066852 0.056676 0.155626 0.129928 -0.036882 -0.111776 DECPPT -0.138239 0.282481 0.227384 -0.075906 0.044772 -0.161629 -0.088709 0.065427 JANPPT -0.166515 0.277492 0.198122 -0.109604 0.070986 -0.099771 -0.074279 0.016791 FEBPPT -0.105446 0.325719 0.138919 -0.089833 0.100507 -0.234046 0.031496 0.090051 MARPPT -0.011793 0.322652 -0.189746 -0.090323 0.130024 0.144684 0.21027 0.092653 APRPPT 0.12589 0.222646 -0.214586 0.103998 0.101887 0.35029 0.101169 -0.076535 MAYPPT 0.051751 0.302206 -0.10167 -0.20908 0.031588 -0.046476 0.111555 0.152106 JUNPPT -0.184161 0.027483 -0.024449 0.228688 0.07224 0.035681 0.344623 0.11 3315 JULPPT -0.089432 0.062907 -0.01769 0.119139 -0.019355 -0.163074 0.302422 0.368208 AUGPPT -0.002944 0.148946 0.136585 0.218903 0.10656 -0.072765 0.178583 0.002103 SEPPPT -0.100682 0.189382 0.147869 0.18204 0.00648 0.432636 0.057727 0.043886 OCTPPT -0.186703 0.191555 0.193047 0.020856 0.042871 0.188666 -0.18611 -0.100952 NOVPPT -0.220331 0.193587 -0.061117 0.013796 0.109452 0.077846 0.017458 -0.033207 v-. CUMGDA 0.269991 0.001794 0.09995 0.090322 0.036737 -0.025852 0.057346 0.037878 Table 6 - Continued Variable Prinl Prin2 Prin3 Prin4 Prin5 Prin6 Prin7 Prin8 CUMGDM 0.271835 0.001062 0.080209 0.085978 0.035384 -0.023416 0.062328 0.040712 APRGDD 0.209283 0.010132 0.317353 0.128291 0.047321 -0.050714 -0.009467 -0.000885 MAYGDD 0.2195 -0.053455 0.214383 0.21737 0.068074 -0.058245 0.0497 -0.010501 JUNGDD 0.259673 -0.051688 0.086571 0.151194 0.049962 -0.020621 0.091288 0.039549 JULGDD 0.268282 -0.012365 0.022007 0.103876 0.02812 -0.007035 0.1053 0.072911 AUGGDD 0.273622 0.06451 -0.001098 -0.01749 0.004712 -0.010251 0.054082 0.061255 SEPGDD 0.263918 0.080411 0.06756 -0.081026 0.012261 -0.018846 -0.029682 0.020064 CUMWIN 0.207925 0.118815 0.070032 -0.227475 0.047257 0.159805 0.007939 0.153336 SPRFST -0.221553 -0.131546 0.221284 0.04573 -0.01687 -0.10085 -0.135856 -0.057692 FALFST 0.206425 0.192495 -0.098829 -0.16775 -0.008064 0.055738 -0.089123 -0.031088 CODE_4 0.170298 0.216555 0.101841 -0.053453 0.072905 -0.054919 -0.198951 -0.172226 CODE_6 -0.134147 -0.Q19252 -0.210728 0.142883 -0.32607 -0.083596 0.225461 -0.018448 CODE12 0.024845 -0.100005 0.116329 0.219115 -0.040581 0.248136 -0.178347 0.148287 CODE13 -0.03121 -0.056988 0.250575 -0.209951 -0.079201 0.072029 0.117701 0.408149 CODE14 -0.037246 -0.08848 0.215469 0.096146 0.237854 0.206508 0.220695 -0.182813 CODE15 -0.000375 -0.218978 -0.16255 -0.245309 0.265335 0.005433 -0.086046 0.074012 CODE17 -0.07589 -0.001497 0.071511 0.143728 0.254242 -0.072538 -0.208892 0.156368 QUAT -0.091048 -0.27668 0.06621 -0.091483 0.303805 0.137621 0.003199 0.242947 PCTGRA -0.041587 -0.065249 -0.149601 0.147197 0.433858 -0.138402 0.07087 -0.037742 PH 0.161664 -0.007563 -0.072377 -0.10155 0.039639 -0.192552 -0.056417 0.153399 PCTSAN 0.036356 0.04734 0.171435 0.001349 -0.47096 0.283256 -0.008481 0.01852
VI � Table 6 - Continued Variable Prin9 PrinlO Prinll Prin12 Prin13 Prin14 Prin15 Prin16 NED 0.105301 -0.219431 0.03922 -0.230788 0.043853 0.101382 -0.050192 0.012168 SLOPE 0.199068 -0.07964 0.364465 -0.006908 -0.178777 0.089765 0.047208 0.145614 COSASP 0.08795 0.38061 -0.197646 -0.10076 0.065753 0.14465 0.246238 -0.219095 SINASP 0.216301 -0.102189 0.241993 0.080682 0.347775 -0.275334 0.400201 0.195165 COSDIR -0.034041 -0.074145 0.149223 0.261905 0.183995 0.162415 0.035853 -0.620185 SINDIR -0.239347 -0.256598 -0.284612 0.062398 0.534748 0.332476 -0.143049 0.012333 DISTSH -0.231819 -0.182952 -0.090448 -0.143477 -0.102952 -0.094304 0.133698 0.223205 GROPPT 0.021806 0.242813 0.251096 0.384084 -0.124479 0.103011 -0.409422 0.16022 DECPPT -0.078699 0.089167 -0.090153 0.028289 -0.092125 -0.108567 0.058848 -0.087773 JANPPT -0.025225 0.160774 0.01899 0.050725 -0.047798 -0.032497 0.000586 0.060773 FEBPPT 0.01406 0.161155 -0.019188 0.022257 -0.056966 -0.090564 -0.024614 -0.038283 MARPPT 0.036327 0.007917 0.052831 -0.142458 0.060699 0.259369 -0.075339 0.176835 APRPPT 0.026309 -0.097784 -0.068972 -0.018175 -0.007017 0.044522 0.127538 -0.013053 MAYPPT -0.133504 -0.11797 0.224363 -0.110584 -0.003798 -0.017268 0.065024 0.224084 JUNPPT -0.037972 0.049914 0.159727 -0.070207 0.103898 0.131712 -0.17412 -0.035625 JULPPT -0.021968 -0.210436 0.079392 0.409711 -0.187815 -0.287488 -0.012203 -0.236207 AUGPPT -0.502903 -0.017009 0.159017 -0.300891 -0.139335 0.151153 -0.025042 -0.102198 SEPPPT 0.184764 -0.047664 -0.063451 0.054998 0.114427 -0.035701 0.218264 0.001172 OCTPPT 0.075217 0.125419 -0.000592 0.067899 0.134914 -0.007569 0.140285 0.044374 NOVPPT 0.156415 0.063513 -0.023827 -0.038095 0.170903 0.076942 -0.050639 0.018982 CUMGDA 0.067007 0.07279 -0.007126 0.030004 -0.021127 0.05198 -0.022925 0.043412 CUMGDM 0.069588 0.060126 -0.00753 0.039218 -0.024087 0.052058 -0.022005 0.045982 APRGDD 0.026994 0.211007 -0.001349 -0.08255 0.016703 0.043542 -0.030417 0.00696 MAYGDD 0.050276 0.172944 0.010712 0.037157 -0.003739 0.151113 -0.064293 0.135227 JUNGDD 0.070097 0.055726 0.010481 0.058464 -0.002096 0.075626 0.00483 0.076419 Vl Vl Table 6 - Continued Variable Prin9 PrinlO Prinl 1 Prin12 Prin13 Prin14 Prin15 Prin16 JULGDD 0.082863 0.004958 -0.000827 0.114215 -0.02704 0.025576 0.022567 0.044705 AUGGDD 0.090586 0.017138 -0.02553 0.029599 -0.049776 0.032394 -0.075093 0.002054 SEPGDD 0.029367 0.046978 -0.038606 -0.084763 -0.037144 -0.042844 -0.011662 -0.054505 CUMWIN -0.016466 0.092705 0.137192 -0.01294 0.115882 -0.112413 0.00864 0.129527 SPRFST 0.042545 0.108976 -0.018243 -0.04562 0.125313 0.009055 0.072052 0.097912 FALFST -0.002835 0.053068 -0.123261 0.024611 -0.064315 -0.019827 0.03832 -0.111744 CODE_4 0.047278 -0.297519 -0.00505 -0.049814 0.036344 -0.131164 -0.089298 -0.030423 CODE_6 -0.016772 0.291959 -0.069681 -0.026863 -0.134345 0.122084 0.028553 0.063242 CODE12 -0.050683 0.151082 0.414803 -0.367518 0.121212 -0.207066 0.036011 -0.346982 CODE13 0.348477 -0.015246 -0.125971 -0.009147 0.079034 0.076604 -0.190819 -0.13045 CODE14 -0.238076 0.041904 -0.369942 0.139088 -0.031649 -0.346018 -0.01382 0.102222 CODE15 -0.131547 -0.001761 0.262318 0.186603 0.25843 0.077738 0.00342 0.127752 CODE17 0.079263 -0.167149 -0.024,522 0.065015 -0.386187 0.437224 0.496046 -0.053121 QUAT -0.059971 0.058786 0.078244 0.139869 0.066926 0.101931 0.142991 0.005373 PCTGRA 0.359841 -0.057466 -0.129776 -0.221139 0.04916 -0.045866 -0.082852 0.039636 PH -0.230443 0.332879 -0.009556 0.124125 0.218788 -0.026604 0.300381 0.082301 PCTSAN -0.087414 -0.132952 0.078114 0.248319 -0.003012 0.2105 0.081109 0.125007
°'VI Table 6 - Continued Variable Prin17 Prin18 Prin19 Prin20 Prin21 Prin22 Prin23 Prin24 NED 0.093553 0.035254 -0.233463 0.225031 0.388193 0.132028 0.088396 0.414201 SLOPE -0.007852 0.269502 0.041385 -0.300563 -0.156598 0.461062 -0.067758 -0.057388 COSASP 0.470627 -0.099521 0.270486 -0.247111 0.180028 -0.179708 -0.063106 -0.074715 SINASP 0.036112 -0.326102 0.250077 0.292857 -0.084862 -0.005826 0.02268 0.14703 COSDIR -0.210335 -0.009859 -0.265584 0.172313 -0.171292 -0.202692 0.129292 0.027998 SINDIR 0.329956 0.260624 0.080475 0.060213 -0.183259 0.170472 -0.066712 -0.103346 DISTSH 0.040608 0.022138 -0.095416 0.358357 -0.008009 -0.049643 -0.08915 -0.505454 GROPPT 0.464342 -0.254748 -0.054728 0.26337 -0.014173 0.044832 0.075423 0.022251 DECPPT -0.070106 0.070648 0.184138 0.061838 0.040042 0.106188 0.23351 -0.092115 JANPPT 0.021046 0.075969 0.04443 0.026476 -0.05597 -0.074291 0.096551 -0.006311 FEBPPT -0.089997 0.144725 0.103136 -0.003815 -0.091165 -0.061416 -0.08245 -0.053701 MARPPT -0.106673 -0.090001 0.008312 -0.129967 -0.089169 0.084585 0.10789 -0.068223 APRPPT -0.038251 -0.040038 0.134726 0.036038 -0.081475 0.29071 0.0611 -0.106067 MAYPPT 0.175104 0.210466 -0.165786 -0.106645 -0.239756 -0.379558 0.11216 0.215155 JUNPPT -0.108343 0.008726 -0.059885 -0.124978 0.118425 -0.059934 -0.524537 0.115693 JULPPT 0.109183 0.179437 -0.014425 -0.133144 0.195301 0.076302 -0.057615 -0.206772 AUGPPT -0.084019 -0.293969 0.150154 -0.043199 0.14991 0.100219 0.259893 0.040327 SEPPPT 0.057361 0.165628 -0.134586 -0.03332 0.202492 -0.022209 0.244222 -0.10632 OCTPPT -0.071924 0.071322 -0.143647 0.058861 0.23748 0.04072 -0.101529 0.01698 NOVPPT -0.24123 0.028815 -0.001111 0.059679 0.111968 0.042022 -0.266565 -0.006662 CUMGDA -0.031078 0.068265 0.025912 0.01538 0.035111 -0.04688 0.006943 -0.006539 CUMGDM -0.020737 0.073325 0.023561 0.012325 0.028879 -0.041584 0.018754 -0.001334 APRGDD -0.148042 -0.001039 0.049773 0.049032 0.103239 -0.102304 -0.132788 -0.066728 MAYGDD -0.046214 0.047549 -0.008021 -0.014661 0.096384 -0.069711 0.084557 -0.067316 JUNGDD -0.033807 0.053435 -0.033818 -0.062378 0.042714 -0.045661 0.056472 -0.077506 VI --....l Table 6 - Continued Variable Prin17 Prin18 Prin19 Prin20 Prin21 Prin22 Prin23 Prin24 JULGDD 0.037818 0.099208 -0.035422 -0.049709 0.042235 -0.012427 0.078697 -0.034038 AUGGDD 0.005769 0.053123 0.04893 0.071365 0.00167 -0.018556 -0.022647 0.106085 SEPGDD -0.07476 0.090997 0.177128 0.157188 -0.05817 -0.056292 -0.141988 0.102316 CUMWIN 0.090918 0.00171 -0.106725 0.079847 -0.154364 -0.035637 -0.274037 -0.089423 SPRFST -0.128252 0.045492 -0.014967 -0.119469 -0.126685 -0.216568 0.086669 -0.123914 FALFST 0.076077 0.190844 0.165623 0.226442 0.162512 0.279398 -0.056005 0.239298 CODE_4 0.123393 -0.260024 -0.049982 -0.228315 0.191432 -0.089736 -0.137381 -0.112408 CODE_6 -0.096544 0.24102 -0.140709 0.308375 -0.098194 0.024285 0.108494 -0.001098 CODE12 0.264577 0.202334 0.008418 -0.010802 -0.175679 0.100927 0.003298 -0.021399 CODE13 -0.119776 -0.322912 0.054097 -0.060431 -0.328514 0.192691 0.114942 -0.070041 CODE14 -0.005875 0.022052 0.002628 -0.186575 -0.220053 0.042989 -0.056819 0.443073 CODE15 -0.146543 0.157656 0.321798 -0.024551 0.292981 -0.048504 0.113973 -0.04998 CODE17 0.147729 -0.077699 -0.049311 0.07529 -0.132552 -0.044832 -0.235654 0.0891 QUAT -0.069683 0.094645 0.234787 -0.017414 -0.114977 0.070779 0.04766 0.16084 PCTGRA 0.134797 0.14171 -0.151606 -0.088062 0.046721 -0.071181 0.300987 0.030595 PH -0.006872 -0.181091 -0.517146 -0.197643 0.056885 0.360162 0.026278 -0.018938 PCTSAN -0.065087 0.001787 0.076432 -0.230981 0.038035 -0.17369 0.111923 0.130564
VI 00 Table 6 - Continued Variable Prin25 Prin26 Prin27 Prin28 Prin29 Prin30 Prin31 Prin32 NED 0.169669 0.225325 -0.056395 -0.240132 -0.023925 -0.023874 -0.096599 0.053608 SLOPE 0.021529 -0.098522 -0.066572 0.07866 0.050381 0.059493 -0.006783 -0.041368 COSASP 0.09192 0.035087 -0.018087 0.015926 -0.03107 0.013051 0.042539 0.003385 SINASP -0.072154 -0.040237 0.05596 -0.005416 -0.054283 -0.011479 -0.001179 0.000191 COSDIR -0.022403 -0.021226 0.038265 -0.05983 -0.017625 -0.02235 0.014984 -0.017245 SINDIR 0.058379 -0.052723 -0.021996 0.043123 -0.003341 0.027375 -0.029605 0.017671 DISTSH -0.227569 0.097303 0.208407 0.128336 -0.037747 0.047381 0.037015 0.052655 GROPPT 0.004767 0.12239 0.028971 0.047311 0.06921 0.072617 -0.03518 -0.046514 DECPPT 0.016486 -0.010383 0.067841 -0.328694 0.083983 0.156728 0.232021 -0.098541 JANPPT -0.173625 -0.07983 0.003882 -0.122708 0.058183 0.066799 0.049088 0.419287 FEBPPT -0.080344 0.290726 0.086793 0.07885 0.059215 -0.28647 -0.561314 0.015727 MARPPT -0.103105 -0.148054 0.112712 -0.276899 -0.500207 0.114025 -0.054257 0.104388 APRPPT 0.273357 0.475339 -0.061969 -0.093458 0.328795 -0.110947 0.086027 0.037831 MAYPPT 0.024474 0.159801 -0.188591 0.325742 -0.002837 0.013556 0.208619 -0.219207 JUNPPT -0.361448 -0.015686 -0.031006 -0.099525 0.339666 -0.043594 0.150574 0.094768 JULPPT 0.192278 -0.026423 0.08535 0.025165 -0.119414 0.075522 0.141502 -0.065152 AUGPPT 0.138857 -0.171198 -0.021498 0.191749 0.121021 -0.1096 0.030593 -0.009005 SEPPPT -0.217891 -0.19939 -0.380452 0.003205 0.174241 0.184399 -0.271887 -0.166731 OCTPPT 0.226931 -0.153977 0.01621 0.38806 -0.157436 -0.213158 0.338881 0.315654 NOVPPT 0.217846 0.269074 0.182476 0.110866 -0.224024 0.218029 0.016601 -0.222361 CUMGDA 0.006477 0.054716 -0.025035 0.003022 -0.028258 0.028988 0.04259 0.083199 CUMGDM -0.006607 0.068905 -0.028997 -0.014627 -0.027843 0.024629 0.069398 0.111322 APRGDD 0.159218 -0.119847 0.025125 0.209873 -0.029052 0.07599 -0.27845 -0.259146 MAYGDD -0.098087 0.116916 -0.00543 -0.166795 -0.163498 -0.000328 0.284172 -0.409436
Vl JUNGDD 0.041572 0.089126 -0.03909 -0.023893 -0.118303 -0.233124 -0.007356 0.222813 \0 Table 6 - Continued Variable Prin25 Prin26 Prin27 Prin28 Prin29 Prin30 Prin31 Prin32 JULGDD -0.022559 0.117798 -0.076442 0.003124 -0.078024 -0.278942 -0.025501 0.251839 AUGGDD -0.053488 -0.040208 -0.045285 0.017156 0.021922 0.319002 0.023549 0.253644 SEPGDD 0.095367 0.018198 0.047529 0.104552 0.256699 0.484602 0.098435 0.142297 CUMWIN 0.378187 -0.415148 0.059799 -0.368281 0.206553 -0.259979 -0.007112 -0.13683 SPRFST -0.033045 0.236245 -0.062388 -0.216201 0.152043 -0.122085 0.286597 -0.044642 FALFST -0.446738 -0.08503 0.157679 0.091885 -0.018478 -0.314139 0.190022 -0.269578 CODE_4 -0.091179 0.074409 -0.002511 -0.046866 -0.008626 0.011671 0.013309 -0.004781 CODE_6 0.113697 -0.089954 -0.00241 -0.001667 0.046319 -0.018468 -0.003913 0.004485 CODE12 -0.074445 0.152925 0.180402 -0.05041 -0.196853 0.05771 -0.015847 0.069838 CODE13 -0.084466 -0.033679 -0.05564 0.280802 0.068924 -0.081943 0.135196 -0.049765 CODE14 0.050376 -0.000427 0.015638 -0.069316 -0.146578 0.026496 -0.028684 -0.007709 CODE15 0.007419 -0.005086 -0.055624 0.008845 0.075298 0.011798 -0.060676 0.015517 CODE17 0.008538 -0.026346 0.027633 -0.06493 -0.030027 0.021026 -0.029598 -0.024625 QUAT 0.009658 -0.014008 -0.004666 0.049489 -0.025936 0.007152 -0.026103 -0.00186 PCTGRA 0.049554 -0.167455 0.495111 0.085897 0.26842 -0.027436 0.012835 -0.002675 PH -0.111821 0.12232 0.110615 0.058043 0.123175 0.183364 -0.039735 -0.005839 PCTSAN -0.025305 0.038324 0.59004 0.009585 0.145462 0.015972 -0.081 0.005843
0\ 0 Table 6 - Continued Variable Prin33 Prin34 Prin35 Prin36 Prin37 Prin38 Prin39 Prin40 NED 0.074906 -0.066873 -0.021662 0.030275 0.000894 0.002592 0 0 SLOPE -0.014054 0.048284 0.007639 -0.006778 0.003112 -0.000743 0 0 COSASP -0.026144 0.015238 0.001359 0.004903 0.001919 0.000889 0 0 SINASP 0.002305 -0.017887 0.006773 0.005339 -0.002428 0.001097 0 0 COSDIR 0.005056 -0.023635 -0.001754 -0.000251 -0.001157 -0.000928 0 0 SINDIR 0.004035 -0.004902 -0.002542 0.004009 0.00132 -0.000481 0 0 DISTSH -0.045137 0.009143 0.039765 -0.017653 0.009438 -0.001969 0 0 GROPPT 0.118964 0.070752 0.087266 -0.062246 -0.048859 0.039108 0 0 DECPPT -0.273495 -0.06446 0.276653 -0.454231 -0.202524 0.119558 0.000001 0 JANPPT -0.041412 -0.115491 -0.594042 0.054176 0.388555 -0.018965 -0.000001 -0.000001 FEBPPT -0.063578 0.011589 0.169126 0.297322 -0.214782 -0.080606 0 0 MARPPT 0.344145 -0.11237 0.127921 0.028352 -0.113186 -0.026951 0 0 APRPPT 0.046115 -0.311632 -0.049719 0.046428 0.139086 0.019362 0 0 MAYPPT -0.046353 -0.06945 0.013583 -0.127684 0.020642 0.080293 0 0 JUNPPT -0.061893 -0.127525 0.066949 -0.142329 -0.080636 0.032414 0 0 JULPPT 0.232555 -0.022651 -0.033885 0.140114 0.096596 0.010919 O· 0 AUGPPT 0.008265 0.288496 -0.008714 0.125121 0.069663 -0.058108 0 0 SEPPPT 0.020599 0.18666 -0.015932 0.047964 -0.050137 0.015953 0 0 OCTPPT -0.014796 -0.182459 0.191534 0.129039 -0.192576 -0.069833 0 0 NOVPPT -0.192012 0.483719 -0.172396 -0.123284 0.212729 0.01141 0 0 CUMGDA -0.010483 0.062487 0.00745 -0.015659 -0.020537 -0.003079 -0.925779 0 CUMGDM -0.03606 0.102546 0.005358 0.010661 -0.048575 -0.010233 0.159382 -0.902941 APRGDD 0.291452 -0.417053 0.030963 -0.32253 0.311778 0.081444 0.07347 0.000001 MAYGDD -0.257802 -0.19542 -0.197859 0.381815 -0.136591 -0.228702 0.13554 0.17395 JUNGDD -0.039535 0.185838 -0.112626 -0.053426 -0.131936 0.750862 0.172534 0.221434 Table 6 - Continued Variable Prin33 Prin34 Prin35 Prin36 Prin37 Prin38 Prin39 Prin40 JULGDD 0.025698 0.234928 0.001196 -0.478622 0.022261 -0.565404 0.171568 0.220189 AUGGDD -0.259987 0.054505 0.540494 0.273731 0.46259 0.011723 0.13253 0.170091 SEPGDD 0.356237 0.146053 -0.167374 0.082889 -0.445109 -0.07903 0.130363 0.167307 CUMWIN -0.073813 0.170765 -0.015482 0.086915 0.045159 -0.040107 0 0 SPRFST 0.513642 0.249151 0.254584 0.127372 0.219481 0.003586 0 0.000001 FALFST 0.225834 0.129952 -0.008087 0.013492 0.148675 0.096395 0 0 CODE_4 0.014585 0.009306 -0.000923 -0.000198 -0.00164 0.002189 0 0 CODE_6 0.013734 0.001758 0.002638 0.001341 0.000996 -0.000852 0 0 CODE12 -0.031713 -0.010373 0.014602 -0.006081 0.010842 -0.001992 0 0 CODE13 -0.055491 0.010653 -0.044677 -0.005923 -0.006544 0.001702 0 0 CODE14 0.016026 0.015498 0.009205 -0.002603 -0.000707 0.00214 0 0 CODE15 -0.016148 -0.041704 0.005891 0.007388 -0.000803 -0.003727 0 0 CODE17 0.006833 0.025903 0.014093 -0.004184 0.003901 -0.000165 0 0 QUAT -0.030308 -0.014817 0.001275 -0.000364 0.001037 -0.002259 0 0 PCTGRA -0.009479 -0.024572 0.006914 0.002015 0.009958 -0.06619 0 0 PH 0.028757 0.013242 0.004244 -0.004435 -0.001472 0.006334 O· 0 PCTSAN -0.042546 0.001545 0.007807 -0.011316 0.000929 -0.00237 0 0
0\ N Table 6 - Continued Variable Prin41 Prin42 NED 0 0 SLOPE 0 0 COSASP 0 0 SINASP 0 0 COSDIR 0 0 SINDIR 0 0 DISTSH 0 0 GROPPT 0 0 DECPPT 0 0 JANPPT 0 0 FEBPPT 0 0 MARPPT 0 0 APRPPT 0 0 MAYPPT 0 0 JUNPPT 0 0 JULPPT 0 0 AUGPPT 0 0 SEPPPT 0 0 OCTPPT 0 0 NOVPPT 0 0 CUMGDA 0 0 CUMGDM 0 0 APRGDD 0 0 MAYGDD 0 0 JUNGDD 0 0 uJ°' Table 6 - Continued Variable Prin41 Prin42 JULGDD 0 0 AUGGDD 0 0 SEPGDD 0 0 CUMWIN 0 0 SPRFST 0 0 FALFST 0 0 CODE_4 0.328425 0.611808 CODE_6 0.13193 0.614814 CODE12 -0.110309 0.14667 CODE13 -0.188061 0.205935 CODE14 -0.22124 0.205935 CODE15 -0.427702 0.346197 CODE17 -0.228461 0.14667 QUAT 0.736971 0 PCTGRA 0 0 PH 0 0 PCTSAN 0 0 Highest eigenvector value within the component
Within 0.1 of the highest eigenvector value within the component
i aspect and growing season precipitation either alone or in conjunction with other
variables (PC 15, 17, 18, 20).
All 42 of the variables load heavily on at least one of the first 11 components,
except growing season precipitation and exposed bedrock. End moraines of coarse textured till does not load heavily until component 11. Dune sand, lacustrine sand and
gravel, and pH do not load heavily on a component until component 10 (Table 6).
Both the z-tests and the PCA of the 42 variables represented at 10m resoluti©n
suggested that mean April, June and July precipitation, cumulative mean growing season
precipitation, elevation, distance to shore, dune sand as the quaternarybedrock type and
percent sand were important variables for describing suitable habitat (Tables 3 and 6).
The z-test results also demonstrated significance for November precipitation and the
quaternary layer as a whole (Table 3), but those two habitat variables did not correlate heavily with any of the middle components (PC 12-27) (Table 6). Lake Huron tansy was found at lower elevations, closer to the shoreline and on sandier soils compared to the
study area as a whole. The test populations on average experienced higher precipitation in April and overall throughout the growing season, but less precipitation in June, Jl!lly
and November than the study area as a whole.
Several variables that were not significantfor the z-test did strongly correlate with the middle components: forexample, pH, percent gravel, winter temperature. The
absence of significance in these variables in z-test results may be due to the fact that
principal components analysis allows for interactions among variables.
An effortwas made to understand relationships described by components 12 - 27
based on the variable(s) that correlated strongly with each. Components 13, 16, 19, and
65 · 23 each had only one correlated variable: distance to shore, direction to shore, pH, and
June precipitation, respectively (Table 6). Component 14 was represented by two
quaternaryclasses (end moraines of coarse textured till and exposed bedrock) and
component 27 was represented by two soil parameters (percent gravel and percent sand).
The remaining 10 components showed interactions that in many cases defieddiscrete
description. Component 12 represented an interaction among growing season
precipitation, July precipitation and medium textured till; component 15 represented the
interaction among aspect, growing season precipitation and exposed bedrock; and
component 18 represented the interaction among 8 habitat variables. The majority of the
middle components (12 - 27) are represented by interactions among disparate variables,
aspect with precipitation or precipitation with bedrock. The apparent significant
interaction among the differentvariables supports the use of partitioned Mahalanobis
distance as described in the literature for modeling suitable Lake Huron tansy habitat.
Habitat Models
The variables that were significantin PCA and z-tests were included in the 11
variables and seven variables models. Both PCA and the z-test found April precipitation,
June precipitation, July precipitation, growing season precipitation, dune sand as a
quaternarylayer, percent sand, distance to the shore, and elevation to be important habitat
variables to describe habitat use by the Lake Huron tansy. Because April, June, and July
precipitation were included in growing season precipitation, they were not included
individually in the 11 variables models. The use of both the dune sand layer and the
percent sand layer seemed redundant, so percent sand was included in the 11 variables
66 models because it appeared to be more informative; the percent sand layer was a
quantitative layer. The slope, cumulative growing degree days (May - September) and
sine and cosine of aspect were included in the 11 variable models because preliminary
research (results not shown) had indicated that those layers were useful. Aspect and
growing season precipitation each correlated with at least one of the middle components in the initial PCA (Table 6). Research indicated that Lake Huron tansy is a calciphile
(Ostlie 1991) and that the seeds are cold stratified (Nichols 1934), so pH and cumulative
winter temperature were included as habitat variables in the 11 variable models. Percent
gravel was included because some populations were found on medium to coarse textured
till and personal observation indicated that the species is often found in a gravelly sand
mix. All three of the variable previously mentioned also correlated with at least one of
the middle components in the initial PCA (Table 6).
Eleven Vriables
PCA of the eleven variables (NED, SLOPE, COSASP, SIN ASP, DISTSH,
GROPPT, CUMGDM, CUMWIN, PCTSAN, PCTGRA, PH) measured at 10 meter
resolution resulted in seven principal components with A< 1 (Table 7), which corresponds
with the elbow in the scree plot (Fig. 7) at Component 5, at a value of 0.92144443 (Table
7). Components 5 - 11 explained 33.23% of the variation in the data (Table 7). The
variables that strongly correlated with the components having 'A,< 1 were aspect, growing
season precipitation, aspect and slope, pH, elevation and distance to shore, winter
temperature and cumulative growing degree days and percent gravel with percent sand
(Table 8). The variables that loaded heaviest on the components with "A�1 were
cumulative growing degree days with winter temperature and pH, elevation with distance
67 to shore, percent sand and percent gravel, percent sand with percent gravel, and aspect
(Table 8).
Table 7
Eigenvalues obtained for 11 variable model in SAS
Com2onent Eigenvalue Difference Pro2ortion Cumulative 1 2.58782335 0.52057893 0.2353 0.2353 2 2.06724441 0.53819651 0.1879 0.4232 3 1.52904790 0.36819647 0.1390 0.5622 4 1.16085143 0.23940700 0.1055 0.6677 5 0.92144443 0.06418193 0.0838 0.7515 6 0.85726250 0.26674280 0.0779 0.8294 7 0.59051970 0.11638274 0.0537 0.8831 8 0.47413696 0.05619685 0.0431 0.9262 9 0.41794011 0.15316356 0.0380 0.9642 10 0.26477655 0.13582391 0.0241 0.9883 11 0.12895264 0.0117 1.0000
Partitioned Mahalanobis Distance (k = 7) (Model A)
Seven principal components had eigenvalues less than one (Table 7) which corresponded to the elbow in the scree plot (Fig. 7). Partitioned Mahalanobis distance was, therefore, calculated based on the last seven principal components. The distance values for the study area ranged from 77 .663 to 4,262,033 (mean= 934,342.560; SD =
860,662.941). The test location (n = 71) distances ranged from1,407.007 to
1,033,401.438 (mean= 148,741.969; SD= 208,964.448) while the null model (n= 100) ranged from1,924.041 to 2,940,397.25 (mean= 991,499.456; SD= 894,160.376). The model was consistent and moderately better than random at predicting suitable habitat
(Fig. 8). The threshold value used to determine habitat suitability was D2 :S500,000, which resulted in 43.66% of the study area being classified suitable (Fig. 9; Table 9),
68 2.00
Q)
1.50 ·-Q) 1.00
0 1 2 3 4 5 6 7 8 9 10 11 12 Principal Component
Figure 7. Scree plot of 11 variable Principal Components Analysis
92.96% of the test populations and 100% of the validation locations being correctly classified (Table 9).
Partitioned Mahalanobis Distance (k = 11) (Model B)
The partitioned Mahalanobis distance that used all 11 principal components resulted in distance values that ranged from 117.374 to 4,955,126.5 (mean=
1,079,569.042; SD= 1,003,053.997)for the study area. The distance values associated with test population locations ranged from 1,579.777 to 1,169,682 (mean= 162,510.727;
SD= 228,146.923) and ranged from2,144.895 to 3,408,138.25 (mean= 1,148,796.444;
SD= 1,044,284.707) forthe null model. The model was both consistent and better than
69 Table8 Eigenvector values obtained fromPrincipal Components Analysis of 11 variables measured at 10 meter scale
Abbreviated Variable PC 1 PC2 PC3 PC4 PCS PC6 PC7 PCS NED -0.226324 0.477619 0.209476 0.058500 -0.194909 -0.171324 0.282436 -0.325631 SLOPE -0.183776 0.325757 0.110408 0.515701 -0.045213 0.434563 -0.461678 -0.330572 COSASP -0.108608 0.260961 0.282240 -0.012411 0.822141 -0.101153 -0.196780 0.307150 SINASP -0.002735 -0.148841 -0.116420 0.789552 0.150781 -0.150029 0.511028 0.167778 DISTSH -0.107781 0.430538 0.406504 -0.123939 -0.258367 -0.008009 0.332011 0.337441 CUMGDM 0.507472 -0.009810 0.169336 0.207177 -0.192761 0.223423 -0.189364 0.282176 GROPPT -0.318198 -0.081146 -0.201992 -0.171273 0.186472 0.756478 0.381506 0.042413 CUMWIN 0.488259 0.160896 0.168629 -0.042057 -0.022898 0.347172 0.163479 0.193226 PCTGRA -0.234425 -0.430917 0.464531 0.112908 -0.157812 0.034802 -0.124021 0.165956 PH 0.460773 -0.055983 0.239928 -0.053565 0.311349 0.013737 0.256214 -0.606905 PCTSAN 0.164749 0.410796 -0.560541 0.045618 -0.016299 -0.069952 -0.088446 0.183566
--..) 0 Table8 - Continued Abbreviated Variable PC9 PC 10 PC ll NED 0.615222 0.164651 -0.120832 SLOPE -0.213377 -0.132939 0.073863 COSASP 0.121208 0.064268 -0.047504 SINASP -0.047599 -0.061564 -0.017181 DISTSH -0.564094 0.081259 0.081811 CUMGDM 0.131532 0.531406 -0.410523 GROPPT 0.074023 0.245792 -0.041953 CUMWIN 0.324179 -0.602181 0.229526 PCTGRA 0.241992 0.219956 0.595684 PH -0.223959 0.277650 0.256451 PCTSAN 0.064983 0.331353 0.571945 Highest eigenvector value within the component Within 0.1 of the highest eigenvector value within the component 1.2
1
0.8 --+-- Random 0.6 --Test
- -Ir - Validation � 0.4
0.2
0 0 1000000 2000000 3000000 4000000 Partitioned Mahalanobis Distance
Figure 8. Cumulative frequencygraph for D2(k=7) for 10 meter, 11 variable mode] random at predicting suitable tansy habitat, according to the cumulative frequencygraph
(Fig. 10). A threshold value of D2 :S527,879.8125 was chosen based on the results of the cumulative frequencygraph to distinguish suitable habitat. Slightly less than 42% of the study area was classifiedas suitable (Fig. 11; Table 9). As with the D2ck=7) model,
92.96% of the test locations and 100% of the validation locations were correctly classified (Table 9). The percentage of predicted suitable land was very similar for
Models A and B.
Seven Variables
The Mahalanobis distance extension (Jenness 2003) is limited to eight variables.
Results obtained fromthe 11 variable models informed the choice of variables forthe seven variable models. Slope, elevation, aspect (cosine and sine) and distance to shore were kept. The predominance of correlation of interpolated layers to the components
72 :-11'11rt,✓ cA.l:;:, �, ·IJ <. Lake Huron Tansy Habitat , Suitability based on D2(k=7) value of 500,000
- Unsulable - Suitabe .. s:i
I N �
O ,s ,o "'""" i + J
Figure 9. Suitable habitat for Lake Huron tansy based on D\k=7) :'.S 500,000 using the IO meter, l l variable model w--..) Table 9
Suitability data for the study area and the test populations
Percent Percent Number Percent Suitable Unsuitable Test Suitable Unsuitable Validation of Suitable Test Test Correctly Validation Validation Correctly Distance La}'.er Variables Land Po2ulations PoQulations Placed Po2ulations PoQulations Placed Model A 11 43.66 66 5 92.96 26 0 100.00 ModelB 11 41.91 66 5 92.96 26 0 100.00 ModelC 7 16.08 83 7 92.22 28 3 90.32 ModelD 7 14.06 85 5 94.44 30 1 96.77 Model E 7 13.66 85 5 94.44 29 2 93.55
-....J +'" 1.2
1
0.8 --+-- Rand0m 0.6 �Test 0.4 - -• - Validation 0.2
0 0 1000000 2000000 3000000 4000000 Partitioned Mahalanobis Distance
Figure 10. Cumulative frequency graph for D2ck=l 1) for 10 meter, 11 variable model with eigenvalues close to zero raised concernsfor the utility of interpolated layers in these models. A limited number of interpolated layers were included in the 11 variable models because preliminary work had indicated their usefulness and the chosen interpolated variables appeared to be biologically relevant. However, because the number of variables that can be included in the Mahalanobis distance extension is limited, no interpolated layers were included in the seven variables models, thus removing winter temperature, cumulative growing degree days (May- September) and growing season precipitation. Percent sand, percent gravel and pH were also not considered in the seven variable models because based on the results of the 11 variable models, it was hypothesized that those variables were not represented at a useful scale
(See Discussion). Instead, cosine and sine of direction to the shore were used beca\!lse those variables were accurately represented at 10m and 15m resolution and direction to
75 �1,r A,,f!:::, �, , 1, ·(J (_ Lake Huron Tansy Habitat , Suitability based on D2(k=11) value of 527,880
- Unsu1able -Suitable
N + 0 15 30 6 Miles
Figure l I. Suitable habitat for Lake Huron tansy based on D2ck= 11) S 527,880 using the l O meter, 11 variable model --..J 0\ shore correlated with at least one of the middle components in the initial PCA.
PCA of the seven variables (NED, SLOPE, COSASP, SINASP, DISTSH,
COSDIR, SINDIR) measured at 15 meter resolution resulted in four principal components with A< 1 (Table 10). The elbow in the scree plot was located at
Component 2 (Fig. 12), which has a value of 1.23 (Table 10). Components 4- 7, those components with an eigenvalue less than 1, explained 41.59% of the variation in the data and components 2 - 7, those components at the elbow of the scree plot and beyond,. explained 74.79% of the variation in the data (Table 10). The variables that correlated most strongly with the components that had A< 1.0 were elevation, distance from shore, direction from shore and slope (Table 11). The variables that correlated strongly with the components having A� 1.0 were aspect and slope, aspect and distance to shore with aspect and elevation.
Table 10
Eigenvalues for seven variable model obtained from SAS
Com2onent Eigenvalue Difference Pro2ortion Cumulative 1 1.76464162 0.52970649 0.2521 0.2521 2 1.23493513 0.14565423 0.1764 0.4285 3 1.0892809 0.16788562 0.1556 0.5841 4 0.92139529 0.1025936 0.1316 0.7158 5 0.81880169 0.15754172 0.117 0.8327 6 0.66125996 0.15157456 0.0945 0.9272 7 0.5096854 0.0728 1.0000
77 2 1.8 1.6
Cl) 1.4 (l) 1.2 1 .....(l) 0.8 0.6 0.4 0.2 0 1 2 3 4 5 6 7 8 Principal Component
Figure 12. Scree plot of seven variable Principal Components Analysis
Full Mahalanobis Distance (Model C)
The seven habitat variable layers and the test population locations were run in the
Mahalanobis distance extension (Jenness 2003) in ArcView 3.3. Mahalanobis distance values for the study area ranged from3.122 to 832.531 (mean= 50.534; SD= 45.701).
The mean D2 value was 6.923 (range= 3.407 - 71.861; SD= 10.432) for the test populations, and 50.444 (range= 3.673 - 145.103; SD= 42.127) for the null model locations. The cumulative frequencygraph for the test population locations and the validation locations were similar indicating model consistency. The cumulative frequencygraph forthe test locations was different fromthe cumulative frequencyof the random locations indicating that the model was better than random at findingsuitable
2 habitat (Fig. 13). A threshold value of D � 7.3 was chosen to definesuitable Lake
Huron tansy habitat based on the cumulative frequencydistribution. Using a threshold of
7 .3, 92.22% of the test populations and 90.32% of the validation populations were correctly classified in suitable habitat (Table 9), while suitable habitat was restricted to
78 Table11
Eigenvector values obtained fromPrincipal Components Analysis of seven variables measured at15 meter scale
Abbreviated Variable PC1 PC2 PC3 PC4 PC5 PC6 PC7 NED 0.162495 0.389750 -0.518913 0.539695 0.476879 0.069111 0.170171 COSASP -0.049493 -0.577609 0.413077 0.397243 0.440748 0.375385 -0.017633 SINASP 0.572883 -0.077590 0.008543 -0.349704 -0.024599 0.393746 0.622718 SLOPE 0.593446 0.197036 0.101412 -0.090587 0.072240 0.246859 -0.724120 DISTSH 0.175986 0.367101 0.534671 0.544911 -0.460897 -0.026585 0.195785 COSDIR -0.133651 0.469735 0.511408 -0.339418 0.580754 -0.174137 0.130940 SINDIR 0.491872 -0.337943 0.048251 0.091082 0.151005 -0.779297 0.055912 Highest eigenvector value within the component Within 0.1 of the highest eigenvector value within the component
'°-....} 1.2 1 ------• 0.8 ---+--- Random --Test � 0.6 - -• - Validation ...♦------..· ...... - [.I.; 0.4 ♦-♦---♦----- ·•----♦--♦- 0.2 ...,✓-- ♦-♦ 0 0 5 10 15 20 25 30 35 40 Mahalanobis Distance
Figure 13. Cumulative frequencygraph for D2 of 15 meter, seven variable data
16.08% of the study area (Fig. 14; Table 9).
Partitioned Mahalanobis Distance (k = 7) (Model D)
The partitioned Mahalanobis distance model that used all seven principle
components resulted in distance values that ranged from 2.842 to 3,172,450 (mean=
856,955.919; SD= 894,251.085) forthe study area. The mean distance for test
populations was 24,860.664 (range= 9.672- 1,160,432.5; SD= 137,966.276) and the
mean for the null model was 869,074.974 (range= 95.604 - 2871071.5; 854,992.235).
The cumulative frequency graph indicated that the model was both consistent and better
than random at predicting suitable habitat (Fig. 15). Suitable tansy habitat was
determined using the distance threshold value of D2 ::S 11,921. Using the threshold ©f
11,921, 14.06% of the study area was deemed suitable (Fig. 16; Table 9) and 94.44% of
the test populations were correctly classified,as were 96.77% of the validation
80 . ,_, I • IJ
•J , Lake Huron Tansy Habitat , Suitability based on 02 value of 7.3
- Unsutable ., -Suitable ..;J .
N '1 + 0 15 30 60Miles (
2 Figure 14. Suitable habitat for Lake Huron tansy based on D � 7.3 using the 15 meter, seven variable model 0..... 1.2
1
0.8 --+-- Random § 0.6 -Test - -.tr - Validation d: 0.4
0.2 · - ---+------+------� __ ------0 ...... 0 5000 10000 15000 20000 25000 30000 35000 40000 Partitioned Mahalanobis Distance
Figure 15. Cumulative frequencygraph forD 2ck=7) of 15 meter, seven variable model populations (Table 9).
Partitioned Mahalanobis Distance (k = 4) (Model E)
Four principle components had eigenvalues less than one (Table 10) and an ').., =
0.921 corresponded to an elbow in the scree plot (Fig. 12); therefore, partitioned
Mahalanobis distance was based on the four components with the lowest eigenvalues.
The distance values for the study area ranged from0.0386 to 2,727,167.75 (mean=
726,979.064; SD= 759,926.089). The distance values for the test population locations ranged from3.426 to 987,386 (mean= 20,840.089; SD= 116,992.125). The null model locations had a mean of 736,016.589 (range= 84.651-2,445,096; SD= 725,987.406).
The model was both consistent and better than random for predicting suitable habitat
(Fig. 17). Suitable tansy habitat was determined using a threshold distance value oii D2
S 8,742; 13.66% of the study area was considered suitable (Fig. 18; Table 9), 94.44% of
82 . ..__,,._ n.J& --� �- . ".J ' • {J � ' Lake Huron Tansy Habitat , Suitability based on D2(k=7) value of 11,921
- Unsulable .... -Suitable .. Q.
N + O 15 30 60 Miles
Figure 16. Suitable habitat for Lake Huron tansy based on D2ck=7) :S 11,921 using the 15 meter, seven variable model
00 t.,.;) 1.2 1 __ ,. 0.8 --+-- Random § 0.6 -a-Test
� 0.4 - -• - Validatiion
0.2 ....------•------♦------· .#♦--;-- 0 0 5000 10000 15000 20000 25000 30000 35000 40000 Partitioned Mahalanobis Distance
2 Figure 17. Cumulative frequency graph for D (k=4) of 15 meter, seven variable mo0�l the test populations and 93.55% of the validation populations were correctly classifie (Table 9). 84 ...�� . .__, :1 , Lake Huron Tansy Habitat , �D Suitability based on D2(k=4) value of 8,742 - Unsutable :.,. -Suitable .. Q. N + 0 15 30 60 Miles Figure 18. Suitable habitat for Lake Huron tansy based on D2ck=4) � 8,742 using the 15 meter, seven variable model 00 u, CHAPTERS DISCUSSION AND CONCLUSIONS The results of this study indicated that the partitioned Mahalanobis distance model was not effective in establishing narrow spatial limits to the Lake Huron tansy habitat, especially for the models that were based on 11 variables. The habitat suitability maps that were based on partitioned D2 were not useful for narrowing the habitat range because each contained a consistent band of habitat suitability along the shoreline, varying in width depending on the model (Figs. 19, 20, 21 and 22). While the tansy is rare in Michigan, none of the partitioned Mahalanobis distance models contained a break in the suitability band that would predict that any portion of the shore adjacent to the Great Lakes (approximately 800 miles) was unsuitable. The habitat suitability map1 that was generated fromthe Mahalanobis distance model run by the extension in Arc View 3.2 did contain portions of unsuitable shoreline (Fig. 23), which was the predicted outcome based on observations in the field. All of the habitat suitability maps show suitable habitat further south and west than the species has been foundto date. The apparent significantinteraction among the differenthabitat variables supports the use of partitioned Mahalanobis distance as described in the literature for modeling suitable Lake Huron tansy habitat. Initial steps in both types of Mahalanobis distanee models indicated good fitbetween model specificationsand the tansy. Cumulative frequencygraphs of the models were consistent and better than random at predicting suitable locations, and the two partitioned D2 models using seven variables did seellil to 86 Lake Huron Tansy Habitat Suitability based on D2(k=4) value of 8742 - Unsulable -Surabe 0 0 5 1 2 l,11les Figure 19. A portion of the habitat suitability map for Lake Huron tansy based on D2(k=4) :S 8.742 using the 15 meter, seven variable model distinguish well between the null model points and the test populations; additionally, the validation locations matched well with the test locations (Figs. 15 and 17). So according to the cumulative frequency curves, partitioned D2 did distinguish land with a higher probability of being suitable for tansy. The same was true for the cumulative frequency graph associated with Mahalanobis distance calculated in Arc View 3.3 (Fig. 13). While the distance between the null model points curve and the test population points curve was not as great for the models where 11 variables were used (Figs. 8 and I 0) as they had been for the seven variable models, there was still a difference between the two curves for both partitioned D2 models. Also, the validation population curve 87 Lake Huron Tansy Habitat Suitability based on D2(k=7) value of 11921 - Unsutable -Suitable 0 0 5 1 2 Miles Figure 20. A portion of the habitat suitability map for Lake Huron tansy based on D\k=7) :S11,921 using the 15 meter, seven variable model closely matched, even exceeded, the test population points curve for both 11 variable models. The problem then seems to be that the variables used in the models do not vary enough along the shorelines to show patchy suitability. Broadly speaking, the results of the habitat suitability maps could be interpreted two ways. The first way to explain the results is that the models all reflect reality, the entire northern Great Lakes shoreline within Michigan is suitable habitat for Lake Huron tansy. If the entire northern shoreline is suitable, then why is Lake Huron tansy rare enough in the state to be considered a threatened species? The models suggest that the physical environment is not what limits the tansy, as the species is rare some other 88 Lake Huron Tansy Habitat Suitability based on D2(k=7) value of 500,000 - Unsutable -Sult8ble 0 0 5 1 2 I.tries Figure 21. A portion of the habitat suitability map for Lake Huron tansy based on 2 D (k=7) :S500,000 using the 10 meter, 11 variable model factor(s) must limit it. The second interpretation is that the tansy does have a narrower range than reflected in the habitat suitability maps, but the models and/or variables lack the sensitivity needed to narrow the habitat. If the models are not able to narrow the range of suitable habitat, in what ways could the included variables or models have lacked sensitivity? The Discussion will first address potential factors that are related to the biology of Lake Huron tansy that might limit the distribution of the species but would not be reflected in habitat suitability models. The biological factors suggested in the discussion are primarily non-spatial; those with a distinct spatial dimension are still grounded in the 89 Lake Huron Tansy Habitat Suitability based on D2(k=11) value of 527,000 -Unsulable -Sunable 0 0 5 1 2 l,hles Figure 22. A portion of the habitat suitability map for Lake Huron tansy based on D\k=11) :S527,000 using the 10 meter, 11 variable model biology of the species. The Discussion will then address potential limits of the variables and limits of the methods that might have reduced the sensitivity of the models. The chapter ends with the conclusions that can be drawn from the present study. Biological Factors Assuming that the results from partitioned Mahalanobis distance are correct, the physical environment is not what is limiting Lake Huron tansy distribution, but the species is still rare enough to be considered threatened in Michigan. Lake Huron 90 Lake Huron Tansy Habitat Suitability based on D2 value of 7 .3 - Unsulable -Sutabe 0 0 5 1 2 f,hles Figure 23. A portion of the habitat suitability map for Lake Huron tansy based on D2 S 7.3 using the 15 meter, seven variable model tansy populations may then be limited by other factors. Aspects of the species biology may limit the establishment of Lake Huron tansy. Non-spatial Biological Factors If seed set, that is the number of viable seeds that are produced by the parent plant, is low, there would be few seeds to germinate in the suitable landscape. Ostlie (1991) states that Lake Huron tansy has abundant seed production, but also says that assessment of seed production per flowering head should be made, implying that seed set is not known. McIntyre (1996) pointed out that seedling regeneration is required for successful exploitation of sites and added that poor seed quality may have contributed to 91 the limited distribution of rare grassland species. She noted that her rarer, native species (Cymbonatus lawsonianus and Microseris lanceolata) produced more damaged and inviable seeds than the abundant exotic species. The USDA Forest Service (2002) stated that little is known about seed dispersal and fertilityof Lake Huron tansy. Limited dispersal ability can prevent plant species fromoccupying suitable habitats (Boetsch et al. 2003). If abundant seeds are produced but many seeds are not viable or if something impedes dispersal, Lake Huron tansy will not be able to rapidly colonize new sites from seed. Tanacetum huronense fruits do not have plumose structures to aid in wind dispersal. Fruits fromthe previous season can persist on the floweringheads until the following spring (personal observation). It is possible that the whole head of fruits falls to the ground and germinates at the footof the parent plant as is known to occasionally occur with Pitcher's thistle (Loveless 1971). Also, once the head falls to the ground the fruits could break apart and be blown along the dune surfacewith the sand. If seed set is an issue for Lake Huron tansy, the species is able to compensate by reproducing vegetatively via rhizomes, a strategy that is common fordune plants (Wilson 1991; Davy and Figueroa 1993). The ability to produce more ramets via rhizomes would increase the number of stems in a given population. Additionally, there is some evidence that many dune plants establish new populations via fragmentsof rhizomes and stolons (horizontal, above ground stems) that are washed offthe shore at one location and washed onto shore at another location by waves (Wilson 1991; Davy and Figueroa 1993). Colonization via plant fragments allows the plants to avoid the colonization constraints associated with recruitment fromseeds (Lichter 1998). Chadde (1999) stated that T. huronense does not form large patches, and it is unknown to what extent Lake Huron 92 · tansy reproduces via rhizomes compared to by seed. Lake Huron tansy may also be functioning under metapopulation dynamics. A number of disturbance-dependent plant species are said to functionas metapopulations, including Pitcher's thistle (McEachem 1992) and Furbish's lousewort (Menges 1990). The USDA Forest Service (2002) suggested monitoring existing populations of T. huronense to better understand its metapopulation dynamics, among other things. With metapopulation dynamics, under normal circumstances, individual populations wink in and out of existence, but the overall number of populations remains stable. If metapopulation dynamics were at play in T. huronense, it would make sense that the whole shoreline could potentially be suitable but tansy populations would not be found everywhere. In the case of Furbish's lousewort, a species found on river banks, ice scour and riverbank collapse cause local extinction of populations, but the same stochastic events also create the disturbed, open habitat that the species requires for establishment (Menges 1990). In the case of Lake Huron tansy, storm surges, dune movement and ice scour may remove populations of the tansy, and/or those events may also promote the establishment of new populations by removing competing vegetation and creating a disturbed landscape that appears to be required by the tansy. The storm surges may also pick up/drop off plant fragmentsthat may then become established in a new location to start a new population. Biological Factors with a Spatial Component Herbivores may be limiting plant success. The herbivores could be those that consume all above ground parts, just consume leaves, thus reducing the surface area available to photosynthesize, they could be seed predators, or the herbivore could be 93 · feeding on below ground parts, such as roots or rhizomes. One observation has been made of a cutworm moth caterpillar feedingon below ground parts of T. huronense (USDA Forest Service 2002). The influence of herbivory on plant commonness is supported by results obtained by McIntyre (1996), who foundthat the native plants in her study (Cymbonatus lawsonianus and Microseris lanceolata) had more potential predators than the exotic species (Hypochoeris radicata), and that grazing had led to rarity. Additionally, she suggested that seed predation may have limited the dispersal ability of the rare plants she was studying. McGraw and Furedi (2005) also saw the influenceof herbivory on plant abundance. These researchers found that deer browsing had reduced the abundance of individuals in the forest understory. However, there is no indication that deer browse on Lake Huron tansy, although deer do browse on Pitcher's thistle (Phillips and Maun 1996), a species that co-occurs with Lake Huron tansy. Additionally, the common tansy, T. vulgare, is unpalatable, and possibly toxic, to most livestock species. There is, however, little evidence of grazing or herbivory of any kind in Lake Huron tansy. Anthropogenic forces could be limiting the distribution of Lake Huron tansy populations. It could be that the physical environment is suitable forthe tansy but that houses, fences,etc. are on the land that the tansy would otherwise use. Landuse and land ownership were not used as variables in the models generated in the present study. Tanacetum huronense has a coefficientof conservatism value of 10 (Michigan Department of Natural Resources 2001). The coefficientof conservatism (C) values range from O - 10, fornative plants within the state. A value of zero indicates that the species has no fidelityto areas that are similar to presettlement conditions. By contrast, a 94 value of 10 indicates that the species has a high fidelityto presettlement conditions. The tansy's high C value indicates that the species requires the presettlement conditions, conditions that are difficultto find along the modem Great Lakes shores. If seed set, dispersal mechanisms, metapopulation dynamics and/or disturbance regimes are the reason forthe models' inability to narrow the habitat, this presents interesting implications forthe use of partitioned Mahalanobis distance. Limits to Model Sensitivity The second interpretation of the results in the present study is that the models lack the sensitivity needed to narrow the limits of habitat suitability. If the models lack sensitivity, the lack could be due to limitations of the data, encompassing limits of the included data, data that were unavailable or were not included, issues of data scale, and the temporal nature of the included data. The lack of sensitivity could also reflect limits of the method, including the choice of components, the scale at which the models were generated, violation of assumptions, and the types of models and tools chosen foruse within the present study. Limitations of Data Included Variables Several factors could have influenced the data. Browning et al. (2005) stressed the importance of basing variable selection on solid natural history. The natural history of Lake Huron tansy is only moderately known. Based on the variables that were shared as important between PCA and the z-test, it would seem that growing season precipitation, the presence of sand, and disturbance are important to tansy success. The 95 assumption was made that distance to shore and NED are correlated and that together they act as a surrogate for disturbance. Rotenberry et al. (2002) proposed partitioned Mahalanobis distance as a method that would be suitable formodeling species associated with dynamic habitats. The initial steps of the present study indicated that the models functioned well in distinguishing suitable and unsuitable Lake Huron tansy habitat. The dynamic nature of the dune environment, however, created some challenges with respect to variables included in the models. One way this information affected the model was the data within a given dataset (STATSGO data for example) were collected over a number of years and the different datasets (STATSGO, climate variables, etc.) were collected in differentyears. The shorelines differed among the STATGO layers, the NED based layers, and quaternary layers, with the ST A TSGO layer being the most limiting. The ST ATSGO layer did not include some of the islands on which the tansy is found and the shoreline was a little short, comparatively, in areas. As a consequence, forthe analysis of data collected at 10m resolution, only 97 (71 test populations; 26 verification populations) of the original 125 population locations could be used. The coordinates of the remaining population locations placed them in the lakes. Because the models based on variables that were measured at 15m resolution did not contain STATSGO data, 121 locations (90 test populations; 31 verification populations) were used to develop and verify the model. The inclusion of the extra 19 test populations may have contributed to the greater effectiveness of the seven variable models. While the STATSGO data are not as detailed as the SSURGO data, the STATSGO files had soil data such as pH, percent sand, and percent gravel for soils along 96 · the lakes, whereas the SSURGO files did not contain those data for all soil types. van Manen et al. (2005) considered using soil type, because soil type is a potentially important habitat variable forplants, but the only consistent GIS soil data available was STA TSGO data. They decided that the ST ATSGO mapping scale was too coarse for their species of interest. Browning et al. (2005) were surprised that soil properties did not contribute more heavily to overwintering site selection for timber rattlesnakes. They suggested that the soil properties were too crudely definedin the GIS (30m resolution) to adequately represent soil properties from a snake's perspective. Given the results of the present study, the STATSGO data may have been at too coarse a scale for modeling Lake Huron tansy habitat as well. The pH of the upper 15cm of young dunes at Wilderness State Park was 8.5 (Lichter 1998), substantially higher than the mean pH of test populations, possibly another indication that the STATSGO layer did not provide enough resolution forthis parameter. However, percent sand was significant, even at the wrong resolution, but might have provided further narrowing of suitable habitat if the data were available at a finer resolution. Another set of data for which the available scale may have lacked the resolution needed forsensitivity was all of the climate variables. The climate variables for the present study were based on interpolating data collected at a number of weather stations distributed throughout northern Michigan. Interpolation could not pick up microscale variations in climate that could dictate tansy presence. The population location data were collected by a number of people over time using a variety of methods, calling into question the precision of some of the data points. Lake levels have changed over the last 100 years (Albert 2000, Peach 2006). Population 97 locations whose geographic coordinates presently placed them in the lake may have been on dry land at the time of observation. The percentage of suitable habitat within the study area was considerably higher for the 11 variable models (43.66% fork= 7; 41.91% fork= 11) than forthe seven variable models (17 .09% fork= 4; 14.06% fork= 7), which was unexpected. Usually the addition of variables improves the fit of the model. The observed results may be due to the variables that were used foreach model. As described earlier, there were concerns about the interpolated layers and the layers that were derived fromSTA TSGO data. Both of the mentioned data types were included in the 11 variable models but not in the seven variable models. The habitat variables that were used in the seven variable models were all based on the 1/3 arc second NED data (NED, SLOPE, COSASP, SINASP) or based on the shoreline (DISTSH, COSDIR, SINDIR). These layers are reliable at both 10m and 15m resolution. The seven variable models may have resulted in less of the study area being classified as suitable because the variables used most accurately depicted the population locations. Unavailable or Unused Data Many habitat variables were tested in the present study, but there could be other variables that would have been more informative. Given the importance of wind in dune formation (Van Dijk 2004) and its presumed importance as a disturbance forcefor dune species (Maun 1989; Choberka et al. 2001) wind would have been a useful variable to consider forthe Lake Huron tansy models, but enough data could not be found. Other studies that have modeled plant habitat suitability have used solar insolation, terrain shape index, topographic relative moisture index (Boetsch et al. 2003; van Manen et al. 98 2005; Thompson et al. 2006)a Beers' transformationof aspect, instead of the cosine and sine of aspect, and topographic convergence index (Boetsch et al. 2003; van Manen et al. 2005). Mean temperature for each month was interpolated, but it may be the extremes in temperature that limit the tansy. The sand on the dunes can reach 120°F (Albert 2000). McIntyre (1996) suggested that the native species in her study were less common than the weedy species because the native plants had narrower environmental tolerance. The results of the habitat suitability maps in the present study suggest that this may not be the case for Lake Huron tansy. However, one environmental variable that McIntyre (1996) addressed for the rare species Cymbonotus lawsonianus was its apparent disturbance-dependence. McIntyre suggested that the disturbance requirements of C. lawsonianus are quite specific,but only met rarely under current regimes. Rare species that are dependent on disturbance may become refugees, neither competing in undisturbed areas, nor effectively colonizing after human disturbances; the problem can be exacerbated by the increased competition resulting fromexotic species that are successfulin the present disturbance regime. If Lake Huron tansy has highly specific disturbance requirements, which seems possible given its evolution on the Great Lakes shores, those disturbance requirements would likely be hard to model, if they were known. Some indirect gradients associated with plant responses may not be well represented with GIS data (van Manen et al. 2005). Model improvements may be possible once more accurate and consistent regional data for soil, climate and geology become available. Future GIS layer needs include: more finely resolved soil data, good GPS locations fortansy presence and consistent Michigan shoreline data. Location 99 · accuracy may affect model performance(van Manen et al. 2005). While a plethora of habitat variables were tried, it is possible that all of the important habitat variables were not included in these models. Limitations of the Methods Choice of Included Components The choice of habitat variables to use in both Mahalanobis distance models was determined based on the results of the initial PCA, where the last 15 components had eigenvalues essentially equal to zero. Browning et al. (2005) urged carefullyconsidering components with zero eigenvalues beforeeliminating them fromthe model because those components may represent purely deterministic habitat requirements. In the present study, the variables that correlated with components having zero eigenvalues were all interpolated variables. When partitioned Mahalanobis distance was calculated using the components having eigenvalues of zero, the resulting suitability maps were very uninformative, having one small circular patch of unsuitable habitat and the rest of the study area was characterized as suitable (results not shown). The correlation of climatic data with the components having extremely low eigenvalues is thought to be an artifact of interpolation, either the method, the number of climate stations used, the location of the climate stations used, or a combination of these factors. The z-tests and PCA indicated that a few habitat variables that were interpolated may be important for tansy success. Few, if any, of the middle components could be neatly classified. When scatterplots were generated forthree of the components (PC 12, 15, and 24), they indicated that the components were picking up on only a couple of populations each that shared those habitat variables (Figs. 24, 25, and 26 respectively). It is possible that the 100 · differentparts of Michigan offerdifferent microhabitats and order for Lake Huron tansy to succeed it requires different combinations of variables in each of the microhabitats. For example, the western half of the lower peninsula will potentially experience more on shore wind and greater precipitation than the eastern half of the lower peninsula. If this is true, then perhaps on the easternhalf of the lower peninsula Lake Huron tansy requires substrate higher in organic matter that holds more water. Each microhabitat is suitable for Lake Huron tansy, but by trying to model the northern part of the state as a whole results in too general of a model. Browning et al. (2005) used bootstrapping techniques, cross-validation and jackknifing to determine the appropriate k subset of principal components, determining the effectindividual test locations had on D2(k) values, and assess the predictive ability of their partitioned Mahalanobis distance model, respectively. The use of these methods in this Lake Huron tansy study may have yielded better results. The choice of k components in this study was somewhat subjective and the effect of individual test locations on D2(k) was not determined. However, increasing kin the present study only appeared to reduce the width of the band of suitable habitat, it did not result in a substantially more useful map (Figs. 19 and 20; Figs. 21 and 22). Assumptions Some assumptions made when using GIS and location data to generate a habitat suitability model are: that plant locations are representative of the whole population; that the GIS layers and the location data are accurate; and that the GIS layers chosen are relevant to the ecology of the species of interest, and that past habitat presence is indicative of where the species will occur in the future (Clark et al. 1993). Some of the 101 Quaternary Not med. textured til 3.0 ' Med. textured till E- 2.75 0. 2.5 2.25 l - -, - , -- 14.00 15.00 16.00 GROPPT Figure 24. Scatterplot of the test population values for July precipitation, growing season precipitation, and the presence of medium textured till, variables that were strongly correlated with Component 12 from Principal Components Analysis of 42 variables 1.0 Quaternary Not bedrock ' Bedrock 0.5 0. r:/J 0.0 r:/J -0.5 14.00 15.00 16.00 GROPPT Figure 25. Scatterplot of the test population values for sine aspect, growing season precipitation, and the presence of exposed bedrock, variables that were strongly correlated with Component 15 from Principal Components Analysis of 42 variables 102 Quaternary Not coarse textu red ti! 260.0� ' Coarse textured till 240.0� Q � 220.01 0.00 250.00 500.00 750.00 l 000.00 DISTH Figure 26. Scatterplot of the test population values for elevation, distance to shore, and the presence of coarse textured till, variables that were strongly correlated with Component 24 from Principal Components Analysis of 42 variables assumptions of Mahalanobis distance and partitioned Mahalanobis distance may have been violated in the present study. The multivariate mean for the full Mahalanobis distance probably does not describe the optimum because there exists differential success on the foredune versus the more stable dune areas (USDA Forest Service 2002; Weatherbee 2006). Lake Huron tansy is not a good competitor on stable dunes; active dunes, however, encourage flowering (Weatherbee 2006). Thompson et al. (2006) point out the importance of test locations being a representative sample of population locations. It seems likely, that with tansy location being collected over time that the locations were indeed representative of the population. Boetsch et al. (2003) points out that a characteristic of a species which is going to be amenable to landscape-scale habitat modeling is that the species respond to large-scale gradients that can be simulated using 103 GIS surrogate predictors. It is possible that Lake Huron tansy responds to micro-scale variables that do not lend themselves well to being represented by GIS layers, even at 1Om resolution. The microhabitat of a given tansy genet may have changed fromthe time of establishment (on a foredune,perhaps) to the time of data collection (when NED data were collected the same genet may have been located on the backdune). Lake Huron tansy experiences differentialsuccess at different locations along the shore (USDA Forest Service 2002; Weatherbee 2006). The habitat condition at the time of data collection may not represent optimal habitat, a violation of a model assumption. It was hoped that using only population data from 1970 to the present would minimize this effect,but there was no way of knowing how long the populations had existed at each given location. Model Choice Previous plant studies using full Mahalanobis distance have examined plants associated with later successional, more stable communities (Boetsch et al. 2003; van Manen et al. 2005; Thompson et al. 2006). T. huronense is considered an early to mid successional species (Jolls and Sellars 1999). Partitioned Mahalanobis distance was recommended forspecies found in dynamic environments (Rotenberry et al. 2002). While partitioned Mahalanobis distance has been used to study bats (Watrous et al. 2006) and rattlesnakes (Browning et al. 2005), it apparently has not been used to study a plant species, nor has it been used for a species that is associated with a dynamic environment. Based on the results of the present study, it is possible that both Mahalanobis distance and partitioned Mahalanobis distance models lack the sensitivity needed to map Lake Huron tansy habitat. 104 Partitioned Mahalanobis distance calculated with all principal components should yield the same results as traditional Mahalanobis distance (Rotenberry et al. 2002). When comparing the results of the seven variables models, the results obtained from the full Mahalanobis distance model calculated with the Arc View 3.3 extension were not the same as the results obtained frompartitioned Mahalanobis distance model where k = 7 (Table 9). The full Mahalanobis distance model predicted patchy distribution along the shore (Fig. 23), whereas the partitioned Mahalanobis distance model with all components predicted the whole shoreline to be suitable (Fig. 20). The black box method employed by the Arc View extension does not allow direct comparison of matrices, but the difference in results may indicate an implementation of D2 in the Arc View Mahalanobis distance extension that differs slightly from standard statistical practices. The means 2 calculated by the D extension differed forNED, SINASP, SINDIR, and SLOPE compared to the means calculated by SAS (Table 12). Table 12 Comparison of means obtained from Mahalanobis distance extension (Jenness 2003) and means calculated within SAS forthe seven variables measured at 15 meter resolution Variable D Extension SAS COSASP 0.06310 0.06310 COSDIR 0.09825 0.09825 DISTSH 68.29133 68.29133 NED 181.45249 181.46532 SINASP -0.04722 -0.05477 SINDIR 0.17489 0.19836 SLOPE 2.47329 2.59818 As expected when comparing the results of partitioned Mahalanobis distance models using the same number of variables (Watrous et al. 2006), the amount of suitable 105 habitat was less when all components were considered compared to when only a subset of the components were considered (Table 9). Like adding more variables to a model, adding more components should increase the specificity of the model, resulting in less of the study area being suitable. Conclusions PCA and z-tests indicated that potentially important habitat variables for Lake Huron tansy success include elevation, distance to shore, growing season precipitation, April, June, July, and November precipitation, bedrock type, specifically dune sand, percent sand, percent gravel and soil pH. PCA of the 11 variables (elevation, slope, cosine aspect, sine aspect, distance to shore, growing season precipitation, cumulative growing degree days May-September, cumulative winter temperature December February, percent sand, percent gravel and soil pH) represented at 10m resolution resulted in 11 components with non-zero eigenvalues, seven of which had eigenvalues less than one. D2(k) was calculated using those seven components (Model A) and using all 11 components (Model B). Both Models A and B were consistent and better than random at predicting suitable population locations. Model A resulted in a classification of 43.66 percent of the study area as suitable and Model B classified 41.91 percent of the study area as suitable. Mahalanobis distance calculated with seven variables (elevation, slope, cosine aspect, sine aspect, distance to shore, cosine direction to shore, and sine direction to shore) represented at 15m resolution (Model C) was consistent and better than random at predicting suitable locations. Sixteen percent of the study area was classifiedas suitable. PCA of the data fromthe seven variables resulted in seven 106 components with non-zero eigenvalues, four of which had eigenvalues less than one. D2(k) was calculated using those four components (Model E) and all seven components (Model D). Both Models D and E were consistent and better than random at predicting suitable locations. Model D resulted in 14.06 percent of the study area classified as suitable and Model E resulted in 13.66 percent of the study area classifiedas suitable. Mahalanobis distance and partitioned Mahalanobis distance have both worked effectivelyin previous studies to distinguish suitable species habitat. Partitioned Mahalanobis distance especially has been recommended for use with species found in dynamic environments. Watrous et al. (2006) recommend the use of partitioned D2 for modeling habitat suitability because relationships among habitat characteristics are often complex and difficultto model, multivariate statistics account for interactions between predictor variables while making no demands on variable distributions, and there is no need to survey random or unused sites. Browning et al. (2005) support the use of partitioned Mahalanobis distance because the "approach involves removing the most variable aspects of the observed use sites (leaving only what the sites have most in common) to definespecies requirements and produce a more refined, precise form of 2 D ". Despite using models that were recommended for a protected species in a dynamic environment, the resulting habitat suitability models in this study were not useful for field work. The four maps based on partitioned Mahalanobis distance each showed bands of habitat suitability along the entire study area shoreline. The suitability map based on Mahalanobis distance showed patchy distribution, but too much of the study area was still considered suitable forthe map to be useful in the field. 107 2 While the maps based on partitioned D did not distinguish which parts of the shoreline were important it is evident that shoreline is important to Lake Huron tansy and as an apparently obligate shoreline species in Michigan it is important to consider the conservation of the dunes as a way of conserving Lake Huron tansy. The aspects of the dunes that appear to favor tansy success are sand movement and natural fluctuations in lake levels. Both act as disturbance forces and aid in creating new habitat and possibly in dispersal by seed or plant fragment. Therefore, it is important to carefully consider the use and placement of any structures that impede the movement of sand. These structures could be sand fences, houses, and stabilizing vegetation. One management concern is that landowners will plant species, often non-native, to stabilize the dunes on their property (Albert 2000). Also, it is important to consider any activities that will stabilize lake levels. Many alterations to the dunes have already taken place, but at least some natural processes can be restored. Peach (2006) discussed grassroots efforts that have made a positive impact on Lake Huron beaches in Canada. Stabilization of the dunes could be detrimental not only to Lake Huron tansy, but also to Pitcher's thistle, another protected species found on the Great Lakes dunes, which requires some burial in order for the seeds to germinate (Hamze and Jolls 2000). Hamze and Jolls state that the previously mentioned finding supports previous recommendations that conservation efforts should maintain the natural sand erosion and accretion regimes for the preservation and restoration of Pitcher's thistle. If T. huronense displays metapopulation dynamics, protecting only the best populations will not conserve the species. Stochastic events remove populations and new areas for colonization must be available (Krebs 2001). The most conservative approach 108 to protecting the habitat would be to protect both existing populations and some potential habitat areas (Elzinga et al. 2001; Krebs 2001). However, the fragmentedlandscape may not allow the dispersal mechanisms necessary for metapopulation dynamics to function effectively (Elzinga et al. 2001). As explained in Chapter 2, many plant taxonomists consider T. huronense a subspecies of T. bipinnatum, an abundant boreal species. If this is the case then T. huronense is at the southernedge of the species range. It is important to consider T. huronense even if it is a subspecies of T. bipinnatum because species at the margins of their range are an important part of the evolutionary laboratory (TNC 1994) and because they are part of the local biodiversity and may serve a vital function within the ecosystems where they are found (Hunter and Hutchinson 1994). We need to support the natural processes necessary for the evolution of the species to continue. Hunter and Hutchinson (1994) state there is value to studying and protecting locally rare but globally abundant species. Oftentimes species are locally rare when they are found on the edge of their range. Hunter and Hutchinson point out that if too many species are lost froman ecosystem, the ecosystem collapses. Shoreline habitat is in danger of losing many species because of the many factors that disrupt the natural dynamics of the ecosystem. Research that can be done in the future with the data that already exist include examining the effects of differentscales on the models, and determining the effectof using only weather stations located within 20 miles of the Great Lakes' shorelines to interpolate climate data. 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