Approaches to mathematical modeling of biological invasions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin
Logos Verlag
2020
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | xix, 224 Seiten Illustrationen 24 cm |
| ISBN: | 9783832551513 3832551514 |
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MARC
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| 100 | 1 | |a Köhnke, Merlin Christopher |e Verfasser |0 (DE-588)1219669016 |4 aut | |
| 245 | 1 | 0 | |a Approaches to mathematical modeling of biological invasions |c Merlin Christopher Köhnke |
| 264 | 1 | |a Berlin |b Logos Verlag |c 2020 | |
| 300 | |a xix, 224 Seiten |b Illustrationen |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |b Dissertation |c Universität Osnabrück |d 2020 | ||
| 650 | 0 | 7 | |a Mathematische Modellierung |0 (DE-588)7651795-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Invasion |g Biologie |0 (DE-588)4335542-0 |2 gnd |9 rswk-swf |
| 653 | |a Dynamical Systems | ||
| 653 | |a Mathematical Biology | ||
| 653 | |a Biological Invasions | ||
| 653 | |a Modeling | ||
| 653 | |a Population Dynamics | ||
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Invasion |g Biologie |0 (DE-588)4335542-0 |D s |
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Record in the Search Index
| _version_ | 1804181945531236352 |
|---|---|
| adam_text | T
ABLE
OF
C
ONTENTS
PAGE
LIST
OF
PUBLICATIONS IX
LIST
OF
TABLES
XV
LIST
OF
FIGURES
XVII
1
INTRODUCTION
1
1.1
WHAT
ARE
BIOLOGICAL
INVASIONS?
................................................................................
1
1.2
THE
RELEVANCE
OF
BIOLOGICAL
INVASIONS
FOR
SCIENCE
AND
SOCIETY
...................................
3
1.3
MATHEMATICAL
MODELS
IN
INVASION
BIOLOGY
................................................................
6
1.4
DIFFERENTIAL
EQUATIONS
AS
A
TOOL
TO
STUDY
BIOLOGICAL
INVASIONS
................................
8
1.4.1
GROWTH
MODELS
..............................................................................................
8
1.4.2
INTERACTIONS
BETWEEN
TWO
SPECIES
................................................................
11
1.4.3
INTERACTIONS
BETWEEN
MORE
THAN
TWO
SPECIES
..............................................
15
1.4.4
SPATIAL
MODELS
..............................................................................................
16
1.4.5
STOCHASTIC
DIFFERENTIAL
EQUATIONS
...................................................................
26
1.5
OUTLINE
......................................................................................................................
29
2
WAVE
PINNING
IN
COMPETITION-DIFFUSION
MODELS
IN
VARIABLE
ENVIRONMENTS
33
2.1
INTRODUCTION
..............................................................................................................
34
2.2
MODEL
AND
METHODS
...................................................................................................
36
2.2.1
DETERMINISTIC
MODEL
......................................................................................
36
2.2.2
STOCHASTIC
MODEL
...........................................................................................
41
2.2.3
NUMERICAL
TREATMENT
...................................................................................
44
2.3
WAVE
PINNING
........................................................................................................
44
2.3.1
ANALYTICAL
REVIEW
...........................................................................................
44
2.3.2
NUMERICAL
RESULTS
........................................................................................
46
2.3.3
STABILITY
AGAINST
ENVIRONMENTAL
PERTURBATIONS
...........................................
47
2.4
DISCUSSION
AND
CONCLUSIONS
......................................................................................
51
TABLE
OF
CONTENTS
3
INVASION DYNAMICS
IN
AN
INTRAGUILD
PREDATION
SYSTEM
WITH
PREDATOR-INDUCED
DEFENSE
55
3.1
INTRODUCTION
...............................................................................................................
56
3.2
MODEL
AND
METHODS
....................................................................................................
57
3.3
ANALYTICAL
RESULTS
.......................................................................................................
61
3.3.1
STATIONARY
SOLUTIONS
.......................................................................................
61
3.3.2
MODEL
WITH
ADAPTIVITY
....................................................................................
63
3.4
NUMERICAL
RESULTS
.......................................................................................................
64
3.4.1
NONSPATIAL
RESULTS
..........................................................................................
65
3.4.2
SPATIAL
RESULTS
...............................................................................................
70
3.5
DISCUSSION
AND
CONCLUSIONS
.......................................................................................
74
3.
A
APPENDIX
...................................................................................................................
76
3.
A.1
JACOBIAN
MATRIX
FOR
THE
MODEL
WITHOUT
ADAPTATION
......................................
76
3.
A.2
NULLCLINES
OF
THE
MODEL
WITH
ADAPTATION
......................................................
77
4
A
TYPE
IV
FUNCTIONAL
RESPONSE
WITH
DIFFERENT
SHAPES
IN
A
PREDATOR-PREY
MODEL
79
4.1
INTRODUCTION
...............................................................................................................
80
4.2
GENERAL
MODEL
.............................................................................................................
81
4.3
MODEL
WITH
A
GIVEN
CATCH
RATE
....................................................................................
86
4.4
DISCUSSION
AND
CONCLUSIONS
.......................................................................................
92
4.
A
APPENDIX
....................................................................................................................
94
4.
A.1
TIMESCALE
SEPARATION
....................................................................................
94
4.
A.2
LIMIT
OF
77 V)
.....................................................................................................
96
5
TAXIS-DRIVEN
PATTERN
FORMATION
IN
A
PREDATOR-PREY
MODEL
WITH
GROUP
DEFENSE
97
5.1
INTRODUCTION
...............................................................................................................
98
5.2
MODEL
AND
METHODS
.......................................................................................................
100
5.3
RESULTS
..........................................................................................................................
102
5.3.1
TAXIS-DRIVEN
INSTABILITY
....................................................................................
102
5.3.2
PATTERNS
IN
EXCITABLE
MEDIA
...............................................................................
104
5.3.3
PREYTAXIS
IN
EXCITABLE
MEDIA
............................................................................
ILL
5.4
DISCUSSION
AND
CONCLUSION
............................................................................................
114
5.
A
APPENDIX
.......................................................................................................................
118
5.
A.1
DIMENSIONS
......................................................................................................
116
6
DISEASE-INDUCED
CHAOS,
COEXISTENCE,
OSCILLATIONS,
AND
INVASION
FAILURE
IN
A
COMPETITION-MODEL
WITH
STRONG
ALLEE
EFFECT
117
6.1
INTRODUCTION
..................................................................................................................
118
6.2
ALLEE
EFFECT
IN
A
SINGLE
SPECIES
.......................................................................................
119
XII
TABLE
OF
CONTENTS
6.3
DISEASE-FREE
COMPETITION
BETWEEN
TWO
SPECIES
...........................................................
122
6.4
COMPETITION-FREE
SI-DYNAMICS
...................................................................................
123
6.4.1
SPATIAL
ANALYSES
..............................................................................................
127
6.5
MODEL
INCLUDING
INFECTION
AND
COMPETITION
................................................................
131
6.6
IMPACT
OF
THE
DISEASE
ON
INVASION
DYNAMICS
..............................................................
134
6.6.1
INVASION
DYNAMICS
WITH
STRONG
COMPETITIVE
PRESSURE
...................................
136
6.6.2
INVASION
DYNAMICS
WITH
WEAK
COMPETITIVE
PRESSURE
......................................
139
6.6.3
SPATIAL
PHENOMENA
...........................................................................................
140
6.7
CONCLUSIONS
...................................................................................................................
143
6.
A
APPENDIX
......................................................................................................................
146
6.
A.1
WAVE
SPEED
IN
THE
SINGLE-SPECIES
MODEL
........................................................
146
6.
A.2
NONSPATIAL
SI-
MODEL
.........................................................................................
146
6.
A.3
SPATIAL
SI-MODEL
..............................................................................................
149
7
THE
NECESSITY
OF
TAILORED
CONTROL
OF
IRRUPTING
PEST
POPULATIONS
DRIVEN
BY
PULSED
RESOURCES
151
7.1
INTRODUCTION
.................................................................................................................
152
7.2
MODEL
............................................................................................................................
153
7.2.1
PULSED
RESOURCE
.................................................................................................
154
7.2.2
GENERALIST
CONSUMER
.........................................................................................
155
7.2.3
GENERALIST
PREDATOR
.........................................................................................
158
7.2.4
METAPOPULATION
MODEL
......................................................................................
159
7.2.5
PLAGUE
METRIC
...................................................................................................
160
7.3
RESULTS
.........................................................................................................................
161
7.3.1
LOCAL
DYNAMICS
.................................................................................................
161
7.3.2
METAPOPULATION
DYNAMICS
................................................................................
162
7.4
DISCUSSION
....................................................................................................................
164
7.4.1
CONTROL
TIMING
.................................................................................................
164
7.4.2
CONTROL
INTENSITY
..............................................................................................
165
7.4.3
CONTROL
STRATEGY
..............................................................................................
166
7.5
CONCLUSIONS
...................................................................................................................
166
7.
A
APPENDIX
.....................................................................................................................
168
7.
A.1
PARAMETERS
......................................................................................................
168
7.
A.2
KILLING
PROPORTION
...........................................................................................
170
7.
A.3
REINVASION
TIME
.............................................................................................
171
8
DISCUSSION
AND
CONCLUSIONS
173
8.1
SUMMARY
......................................................................................................................
173
8.2
DISCUSSION
...................................................................................................................
175
XIII
TABLE
OF
CONTENTS
8.2.1
GENERAL
IMPLICATIONS
..........................................................................................
175
8.2.2
GENERAL
UNCERTAINTIES
AND
LIMITATIONS
............................................................
175
8.2.3
RECOMMENDATIONS
............................................................................................
177
8.3
OUTLOOK
..........................................................................................................................
179
8.3.1
ENVIRONMENTAL
STOCHASTICITY
............................................................................
179
8.3.2
DISPERSAL
............................................................................................................
180
8.3.3
MANAGEMENT
....................................................................................................
182
REFERENCES
185
XIV
|
| adam_txt |
T
ABLE
OF
C
ONTENTS
PAGE
LIST
OF
PUBLICATIONS IX
LIST
OF
TABLES
XV
LIST
OF
FIGURES
XVII
1
INTRODUCTION
1
1.1
WHAT
ARE
BIOLOGICAL
INVASIONS?
.
1
1.2
THE
RELEVANCE
OF
BIOLOGICAL
INVASIONS
FOR
SCIENCE
AND
SOCIETY
.
3
1.3
MATHEMATICAL
MODELS
IN
INVASION
BIOLOGY
.
6
1.4
DIFFERENTIAL
EQUATIONS
AS
A
TOOL
TO
STUDY
BIOLOGICAL
INVASIONS
.
8
1.4.1
GROWTH
MODELS
.
8
1.4.2
INTERACTIONS
BETWEEN
TWO
SPECIES
.
11
1.4.3
INTERACTIONS
BETWEEN
MORE
THAN
TWO
SPECIES
.
15
1.4.4
SPATIAL
MODELS
.
16
1.4.5
STOCHASTIC
DIFFERENTIAL
EQUATIONS
.
26
1.5
OUTLINE
.
29
2
WAVE
PINNING
IN
COMPETITION-DIFFUSION
MODELS
IN
VARIABLE
ENVIRONMENTS
33
2.1
INTRODUCTION
.
34
2.2
MODEL
AND
METHODS
.
36
2.2.1
DETERMINISTIC
MODEL
.
36
2.2.2
STOCHASTIC
MODEL
.
41
2.2.3
NUMERICAL
TREATMENT
.
44
2.3
WAVE
PINNING
.
44
2.3.1
ANALYTICAL
REVIEW
.
44
2.3.2
NUMERICAL
RESULTS
.
46
2.3.3
STABILITY
AGAINST
ENVIRONMENTAL
PERTURBATIONS
.
47
2.4
DISCUSSION
AND
CONCLUSIONS
.
51
TABLE
OF
CONTENTS
3
INVASION DYNAMICS
IN
AN
INTRAGUILD
PREDATION
SYSTEM
WITH
PREDATOR-INDUCED
DEFENSE
55
3.1
INTRODUCTION
.
56
3.2
MODEL
AND
METHODS
.
57
3.3
ANALYTICAL
RESULTS
.
61
3.3.1
STATIONARY
SOLUTIONS
.
61
3.3.2
MODEL
WITH
ADAPTIVITY
.
63
3.4
NUMERICAL
RESULTS
.
64
3.4.1
NONSPATIAL
RESULTS
.
65
3.4.2
SPATIAL
RESULTS
.
70
3.5
DISCUSSION
AND
CONCLUSIONS
.
74
3.
A
APPENDIX
.
76
3.
A.1
JACOBIAN
MATRIX
FOR
THE
MODEL
WITHOUT
ADAPTATION
.
76
3.
A.2
NULLCLINES
OF
THE
MODEL
WITH
ADAPTATION
.
77
4
A
TYPE
IV
FUNCTIONAL
RESPONSE
WITH
DIFFERENT
SHAPES
IN
A
PREDATOR-PREY
MODEL
79
4.1
INTRODUCTION
.
80
4.2
GENERAL
MODEL
.
81
4.3
MODEL
WITH
A
GIVEN
CATCH
RATE
.
86
4.4
DISCUSSION
AND
CONCLUSIONS
.
92
4.
A
APPENDIX
.
94
4.
A.1
TIMESCALE
SEPARATION
.
94
4.
A.2
LIMIT
OF
77 V)
.
96
5
TAXIS-DRIVEN
PATTERN
FORMATION
IN
A
PREDATOR-PREY
MODEL
WITH
GROUP
DEFENSE
97
5.1
INTRODUCTION
.
98
5.2
MODEL
AND
METHODS
.
100
5.3
RESULTS
.
102
5.3.1
TAXIS-DRIVEN
INSTABILITY
.
102
5.3.2
PATTERNS
IN
EXCITABLE
MEDIA
.
104
5.3.3
PREYTAXIS
IN
EXCITABLE
MEDIA
.
ILL
5.4
DISCUSSION
AND
CONCLUSION
.
114
5.
A
APPENDIX
.
118
5.
A.1
DIMENSIONS
.
116
6
DISEASE-INDUCED
CHAOS,
COEXISTENCE,
OSCILLATIONS,
AND
INVASION
FAILURE
IN
A
COMPETITION-MODEL
WITH
STRONG
ALLEE
EFFECT
117
6.1
INTRODUCTION
.
118
6.2
ALLEE
EFFECT
IN
A
SINGLE
SPECIES
.
119
XII
TABLE
OF
CONTENTS
6.3
DISEASE-FREE
COMPETITION
BETWEEN
TWO
SPECIES
.
122
6.4
COMPETITION-FREE
SI-DYNAMICS
.
123
6.4.1
SPATIAL
ANALYSES
.
127
6.5
MODEL
INCLUDING
INFECTION
AND
COMPETITION
.
131
6.6
IMPACT
OF
THE
DISEASE
ON
INVASION
DYNAMICS
.
134
6.6.1
INVASION
DYNAMICS
WITH
STRONG
COMPETITIVE
PRESSURE
.
136
6.6.2
INVASION
DYNAMICS
WITH
WEAK
COMPETITIVE
PRESSURE
.
139
6.6.3
SPATIAL
PHENOMENA
.
140
6.7
CONCLUSIONS
.
143
6.
A
APPENDIX
.
146
6.
A.1
WAVE
SPEED
IN
THE
SINGLE-SPECIES
MODEL
.
146
6.
A.2
NONSPATIAL
SI-
MODEL
.
146
6.
A.3
SPATIAL
SI-MODEL
.
149
7
THE
NECESSITY
OF
TAILORED
CONTROL
OF
IRRUPTING
PEST
POPULATIONS
DRIVEN
BY
PULSED
RESOURCES
151
7.1
INTRODUCTION
.
152
7.2
MODEL
.
153
7.2.1
PULSED
RESOURCE
.
154
7.2.2
GENERALIST
CONSUMER
.
155
7.2.3
GENERALIST
PREDATOR
.
158
7.2.4
METAPOPULATION
MODEL
.
159
7.2.5
PLAGUE
METRIC
.
160
7.3
RESULTS
.
161
7.3.1
LOCAL
DYNAMICS
.
161
7.3.2
METAPOPULATION
DYNAMICS
.
162
7.4
DISCUSSION
.
164
7.4.1
CONTROL
TIMING
.
164
7.4.2
CONTROL
INTENSITY
.
165
7.4.3
CONTROL
STRATEGY
.
166
7.5
CONCLUSIONS
.
166
7.
A
APPENDIX
.
168
7.
A.1
PARAMETERS
.
168
7.
A.2
KILLING
PROPORTION
.
170
7.
A.3
REINVASION
TIME
.
171
8
DISCUSSION
AND
CONCLUSIONS
173
8.1
SUMMARY
.
173
8.2
DISCUSSION
.
175
XIII
TABLE
OF
CONTENTS
8.2.1
GENERAL
IMPLICATIONS
.
175
8.2.2
GENERAL
UNCERTAINTIES
AND
LIMITATIONS
.
175
8.2.3
RECOMMENDATIONS
.
177
8.3
OUTLOOK
.
179
8.3.1
ENVIRONMENTAL
STOCHASTICITY
.
179
8.3.2
DISPERSAL
.
180
8.3.3
MANAGEMENT
.
182
REFERENCES
185
XIV |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Köhnke, Merlin Christopher |
| author_GND | (DE-588)1219669016 |
| author_facet | Köhnke, Merlin Christopher |
| author_role | aut |
| author_sort | Köhnke, Merlin Christopher |
| author_variant | m c k mc mck |
| building | Verbundindex |
| bvnumber | BV046998417 |
| classification_rvk | WI 6400 WI 1500 SK 950 |
| ctrlnum | (OCoLC)1196870346 (DE-599)DNB1216960658 |
| discipline | Biologie Mathematik |
| discipline_str_mv | Biologie Mathematik |
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| index_date | 2024-07-03T15:55:54Z |
| indexdate | 2024-07-10T08:59:43Z |
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| isbn | 9783832551513 3832551514 |
| language | English |
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| physical | xix, 224 Seiten Illustrationen 24 cm |
| publishDate | 2020 |
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| publisher | Logos Verlag |
| record_format | marc |
| spelling | Köhnke, Merlin Christopher Verfasser (DE-588)1219669016 aut Approaches to mathematical modeling of biological invasions Merlin Christopher Köhnke Berlin Logos Verlag 2020 xix, 224 Seiten Illustrationen 24 cm txt rdacontent n rdamedia nc rdacarrier Dissertation Universität Osnabrück 2020 Mathematische Modellierung (DE-588)7651795-0 gnd rswk-swf Invasion Biologie (DE-588)4335542-0 gnd rswk-swf Dynamical Systems Mathematical Biology Biological Invasions Modeling Population Dynamics (DE-588)4113937-9 Hochschulschrift gnd-content Invasion Biologie (DE-588)4335542-0 s Mathematische Modellierung (DE-588)7651795-0 s DE-604 Logos Verlag Berlin (DE-588)1065538812 pbl X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=dab1550d7a4343ca9ee035d62db92602&prov=M&dok_var=1&dok_ext=htm Inhaltstext B:DE-101 application/pdf https://d-nb.info/1216960658/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032406111&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p dnb 20200930 DE-101 https://d-nb.info/provenance/plan#dnb 2\p dnb 20200930 DE-101 https://d-nb.info/provenance/plan#dnb |
| spellingShingle | Köhnke, Merlin Christopher Approaches to mathematical modeling of biological invasions Mathematische Modellierung (DE-588)7651795-0 gnd Invasion Biologie (DE-588)4335542-0 gnd |
| subject_GND | (DE-588)7651795-0 (DE-588)4335542-0 (DE-588)4113937-9 |
| title | Approaches to mathematical modeling of biological invasions |
| title_auth | Approaches to mathematical modeling of biological invasions |
| title_exact_search | Approaches to mathematical modeling of biological invasions |
| title_exact_search_txtP | Approaches to mathematical modeling of biological invasions |
| title_full | Approaches to mathematical modeling of biological invasions Merlin Christopher Köhnke |
| title_fullStr | Approaches to mathematical modeling of biological invasions Merlin Christopher Köhnke |
| title_full_unstemmed | Approaches to mathematical modeling of biological invasions Merlin Christopher Köhnke |
| title_short | Approaches to mathematical modeling of biological invasions |
| title_sort | approaches to mathematical modeling of biological invasions |
| topic | Mathematische Modellierung (DE-588)7651795-0 gnd Invasion Biologie (DE-588)4335542-0 gnd |
| topic_facet | Mathematische Modellierung Invasion Biologie Hochschulschrift |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=dab1550d7a4343ca9ee035d62db92602&prov=M&dok_var=1&dok_ext=htm https://d-nb.info/1216960658/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032406111&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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