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Stage-Structured Sensitivity Analysis
THE EFFECT OF
POST-DISPERSAL SEED PREDATION
ON ATTALEA HUMILIS
Casey Trout and Justin Tirrell
December 4, 2018
Utah State University
Theoretical Ecology BIOL4270
Content
• Background on A. humilis
• Fragment 1 and 3: Differences and Similarities
• Methods
• Results
• Discussion
A. humilis
TRAITS
• Less than 1 m tall
• A tropical species
• Predated on by Beetle
Predators
https://cropscience.bayer.co.uk/threats/pest-and-
slugs/bruchid-beetle/
https://commons.wikimedia.org/wiki/File:Palmeira_de_indai%C3%A1_REFON.jpg
Research Question: Do changing rates of Bruchid Beetle
predation have a significant effect on the survivorship and
equilibrium stage structure of A. humilis?
NULL HYPOTHESIS
• The population persistence
and equilibrium stage structure
of A. humilis is not strongly
affected by Bruchid Beetle
predation
• Leading eigenvalue and
eigenvector of the stage-
structured matrix will be
relatively similar with different
levels of predation
ALTERNATIVE HYPOTHESIS
• The population persistence
and equilibrium stage structure
of A. humilis is strongly
impacted by Bruchid Beetle
predation
• Leading eigenvalue and
eigenvector of the stage-
structured matrix will be
significantly different with
different levels of predation
Forest Fragments
FRAGMENT 1
• A smaller fragment
FRAGMENT 3
• A larger fragment
• Part of a study of A. humilis
response to fire in various
fragments in Northern Brazil
Figure 1. Life cycle diagram for A. humilis in two forest fragments. Values
along arrows represent transition probabilities between stages (from one
circle to another), or stasis probabilities (from a circle to the same one). S
= seedling, J = juvenile, I = immature, V = virgin, R = reproductive.
Reprinted from Souza and Martins.
STAGE CLASSES
Seed Seedling
Juvenile Immature
Virgin Reproductive
Stage-Structured Matrices
Table 1. Stage-structured matrices for fragment 1 and
fragment 3 as extracted from the Souza and Martins study.
The survivorship of seeds to seedlings (the box with an “x”)
was modified for our sensitivity analysis to summarize the
effect of varying rates of predation by Bruchid Beetles.
Method: Stage Class Population Projection Matrices
Key Concept: Eigenvalue
• A is a
matrix:
• V is a vector: • w is A x v:
• λ is a scalar: • w is λ x v:• V is a vector:
Calculating Eigenvalues
• Create the stage-structured
matrix
• Create an Index for seed
survival to seedling stage
class
• Calculate eigenvalues for
the index
… And plot!
Figure 2. Sensitivity analysis of seed survivorship on population growth rate. At eigenvalues smaller
than 1 the population is declining while at eigenvalues larger than 1 the population is growing. It
appears that the seed survivorship needs to be very small before the population will begin declining.
Calculating Eigenvectors
• Store matrices for the desired
index range
• Print eigenvector
• …and…
Eigenvector Analysis
Fragment 1 Fragment 3
Survivorship 0.01% 1% 0.01% 1%
Seed 98.03% 95.50% 99.61% 96.65%
Seedling 0.05% 2.48% 0.03% 1.62%
Juvenile 0.01% 0.39% ~0.00% 0.08%
Immature 0.24% 0.61% 0.22% 1.47%
Virgin 1.52% 0.85% ~0.00% ~0.00%
Reproductive 0.15% 0.17% 0.14% 0.17%
Table 2. Equilibrium stage structure
of the two populations of A. humilis
with a seed survivorship of 0.01%
and 1%. We see that as seed
survivorship increases, the proportion
of individuals in the seed stage class
decreases and the proportion of
individuals in the other stage classes
increases (except for the virgin stage
class in fragment 1).
Results
• Beetle predation needs to be relatively
high in fragment 1 and 3 to drive the two
populations of A. humilis to extinction
• Seed survivorship of 0.04% in
fragment 1 and 0.09% in fragment 2
• Higher levels of seed survivorship result
in a smaller proportion of seeds and a
larger proportion of individuals in all
other stage classes
https://www.monaconatureencyclopedia.com/attalea-humilis-2/?lang=en
https://www.fginsight.com/news/news/bruchid-beetles-threaten-bean-
crops-61435
Discussion
• Previous research has shown that A. humilis is more effective at
dispersing seeds in smaller fragments than most palms
• Higher survivorship of the seeds in the small (I) fragment
• Lower rates of predation correspond to a more diverse stage structure
(healthier population of A. humilis overall)
• Our findings (resilience of the population under high rates of seed
predation) support previous findings that palm populations are
generally quite resilient to beetle predation
Discussion – future work
• The stage structures in our analysis came from a study at a very specific
location in Northern Brazil
• Stage structure between fragment 1 and fragment 3 varied
markedly (high variability in stage-structured matrices of A.
humilis)
• Meta-sample the reproduction and fecundity of A. humilis throughout
Central and South America to better understand stage-structured
variability
• Conduct eigenvalues and eigenvectors for each sample
• Summarize the range and variance in potential predation rates that
could drive any local population of A. humilis extinct
Literature Sources
• Andreazzi, Cecilia & S. Pimenta, Clarissa & Pires, Alexandra & Fernandez,
Fernando & Oliveira-Santos, Luiz & Menezes, Jorge. (2011). Increased
Productivity and Reduced Seed Predation Favor a Large‐seeded Palm in Small
Atlantic Forest Fragments. Biotropica. 44. 237 - 245. 10.1111/j.1744-
7429.2011.00782.
• Connell, J.H. (1971). On the Role of Natural Enemies in Preventing Competitive
Exclusion in Some Marine Animals and in Rain Forest Trees. In: Den Boer, P.J. and
Gradwell, G.R., Eds., Dynamics of Populations, Centre for Agricultural Publishing
and Documentation, Wageningen, The Netherlands.
• Elwood, E. C., Lichti, N. I., Fitzsimmons, S. F. & Dalgleish, H. J. (2018).
Scatterhoarders drive long‐and short‐term population dynamics of a
nut‐producing tree, while pre‐dispersal seed predators and herbivores have little
effect. Journal of Ecology 106, 1191–1203.
• Janzen, D. H. (1970). Herbivores and the Number of Tree Species in Tropical
Forests STOR ®. The American Naturalist, 104(940), 501–528. Retrieved from
http://links.jstor.org/sici.
• Souza, A. F. & Martins, F. R. (2004). Population structure and dynamics of a
neotropical palm in fire-impacted fragments of the Brazilian Atlantic Forest.
Biodiversity and Conservation, 13: 1611-1632. Retrieved from:
https://www.researchgate.net/publication/227158775_Population_structure_an
d_dynamics_of_a_Neotropical_palm_in_fire-
impacted_fragments_of_the_Brazilian_Atlantic_Forest.
• Wright, S. J., & Duber, H. C. (2001). Poachers and Forest Fragmentation Alter
Seed Dispersal, Seed Survival, and Seedling Recruitment in the Palm Attalea
butyraceae, with Implications for Tropical Tree Diversity1. Biotropica, 33(4), 583–
595. https://doi.org/10.1111/j.1744-7429.2001.tb00217.x
https://commons.wikimedia.org/wiki/File:Palmeira_de_indai%C3%A1_REFON.jpg

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Fall18 theoretical-ecology presentation

  • 1. Stage-Structured Sensitivity Analysis THE EFFECT OF POST-DISPERSAL SEED PREDATION ON ATTALEA HUMILIS Casey Trout and Justin Tirrell December 4, 2018 Utah State University Theoretical Ecology BIOL4270
  • 2. Content • Background on A. humilis • Fragment 1 and 3: Differences and Similarities • Methods • Results • Discussion
  • 3. A. humilis TRAITS • Less than 1 m tall • A tropical species • Predated on by Beetle Predators https://cropscience.bayer.co.uk/threats/pest-and- slugs/bruchid-beetle/ https://commons.wikimedia.org/wiki/File:Palmeira_de_indai%C3%A1_REFON.jpg
  • 4. Research Question: Do changing rates of Bruchid Beetle predation have a significant effect on the survivorship and equilibrium stage structure of A. humilis? NULL HYPOTHESIS • The population persistence and equilibrium stage structure of A. humilis is not strongly affected by Bruchid Beetle predation • Leading eigenvalue and eigenvector of the stage- structured matrix will be relatively similar with different levels of predation ALTERNATIVE HYPOTHESIS • The population persistence and equilibrium stage structure of A. humilis is strongly impacted by Bruchid Beetle predation • Leading eigenvalue and eigenvector of the stage- structured matrix will be significantly different with different levels of predation
  • 5. Forest Fragments FRAGMENT 1 • A smaller fragment FRAGMENT 3 • A larger fragment • Part of a study of A. humilis response to fire in various fragments in Northern Brazil Figure 1. Life cycle diagram for A. humilis in two forest fragments. Values along arrows represent transition probabilities between stages (from one circle to another), or stasis probabilities (from a circle to the same one). S = seedling, J = juvenile, I = immature, V = virgin, R = reproductive. Reprinted from Souza and Martins.
  • 6. STAGE CLASSES Seed Seedling Juvenile Immature Virgin Reproductive
  • 7. Stage-Structured Matrices Table 1. Stage-structured matrices for fragment 1 and fragment 3 as extracted from the Souza and Martins study. The survivorship of seeds to seedlings (the box with an “x”) was modified for our sensitivity analysis to summarize the effect of varying rates of predation by Bruchid Beetles.
  • 8. Method: Stage Class Population Projection Matrices
  • 9. Key Concept: Eigenvalue • A is a matrix: • V is a vector: • w is A x v: • λ is a scalar: • w is λ x v:• V is a vector:
  • 10. Calculating Eigenvalues • Create the stage-structured matrix • Create an Index for seed survival to seedling stage class • Calculate eigenvalues for the index
  • 11. … And plot! Figure 2. Sensitivity analysis of seed survivorship on population growth rate. At eigenvalues smaller than 1 the population is declining while at eigenvalues larger than 1 the population is growing. It appears that the seed survivorship needs to be very small before the population will begin declining.
  • 12. Calculating Eigenvectors • Store matrices for the desired index range • Print eigenvector • …and…
  • 13. Eigenvector Analysis Fragment 1 Fragment 3 Survivorship 0.01% 1% 0.01% 1% Seed 98.03% 95.50% 99.61% 96.65% Seedling 0.05% 2.48% 0.03% 1.62% Juvenile 0.01% 0.39% ~0.00% 0.08% Immature 0.24% 0.61% 0.22% 1.47% Virgin 1.52% 0.85% ~0.00% ~0.00% Reproductive 0.15% 0.17% 0.14% 0.17% Table 2. Equilibrium stage structure of the two populations of A. humilis with a seed survivorship of 0.01% and 1%. We see that as seed survivorship increases, the proportion of individuals in the seed stage class decreases and the proportion of individuals in the other stage classes increases (except for the virgin stage class in fragment 1).
  • 14. Results • Beetle predation needs to be relatively high in fragment 1 and 3 to drive the two populations of A. humilis to extinction • Seed survivorship of 0.04% in fragment 1 and 0.09% in fragment 2 • Higher levels of seed survivorship result in a smaller proportion of seeds and a larger proportion of individuals in all other stage classes https://www.monaconatureencyclopedia.com/attalea-humilis-2/?lang=en https://www.fginsight.com/news/news/bruchid-beetles-threaten-bean- crops-61435
  • 15. Discussion • Previous research has shown that A. humilis is more effective at dispersing seeds in smaller fragments than most palms • Higher survivorship of the seeds in the small (I) fragment • Lower rates of predation correspond to a more diverse stage structure (healthier population of A. humilis overall) • Our findings (resilience of the population under high rates of seed predation) support previous findings that palm populations are generally quite resilient to beetle predation
  • 16. Discussion – future work • The stage structures in our analysis came from a study at a very specific location in Northern Brazil • Stage structure between fragment 1 and fragment 3 varied markedly (high variability in stage-structured matrices of A. humilis) • Meta-sample the reproduction and fecundity of A. humilis throughout Central and South America to better understand stage-structured variability • Conduct eigenvalues and eigenvectors for each sample • Summarize the range and variance in potential predation rates that could drive any local population of A. humilis extinct
  • 17. Literature Sources • Andreazzi, Cecilia & S. Pimenta, Clarissa & Pires, Alexandra & Fernandez, Fernando & Oliveira-Santos, Luiz & Menezes, Jorge. (2011). Increased Productivity and Reduced Seed Predation Favor a Large‐seeded Palm in Small Atlantic Forest Fragments. Biotropica. 44. 237 - 245. 10.1111/j.1744- 7429.2011.00782. • Connell, J.H. (1971). On the Role of Natural Enemies in Preventing Competitive Exclusion in Some Marine Animals and in Rain Forest Trees. In: Den Boer, P.J. and Gradwell, G.R., Eds., Dynamics of Populations, Centre for Agricultural Publishing and Documentation, Wageningen, The Netherlands. • Elwood, E. C., Lichti, N. I., Fitzsimmons, S. F. & Dalgleish, H. J. (2018). Scatterhoarders drive long‐and short‐term population dynamics of a nut‐producing tree, while pre‐dispersal seed predators and herbivores have little effect. Journal of Ecology 106, 1191–1203. • Janzen, D. H. (1970). Herbivores and the Number of Tree Species in Tropical Forests STOR ®. The American Naturalist, 104(940), 501–528. Retrieved from http://links.jstor.org/sici. • Souza, A. F. & Martins, F. R. (2004). Population structure and dynamics of a neotropical palm in fire-impacted fragments of the Brazilian Atlantic Forest. Biodiversity and Conservation, 13: 1611-1632. Retrieved from: https://www.researchgate.net/publication/227158775_Population_structure_an d_dynamics_of_a_Neotropical_palm_in_fire- impacted_fragments_of_the_Brazilian_Atlantic_Forest. • Wright, S. J., & Duber, H. C. (2001). Poachers and Forest Fragmentation Alter Seed Dispersal, Seed Survival, and Seedling Recruitment in the Palm Attalea butyraceae, with Implications for Tropical Tree Diversity1. Biotropica, 33(4), 583– 595. https://doi.org/10.1111/j.1744-7429.2001.tb00217.x https://commons.wikimedia.org/wiki/File:Palmeira_de_indai%C3%A1_REFON.jpg