Date of Award:

5-2015

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Committee Chair(s)

James Powell

Committee

James Powell

Committee

Brynja Kohler

Committee

Richard Cutler

Committee

Nghiem Nguyen

Committee

Thomas Edwards

Abstract

The spread of fruiting tree species is strongly determined by the behavior and range of fruit-eating animals, particularly birds. Birds either consume and digest seeds or carry and cache them at some distance from the source tree. These carried and settled seeds provide some form of distribution which generates tree spread to the new location. Firstly, we modal seed dispersal by birds and introduce it in a dispersal model to estimate seed distribution. Using this distribution, we create a population model to estimate the speed at which juniper and pinyon forest boundaries move.

Secondly, we introduce a fact that bird movement occurs based on local habitat type to receive modified dispersal model. Birds can easily move many kilometers but habitat changes on the scale of tens of meters with rapidly varying. We develop a new technique to solve the modified dispersal model and approximate the form of transported seed distributions in highly variable landscapes. Using a tree population model, we investigate the rate of forest migration in variable landscapes. We show that speeds calculated using average motility of animals and mean seed handling times accurately predict the migration rate of trees.

Regional scale forest distribution models are frequently used to project tree migration based on climate and geographic variables such as elevation, and regional presence-absence data. It is difficult to accurately use dispersal models based on large-scale presence-absence data, particularly for tree species dispersed by birds. The challenge is that variables associated with seed dispersal by birds are represented only few meters while the smallest pixel size for the distribution models begins with few kilometers. Transported seed distribution estimated in the variable landscape offers a tool to make use of this scale separation. Finally, we develop a scenarios that allows us to find large scale dispersal probabilities based on small scale environmental variables.

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