Interactions between wolves and livestock depending on abundance

The purpose of this deer management model is to explore the capacity of wildlife management actions to help us adapt to the effects of climate change.

Simple BIDE model

A simulation illustrating how the size of a fish population affects the number of fish caught and vice versa.

This is a basic model for use with our lab section.  The full BIDE options.

This is a basic BIDE (birth, immigration, death, emigration) model.  Not all parts are implemented, however Birth and Death are.

This model illustrates predator prey interactions using real-life data of fox and rabbit populations.

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale. It was "cloned" from a model that InsightMaker provides to its users, at
https://insightmaker.com/insight/2068/Isle-Royale-Predator-Prey-Interactions
Thanks Scott Fortmann-Roe.

I've created a Mathematica file that replicates the model, at
http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/Moose-n-Wolf-InsightMaker.nb

It allows one to experiment with adjusting the initial number of moose and wolves on the island.

I used steepest descent in Mathematica to optimize the parameters, with my objective data being the ratio of wolves to moose. You can try my (admittedly) kludgy code, at
http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/Moose-n-Wolf-InsightMaker-BestFit.nb

{WolfBirthRateFactorStart,
WolfDeathRateStart,
MooseBirthRateStart,
MooseDeathRateFactorStart,
moStart,
woStart} =
{0.000267409,
0.239821,
0.269755,
0.0113679,
591,
23.};

This non-dimensionalized, sleekest most neatest model illustrates predator prey interactions using logistic growth for the moose population, for the wolf and moose populations on Isle Royale.

Thanks Scott Fortmann-Roe for the original model.

I've added in an adjustment to handle population sizes, by dividing by moose carrying capacity.

Time is scaled by the moose birth parameter:
tau=bm*t

There are therefore only three parameters left to account for any dynamics:

beta = bw/bm (relative wolf to moose births)
delta = dm/bm (relative death to birth ratio for moose)
gamma = dw/bm (wolf deaths to moose births)

The equations are thus

dM/dtau = M [ (1-M) - delta W ]
dW/dtau = W [beta M - gamma ]

There is a stable equilibrium pair of population values, relative to the carrying capacity:

M^* = gamma / beta
W^* = (1-gamma / beta) / delta

I have a sleek version with a logistical growth term for the moose, at

http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/Moose-n-Wolf-InsightMaker-sleek.nb

A collaborative class project with each participant creating an animal/plant sub-model​ to explore the greater population/community dynamics of the Yellowstone ecosystem.

The body of research and studies generated on the Fryingpan River between the 1940s and the present supports the development of a conceptual model of ecosystem responses to hydrological regime behavior and streamflow management activities. This conceptual model should encourage conversations about system behavior and collective understanding among stakeholders regarding connections between specific hydrological regime characteristics affected by management of Ruedi Reservoir and the ecological or biological variables important to local communities. For the sake of simplicity, the model includes mostly unidirectional relationships—feedback loops are exploded to reveal intermediate connections between variables. This approach increases the number of variables represented in the system, perhaps increasing its complexity at first glance. However, the primary benefit to the end user is that the model becomes more readable and explicit in its representation of system behavior. 

 

The conceptual model presented here likely differs by degrees from those held by the various investigators who considered Fryingpan River processes over the previous 80 years. However, it affectively aggregates the ideas main presented by each of those individuals. This model focuses on hydrological and biological variables and does not incorporate the entire diversity of human uses and needs for water from the Fryingpan River (e.g. hydropower production for the City of Aspen, revenue generated in the Town of Basalt by angling activities, etc.).  Rather it attempts to illustrate how the conditional state of important ecosystem characteristics might respond to reservoir management activities that impact typical spring flows, peak flow timing and magnitude, summer flows, fall flows, and winter flows. 

Dynamic system modelling the effect of pest population reductions in transport vectors hubs (e.g. marina or port), by means of a biocontrol agent (e.g. gastropod snail), on the spread of marine pests into new areas.

This is a simulation that represents the populations of lions in the world over the last 200 years.

This is a model which explains the difference between Mountain bikes riding compared to logging in the Tasmanian forests.

There is a concern that Logging has an adverse effect on the experience of tourist mountain bikers looking for nature experiences in Derby, Tasmaina.

Model created by Scott Fortmann-Roe.  This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

Experiment with adjusting the initial number of moose and wolves on the island.

This is my first Insight from the BIDE model of environmental science for BIO 190

This very simple model generates a tidal curve and a light climate at the sea surface to illustrate the non-linearity of the diel and tidal cycles. This has repercussions on benthic primary (and therefore also secondary) production.