Ash Reduction Model Tutorial

Version 2.0





Tara L. Eberhart, Andrew J. Storer, Linda M. Nagel







© Michigan Technological University

1400 Townsend Dr.

Houghton MI, 49931

Updated April 2, 2007






            The Ash Reduction Model is a website intended to help forest resource managers reduce the amount of ash resource available to emerald ash borer (Agrilus planipennis) and thereby reduce the insect’s potential population density.  Version 2.0 of the model was formulated with phloem thickness data collected from over 500 ash trees in order to find the average phloem basal area of any given ash (Fraxinus spp., Oleaceae) tree within a desired size class. 


            The phloem tissue is the critical resource utilized by emerald ash borer.  Ash Reduction Model 2.0 takes into consideration ash tree phloem basal area, which is a good indicator of the relative amount of phloem available to emerald ash borer based on the size of the tree and its growing conditions.   Using Trees per Acre as the input data, managers can view the model outputs which include the diameter limit for removal of ash to achieve the specific reduction target percentage.  


Use of the model will limit the population potential of emerald ash borer, thereby reducing its impacts and potential spread.  Using diameter limit cutting on ash trees in a stand allows for retention of some trees in order to help preserve ash genetics and maintain it as a viable part of our forest.  The model shows outputs for retaining small trees as well as large diameter ash trees, depending on the manager’s decision.  This manual gives an example using real stand information that explains where to find the model, how to input data, and read the results.  Future models may incorporate ash species, growing conditions, geographic location, and remaining stand basal area. 










Welcome to the Ash Reduction Model – a website created to help with management decisions in removal of ash trees to reduce the population densities of emerald ash borer.  This tutorial provides background on the model, instructions for inputting data and how to use the information given by the model.


The model is designed to work with diameter limit harvesting silvicultural proscriptions.  This short tutorial will be useful to first time users of the model for reading the outputs and to see what data they need to enter into the model.  As the model versions progress with additional factors taken into consideration, the tutorials will be updated.


Why use this type of model?

At high population densities, this insect is capable of attacking and killing green, black and white ash. Long-term prospects for management include biological control to reduce population densities of the insect, and resistance or tolerance of ash trees to reduced population densities of the pest. In the short term, reduction of pest populations in local areas is achievable by removal of its breeding substrate.


Removal of ash from stands such as those in close proximity to outlier populations will reduce the population density of this insect, thereby reducing EAB impacts and potential spread.  The amount of phloem available to the insect in a forest stand containing ash can be measured from tree cores and samples removed from down trees.  Models of the amount of ash tree removal necessary to reduce EAB breeding substrate by a target percentage have been developed.


How does the model work?

The Ash Reduction Model Version 2.0 is based on ash species specific phloem.  The data used to calibrate the model comes from over 500 ash trees in a variety of rural sites throughout Michigan and northern Wisconsin that were measured in 2005.  The models find the percent phloem basal area by diameter of ash in a stand were developed from basal area of the tree minus the phloem tissue.  This is representative of the phloem in a tree that is available to emerald ash borer as phloem thickness is dependent on size of the tree and growing conditions.



Getting Started


Input Requirements Version 2.0

You will need the following information to run the Ash Reduction Model found at

  • Number of Trees per Acre of ash (Fraxinus) species
    • This is a measurement of tree density and can be determined from stock and stand tables.  Use only ash species in the stand, not total Trees/Acre.  Contact your local forester for more information.  Diameter class can be 2”, 1”, or 2cm, 1cm classes. 


Note:  This model only works with the ash component of a stand regardless of total stand size, other tree species presence, or how much total ash there is present. 


Using the Model

The model can be found at


Figure 1 – Ash Reduction Model homepage



At the bottom of the page is a link to this manual and below that a link to the model input page (Model Version 2.0).  Click on this to open the input page.


The Input Page

Once the input page is open, the user can scroll down and see information about the model, two tables of target percentages, an empty chart, and to the left a column of diameter classes and empty green cells for the user’s Trees per Acre data. 


Figure 2 – Top of Model input page


 Notice the 3 buttons at the top and bottom of the page:

Update – after data has been entered in the green columns, Update will refresh the page to reflect the correct % Surface Area and Diameter Limit to cut

            Clear – will erase data in the green columns and start the page blank

            Print – will print the outputs


Multiple Diameter Class Models

The user will have noticed that there are 4 model versions available, which may be used depending on the type of data information the user has.  1”, 2”, 1 cm, and 2 cm models are available to allow for different inventory data.


Entering Data

The Ash Reduction Model will automatically start with 0.0 in each of the green Number Trees/Acre cells.  This is where the user will enter their data.  After all of the numbers have been entered the user may click update to refresh the page or hit the Tab key on their keyboard after each entry to update the page automatically




Figure – 3 Empty input page


The example in Figure 4 shows real stand data that has been entered, with the % Surface Area that the Trees per Acre in that stand represent.  The Cumulative Percent Surface Area in the chart shows what Diameter limit corresponds with the cumulative percent.  The Target Percentage tables at the top show specific diameter limits for target percentages of surface area that may be chosen to remove.


Interpreting Outputs of the Model

% Surface Area Column - The column to the right of the green Trees per Acre column shows what percent of the total surface area in the stand that that particular diameter size class represents.  This information is used to compile the cumulative surface area that is graphed in the charts.


Relationship Cumulative Surface Area and DBH charts & Target % tables – Notice the output charts cumulative surface area to retain small trees, the most common type of diameter limit harvesting, which is removing all trees above a specified diameter at breast height. 



Figure 4 –Output chart


The first chart corresponds with most common type of diameter limit harvesting of retaining small trees, which is removing all trees above a specified diameter at breast height.  This chart matches up with the first table on the top left Retaining Small Trees that shows what the specific diameter limit is when targeting a certain percent removal of ash surface area as shown in Figure 4.  In this example, to remove 95 % of the surface area available to EAB, all ash trees greater than 4.4 inches should be removed.


Another way diameter limit harvesting is done is by removing trees to retain large trees.  An output of this type of modeling would be the same graph but with the cumulative surface area ascending. The user will see that the diameter limits shown in the bottom table on the right to retain large trees are much larger than in the table to retain small trees. 


With this type of harvesting, the forest manager can still remove a target amount of surface area or phloem available to emerald ash borer but retain seedlings (trees to small to be cut at all) and the larger diameter trees.  The diameter limit given for this type of harvesting indicates the size at which trees are left rather than cut, so all trees less than the specific diameter are removed.  Using this example, to retain large trees and still remove 95 % of the ash surface area, all trees less than 19.6 inches should be removed.




These models are available to forest resource managers so that they may be used to determine a diameter limit to retain ash trees as a component of our forests.  This management strategy will not eliminate emerald ash borer from our forests but it may reduce their population impacts on our remaining trees after the diameter limit harvest.  The model can be used with 1 or 2 inch diameter classes as well as metric data and will find diameter limits to retain large or small ash trees. 



Common Questions about the Ash Reduction Model

  1. Do all diameter classes need to have trees per acre?

No, a diameter class with no trees in it may be left blank and the model will still work.  A straight line may appear in the chart output; however this has no negative effect on the calculations and a target % may still be found.

  1. Where can I get trees per acre information from if I don’t have a stand table?

Contact your local forester, a forestry extension official from a university, or a consulting forester.  Trees per Acre is a measure of stand density that is calculated from stand basal area.

  1. Will my remaining ash trees be protected from emerald ash borer?

No, that is not the purpose of the model.  Using target ash reduction as a management tool will reduce the population potential of eab by taking away a targeted % of their critical resource, ash phloem.  This will reduce the potential for eab population buildup in an area, therefore minimizing its impact and possibly slowing its spread.





    1. Diameter class – any tree with a Diameter at Breast Height (dbh) may fit within a specified category ranging from 3” to 20”+, either within a 1” class or a 2” class, with each class being indicated by its midpoint diameter.  In the 2” class, diameter class 4 is for trees ranging in diameter from 3 to 5.9”.
    2. Diameter limit cutting – a harvesting method in which trees larger than a given diameter, based on the managers decision, are harvested, retaining the smaller trees less than the given diameter.  A reverse diameter limit cut may also occur, where larger trees are retained and all trees in the stand smaller than a given diameter are removed.  This may be done for wildlife benefits or aesthetics. 
    3. Fraxinus spp. – any Ash Tree species within the family Oleaceae, specifically including white, black, green, pumpkin, and blue ash (Fraxinus americana, Fraxinus nigra, Fraxinus pennsylvanica, Fraxinus profunda, Fraxinus quadrangulata respectively).  Mountain ash is not a true ash, belonging instead to the Rosaceae family.
    4. Phloem – the living tissue between the vascular cambium and the cork cambium of the outer bark.
    5. Basal area – the area of a cross section of a tree measured at breast height (1.3 meters above the ground), which is a useful description per unit area of a forest stand.
    6. Trees per acre – one of the most common descriptors of a stand found in a stand table, useful for describing the density of a stand per unit area by species and dbh class.




Funding for this research was provided by the USDA Forest Service Northeastern Area and was conducted at the School of Forest Resources and Environmental Science, Michigan Technological University, Houghton, Michigan.  We would also like to thank the many field consultants and lab technicians for their contribution in data collection.


Links for more information on Emerald Ash Borer







Contact Information:

Tara L. Eberhart


Andrew J. Storer


Linda M. Nagel


Mike Hyslop



About the Authors

Tara Eberhart is a Graduate Research Assistant., Andrew Storer is Associate Professor of Forest Insect Ecology, Linda Nagel is Assistant Professor of Silviculture, and Mike Hyslop is a GIS analyst in the School of Forest Resources and Environmental at Michigan Tech.


School of Forest Resources and Environmental Science

Michigan Technological University

1400 Townsend Dr.

Houghton, MI 49930

Fax: (906) 497 – 2915







Photo credits

Cover photo by Jessica Metzger

Emerald ash borer photo by Andrew Storer