Modeling the performance over a range of sites using

genetic flexibility (plasticity)

Dag Lindgrenat

Plasticity Adaptation in Forest Trees Madrid (Spain), 27th - 29th February 2008

A mathematical method for systematizing and utilizing the variation over a range, Can be applied to any regeneration material and range, but here applied to provenances and seed orchards over latitudes in Sweden.

http://www-genfys.slu.se/staff/dagl/TREEBREEDEX/MadridMeeting.htm

One of the plus trees grafted at the seed orchard Västerhus designed AC 3033

Swedish seed orchards have clones from plus trees, which grows in different places (to avoid relatives and contribute to diversity)

A Swedish seed orchard with tested clones

Västerhus

Photo: Anders Fries Oct 2007

Plantation with Västerhus seedlings

Photo Dag Lindgren

     

                                                                                                        

     

Recommended area for using the seed orchard (Planter’s guide 2008-01-01)

Västerhus (T10)

Latitude for plus tree origin 63°30'Category: TestedLocation:Latitude 63,8 NElevation 15 mEstablished 1991

     

The range a material could be used over?

• Problem: What is the cost of using the same material over a wide range?

• Problem: What is the cost of having a forest reproductive material composed of components best adapted for different environments?

• etc

The information for Sweden is quantified into “planter’s guide” on the web

• Transfer of stand and seed orchard seeds• http://www.skogforsk.se/KunskapDirekt/default.aspx?p=20295&bmp=11727

Hannerz and Eriksson 2008

In seed orchard proceedings

Planter’s guide was used

• The following shows what I found for stand seeds

• There are legal limits, most but not all transfers shown are allowed

• I make the best transfer = 100 and relate to that for other alternatives at the site

• Figures should be compared horizontally and shows how the performance of a provenance varies over plantation latitudes (at a given altitude)

Performance of a provenance at a plantation site in percent of optimal transfer

Performance of a provenance at a plantation site in percent of best transfer

Comments

• A general problem: Planter’s guide often advices an optimum at the extreme of what is available as input.

• For Norway spruce: you would like to see what happens if you transfer more to the north.

• For Scots pine: too narrow range and not suboptimal northern provenances in the north..

• For Scots pine I tried specific seed orchards also

Relative performance over plantation sites compared to an optimal seed orchard (=100%)

About fits to field data

• Data from a provenance series extending over Sweden (the Eiche series with Scots pine) was fitted, this may be one of the best series (30 sites in Sweden)

• However, it is few provenances which are at many places and individual values vary wildly. Statistical variation in index may be 10%.

• Therefore no good fit is possible, polynomials give vary variable result, we fitted to a standard curve instead (Raymond and Lindgren 1990).

• Field data are always very imprecise and statistical fits with many degrees of freedom give unreliable information.

• Model developed by Lindgren and Ying (2000)

• “Cauchy-distribution”• Y (X) is performance in environment X• Symmetric around B (the environment

where the material is best adapted)• C is a measure of flexibility (plasticity,

adaptability)

2

1

1)(

CBX

XY

Adaptation over environments

(Systematic G*E)Plantation sites and seed origins described by a single value

Flexibility (C) of seed source best adapted at B.Cauchy function

0

1

Site type value

Per

form

ance

C

B

Scots pine optimal at lat 60 Performance compared to best provenance

0.000.100.200.300.400.500.600.700.800.901.00

55 57 59 61 63 65Plantation site (latitude)

Pe

rfo

rma

nc

e v

s b

es

t o

rig

in

Cauchy with flexibility 5 latitudes gives reasonable fits

Environment - adaptation

Wider zones = lower average maladaptation

Performance as a function of zone size

0

0.2

0.4

0.6

0.8

1.0

1.2

0Zone size

Pe

rfo

rma

nc

e (m

ax=

1)

at zone periphery

average over zone

The Cauchy get an integral

Loss over a range (zone size) z

(approx small z) 3

arctan 2z

z

z

Components of the seed source have the range v, the loss is (approx for small z and v) 63

22 vz

z and v are ranges expressed as fractions of 2C

C= flexibility = 5 latitudes! (from Scots pine Swedish data).

Thus a Scots pine seed source produces 80% of optimum over a range of 5 latitudes

Origin of clones at Västerhus

0

100

200

300

400

500

600

61 62 63 64 65 66

Latitude

Alt

itu

de

Range of origins = v = 3 latitudes, but considering pollen, range of halfsibfamilies =v/2 = 1.5 latitude

Plust tree origins

Seed orchard location

Inoptimality loss as function of zone size and origin range (latitudes,

flexibility = 5 latitudes)Zone size Range of

originsLoss (%)

4 0 5.3

2 0 1.3

2 2 2.0

2 4 4.0

Conclusions:

• Zone size 2 latitudes is OK (as used)

• Avoid larger origin range than 2-3 latitudes in seed orchards

Useful links and referenceshttp://www-genfys.slu.se/staff/dagl/TREEBREEDEX/MadridMeeting.htmhttp://www-genfys.slu.se/staff/dagl/Breed_Home_Page/SiteNrRange/Sites_Menu.html

References:• Hannerz M and Ericsson T 2008. Planter's guide - a

decision support system for the choice of reforestation material In Lindgren D (editor) Proceedings of a Seed Orchard Conference, Umeå, Sweden, 26-28 September 2007. p 88-94.

• Lindgren D & Ying CC 2000. A model integrating seed source adaptation and seed use. New Forest 20: (1) 87-104

• Raymond, C.A. and Lindgren, D. 1990. Genetic flexibility - a model for determining the range of suitable environments for a seed source. Silvae Genet. 39: 112-120.