Topics

Z16357 In-depth Age Analysis

Jared Smith
 

Aging our ancestors using Y-DNA data is far from an exact science. I'd
be happy to have you poke holes in any of this.

An analysis of the 11 Z16357 people who have taken Big-Y results in
the following number of 'good', unique/novel variants/mutations:

C. Hays 4
R. Hays 3
Pillsbury 5
Merrick 11
Thomas 6
Phillips 7
Bennett 9
M. Hartley 5
J. Hartley 5
J. Smith 12
Smith 27

These are variants that each person has that are not shared with
anyone else who has tested. The higher the number of novel variants,
the further back one would expect to be related to someone else
listed. I use the same metric for a 'good' variant as Alex does on his
Big Tree. This is a bit more aggressive than what YFull uses.

There are, however, some inconsistencies with this. Merrick, for
example, has nearly twice as many novel variants as Thomas, even
though Merrick connects lower/later on the tree than Thomas - one
would thus expect Merrick to have fewer novel variants. This is
primarily a factor of test coverage, but this is all we have to work
with, so we partially account for this variability by averaging. This
is why each new Big-Y test gives us increased accuracy.

When I add the novel variants above to the number of 'good' SNPs in
each block or haplogroup of our tree and average the results, I end up
with the following average number of variants downstream from each
listed SNP block:

ZS349 - 3.5
Z16854 - 9.3
BY15420 - 8.0
BY15419 - 9.7
Y29969 - 9.5
A11132 - 5
Z17911 - 10.9
Z16343 - 13
Z16357 - 36.1

This means, for example, that there's an average of 3.5 variants that
were formed after the most recent ZS349 ancestor that the two Hays men
share. For Z17911, we average 10.9 variants downstream (more recent
than) our most recent common Z17911 ancestor. Altogether, we average
36.1 SNPs downstream of Z16357.

To use these variant numbers to help us in aging, we need to calculate
a "years per SNP" value. YFull has our last Z16357 ancestor at around
3300 years ago (though they've acknowledged this is probably too
high). Other recent estimates put it as young as 2300 years ago. Until
someone digs up some Z16357 remains or we get enough DNA testers to
give us better data, we have to use our best informed estimate. I'll
assume our most recent Z16357 ancestor lived a minimum of 2500 and
maximum of 3000 years ago.

If we divide these age estimates by 36.1 SNPs (on average), this is a
minimum of 69.3 years per SNP and a maximum of 83.1 years per SNP. We
can then use these values to assign age estimates to notable
branchings as follows:

ZS349 - 327-376 years before present
Z16854 - 732-861
BY15420 - 639-750
BY15419 - 755-889
Y29969 - 743-875
A11132 - 431-501
Z17911 - 837-987
Z16343 - 986-1166
Z16357 - 2585-3085

The values are years before present, and include an additional 35
years (one generation?) to account for the age of the last ancestor
that had this SNP - and also adds 50 years as a guessed average of how
old the 11 Z16357 people are.

So this estimates that the common ZS349 ancestor for Hays was born
347-376 years ago. We know this ancestor was George Hays who was born
in 1655 - 362 years ago, so these numbers align perfectly!

This places our Z17911 ancestor being born between 837 and 987 years
ago. It places the Hartley common ancestor between 431 and 501 years
ago, the Bennett/Phillips ancestor 639-750 years ago, etc.

Do keep in mind that accuracy is more variable near the end of the
branches (closer to present day), especially with data from only 2 or
3 people. And SNPs are not always formed at a consistent rate. So this
all a bit rough, but should give us fairly reasonable estimations.

Jared

Joel Hartley
 

This sounds reasonable to me. I'd like to hear what folks at the L513 Yahoo Forum would have to say about it.

Joel

On 3/20/2017 10:52 AM, Jared Smith wrote:
Aging our ancestors using Y-DNA data is far from an exact science. I'd
be happy to have you poke holes in any of this.

An analysis of the 11 Z16357 people who have taken Big-Y results in
the following number of 'good', unique/novel variants/mutations:

C. Hays 4
R. Hays 3
Pillsbury 5
Merrick 11
Thomas 6
Phillips 7
Bennett 9
M. Hartley 5
J. Hartley 5
J. Smith 12
Smith 27

These are variants that each person has that are not shared with
anyone else who has tested. The higher the number of novel variants,
the further back one would expect to be related to someone else
listed. I use the same metric for a 'good' variant as Alex does on his
Big Tree. This is a bit more aggressive than what YFull uses.

There are, however, some inconsistencies with this. Merrick, for
example, has nearly twice as many novel variants as Thomas, even
though Merrick connects lower/later on the tree than Thomas - one
would thus expect Merrick to have fewer novel variants. This is
primarily a factor of test coverage, but this is all we have to work
with, so we partially account for this variability by averaging. This
is why each new Big-Y test gives us increased accuracy.

When I add the novel variants above to the number of 'good' SNPs in
each block or haplogroup of our tree and average the results, I end up
with the following average number of variants downstream from each
listed SNP block:

ZS349 - 3.5
Z16854 - 9.3
BY15420 - 8.0
BY15419 - 9.7
Y29969 - 9.5
A11132 - 5
Z17911 - 10.9
Z16343 - 13
Z16357 - 36.1

This means, for example, that there's an average of 3.5 variants that
were formed after the most recent ZS349 ancestor that the two Hays men
share. For Z17911, we average 10.9 variants downstream (more recent
than) our most recent common Z17911 ancestor. Altogether, we average
36.1 SNPs downstream of Z16357.

To use these variant numbers to help us in aging, we need to calculate
a "years per SNP" value. YFull has our last Z16357 ancestor at around
3300 years ago (though they've acknowledged this is probably too
high). Other recent estimates put it as young as 2300 years ago. Until
someone digs up some Z16357 remains or we get enough DNA testers to
give us better data, we have to use our best informed estimate. I'll
assume our most recent Z16357 ancestor lived a minimum of 2500 and
maximum of 3000 years ago.

If we divide these age estimates by 36.1 SNPs (on average), this is a
minimum of 69.3 years per SNP and a maximum of 83.1 years per SNP. We
can then use these values to assign age estimates to notable
branchings as follows:

ZS349 - 327-376 years before present
Z16854 - 732-861
BY15420 - 639-750
BY15419 - 755-889
Y29969 - 743-875
A11132 - 431-501
Z17911 - 837-987
Z16343 - 986-1166
Z16357 - 2585-3085

The values are years before present, and include an additional 35
years (one generation?) to account for the age of the last ancestor
that had this SNP - and also adds 50 years as a guessed average of how
old the 11 Z16357 people are.

So this estimates that the common ZS349 ancestor for Hays was born
347-376 years ago. We know this ancestor was George Hays who was born
in 1655 - 362 years ago, so these numbers align perfectly!

This places our Z17911 ancestor being born between 837 and 987 years
ago. It places the Hartley common ancestor between 431 and 501 years
ago, the Bennett/Phillips ancestor 639-750 years ago, etc.

Do keep in mind that accuracy is more variable near the end of the
branches (closer to present day), especially with data from only 2 or
3 people. And SNPs are not always formed at a consistent rate. So this
all a bit rough, but should give us fairly reasonable estimations.

Jared

Charles Thomas
 

Great analysis, Jared, but I think the SNP names are confusing me. Did you include an equivalent to FGC33966 for Martin and me?

Charles


From: Z16357@groups.io <Z16357@groups.io> on behalf of Jared Smith <jared@...>
Sent: Monday, March 20, 2017 9:52 AM
To: Z16357@groups.io
Subject: [Z16357] Z16357 In-depth Age Analysis
 
Aging our ancestors using Y-DNA data is far from an exact science. I'd
be happy to have you poke holes in any of this.

An analysis of the 11 Z16357 people who have taken Big-Y results in
the following number of 'good', unique/novel variants/mutations:

C. Hays 4
R. Hays 3
Pillsbury 5
Merrick 11
Thomas 6
Phillips 7
Bennett 9
M. Hartley 5
J. Hartley 5
J. Smith 12
Smith 27

These are variants that each person has that are not shared with
anyone else who has tested. The higher the number of novel variants,
the further back one would expect to be related to someone else
listed. I use the same metric for a 'good' variant as Alex does on his
Big Tree. This is a bit more aggressive than what YFull uses.

There are, however, some inconsistencies with this. Merrick, for
example, has nearly twice as many novel variants as Thomas, even
though Merrick connects lower/later on the tree than Thomas - one
would thus expect Merrick to have fewer novel variants. This is
primarily a factor of test coverage, but this is all we have to work
with, so we partially account for this variability by averaging. This
is why each new Big-Y test gives us increased accuracy.

When I add the novel variants above to the number of 'good' SNPs in
each block or haplogroup of our tree and average the results, I end up
with the following average number of variants downstream from each
listed SNP block:

ZS349 - 3.5
Z16854 - 9.3
BY15420 - 8.0
BY15419 - 9.7
Y29969 - 9.5
A11132 - 5
Z17911 - 10.9
Z16343 - 13
Z16357 - 36.1

This means, for example, that there's an average of 3.5 variants that
were formed after the most recent ZS349 ancestor that the two Hays men
share. For Z17911, we average 10.9 variants downstream (more recent
than) our most recent common Z17911 ancestor. Altogether, we average
36.1 SNPs downstream of Z16357.

To use these variant numbers to help us in aging, we need to calculate
a "years per SNP" value. YFull has our last Z16357 ancestor at around
3300 years ago (though they've acknowledged this is probably too
high). Other recent estimates put it as young as 2300 years ago. Until
someone digs up some Z16357 remains or we get enough DNA testers to
give us better data, we have to use our best informed estimate. I'll
assume our most recent Z16357 ancestor lived a minimum of 2500 and
maximum of 3000 years ago.

If we divide these age estimates by 36.1 SNPs (on average), this is a
minimum of 69.3 years per SNP and a maximum of 83.1 years per SNP. We
can then use these values to assign age estimates to notable
branchings as follows:

ZS349 - 327-376 years before present
Z16854 - 732-861
BY15420 - 639-750
BY15419 - 755-889
Y29969 - 743-875
A11132 - 431-501
Z17911 - 837-987
Z16343 - 986-1166
Z16357 - 2585-3085

The values are years before present, and include an additional 35
years (one generation?) to account for the age of the last ancestor
that had this SNP - and also adds 50 years as a guessed average of how
old the 11 Z16357 people are.

So this estimates that the common ZS349 ancestor for Hays was born
347-376 years ago. We know this ancestor was George Hays who was born
in 1655 - 362 years ago, so these numbers align perfectly!

This places our Z17911 ancestor being born between 837 and 987 years
ago. It places the Hartley common ancestor between 431 and 501 years
ago, the Bennett/Phillips ancestor 639-750 years ago, etc.

Do keep in mind that accuracy is more variable near the end of the
branches (closer to present day), especially with data from only 2 or
3 people. And SNPs are not always formed at a consistent rate. So this
all a bit rough, but should give us fairly reasonable estimations.

Jared



Jared Smith
 

Charles -

FGC33966 is your terminal SNP shared with Martin, but I only analyzed
Big-Y testers so I could include the novel variants. So FGC33966 is
counted as one of your 6 novel variants.

This methodology is a fairly standard way of doing age estimates, but
I don't think it had been done to this level for our tree before.

Jared

On Mon, Mar 20, 2017 at 3:05 PM, Charles Thomas <charles_002@...> wrote:
Great analysis, Jared, but I think the SNP names are confusing me. Did you
include an equivalent to FGC33966 for Martin and me?

Charles

________________________________
From: Z16357@groups.io <Z16357@groups.io> on behalf of Jared Smith
<jared@...>
Sent: Monday, March 20, 2017 9:52 AM
To: Z16357@groups.io
Subject: [Z16357] Z16357 In-depth Age Analysis

Aging our ancestors using Y-DNA data is far from an exact science. I'd
be happy to have you poke holes in any of this.

An analysis of the 11 Z16357 people who have taken Big-Y results in
the following number of 'good', unique/novel variants/mutations:

C. Hays 4
R. Hays 3
Pillsbury 5
Merrick 11
Thomas 6
Phillips 7
Bennett 9
M. Hartley 5
J. Hartley 5
J. Smith 12
Smith 27

These are variants that each person has that are not shared with
anyone else who has tested. The higher the number of novel variants,
the further back one would expect to be related to someone else
listed. I use the same metric for a 'good' variant as Alex does on his
Big Tree. This is a bit more aggressive than what YFull uses.

There are, however, some inconsistencies with this. Merrick, for
example, has nearly twice as many novel variants as Thomas, even
though Merrick connects lower/later on the tree than Thomas - one
would thus expect Merrick to have fewer novel variants. This is
primarily a factor of test coverage, but this is all we have to work
with, so we partially account for this variability by averaging. This
is why each new Big-Y test gives us increased accuracy.

When I add the novel variants above to the number of 'good' SNPs in
each block or haplogroup of our tree and average the results, I end up
with the following average number of variants downstream from each
listed SNP block:

ZS349 - 3.5
Z16854 - 9.3
BY15420 - 8.0
BY15419 - 9.7
Y29969 - 9.5
A11132 - 5
Z17911 - 10.9
Z16343 - 13
Z16357 - 36.1

This means, for example, that there's an average of 3.5 variants that
were formed after the most recent ZS349 ancestor that the two Hays men
share. For Z17911, we average 10.9 variants downstream (more recent
than) our most recent common Z17911 ancestor. Altogether, we average
36.1 SNPs downstream of Z16357.

To use these variant numbers to help us in aging, we need to calculate
a "years per SNP" value. YFull has our last Z16357 ancestor at around
3300 years ago (though they've acknowledged this is probably too
high). Other recent estimates put it as young as 2300 years ago. Until
someone digs up some Z16357 remains or we get enough DNA testers to
give us better data, we have to use our best informed estimate. I'll
assume our most recent Z16357 ancestor lived a minimum of 2500 and
maximum of 3000 years ago.

If we divide these age estimates by 36.1 SNPs (on average), this is a
minimum of 69.3 years per SNP and a maximum of 83.1 years per SNP. We
can then use these values to assign age estimates to notable
branchings as follows:

ZS349 - 327-376 years before present
Z16854 - 732-861
BY15420 - 639-750
BY15419 - 755-889
Y29969 - 743-875
A11132 - 431-501
Z17911 - 837-987
Z16343 - 986-1166
Z16357 - 2585-3085

The values are years before present, and include an additional 35
years (one generation?) to account for the age of the last ancestor
that had this SNP - and also adds 50 years as a guessed average of how
old the 11 Z16357 people are.

So this estimates that the common ZS349 ancestor for Hays was born
347-376 years ago. We know this ancestor was George Hays who was born
in 1655 - 362 years ago, so these numbers align perfectly!

This places our Z17911 ancestor being born between 837 and 987 years
ago. It places the Hartley common ancestor between 431 and 501 years
ago, the Bennett/Phillips ancestor 639-750 years ago, etc.

Do keep in mind that accuracy is more variable near the end of the
branches (closer to present day), especially with data from only 2 or
3 people. And SNPs are not always formed at a consistent rate. So this
all a bit rough, but should give us fairly reasonable estimations.

Jared



Charles Thomas
 

Thanks, Jared. The new age estimates are very helpful. One more question if I may:

the L513 Descendant Tree Chart has Bennett and I at BY11382. Is that an equivalent for

a SNP included on your Z16357 SNP tree?

Charles




From: Z16357@groups.io <Z16357@groups.io> on behalf of Jared Smith <jared@...>
Sent: Monday, March 20, 2017 8:53 PM
To: Z16357@groups.io
Subject: Re: [Z16357] Z16357 In-depth Age Analysis
 
Charles -

FGC33966 is your terminal SNP shared with Martin, but I only analyzed
Big-Y testers so I could include the novel variants. So FGC33966 is
counted as one of your 6 novel variants.

This methodology is a fairly standard way of doing age estimates, but
I don't think it had been done to this level for our tree before.

Jared



On Mon, Mar 20, 2017 at 3:05 PM, Charles Thomas <charles_002@...> wrote:
> Great analysis, Jared, but I think the SNP names are confusing me. Did you
> include an equivalent to FGC33966 for Martin and me?
>
> Charles
>
> ________________________________
> From: Z16357@groups.io <Z16357@groups.io> on behalf of Jared Smith
> <jared@...>
> Sent: Monday, March 20, 2017 9:52 AM
> To: Z16357@groups.io
> Subject: [Z16357] Z16357 In-depth Age Analysis
>
> Aging our ancestors using Y-DNA data is far from an exact science. I'd
> be happy to have you poke holes in any of this.
>
> An analysis of the 11 Z16357 people who have taken Big-Y results in
> the following number of 'good', unique/novel variants/mutations:
>
> C. Hays 4
> R. Hays 3
> Pillsbury 5
> Merrick 11
> Thomas 6
> Phillips 7
> Bennett 9
> M. Hartley 5
> J. Hartley 5
> J. Smith 12
> Smith 27
>
> These are variants that each person has that are not shared with
> anyone else who has tested. The higher the number of novel variants,
> the further back one would expect to be related to someone else
> listed. I use the same metric for a 'good' variant as Alex does on his
> Big Tree. This is a bit more aggressive than what YFull uses.
>
> There are, however, some inconsistencies with this. Merrick, for
> example, has nearly twice as many novel variants as Thomas, even
> though Merrick connects lower/later on the tree than Thomas - one
> would thus expect Merrick to have fewer novel variants. This is
> primarily a factor of test coverage, but this is all we have to work
> with, so we partially account for this variability by averaging. This
> is why each new Big-Y test gives us increased accuracy.
>
> When I add the novel variants above to the number of 'good' SNPs in
> each block or haplogroup of our tree and average the results, I end up
> with the following average number of variants downstream from each
> listed SNP block:
>
> ZS349 - 3.5
> Z16854 - 9.3
> BY15420 - 8.0
> BY15419 - 9.7
> Y29969 - 9.5
> A11132 - 5
> Z17911 - 10.9
> Z16343 - 13
> Z16357 - 36.1
>
> This means, for example, that there's an average of 3.5 variants that
> were formed after the most recent ZS349 ancestor that the two Hays men
> share. For Z17911, we average 10.9 variants downstream (more recent
> than) our most recent common Z17911 ancestor. Altogether, we average
> 36.1 SNPs downstream of Z16357.
>
> To use these variant numbers to help us in aging, we need to calculate
> a "years per SNP" value. YFull has our last Z16357 ancestor at around
> 3300 years ago (though they've acknowledged this is probably too
> high). Other recent estimates put it as young as 2300 years ago. Until
> someone digs up some Z16357 remains or we get enough DNA testers to
> give us better data, we have to use our best informed estimate. I'll
> assume our most recent Z16357 ancestor lived a minimum of 2500 and
> maximum of 3000 years ago.
>
> If we divide these age estimates by 36.1 SNPs (on average), this is a
> minimum of 69.3 years per SNP and a maximum of 83.1 years per SNP. We
> can then use these values to assign age estimates to notable
> branchings as follows:
>
> ZS349 - 327-376 years before present
> Z16854 - 732-861
> BY15420 - 639-750
> BY15419 - 755-889
> Y29969 - 743-875
> A11132 - 431-501
> Z17911 - 837-987
> Z16343 - 986-1166
> Z16357 - 2585-3085
>
> The values are years before present, and include an additional 35
> years (one generation?) to account for the age of the last ancestor
> that had this SNP - and also adds 50 years as a guessed average of how
> old the 11 Z16357 people are.
>
> So this estimates that the common ZS349 ancestor for Hays was born
> 347-376 years ago. We know this ancestor was George Hays who was born
> in 1655 - 362 years ago, so these numbers align perfectly!
>
> This places our Z17911 ancestor being born between 837 and 987 years
> ago. It places the Hartley common ancestor between 431 and 501 years
> ago, the Bennett/Phillips ancestor 639-750 years ago, etc.
>
> Do keep in mind that accuracy is more variable near the end of the
> branches (closer to present day), especially with data from only 2 or
> 3 people. And SNPs are not always formed at a consistent rate. So this
> all a bit rough, but should give us fairly reasonable estimations.
>
> Jared
>
>
>
>



Jared Smith
 

Charles -

It appears Mike made a mistake when he updated the chart. This should
be FGC33966. None of us have BY11382. I'll let him know.

Thanks,

Jared

On Mon, Mar 20, 2017 at 11:40 PM, Charles Thomas
<charles_002@...> wrote:
Thanks, Jared. The new age estimates are very helpful. One more question if
I may:

the L513 Descendant Tree Chart has Bennett and I at BY11382. Is that an
equivalent for

a SNP included on your Z16357 SNP tree?

Charles



________________________________
From: Z16357@groups.io <Z16357@groups.io> on behalf of Jared Smith
<jared@...>
Sent: Monday, March 20, 2017 8:53 PM
To: Z16357@groups.io
Subject: Re: [Z16357] Z16357 In-depth Age Analysis

Charles -

FGC33966 is your terminal SNP shared with Martin, but I only analyzed
Big-Y testers so I could include the novel variants. So FGC33966 is
counted as one of your 6 novel variants.

This methodology is a fairly standard way of doing age estimates, but
I don't think it had been done to this level for our tree before.

Jared



On Mon, Mar 20, 2017 at 3:05 PM, Charles Thomas <charles_002@...>
wrote:
Great analysis, Jared, but I think the SNP names are confusing me. Did you
include an equivalent to FGC33966 for Martin and me?

Charles

________________________________
From: Z16357@groups.io <Z16357@groups.io> on behalf of Jared Smith
<jared@...>
Sent: Monday, March 20, 2017 9:52 AM
To: Z16357@groups.io
Subject: [Z16357] Z16357 In-depth Age Analysis

Aging our ancestors using Y-DNA data is far from an exact science. I'd
be happy to have you poke holes in any of this.

An analysis of the 11 Z16357 people who have taken Big-Y results in
the following number of 'good', unique/novel variants/mutations:

C. Hays 4
R. Hays 3
Pillsbury 5
Merrick 11
Thomas 6
Phillips 7
Bennett 9
M. Hartley 5
J. Hartley 5
J. Smith 12
Smith 27

These are variants that each person has that are not shared with
anyone else who has tested. The higher the number of novel variants,
the further back one would expect to be related to someone else
listed. I use the same metric for a 'good' variant as Alex does on his
Big Tree. This is a bit more aggressive than what YFull uses.

There are, however, some inconsistencies with this. Merrick, for
example, has nearly twice as many novel variants as Thomas, even
though Merrick connects lower/later on the tree than Thomas - one
would thus expect Merrick to have fewer novel variants. This is
primarily a factor of test coverage, but this is all we have to work
with, so we partially account for this variability by averaging. This
is why each new Big-Y test gives us increased accuracy.

When I add the novel variants above to the number of 'good' SNPs in
each block or haplogroup of our tree and average the results, I end up
with the following average number of variants downstream from each
listed SNP block:

ZS349 - 3.5
Z16854 - 9.3
BY15420 - 8.0
BY15419 - 9.7
Y29969 - 9.5
A11132 - 5
Z17911 - 10.9
Z16343 - 13
Z16357 - 36.1

This means, for example, that there's an average of 3.5 variants that
were formed after the most recent ZS349 ancestor that the two Hays men
share. For Z17911, we average 10.9 variants downstream (more recent
than) our most recent common Z17911 ancestor. Altogether, we average
36.1 SNPs downstream of Z16357.

To use these variant numbers to help us in aging, we need to calculate
a "years per SNP" value. YFull has our last Z16357 ancestor at around
3300 years ago (though they've acknowledged this is probably too
high). Other recent estimates put it as young as 2300 years ago. Until
someone digs up some Z16357 remains or we get enough DNA testers to
give us better data, we have to use our best informed estimate. I'll
assume our most recent Z16357 ancestor lived a minimum of 2500 and
maximum of 3000 years ago.

If we divide these age estimates by 36.1 SNPs (on average), this is a
minimum of 69.3 years per SNP and a maximum of 83.1 years per SNP. We
can then use these values to assign age estimates to notable
branchings as follows:

ZS349 - 327-376 years before present
Z16854 - 732-861
BY15420 - 639-750
BY15419 - 755-889
Y29969 - 743-875
A11132 - 431-501
Z17911 - 837-987
Z16343 - 986-1166
Z16357 - 2585-3085

The values are years before present, and include an additional 35
years (one generation?) to account for the age of the last ancestor
that had this SNP - and also adds 50 years as a guessed average of how
old the 11 Z16357 people are.

So this estimates that the common ZS349 ancestor for Hays was born
347-376 years ago. We know this ancestor was George Hays who was born
in 1655 - 362 years ago, so these numbers align perfectly!

This places our Z17911 ancestor being born between 837 and 987 years
ago. It places the Hartley common ancestor between 431 and 501 years
ago, the Bennett/Phillips ancestor 639-750 years ago, etc.

Do keep in mind that accuracy is more variable near the end of the
branches (closer to present day), especially with data from only 2 or
3 people. And SNPs are not always formed at a consistent rate. So this
all a bit rough, but should give us fairly reasonable estimations.

Jared