Optimal use of genetic markers in conservation programmes

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Optimal use of genetic markers in conservation

programmes

Miguel Toro, Luis Silió, Jaime Rodrigañez, Carmen Rodriguez, Jesús

Fernández

To cite this version:

Note

Optimal

use

of

genetic

markers

in conservation

_programmes

Miguel

Toro*

Luis Silió, Jaime

_{Rodrigañez,}

Carmen

_Rodriguez

Jesús

Fernández

Departamento

de

Mejora

Genética _y

_{Bíotecnología, INIA,}

Ctra. de La Corufia km _7, 28040

_{Madrid, Spain}

(Received

24 November

1998; accepted

26 March

₁₉₉₉₎

Abstract - Monte Carlo simulations were carried out in order to

_study

the benefits of

using

molecular markers to minimize the

_{homozygosity by}

descent in a conservation

scheme of the Iberian

_pig.

A selection criterion is introduced: the overall

_expected

heterozygosity

of the group of selected individuals. The method to

_implement

this criterion

_depends

on the _type of information available. In the absence of molecular information

_breeding

animals are chosen that minimize the _{average group coancestry}

calculated from

_pedigree.

If

_complete

molecular information is known the average group coancestry is calculated either from markers alone or

_{by combining pedigree}

and _genotypes with the markers. When a limited number of markers and alleles _per

marker are

_considered,

the

optimal

criterion is the average group coancestry based on

markers. Other

_{alternatives,}

such as

_{optimal within-family}

selection and

frequency-dependent selection,

are also

_{analysed. ©}

_{Inra/Elsevier,}

Paris

conservation _genetics

_/

molecular markers

_/

average coancestry

Résumé - Utilisation _{optimale des marqueurs génétiques dans les programmes de} conservation. Des simulations Monte Carlo ont été effectuées pour étudier l’intérêt de l’utilisation des _marqueurs moléculaires pour minimiser le taux

_{d’homozygotie}

par

réplication

mendélienne dans un schéma de conservation du porc

ibérique.

Un critère de sélection a été introduit : le taux

_{global espéré d’hétérozygotie}

du

groupe des individus sélectionnés. La méthode pour

appliquer

ce critère

_dépend

du type d’information

disponible.

À

défaut d’information

_{moléculaire,}

on choisit

les animaux

_{reproducteurs}

qui minimisent la

_parenté

_{moyenne du groupe} calculée

d’après

les

généalogies.

En cas d’information

_{moléculaire,}

la

parenté

moyenne est

calculée soit

_d’après

les marqueurs

seuls,

soit en combinant

_{généalogies}

et

_génotypes

aux _marqueurs.

_Lorsque

l’on considère un nombre limité de marqueurs et d’allèles

par marqueur, le critère

optimal

est la

_parenté

moyenne du groupe conditionnée aux

*

Correspondence

and reprints

marqueurs. D’autres

alternatives,

telles que la sélection intra-familiale et la sélection

dépendant

des

fréquences alléliques,

ont été

_{également analysées.}

_©

_{Inra/Elsevier,}

Paris

génétique de

_conservation

_{/ marqueurs génétiques}

_{/ parenté}

moyenne

1. INTRODUCTION

Molecular markers are

_being

advocated as a

_powerful

tool for

_paternity

exclusion and for the identification of distinct

_populations

that need to be conserved

_(1!.

Here we focused on a different

_application,

namely

the use of

markers to

_delay

the loss of

_{genetic variability}

in a

_population

of limited

size. In a

_previous

_paper

_[12]

we conclude that a conventional

_tactic,

such

as the restriction of the variance of

_family

_sizes,

is the most

_important

tool for

maintaining genetic variability.

In this

_context,

_{frequency-dependent}

selection

seems to be a more efficient criterion than selection for

_{heterozygosity,}

but an

expensive

strategy

with

_respect

to the number of

_genotyped

candidates and markers is

_required

in order to obtain substantial benefits.

For this reason, we have considered a new criterion of selection: the overall

expected heterozygosity

of the _group of selected individuals. The

implementa-tion of this criterion

_depends

on the

_type

of information

available,

either from

pedigree

or from molecular markers. A new

_type

of conventional

_tactics,

op-timal

_{within-family}

selection

_(OWFS)

recently proposed by Wang

(14!,

is also considered.

2. SIMULATION

The

_{breeding population}

consisted of

N,

= 8 sires and

N

d

= 24 dams. Each

dam

_produced

three progeny of each sex. These 72

_offspring

of each sex were

candidates for selection to

_breeding

of the next

_generation.

This nucleus mimicked the conservation programme carried out in the

_Guadyerbas

strain of the Iberian

_pig

_(11!.

The

_techniques

of simulation of the genome, marker loci and

frequency-dependent

selection have been

_previously

described

_(12!.

_Here,

we introduced a new

_criterion,

the average

expected heterozygosity

of the group of selected

individuals,

implemented by

three different methods

_depending

on the

_type

of information available:

_a)

_average

_coancestry,

_{including reciprocal}

and

self-coancestries,

calculated from

_pedigree

_{(GCP); b)}

_average

_coancestry

for the

L n

markers

_(GCM),

which can be calculated

_using

1 -

_{L LP7k,}

where pik is

k i

the average

frequency

in the selected

population,

of allele i of locus

k,

n

the number of alleles and L the number of marker

_loci;

and

_c)

the _average

coancestry

calculated

_{by combining}

information

_{given by pedigree}

and

by

molecular markers

_(GCPM).

The calculation of

_coancestry,

based on marker

The

_{implementation}

of this selection criterion would

_require

the examination

of

!!! (3!d)

_N,,!

at all

_possible

combinations and this would be cum

-( N!, ) -( Nd )

bersome even for a small nucleus. It can be solved

_{using integer}

mathematical

programming techniques,

whose

_{computational}

cost would be feasible in most

practical

situations but not for simulation

work,

where the

algorithm

should

be used

_repeatedly.

For this reason we used a simulated

annealing algorithm

[10]

that,

although

not

_assuring

the

_{optimal solution,}

was

_generally

shown to

exhibit a _very

_good

behaviour when

_dealing

with similar

_problems

[5, 8!.

Besides the basic situation of no restriction on the

_{family sizes,}

two

_types

of restrictions were considered:

_a)

within-family

selection

_(WFS)

where each dam

_family

contributes one dam and each sire

_family

contributes one sire to the next

_generation;

and

_b)

optimal

within-family

selection

_(OWFS):

_among the

N

d

dams

mated with each

sire,

one is selected at random to contribute

N,

one _son, another one to contribute two

_daughters

and the

_remaining

C N

d

J -

2

B!

/

contribute one

daughter

each

!14!.

The values of true

_genomic

_homozygosity

_by

descent and

_inbreeding

of evalu-ated individuals at each

_generation

were calculated

_together

with the

_expected

genomic

homozygosity

of individuals selected from the

_previous

_generation

and

averaged

over 100

_replicates.

The various situations

_analysed

were also

com-pared

according

to their rate of

_homozygosity

per

generation

calculated from

Ho(t) - Ho(t - 1)

.

__ , ,

generation

6 to

_generation

15 as OHo

-Ho

t

-Ho

t - 1

where

Ho

(t)

is 1( )

_{ot-1 1) )}

W’!’here

Ho t is the average

homozygosity

by

descent of individuals in

_generation.

The rate of

inbreeding

was calculated in a similar _way. 3. RESULTS AND DISCUSSION

3.1. No molecular information or

_complete

molecular information

Several cases were considered for two extreme situations: the absence of molecular information or the

_{complete knowledge}

of the _genome. The relative

ranking

of the methods was maintained for all

_generations

and the results of

generation

15 are shown in table L With no molecular

_information,

the true

homozygosity

values were almost identical to those calculated from

pedigrees.

Optimal within-family

selection

_[14]

was

_{substantially}

(about

15

%)

more

ef-ficient than classical

_{within-family}

selection. The restrictions on

_family

size distribution are _unnecessary if the method of minimum average _group

coances-try

of selected individuals

_(GCP)

is used. The

_{commonly accepted}

measure of

genetic

variability

of a

population

is the

expected

heterozygosity

[9]

under the

Hardy-Weinberg

equilibrium

(1 - EP

2

).

In the absence of molecular infor-mation the _{average group}

_coancestry

measures the

_expected

_homozygosity

_by

descent

_[4]

and therefore the best method for

_{choosing breeding}

animals should minimize _{the average group}

_coancestry

calculated from

_pedigree

_[2-4,

_7!.

If

_only

full and half-sib

relationships

are

considered,

the criterion would lead to the

When

_using

_complete

molecular information for

_selection,

the best method

was still the same

_although

now the true

_coancestry

for all of the genome

was known. In this case, the

inbreeding

coefficient did not reflect the true

homozygosity,

and the

_discrepancy

could have been considerable.

_Furthermore,

the rate of advance in the true

_{homozygosity,}

unlike the rate of

_inbreeding,

does not attain an

_asymptotic

value after a short number of

_generations

but

decreases

_{continuously.}

The method of _{minimum average group}

_coancestry

_using

all the molecu-lar information

_(GCM)

reduced the rate of

_{homozygosity by}

almost a

_half,

although

the

_algorithm

utilized did not warrant the attainment of the

opti-mal solutions. The

_impact

of

_imposing

additional restriction on

_family

size was

negligible.

In a balanced

_structure,

the minimization of _average

_coancestry

is

mainly

attained,

as

_{previously explained, by selecting}

individuals from different

families.

Frequency-dependent

selection,

very easy to

apply,

can also be efficient as

a conventional

_tactic,

_although

not

_{being theoretically justified}

and therefore

lacking

generality.

The results of

_{frequency-dependent}

selection

_depended

on

family

size restrictions. Without

_{restrictions,}

the results were almost as bad as

when the

_molecular

information was

ignored owing

to an

_increasing

_tendency

to co-select sibs

_[12].

But,

after

_optimal

_family

size restrictions were

_imposed,

the method was as

_good

as the _group

_coancestry

_method,

since the differences

3.2. Limited number of markers and alleles _per marker

The relative

_utility

of the number of markers and alleles _per marker is

presented

in table

_II,

where values of the true

_{genomic homozygosity}

and

inbreeding

are

_given

for three situations: _{average group}

_coancestry

criterion

(GCM),

used either without restriction or with

_optimal

_family

size

_{restrictions,}

and

_{frequency-dependent}

selection with

optimal family

size restrictions. The

cases of

_complete

or null marker information are also

_presented

for

_comparison.

As the number of markers and alleles per marker

increased,

the genome

ho-mozygosity

attained at

_generation

15 decreased

_although

it was not

_adequately

reflected in the

_inbreeding

coefficient. This also confirmed our

_previous

finding

[12]

that the value of a marker is related to the number of alleles: two markers with ten alleles are as valuable as six markers with four alleles.

The results also indicated that the use of the method of minimum _average

group

coancestry

(or

expected

heterozygosity)

based

_only

on ,molecular

data without

_family

restrictions was not a

_good

criterion even with a

_huge

amount

of molecular information. The use of this method while

applying

the

optimal

restrictions on

_family

sizes

_emerged

from table II as a better criterion

(10

%

of

advantage).

Our

_results,

not shown

_here,

also confirmed that

_slight

improve-ments in the conventional tactics could have an

_{important impact}

on the

main-tenance of

_{genetic variability. Thus,}

OWFS with three

_{markers/chromosome}

and four

_{alleles/marker}

was as efficient as WFS with ten

_{markers/chromosome}

and four

_{alleles/marker (14.80}

of genome

homozygosity

at

_generation

15 in both

Finally,

table III shows a

_comparison

of the values for _genome

_homozygosity

when

_using

the method of

_minimizing

_average group

coancestry

for markers

(GCM)

together

with restrictions on

_family

sizes with the

_{theoretically}

optimal

method of

_minimizing

average group

coancestry

based on marker information

(GCPM).

In order to diminish the

_{high computing}

cost of the

_analysis

of

pedigree

involved in the last

_method,

_{the genome size has been reduced} to

_just

one chromosome of 100 cM. Due to this smaller _genome

_size,

selection was more

efficient and the results of the method of the average group marker

coancestry

with

optimal

restrictions were now better than those shown in table II. Results

shown in table III also indicated that the method of average group

coancestry

based on the markers was 20-30

%

more efficient. This

comparison

was

_only

strictly

valid for the _genome size

_considered,

but it can be

safely

concluded that

the last method could contribute

_{substantially}

to the

_efficiency

of a

marker-assisted conservation programme.

Although

the conclusions obtained

_through

simulation

_probably

have some

generalities,

it should be

_recognized

that some theoretical

developments

on

marker-assisted conservation are needed. In recent _years, substantial work has been carried out on the

joint prediction

of

_inbreeding

and

genetic gain

when

selecting

for a

_quantitative

trait

(see

[15],

for the latest

development

of the

theory).

However, predictions

on the rate of advance of the true

_homozygosity

by

descent when the selected trait is the

_{heterozygosity itself,}

measured either

by

molecular or

pedigree information,

is

lacking.

The use of an

optimal

method enhances the

prospectives

of the

application

of

molecular markers in conservation programmes,

although

the future will

depend

multiplex genotyping

is

_used,

but in the near future other DNA

_{polymorphisms}

such as SNP could be the most

_adequate

for routine

_scoring

_[6].

It is also

interesting

to

_emphasize

that the

adequate

use of molecular tools

_requires

increasingly

sophisticated

methods of Monte Carlo

_analysis

of

_pedigree

and

more

_powerful

methods of combinatorial

_{optimization.}

ACKNOWLEDGEMENT

This work was

_{supported by}

the INIA grant SC98-083.

REFERENCES

[1]

Avise

J.C.,

Molecular

_Markers,

Natural

_History

and

Evolution, Chapman

&

Hall,

New

_York,

1994.

[2]

Ballou

_{J.D., Lacy}

_{R.C., Identifying genetically important}

individuals for

man-agement of

_genetic

variation in

_{pedigreed populations,}

in: Ballou

J.D., Gilpin M.A.,

Foose T.J.R.

_(Eds.),

Population Management

for Survival and

_Recovery.

Analyti-cal Methods and

Strategies

in Small

Population Conservation,

Columbia

University

Press, 1995,

pp. 76-111.

[3]

Brisbane

_J.R.,

Gibson

_{J.P., Balancing}

selection response and rate of

_inbreeding

by including genetic relationship

in selection

decisions,

Theor.

_Appl.

Genet. 91

₍₁₉₉₅₎

421-431.

[4]

Caballero

_A.,

Toro

_M.A.,

Interrelations between effective

_population

size and other

pedigree

tools for the management of conserved

populations,

Genet. Res.

(submitted).

[5]

Fernindez

_J.,

Toro

_M.A.,

The use of mathematical

_programming

to control

inbreeding

in selection

schemes,

J. Anim. Breed. Genet.

_{(1999) (in press).}

[6]

Kruglyak L.,

The use of

_genetic

_map of biallelic markers in

_{linkage studies,}

Nat. Genet. 17

₍₁₉₉₇₎

21-24.

[7]

Meuwissen

T.H.E., Maximizing

the response of selection with a

predefined

rate

of

_inbreeding,

J. Anim. Sci. 75

₍₁₉₉₇₎

934-940.

[8]

Meuwissen

_T.H.E.,

Woolliams

_{J.A., Maximizing genetic}

_response in

_breeding

schemes of

_dairy

cattle with constraints on variance of _response, J.

_Dairy

Sci. 77

(1994)

1905-1916.

[9]

Nei

_{M., Analysis}

of gene

diversity

in subdivided

populations,

Proc. Nat. Acad.

Sci. USA 70

₍₁₉₇₃₎

3321-3323.

[10]

Press

_{W.H., Flannery B.P., Teukolsky S.A., Vetterling W.T.,}

Numerical

Recipes, Cambridge University Press, Cambridge,

1989.

!11!

Rodriganez J.,

Sili6

_L.,

Toro

_{M.A., Rodriguez C., Fifty}

years of conservation of

a black hairless strain of Iberian

_pigs,

in: Matassino

_{D., Boyazoglou J., Cappuccio}

A.

(Eds.),

International

Symposium

on Mediterranean Animal

_Germplasm

and Future

Challenges,

EAAP Publication no. _85,

_{Wageningen Pers, 1997,}

_pp. 183-186.

[12]

Toro

M.A.,

Sili6

L., Rodriganez J., Rodriguez C.,

The use of molecular markers in conservation programmes of live

animals,

Genet. Sel. Evol. 30

₍₁₉₉₈₎

585-600.

[13]

Varona

_{L., Pérez-Enciso,}

M., Detecci6n de

_(aTLs

mediante la

_partici6n

de la

varianza

_gen6tica

en funci6n del parentesco atribuible a _segmentos del genoma, ITEA

Producci6n Animal 94A

_{(3) (1998)}

265-270.

[14]

Wang

J., More efficient

breeding

systems for

controlling inbreeding

and effective size in animal

_{populations, Heredity}

79

₍₁₉₉₇₎

591-599.

[15]

Woolliams

_J.,

A recipe for the

_design

of

_{breeding schemes,}

Proc. 6th World

Cong.

Genet.

_Appl.

Livest. Prod. 25

₍₁₉₉₈₎

427-430.