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MHC-based mating rules can evolve as a way to avoid inbreeding or to increase offspring immune competence. While the role of mating preference in the MHC diversity in vertebrates has been acknowledged, its impact on individual MHC diversity has not been considered. Here, we use computer simulations to investigate how simple mating rules favouring MHC-dissimilar partners affect the evolution of the number of MHC variants in individual genomes, accompanying selection for resistance to parasites. We showed that the effect of such preferences could sometimes be dramatic. If preferences are aimed at avoiding identical alleles, the equilibrium number of MHC alleles is much smaller than under random mating. However, if the mating rule minimises the ratio of shared to different alleles in partners, MHC number is higher than under random mating. Additionally, our simulations revealed that a negative correlation between the numbers of MHC variants in mated individuals can arise from simple rules of MHC-disassortative mating. Our results reveal unexpected potential of MHC-based mating preferences to drive MHC gene family expansions or contractions and highlight the need to study the mechanistic basis of such preferences, which is currently poorly understood.
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
!!!"#!#$%&'(
&Bentkowski P, Radwan J. 2020 Mating preferences can drive expansion or contraction of major
histocompatibility complex gene family. Proc. R. Soc. B 20192706. http://dx.doi.org/10.1098/rspb.2019.2706
Mating preferences can drive expansion or contraction of MHC gene family
Piotr Bentkowski, Jacek Radwan 
 !"#$%#&
!'()*                    *        +
,---!'(*-
*"!'(-*'
          -          !'()
  +  -      -  *    !'(        
            ,  -  -  -  +    -
*.
-/**!'(--'
-  -  - + !'( *
-- -        - 
 *- * !'(   
    !'()    0      1      !'()*
!'(1----
--*---
Introduction
2- -*1!'(-
   - *
-
3)4!'( *
*--
 -
-  2)   5    !'()  1  
*   %- 
 * 
-2-
--
--  -    !'(        -#
6 )/)
7)8!'(       

 3  9  %    !'()  
9:
-!'(-;)33
,--  !'(- - *
1    *  - 8  3<)38  -
      -  *    !'(  
1* -
* 39  !'(*  *
+3:)<=-
1"!'(-**
*    +      -    -
+- 
-#  !'(  -* 
!'(    1        *  
-7 <3  -
     --  * <<<4
'-1!'(" *
*----
--  - !'(
 )  -  <7
<>    --  -          
  *  -            
 <8)<:              -
* !'(  -  
    -" <;  - 4=  # 
43*<3.
*--"+-*!'(
 +*1 * -
+-*
-          --        -
*+!'(*39'
-- !'(
-!'(
%!'()  
  - -
"               
3 92- 51 -
- --
1 5* 
*4<!'(
"    "- 44 )  -  1  -
- -   
2---!'(
+-*2-
1--!'(
--
 2) !'( -#-* * 
*--#
- 
       7  .  /
    !'(      -    
---*5
*-*-1
!'(    - --  !'( )
*
.    -     
!'(     
  * 1   47 4> 5-
1
4849  4: * 4; - 7= *
--737<74!)
-)-77)
- * : - -   
)5'
*-    *      +  #
  -  -    )5  ?-
+    +  #  *  16  
  +        
5 !'( -  
5  +      !'(   
1-!'()*  
        5    !'(  
**@
    (  1    !'(
-"--
----5
 *'   
  -        !'()
   +-  !'(
.-
!'()* - 
!'(1!'()*
 --   1 )
5!'(
Methods
,  !'()*  
--!'(**
A
2-)
  -  "        
  -  -      * -
*----1
        -  !'(      *
39  *              -  2-
  "        !'()-  )
    *      -      
- -   !'( 8;
34  .    !'(    *        
        =   3  *    %-
    *    -      *  /
*--@!'(--@
 -   ?
!3
. * - 5 -  - 
*-*""
B39!'(38*)
- * *--   *
-!'(C-3<D<4-
  -  !'(    7>  -  -  -  
--*!'(*
      !  -  
* !'(  
--*
-    -  +  *      0
    * * -!'(

%-@      8===  *)  .  -
  -        38)*)  *)  
---@!'(-*
----
-*-*-
?" 39
1--!'(
?!3   --A  -
-        2)        
<7<>
2---5-
" !'()  -.
-**-
*-"+
*1-/)
--  2-        
- - + 3= 
---
    *  *  2-      
+B--
3===
,          --
- --**
-"2-5---
 * !'(----
!?---?-*
+    - 
        -  
** *  ' -  
-E5-
-              
 2-  
--+
-    -        +    +
  2-    --  %?-    -
-min(|A∩B|/|A∪B|- 
   
 - 
---*!'(
  +    -    *  -  -
!1F+ .   B   
-
2!'(
1 -*    1
!'(
!?-$  !?- * *
  1  !'( 
*  -*  
-%?-$  %?-*
  2-      /    
--
        ?3     
*-2*3
Table 1: Mating preference rules tested in simulations. Scenarios
marked with the asterisk are only presented in the supplementary
materials. The intrinsic cost of expressing too many MHC variants
were modelled as explained in SM1 (eq.2 p.3 in SM1).
Abbrev. Brief description
Number of
mates to chose
from
MinShared
Preference for mates with the
smallest number of identical
MHC variants
10
PropShared
Preference for mates with
minimal proportion of shared
identical MHC variants within the
sum of variants in both partners
10
Random No preference, random matching
of mates N/A
MaxDiffer
Preference for mates with the
largest number of MHC variants
different from the chooser
10
MinSharedUnc*
Preference for mates with the
smallest number of identical
MHC variants
10
PropSharedUnc*
Preference for mates minimising
proportion of identical MHC
variants among the sum of
variants in both partners
10
-+-
!'(*39--
2
Fig."1 )*$%&+"""",$-./"",0-.*
/"1""*),$12)./"*3$%&
/""",4"."!"!,*
"+556+5.*,7/
*.81!"3*"*- *!*"
(1!-+-9
*        -      3=)>
>G3=)>  *    -  
-7:38-
#         *      -
-   -
-    +    * /  
+    --    39  2-
  *      -      -
*!'(- 
* C  *
38    *1  !'(
  *      *  2-
2*<
Table 2: Parameters of the model. 1 total number of pathogen
individuals was equal to Np· S; 2 probability per reproduction event;
3 probability per site (flip of a single bit); 4 probability of change of
the whole MHC (change in any given site); 5 used not in all
scenarios.
Parameter description Symbol Values
Hosts population size (number of individuals) NH1000
Pathogen population size of a species (number of
individuals) 1NP1000
Number of pathogen species in the simulation S4, 8, 16
Antigen length (number of bits) a6000
MHC’s antigen-binding region length (number of bits) m16
Number of pathogens generation per one hosts
generation K10
Total number of hosts generation (a.k.a. simulation
time) G5000
Probability of mutation in antigen (per site) 2,3 μA
10-5 ,
5 · 10-5
Probability of mutation in MHC PBR (per protein) 2,4 μMHC 10-4
Probability of deletion of MHC gene 2μdel 10-3
Probability of duplication of MHC gene 2μdupl 10-3
Cost factor for the host selection function 5α0.02
Number of random partners to select from in sexual
selection P10
-3<>=
-----))
*-*!'(
  *-        1    
  -            !'(  
* *-  -
  -   *    /  !'(    
*--.HI * *
5
-" -  3<>=  - 
? -  -
    .HI        *    -
      -      51  
?B47<78
- 1-- -
  )  - 
- * !'( 2- *
+.HI-
  .HI    -  )  *  )  -
   -   -.HI
-      ?*/    -  -
  -  "  .HI     -  +
* .HI-
.HI  ,    -  *    -  *   !'(
    -  -      -    3<>=
              *
JK  HI        JL=  B  
-      -  J    HI    
*-.HI51
 2-- * -* 
- .HIA # 
<
Results
.  !'()*   -
5 +-*  
.HI 3-- A -*  
-?<2-+
-  -  *    -  !'()*  
2---
"        -  -      !?-
   !'( 1 3 
-      -          
* ?32- -)
*-
3
Fig."2 !"*$%&,:;.*
"**",<=:;.$%&+",
=/""/*!*".!",*+5>56+5.
?
n
/!=="**:;%/!
"!*,7.-7-5
-*-
*  -  +    -      *    .HI    -
B  2*?4   
    39  !?-  -  "  .HI
  -        3  $
%?--.HI
  B      3  1      
*-----
      A      5  -)
  2*  ?7      2-
.HI
    !1F+      3  2*  ?>
  H*  !'(  
A .HI   ?4
    ,  1  --  
 - !'( 
.HI*,-
-- -@.HI
  -     .HI      
-  .HI    -  -      <  2*  ?8)?:
.!?--
5 .HI M  
-  -    *  5      
-  -!?- 2*
?9!1F+-
-    5  )  2*  ?:

Discussion
2--!'()
5+-
!'(-   - 
  *    ;  33  '    -  -  !'(
*    -  -        
/    -      -  *    !'(
-
'-  - +  -
 -  .-
-    *        -  
!?--1-!'(
4
          B"*    
    !'(        
-*-
-    !'(    1  2-
      +  -   -    
-  %?-  
- - -
* **-
+  $-- !'(
    -    /  *  5    
-5
(/    %?-      
-  !'(  1        
  -  *-    /     
!'(    1    *  0    -
  -  +    -    !'()*
*")5
!'(
<;79#<37:
F*-/
 - !'(* - 
*    -      -
      -        
1"B--
*      !'(        
-    4>  -  *      --  
+7;-->=*
, -   - -
  1    2-      
-**
---* 1-*
      !'()    
-- - * - *-
  -  -  !  5-    -  
!'(-!'(
--->3
 - -   - - * 
    -        
?"    -    !'(    -
  "*"        ><
'*"  
    -    *  *    !'(    
 -!'(    
-*1
")*--
*-!'()
*-**
1  - 
-4;7;
.    -    !'()*
-
 *   -- 
--1
-!'(-*
        -        
 --  * 
   - * 
1  *    +        --
*   - -*!'()*
- 3' 1--
    *    !'(       
      *  -  *  *5  
*)-*"*
-      *    --      *  
4<,-"5
*            -  -
-*
      !'()*    
            +
**"*
   -           
-
!)  :  >7  ---  -  
---!'(
-#      )      
1--!'( 
- -  !?-  
---!'(*
        *     !'(
*
  ,  -     -      -
*-- -
*!'(-N
-    "     *        -
+-1!'(
          -   !
-    -        -    -
  *    !'(    ><  >7      *
1  '  -      -  
-1+
-  -    *    !'(      
--**
2--!'(-+.HI
 H-*   1
  --    -        
  .  -  1      -  -    
---
   
-!'(*+.
-        O  P  
-*----
-- *  )>> >8 ' 
 - -  
 -   !'( 2-
  -  *  1  -      O
P*!'()*
            -
  F  *      
-*-
1  -  -    "    -
!'(  ><$ - 1
-
 - 1 * !"
><-**)
  ** - -
*--
(      -  -  
    !'(    -  -  5
/    -      !'(    
1    *    F+   5
-"+
 --   1)5
+   -  *    !'(     F
 -     -
-              
 *  -
 -   - 
-!'()*
Data accessibility
2-        -      *    
-66-*6*""6!'(Q 2-  
      -  F  F  B
-6663=>=8366>9
Acknowledgements
, -"  2 *  R# S  ,#    
          -    
-
5
Founding
2-  -      *  %-  H  ?
( $!0)473 <=346=:6 6HT:6==3>4  
SB(-%#&?
H"(%(??
Authors' contributions
SB - --
        -      
- C %   -
-@
---5
**-*-"
-
References
1. !"  !  <==8  2-    -*  1
1    -  B  
?493>;)3:8
2. I%F? %B B+RB U%,V3;;92-
--*1(
B.39<39;)<<7
3. ?  R U  B-  F?  <=3=  '  -  
    !'(  -    
%    -  B  ?  )  ?
<9938:7;9;);::
4. %  FS  F-  V  U  %  ,V  <==<  !'(
-#            )
%-H ?
-$? ;;3933<8=)33<87
5. %-  V%     <=3:  .     
 -D- %
-H ?33>93>><)3>>9
6. !SUBS <=3> BW  
      !  '*  (1  !'(
%R?(33333==78<9)3==78<9
7. %  FS <==<  2-        *  ?1
    -    -*  1  -
3=:33)<3
8. V20XFV,-'? UH"?
<=37 /!'()*-
     !  <4<3>3>3)
>384
9.  !SBSU, <=37 ?1
  -        -  !  '*
(1%B?R<:3<=37388<
10. ,# S(   <=34 ?1 1 
      -      -*
1  -    %    -  B  ?  )
?<:=398;<=3438=>
11. '"%,3;;<- -
-*134<>9>)>:3
12. 2"- H U H ! 3;;=   
    /)    
- ! '*(1  
3<77;89);9:
13. - S !  S U F  BS <==7 !'(
- -)- .
>>3394<)94;
14. FBS-S !!V(U,
S<==7'#1 ---
--!'(.>>339<>)943
15.  0- ( <==; -  !'(
* -%- B
?)?<9838>98>9)88>
16. '"%,<==<%-
!'(>83=3;=<)3;=:
17. ""  %  U  B  S  <=3;      
-*1*%R0?(
3>>3==9=3>
18. V,!3;;7B')!.5
%('%2)3889
%S.3><:4;=7)4;3<
19. %? <=34 'R (.     -
%) B  F+ ?# E 
.S.3;33<>:43)>:4;
20. R# 2R <=33 (  !'(..)
*           1 )
-8>:<4:=)<4;=
21. #"  <=3:  - 1
  -*  1        
!<933<>;7)<8=4
22. 0X(   ( (V '/ F H S  U
,- '  <=3:  2-           
#  H  U  <>:73)
:7;
23. ! % %"  F %0 U ,-- R <=3:
(H*-!'(I- 2
R33339)<:
24. H"! 2#)'-VU S!3;;<2-
*      -*  1      
%-H ?-
$? :;<<3=:;8)3=:;;
25. !" ! ?* U B S <=3; !
-*1.-2
  %  - H  
?<=3:=9:87
26. ,V!V*!V#SB-2'U!"!<==4
%          ?
4=3>84:3474)3474
27. V- *", ?"UBS<=3=+
 !'()FB  *  -  
    - *"    !    !  
3;<>>)<8>
28. !2U$ <==8!'(. 
-  -S
3;83;94)3;9:
29. V S I"' U , 'S 3;;> !))
!-      $#)!-  )  <  1    ?  
%-.B37484)::
30. "  ?  U  2  S  <===  2-  -  
-* 1 R  - FH /
B'3339)349
31 !"! ?*  V#! V" % UB S
<=39F*-
  )      !'(    .    -  *"  
!'33:747:)4>9
32 (""% U B+F 3;;; .*  -
':4<8=)<9=
33  SR U " 3;;7V.HB(0H.2.0H HF2'
! S0B '.?20(0!% 2..R.2N(0!%RY) H.H2B 2.IBI.,
H374474>)783
34 N#" V   3;98(  
  *      ! ' *  (1  S  
1!377>34<7)344>
35 BS2"# UV- <==:!'(
-*"-337;:<9):44
36 * !B- !  S U ?- (<=3=
! -   *5  - !'(
    -   *  B-    
87838:4)38;8
37 - ??!U, <=3<!
-    -  *  -  '  *
-<47:8;):9:
38 0!<==4!-*1
 -  # % -B? 
R?)?<9=?<>7)?<>8
39 -!    <==; (  !'()
              
%    -  B  ?  )  ?
<9838>;3=:4)3=;<
40 ,"(?*"2U%" S3;;>!'()
-% - B
?R?)?<8=34>;<7>)<7;
41 % ? U%* S! 3;;9 H  
-*  1)         )
      %    -  B  ?  
R?)?<8734:;3:34)3:3;
42  F' , BH "FTUFS
<==;  ()    -      
!'()!
3:3>44=9)443>
43 ,-' <==7 H   !'()* 
          *  !  
34:<78>)<79=
6
44 ,#S(<=3>+-#!'(
        1)      -  
    5-  -    
?*8;47>;)78;
45 ?RS 3;;7(--..
!'( 'R )FB31 -  A#
H48:878:<3>)<<3
46 B ( 2 <=3> B    
    B      ?  (
I 473
47 V-  V #" !V#" !U B S
<=34!'(A- 
  -      !      
<9484>)8>4
48 !!<=38- 
A          5-  H  
7:3=3<=7)3<3=
49 ?- H* ! U ?? <==: (*
  !'()    -        
  %   -  B  ?  )  ?
<9>3847>>>)>87
50 ( %  !?U T BB <=3<
!'()-)
 -:44:79):>8
51 R)T  2      <==7  !'(    .    
-      -      ?
4=8>8;:3=44)3=49
52 !"!<==>!- "*"
*5*!'(%
 - H   ?  - $ ? 
3=<3<7737)773:
53 !SUBS<=3=!'(*"
(
54 ,#S **SR'-'Z["SU#
RT<=39 % !'()    -
  -      )  !  
<8<88:)8::
55 B-2''*!  -%U!"!<==3
"*"1
1!'(-H7378:834==)4=<
56 ! ( %FS U ' ' <=33  -
\\1!'()
        * !(    
333
57 ""%B S<=<=!
1!'(  <F F
3=>=836
7
... Hamilton and Zuk (1982) suggested that female choice for disease resistant males drives the evolution of exaggerated ornaments and mating displays that signal the ability of males to resist infection by pathogens. This selection for disease resistance can also lead to expansion or contraction of MHC gene families (Bentkowski and Radwan 2020). Manakins have elaborate male mating displays and a lek mating system with extreme sexual selection on males (DuVal and Kempenaers 2008). ...
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