(*investigating analytically conditions under which weapons evolve faster than ornaments*)
sz=(-8*(az^3)*(Bzp)*(Gz)+4*cp *(-4+cp*Gp)*((Bzp^2)*cz *cp+2 *cp*Gp+cz*Gz *(2-cp* Gp))-4 *(2*az)*Bzp* cp*(-8+(Bzp^2)* cz* cp+3 *cp* Gp+cz*Gz *(2-cp* Gp))+4*(az^2)*((Bzp^2)* cp *(4+cz* Gz)+Gz*(-8+2* cp* Gp+cz*Gz*(2-cp *Gp))))/(2 cz* cp *(-(2*az)*Bzp+(Bzp^2)*cz*cp+2 *cp* Gp+cz* Gz* (2-cp *Gp))* ((-2* (2*az)* Bzp)+(Bzp^2)*cz*cp-(-4+cz*Gz)* (-4+cp *Gp))*ne);
sw=(2)/(4 cw* ne-(cw^2 )*Gw *ne);
sp=(-2 *(2*az)*Bzp*cz *Gz+2*(Bzp^2)*cz *cp *(-4+cz* Gz)-2*(-4+cz* Gz) *(-2* cp* Gp+cz*Gz *(-2+cp* Gp)))/(cp *(-(2*az)*Bzp+(Bzp^2)*cz *cp+2 *cp* Gp+cz*Gz *(2-cp*Gp))*(-2*(2*az)*Bzp+(Bzp^2)*cz*cp-(-4+cz* Gz) (-4+cp *Gp))*ne);szp=(-2 *(Bzp^3)*cz*(cp^2)+(2*az)*(Bzp^2)*cz* cp*Gz-Bzp*(4*(az^2)+4*cz*cp)*Gz+2* Bzp*(cp^2)*(-2+cz*Gz)*Gp-(2*az)* Gz*(-4+cz*Gz)* (-2+cp* Gp))/(cp *(-(2*az)*Bzp+(Bzp^2)* cz *cp+(2* cp* Gp)+cz*Gz *(2-cp* Gp))*((-2* (2*az)* Bzp)+(Bzp^2) *cz*cp-(-4+cz*Gz)*(-4+cp* Gp))* ne);
Reduce[{sw>sz&&sp>0&&szp>0&&az>0&&2>cz==cw>0&&ne=1&&Gz=1&&Gw=1}]

(*necessary and sufficient conditions for weapons to evolve faster than ornaments. Note: since the variance in ornament (sz) and in weapon (sw) are inversely proportional to effective population size (ne),the ratio of ornament variance to weapon variance is not expected to be related to effective population size->ne=1*)
Bzp>0&&0<cw<2&&az>0&&cp>(az)/(Bzp)&&((-(2*az)* Bzp+2 *cw+(Bzp^2)* cw*cp)/(-2 *cp+(cw* cp)))<Gp<(32*(2*az)+16 *(az^2)* Bzp-32*az* cw-4*(az^2) *Bzp *cw+4*az* (cw^2)-4* az* (Bzp^2)* cw*cp-4 *Bzp*(cw^2)* cp+(2*az)* (Bzp^2)*(cw^2)*cp-2*(Bzp^3)*(cw^2)*(cp^2))/(16 *az* cp-12 *az*cw* cp+(2*az)* (cw^2)* cp+4*Bzp* cw* (cp^2)-2* Bzp* (cw^2)*(cp^2))&&cz==cw