, Animals were held on a 12 h day/night cycle and had access to food and water ad libitum. Animals of both sexes were used for experiments. CD1 mice (Charles River, Lyon, France) were used for in vivo electroporation and expression pattern analyses. Vax1 flox (Vax1cKO) conditional mutants (Hoffman 2016) and Rosa26 tdTomato reporter mice

*. Cd1 and . Background, Vax1flox genotyping was performed with Vax1flox forward: 5'-GCCGGAACCGAAGTTCCTA; Vax1wt forward: 5'-CCAGTAAGAGCCCCTTTGGG, reverse 5'-CGGA TAGACCCCTTGGCATC. Ai14 genotyping was performed with R26wt forward: 5'-AAGGGAGC TGCAGTGGAGTA, reverse 5'-CCGAAAATCTGTGGGAAGTC

. Boutin, Plasmid and in vivo electroporation The full-length rat cDNA sequence of Vax1 was excised from pCMV2-Rn-Vax1-FLAG (a gift of Kapil Bharti) and subcloned into pCAGGS vector to produce pCAG-Vax1. Postnatal day 0 (P0) or day 1 (P1) pups were electroporated as previously described, CRE Recombinase mRNA, pp.130-101, 2007.

A. Alvarez-buylla, M. Kohwi, T. M. Nguyen, and F. T. Merkle, The heterogeneity of adult neural stem cells and the emerging complexity of their niche, Cold Spring Harbor Symposia on Quantitative Biology, pp.357-365, 2008.

A. Alvarez-buylla and J. M. Garcia-verdugo, Neurogenesis in adult subventricular zone, The Journal of Neuroscience, vol.22, pp.629-634, 2002.

A. Angelova, M. C. Tiveron, H. Cremer, and C. Beclin, Neuronal subtype generation during postnatal olfactory bulb neurogenesis, Journal of Experimental Neuroscience, vol.12, p.117906951875567, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02088440

T. L. Bailey, M. Boden, F. A. Buske, M. Frith, C. E. Grant et al., MEME SUITE: tools for motif discovery and searching, Nucleic Acids Research, vol.37, pp.202-208, 2009.

N. Bä-umer, T. Marquardt, A. Stoykova, R. Ashery-padan, K. Chowdhury et al., Pax6 is required for establishing naso-temporal and dorsal characteristics of the optic vesicle, Development, vol.129, pp.4535-4545, 2002.

S. Bertuzzi, R. Hindges, S. H. Mui, D. D. O'leary, and G. Lemke, The homeodomain protein vax1 is required for axon guidance and major tract formation in the developing forebrain, Genes & Development, vol.13, pp.3092-3105, 1999.

C. Boutin, S. Diestel, A. Desoeuvre, M. C. Tiveron, and H. Cremer, Efficient in vivo electroporation of the postnatal rodent forebrain, PLOS ONE, vol.3, p.1883, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00409149

S. Bugeon, A. De-chevigny, C. Boutin, N. Coré, S. Wild et al., Direct and efficient transfection of mouse neural stem cells and mature neurons by in vivo mRNA electroporation, Development, vol.144, pp.3968-3977, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01690045

Z. Chaker, P. Codega, and F. Doetsch, A mosaic world: puzzles revealed by adult neural stem cell heterogeneity, Wiley Interdisciplinary Reviews: Developmental Biology, vol.5, pp.640-658, 2016.

J. Chen, Y. Huang, E. O. Mazzoni, G. C. Tan, J. Zavadil et al., Mir-17-3p controls spinal neural progenitor patterning by regulating Olig2/Irx3 Cross-Repressive loop, Neuron, vol.69, pp.721-735, 2011.

A. De-chevigny, N. Coré, P. Follert, M. Gaudin, P. Barbry et al., miR-7a regulation of Pax6 controls spatial origin of forebrain dopaminergic neurons, Nature Neuroscience, vol.15, pp.1120-1126, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00724257

A. De-chevigny, N. Core, P. Follert, S. Wild, A. Bosio et al., Dynamic expression of the pro-dopaminergic transcription factors Pax6 and Dlx2 during postnatal olfactory bulb neurogenesis, Frontiers in Cellular Neuroscience, vol.6, p.6, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00843367

F. Doetsch, L. Petreanu, I. Caille, J. M. Garcia-verdugo, and A. Alvarez-buylla, EGF converts transit-amplifying neurogenic precursors in the adult brain into multipotent stem cells, Neuron, vol.36, pp.1021-1034, 2002.

M. E. Ferná-ndez, S. Croce, C. Boutin, H. Cremer, and O. Raineteau, Targeted electroporation of defined lateral ventricular walls: a novel and rapid method to study fate specification during postnatal forebrain neurogenesis, Neural Development, vol.6, p.13, 2011.

R. Fiorelli, K. Azim, B. Fischer, and O. Raineteau, Adding a spatial dimension to postnatal ventricularsubventricular zone neurogenesis, Development, vol.142, pp.2109-2120, 2015.

N. Flames, R. Pla, D. M. Gelman, J. L. Rubenstein, L. Puelles et al., Delineation of multiple subpallial progenitor domains by the combinatorial expression of transcriptional codes, Journal of Neuroscience, vol.27, pp.9682-9695, 2007.

M. Furimsky and V. A. Wallace, Complementary gli activity mediates early patterning of the mouse visual system, Developmental Dynamics, vol.235, pp.594-605, 2006.

F. Guillemot, Spatial and temporal specification of neural fates by transcription factor codes, Development, vol.134, pp.3771-3780, 2007.

M. A. Hack, A. Saghatelyan, A. De-chevigny, A. Pfeifer, R. Ashery-padan et al., Neuronal fate determinants of adult olfactory bulb neurogenesis, Nature Neuroscience, vol.8, pp.865-872, 2005.
URL : https://hal.archives-ouvertes.fr/pasteur-00163055

M. Hallonet, T. Hollemann, R. Wehr, N. A. Jenkins, N. G. Copeland et al., Vax1 is a novel homeobox-containing gene expressed in the developing anterior ventral forebrain, Development, vol.125, pp.2599-2610, 1998.

M. Hallonet, T. Hollemann, T. Pieler, and P. Gruss, Vax1, a novel homeobox-containing gene, directs development of the basal forebrain and visual system, Genes & Development, vol.13, pp.3106-3114, 1999.

H. M. Hoffmann, C. Trang, P. Gong, I. Kimura, E. C. Pandolfi et al., Deletion of Vax1 from Gonadotropin-Releasing hormone (GnRH) Neurons abolishes GnRH expression and leads to hypogonadism and infertility, Journal of Neuroscience, vol.36, pp.3506-3518, 2016.

R. A. Ihrie, J. K. Shah, C. C. Harwell, J. H. Levine, C. D. Guinto et al., Persistent sonic hedgehog signaling in adult brain determines neural stem cell positional identity, Neuron, vol.71, pp.250-262, 2011.

T. M. Jessell, Neuronal specification in the spinal cord: inductive signals and transcriptional codes, Nature Reviews Genetics, vol.1, pp.20-29, 2000.

M. Kohwi, N. Osumi, J. L. Rubenstein, and A. Alvarez-buylla, Pax6 is required for making specific subpopulations of granule and periglomerular neurons in the olfactory bulb, Journal of Neuroscience, vol.25, pp.6997-7003, 2005.

H. C. Lai, R. P. Seal, and J. E. Johnson, Making sense out of spinal cord somatosensory development, Development, vol.143, pp.3434-3448, 2016.

P. M. Lledo, F. T. Merkle, and A. Alvarez-buylla, Origin and function of olfactory bulb interneuron diversity, Trends in Neurosciences, vol.31, pp.392-400, 2008.

M. A. Long and F. M. Rossi, Silencing inhibits Cre-mediated recombination of the Z/AP and Z/EG reporters in adult cells, PLOS ONE, vol.4, p.5435, 2009.

S. Lugert, O. Basak, P. Knuckles, U. Haussler, K. Fabel et al., Quiescent and active hippocampal neural stem cells with distinct morphologies respond selectively to physiological and pathological stimuli and aging, Cell Stem Cell, vol.6, pp.445-456, 2010.

L. Luo, M. C. Ambrozkiewicz, F. Benseler, C. Chen, E. Dumontier et al., Optimizing nervous System-Specific gene targeting with cre driver lines: prevalence of germline recombination and influencing factors, Neuron, vol.106, pp.37-65, 2020.

F. T. Merkle, Z. Mirzadeh, and A. Alvarez-buylla, Mosaic organization of neural stem cells in the adult brain, Science, vol.317, pp.381-384, 2007.

X. Morin, F. Jaouen, and P. Durbec, Control of planar divisions by the G-protein regulator LGN maintains progenitors in the chick neuroepithelium, Nature Neuroscience, vol.10, pp.1440-1448, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00306564

S. H. Mui, J. W. Kim, G. Lemke, and S. Bertuzzi, Vax genes ventralize the embryonic eye, Genes & Development, vol.19, pp.1249-1259, 2005.

K. Ohsaki, T. Morimitsu, Y. Ishida, R. Kominami, and N. Takahashi, Expression of the vax family homeobox genes suggests multiple roles in eye development, Genes to Cells, vol.4, pp.267-276, 1999.

J. C. Platel, A. Angelova, S. Bugeon, J. Wallace, T. Ganay et al., Neuronal integration in the adult mouse olfactory bulb is a non-selective addition process, vol.8, p.44830, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02382367

A. Sagner and J. Briscoe, Establishing neuronal diversity in the spinal cord, Development, vol.146, p.182154, 2019.

J. Schindelin, I. Arganda-carreras, E. Frise, V. Kaynig, M. Longair et al., Fiji: an open-source platform for biological-image analysis, Nature Methods, vol.9, pp.676-682, 2012.
URL : https://hal.archives-ouvertes.fr/pasteur-02616466

J. M. Soria, P. Taglialatela, S. Gil-perotin, R. Galli, A. Gritti et al., Defective postnatal neurogenesis and disorganization of the rostral migratory stream in absence of the Vax1 homeobox gene, Journal of Neuroscience, vol.24, pp.11171-11181, 2004.

A. Stoykova, D. Treichel, M. Hallonet, and P. Gruss, Pax6 modulates the dorsoventral patterning of the mammalian telencephalon, The Journal of Neuroscience, vol.20, pp.8042-8050, 2000.

P. Taglialatela, J. M. Soria, V. Caironi, A. Moiana, and S. Bertuzzi, Compromised generation of GABAergic interneurons in the brains of Vax1-/-mice, Development, vol.131, pp.4239-4249, 2004.

M. Take-uchi, J. D. Clarke, and S. W. Wilson, Hedgehog signalling maintains the optic stalk-retinal interface through the regulation of vax gene activity, Development, vol.130, pp.955-968, 2003.

M. Tiveron, M. Hirsch, and J. Brunet, The expression pattern of the transcription factor Phox2 delineates synaptic pathways of the autonomic nervous system, The Journal of Neuroscience, vol.16, pp.7649-7660, 1996.

M. C. Tiveron, C. Beclin, S. Murgan, S. Wild, A. Angelova et al., Zic-Proteins are repressors of dopaminergic forebrain fate in mice and C. elegans, The Journal of Neuroscience, vol.37, pp.10611-10623, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01690610

R. E. Ventura and J. E. Goldman, Dorsal radial Glia generate olfactory bulb interneurons in the postnatal murine brain, Journal of Neuroscience, vol.27, pp.4297-4302, 2007.

F. Weinandy, J. Ninkovic, G. , and M. , Restrictions in time and space-new insights into generation of specific neuronal subtypes in the adult mammalian brain, European Journal of Neuroscience, vol.33, pp.1045-1054, 2011.

M. C. Whitman and C. A. Greer, Adult-generated neurons exhibit diverse developmental fates, Developmental Neurobiology, vol.67, pp.1079-1093, 2007.

M. C. Whitman and C. A. Greer, Adult neurogenesis and the olfactory system, Progress in Neurobiology, vol.89, pp.162-175, 2009.

L. Zhao, H. Saitsu, X. Sun, K. Shiota, and M. Ishibashi, Sonic hedgehog is involved in formation of the ventral optic cup by limiting Bmp4 expression to the dorsal domain, Mechanisms of Development, vol.127, pp.62-72, 2010.