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When a female mammal makes thetransition from virginity to mother-hood, she is forced to refocus her

activities dramatically. She must adapt to amultitude of new demands by her offspringor risk losing a significant metabolic andgenetic investment. She needs to find andremember the location of food stores, watersources and nest sites, and be able to exploitthem to her offspring’s advantage. The per-formance of these tasks may depend on asharpening of her cognitive abilities. Wehave tested this idea by using two differentstrains of rat and two separate spatial tasks,and find that pregnancy and a litter of pupsmay combine to stimulate spatial learningand memory in females.

In the oestrous cycle, which occurs pre-paratory to mating, steroid hormones suchas oestradiol and progesterone markedlyincrease the concentration of hippocampalapical dendritic spines in adult females, par-ticularly when oestradiol levels are raised1.Because dendritic spines increase the totalsurface area of the synapse, such neuralchanges may improve learning and mem-ory2. Pregnancy, which raises the amount ofoestradiol and progesterone for significantlylonger than the oestrous cycle, may producelong-lived improvements in behaviours thatare not maternal as such, but which con-tribute to the survival and rearing of pups.The hormones of pregnancy may preparesites that regulate learning and memory3, inmuch the same way that they stimulate themedial preoptic area to respond withmaternal behaviour when pups are born4.

We investigated this idea by testing multi-parous (animals that had given birth and lac-tated twice) and age-matched nulliparous(virgin) Sprague–Dawley females on a 16-day regimen of radial-arm maze tests. On thefirst six days, multiparous females made sig-nificantly more correct choices than nulli-parous females (P*0.0002–0.01; Fig. 1a).

In a second experiment, virgin femaleLong Evans rats were assigned to one ofthree groups: fosters, maternals and nulli-parous. In the dry-land version of the Mor-ris watermaze5, maternal females tooksignificantly less time (43.2 s) than nulli-parous rats (128 s) to recall and locate thefood reward (P*0.05; Fig. 1b). No signifi-cant differences were observed between fos-ter (55 s) and maternal rats.

Taken together, these results show that a combination of reproductive and pupexperience and stimulation is beneficial tolearning and memory in female rats. Hormone-induced modifications to thehippocampus (increases in both long-term

potentiation6 and dendritic spine density1,7)may improve the navigation skills involvedin parental resource-gathering behaviours.For example, hippocampal volume inparental rodents during the breeding seasonis correlated with the size of the homerange8. Concurrent alterations in both thehippocampus and the medial preoptic areamay therefore contribute to the pro-nounced behavioural transition that ischaracteristic of the maternal female, withthe medial preoptic area directly regulatingmaternal behaviour, and the hippocampuscontrolling supporting behaviours such as foraging.

As well as receiving the hormones ofpregnancy, the female’s brain is exposed torich sensory events when pups are born.With each litter of pups comes a plethora ofnew sights, sounds, tastes, and tactile andsuckling stimulation, the last of which canreorganize hypothalamic connections9. Thissensory stimulation may have effects onbrain structure and function that are similarto those caused by other types of enrichedphysical environment, an idea supported bythe observation that the brains of parous,environmentally impoverished rats resemblethose of rats in an enriched environment10.

Dendritic processes called filopodia aretriggered by the excitatory activation of

N-methyl-D-aspartate (NMDA)11, leadingto the formation of synapses. Furthermore,new postsynaptic CA1 dendritic spines arerapidly formed after long-term potentiation(LTP, a learning analogue)12. Neural activitybrought about by pregnancy and the pres-ence of pups may literally reshape the brain,fashioning a more complex organ that canaccommodate an increasingly demandingenvironment.

Little attention has been paid to theremarkable neural plasticity that is inherentin reproduction itself and that underlies thesubsequent behavioural changes, particu-larly those unique to late pregnancy and thepostpartum period. To consider the rela-tionship of a mother caring for her young asunidirectional disregards the potentiallyrich set of sensory cues in the oppositedirection that can enrich the mother’s envi-ronment. By providing such stimuli, thepups may ensure both their own and theirmother’s development and survival.Craig H. Kinsley*, Lisa Madonia*, Gordon W. Gifford*, Kara Tureski*, Garrett R. Griffin*, Catherine Lowry†,Jamison Williams†, Jennifer Collins†,Heather McLearie†, Kelly G. Lambert†*Department of Psychology, University of Richmond,Richmond, Virginia 23173, USAe-mail: ckinsley@richmond.edu

brief communications

NATURE | VOL 402 | 11 NOVEMBER 1999 | www.nature.com 137

Motherhood improves learning and memoryNeural activity in rats is enhanced by pregnancy and the demands of rearing offspring.

Trial day

Foster MaternalNulliparous

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Figure 1 Improvement in spatial learning following reproductive

and pup experience. a, Effects of distal reproductive experience

on spatial learning. Two separate groups of 6–8 adult (~100 days

old) randomly chosen female Sprague–Dawley rats were mated

and allowed to deliver naturally. Litters were culled to 6 pups and

allowed to remain with their mothers until weaning (21 days). Two

weeks after weaning, these newly primiparous females were re-

mated and the sequence repeated. These newly multiparous

females were allowed to remain with their pups until weaning.

Two weeks later, the multiparous females and their age-matched

nulliparous cohorts were tested on the radial-arm maze. b, Effects

of proximal reproductive experience on spatial learning in three

groups of 5 virgin Long Evans rats: nulliparous rats, which had no

mating or pup contact; fosters, for which females were exposed to

three foster pups (exchanged every 24 h for milk-replete pups) for

16 days, when the females met all the criteria for displaying

maternal behaviour (retrieving, grouping and crouching over pups

within 60 min of exposure); and maternals, which are primiparous

females that stayed with pups for 16 days. When pups were

removed, females were weighed, food was restricted and behav-

ioural testing began in a dry land maze5. Further experimental

details are available from the authors.

© 1999 Macmillan Magazines Ltd

6. Warren, S. G. et al. Brain Res. 703, 26–30 (1995).

7. Kinsley, C. H. et al. Soc. Neurosci. Abstr. 24, 952 (1998).

8. Jacobs, L. F., Gaulin, S. J. C., Sherry, D. F. & Hoffman, G. E.

Proc. Natl Acad. Sci. USA 87, 6349–6352 (1990).

9. Modney, B. K. & Hatton, G. I. Mammalian Parenting:

Biochemical, Neurobiological, and Behavioral Determinants

(eds Krasnegor, N. A. & Bridges, R. S.) 305–323 (Oxford Univ.

Press, New York, 1990).

10.Diamond, M. C., Johnson, R. E. & Ingham, C. Int. J. Neurosci.

2, 171–178 (1971).

11.Maletic-Savatic, R., Malinow, R. & Svoboda, K. Science 283,

1923–1927 (1999).

12.Engert, F. & Bonhoeffer, T. Nature 399, 66–70 (1999).

of the mode, which continues down to thediffraction limit of approximately a/4N. Oneven smaller scales, further magnificationdoes not reveal further substructure (Fig. 1,bottom). In the asymptotic limit l↓0(N→÷), the diffractive spreading becomesnegligible, leading to an ideal fractal. Large-N resonators are feasible (for example,N414 has already been realized in ref. 3).

The origin of the self-similarity can beunderstood intuitively: the existence of the round-trip magnification M means thatthe eigenmode must consist of (de)mag-nified copies of itself. Note that the hermite–gaussian modes of stable reson-ators are not self-similar because the round-trip magnification is absent.

A characteristic property of fractals istheir non-integer fractal dimension Df (refs4,5). We found that an accurate determina-tion of Df for two-dimensional modes (asin Fig. 1) would require calculations atmuch higher N than considered here, andhence computational resources beyondthose available; in earlier calculations6 forone-dimensional resonators with N4103,we found that Df was 1.650.1.

It has been shown that a tetraedicalstacking of four reflecting spheres representsa chaotically scattering system with inherentfractal properties7. Our results help toexplain this: light rays repeatedly scatteringin the inner chamber of the tetraedicalstacking undergo geometrical magnificationowing to the reflecting spheres, just as inour unstable resonator. Coincidentally, the‘aperture’ in ref. 7 is approximately triangu-lar, like our aperture in Fig. 1, leading tosimilar patterns. The self-similar aspectseems to be a useful unifying feature of opti-cal-pattern generation, providing insightinto chaotic scattering7 and transverse non-linear optics8. In the latter case, there iscompetition between bulk nonlinear behav-iour and boundary-imposed linear diffrac-tion as pattern-generating mechanisms.G. P. Karman*‡, G. S. McDonald*†, G. H. C. New†, J. P. Woerdman**Leiden University, PO Box 9504, 2300 RA Leiden, The Netherlandse-mail: qo@molphys.leidenuniv.nl†Blackett Laboratory, Imperial College, London SW7 2BZ, UK‡Present address: Philips Research Laboratories,Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands

1. Siegman, A. E. Lasers Ch. 19, 22 (University Science, Mill

Valley, California, 1986).

2. McDonald, G. S. & Firth, W. J. J. Mod. Opt. 40, 23–32 (1993).

3. Cheng, Y.-J., Fanning, C. G. & Siegman, A. E. Phys. Rev. Lett.

77, 627–630 (1996).

4. Falconer, K. Fractal Geometry: Mathematical Foundations and

Applications (Wiley, New York, 1990).

5. Peitgen, H.-O., Jürgens, H. & Saupe, D. Chaos and Fractals

(Springer, New York, 1992).

6. Karman, G. P. & Woerdman, J. P. Opt. Lett. 23, 1909–1911 (1998).

7. Sweet, D., Ott, E. & Yorke, J. A. Nature 399, 315–316 (1999).

8. Lugiato, L. A., Brambilla, M. & Gatti, A. Adv. Atom. Mol. Opt.

Phys. 40, 229–306 (1999).

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†Department of Psychology, Randolph-Macon College, Ashland, Virginia 23005, USA

1. Woolley, C. S., Gould, E., Frankfurt, M. & McEwen, B. S.

J. Neurosci. 10, 4035–4039 (1990).

2. Daniel, J. M., Roberts, S. L. & Dohanich, G. P. Physiol. Behav.

66, 11–20 (1999).

3. Loy, R., Gerlach, J. L. & McEwen, B. S. Brain Res. 467, 245–251

(1988).

4. Numan, M. in The Physiology of Reproduction 2nd edn (eds

Knobil, E. et al.) 221–302 (Raven, New York, 1994).

5. Kesner, R. & Dakis, M. Psychopharmacology 120, 203–208 (1995).

brief communications

Laser optics

Fractal modes inunstable resonatorsOne of the simplest optical systems, consist-ing of two mirrors facing each other to forma resonator, turns out to have a surprisingproperty. Stable resonators, in which thepaths of the rays are confined between thetwo mirrors, have a well known mode struc-ture (hermite–gaussian), but the nature ofthe modes that can occur in unstable reson-ant cavities (from which the rays ultimatelyescape) are harder to calculate, particularlyfor real three-dimensional situations1. Herewe show that these peculiar eigenmodes ofunstable resonators are fractals, a findingthat may lead to a better understanding ofphenomena such as chaotic scattering andpattern formation. Our discovery may havepractical application to lasers based onunstable resonators1.

For a confocal unstable resonator con-sisting of a large concave mirror and a smallconvex feedback mirror sharing a commonfocus, the rays spill over the small mirror sothat its size and shape define the outputaperture (Fig. 1, insets); the other mirror isso large that its size and shape are irrele-vant. The properties of an unstable res-onator are determined by the round-trip magnification M and the (equivalent)Fresnel number N of the resonator:N¬(M11)a2/2lL, where l is the opticalwavelength, 2a is the size of the small mir-ror, and L is the cavity length1. The exist-ence of a round-trip magnification M ischaracteristic for unstable resonators, asstable resonators lack such magnification.The value of M determines the round-tripspill-over loss around the small mirror, andN controls the size of the smallest details inthe transverse mode profile as determinedby diffraction. In an unstable-cavity laser,the losses are compensated by the gain pro-vided by the laser medium.

Free-space propagation of the opticalfield is described by the Huygens–Fresnelintegral1, and cavity eigenmodes u(x,y) aredefined by the requirement that, after oneround trip, the field profile remainsunchanged apart from a complex multiplier

(the eigenvalue of the mode). We have cal-culated the mode patterns for a range ofdifferent aperture shapes, concentratingparticularly on regular polygons and rhom-boids. This calculation is numerically verydemanding, so we used a non-orthogonalgrid2 to increase efficiency. For square orcircular apertures, the diffraction problemcan be reduced to a one-dimensional calcu-lation, with the mode patterns for thesquare factorizing into x and y components.

A typical modal intensity distributionfor triangular aperturing is shown in Fig. 1.Smaller and smaller triangles keep appear-ing as the mode pattern is repeatedly mag-nified. This shows the self-similar nature

L2a

Figure 1 Calculated lowest-loss eigenmode of an unstable res-

onator with a triangular mirror. Left inset, a three-dimensional

view; right inset, a side view. M41.5, N410.5. The intensity

distribution äuä2 on the small mirror is shown: white, high; red,

medium; blue, low. Bottom, magnification of the centre part, with

colour coding adjusted to exploit the full dynamical range.