### Animals

Subjects were adult male Long-Evans Hooded WT and *Fmr1*^{em1/PWC} rats, hereafter referred to as *Fmr1*^{−/y} (for more details on this rat model see [19]). The rats were bred in-house and kept on a 12 h/12 h light/dark cycle with ad libitum access to food and water unless noted below. Following weaning (postnatal day 21) up until the start of the experiment, *Fmr1*^{−/y} and WT littermates were group-housed (3 to 5 rats per cage) in mixed-genotype cages. Animals were selected pseudo-randomly from a litter for use in the experiment (cohorts of 2–6 animals at a time). Each cohort included both WT and *Fmr1*^{−/y} rats. Selection of animals was done by an experimenter not involved in any stage of the experiment, data collection or analysis, by randomly picking rat ID numbers from a given litter (while ensuring balance of WT and *Fmr1*^{−/y} rats). Experimenters involved in data collection and data analysis were blind to the genotype of the subjects throughout all stages of the experiments and data analysis until final statistical analyses were conducted [in line with the ARRIVE (Animal Research: Reporting of In Vivo Experiments) guidelines [35]. All animal experiments were approved by the University of Edinburgh veterinary services before their start. Procedures were performed in accordance with the guidelines established by European Community Council Directive 2010/63/EU (22 September 2010) and by the Animal Care (Scientific Procedures) Act 1986, and under the authority of Home Office Licences.

For ex vivo experiments, subjects were 14 WT and 14 *Fmr1*^{−/y} rats aged 2–3 months. For in vivo experiments, subjects were 7 WT and 7 *Fmr1*^{−/y} adult rats aged 3–4 months at the time of surgery. After surgery, these rats were housed individually in cages designed to minimize head-stage damage, and after recovery from surgery, they were food restricted such that they maintained approximately 90% of their free-feeding weight. All in vivo recordings were conducted during the light phase of the cycle.

### In vivo experiments: electrodes and surgery

The microdrives used for the in vivo recordings were based on a modified tripod design described previously [36]. The drives were loaded with eight tetrodes, each of which was composed of four HML coated, 17 µm, 90% platinum 10% iridium wires (California Fine Wire, Grover Beach, CA). Tetrodes were threaded through a thin-walled stainless steel cannula (23 Gauge Hypodermic Tube, Small Parts Inc, Miramar, FL). The tip of every wire was gold-plated (Non-Cyanide Gold Plating Solution, Neuralynx, MT) to reduce the impedance of the electrode from a resting impedance of 0.7–0.9 MΩ to a plated impedance in the range of 150–250 kΩ (200 kΩ being the target impedance) one to ten hours before surgery. Electrodes were implanted using standard stereotaxic procedures under isoflurane anaesthesia. Hydration was maintained by subcutaneous administration of 2.5 ml 5% glucose and 1 mL 0.9% saline. Animals were also given an anti-inflammatory analgesia (small animal Carprofen/Rimadyl, Pfizer Ltd., UK) subcutaneously. Electrodes were lowered to just above the dorsal CA1 cell layer of the hippocampus (-3.5 mm AP from bregma, + 2.4 mm ML from the midline, − 1.7 mm DV from dura surface). The drive assembly was anchored to the skull screws and bone surface using dental acrylic (Associated Dental Products Ltd. Swindon, UK). Animals were monitored closely for at least two hours in their home cage while recovering from anaesthesia, and then returned to the colony. Following this, at least one week of recovery time passed before access to food was restricted and screening for cellular activity began.

### In vivo unit recording

In vivo single unit and local field potential (LFP) activity was recorded using a 32-channel Axona USB system (Axona Ltd., St. Albans, UK). Mill-Max connectors built into the rat’s microdrive were attached to the recording system via two unity gain buffer amplifiers and a light, flexible, elasticated recording cable. The recording cable passed signals through a ceiling mounted slip-ring commutator (Dragonfly Research and Development Inc., Ridgeley, West Virginia) to a pre-amplifier where they were amplified 1000 times. The signal was then passed to a system unit; for single unit recording the signal was band-pass (Butterworth) filtered between 300 and 7000 Hz. Signals were digitized at 48 kHz (50 samples per spike, 8 bits/sample) and could be further amplified 10–40 times at the experimenter’s discretion. The LFP signals were recorded from one channel of a tetrode located in the pyramidal neuron layer of the dCA1 area. The signals were amplified by a factor of 1000–2000, low-pass filtered at 500 Hz, and sampled at a rate of 4.8 kHz (16 bits/sample). A notch filter was applied at 50 Hz. The position of the animal was recorded by tracking two small light-emitting diodes fixed on the headstage connected to the rat’s microdrive. A ceiling-mounted, infrared sensitive CCTV camera tracked the animal’s position at a sampling rate of 50 Hz. Rats were screened for single unit activity and for the presence of theta oscillations once or twice a day, at least five days a week, while foraging for chocolate treats (CocoPops, Kellogg's, Warrington, UK). The screening environment was a blue, wooden square arena (1 m × 1 m × 52 cm) which was not used during later experiments. At the end of each screening session, rats were removed from the recording apparatus and the electrodes were lowered if no hippocampal unit activity had been observed. Brain tissue was allowed to recover from electrode movement for at least 5 h before a new screening session started.

### In vivo recording protocol

Once at least 10 putative CA1 pyramidal neurons were detected, the rat was transferred to a totally novel grey plastic cylindrical environment (62 cm diameter, 60 cm walls) surrounded by black curtains and different lighting within the same experimental room. The cylinder contained one salient black cue card that remained stable throughout the two days of recording. Three 10-min recording sessions, separated by a 10-min inter-session interval (ISI), took place on each of the two days of the experiment, during which the rat foraged for scattered chocolate cereal treats in the recording arena (six sessions in total) (Fig. 1A). Between sessions of the same day, that rat was placed in a plastic holding bucket (25 cm diameter, sawdust bedding) while remaining tethered.

### Single unit analysis

Single unit activity was analysed offline using a custom-written MATLAB (MathWorks) routine that makes use of the Klustakwik spike-sorting program [37]. Electrophysiological recordings from all six sessions of the experiment were combined before the use of the spike sorting algorithms. This permits tracking of clusters across sessions and days that does not rely on assumptions about stability of cluster boundaries. The dimensionality of the waveform information was reduced to the first principal component, energy, peak amplitude, peak time, and width of the waveform. The energy of a signal *x* was defined as the sum of squared moduli given by the formula:

$$\varepsilon_{x} \triangleq \mathop \sum \limits_{n = 0}^{N - 1} \left| {x_{n} } \right|^{2}$$

Based on these parameters, Klustakwik spike sorting algorithms were then used to distinguish and isolate separate clusters. The clusters were then further checked and refined manually using the manual cluster cutting GUI, Klusters [38]. In addition to the aforementioned waveform features, manual cluster cutting also made use of spike auto- and cross-correlograms to examine refractory period and complex spiking. Cluster quality was operationalized by calculating isolation distance (Iso-D), *L*_{ratio}, and peak waveform amplitude, taken as the highest amplitude reached by the four mean cluster waveforms. For cluster *C*, containing *n*_{c} spikes, Iso-D is defined as the squared Mahalanobis distance of the *n*_{c}*-th* closest *non-c* spike to the centre of *C*. The squared Mahalanobis distance was calculated as:

$$D_{i,C}^{2} = \left( {x_{i} - \mu_{C} } \right)^{T} \Sigma_{c}^{ - 1} \left( {x_{i} - \mu_{C} } \right)$$

where *x*_{i} is the vector containing features for spike *i*, and *μ*_{C} is the mean feature vector for cluster *C*, and *Σ*_{C} is the covariance matrix of the spikes in cluster *C*. A higher value indicates better isolation from non-cluster spikes [39]. The L quantity was defined as:

$$L_{\left( c \right)} = \mathop \sum \limits_{i \notin C} 1 - {\text{CDF}}_{{x_{df}^{2} }} \left( {D_{i,C}^{2} } \right)$$

where \(i \notin C\) is the set of spikes which are not members of the cluster and CDF is the cumulative distribution function of the distribution with 8 degrees of freedom. The cluster quality measure, *L*_{ratio} was thus defined as *L* divided by the total number of spikes in the cluster [40]. Finally, cluster waveforms were visually inspected to ensure that waveforms of a given cluster looked similar across the 6 recording sessions.

A cluster was classified as a pyramidal neuron if it satisfied the following criteria: i) Iso-D > 15 and *L*_{ratio} < 0.2 and ii) the width of its average waveform was > 250 μs and mean firing rate was < 5 Hz. A pyramidal cell was considered to be active in a given session if the mean firing rate was greater than 0.1 Hz (but less than 5 Hz). Only spikes that occurred during periods of animal locomotion (speed > 3 cm/s) were included in the analyses.

To calculate burst probability, we first defined bursts as groups of spikes with interspike interval (ISI) < 10 ms. Using ISIs of 6, 9 and 12 ms yielded consistent results. The number of bursts *N*_{B} and single spikes *N*_{S} in each session were counted for each cell. The burst probability was calculated as *N*_{B}*/*(*N*_{B} + *N*_{S}) [41, 42]. A similar analysis of cell bursting behaviour using a different definition (numbers of spikes in bursts divided by total spikes) [43] yields similar results (data not shown).

Several measures of the spatial activity were calculated for each active pyramidal cell in a given session:

Spatial information content is given by the equation:

$${\text{Information}} \;{\text{content}} = \sum P_{i} \left( {R_{i} {/}R} \right)\log_{2} \left( {R_{i} {/}R} \right)$$

where *i* is the bin number, *Pi* is the probability for occupancy of bin *i*, *Ri* is the mean firing rate for bin *i*, and *R* is the overall average firing rate [44].

Sparsity was calculated as previously[45]:

$${\text{Sparsity}} = \left( {\sum P_{i} R_{i} } \right)^{2} /\sum P_{i} R_{i}^{2}$$

where *i* is the bin number, *Pi* is the probability for occupancy of bin *i* and *Ri* is the mean firing rate for bin *i*.

Firing rate maps were produced for each session by dividing the recording cylinder area into a grid of 2.5 cm square bins. The firing rate in each bin was calculated as the total number of spikes which occurred in that bin divided by the total length of time spent there. Bins in which the rats spent less than 100 ms were treated as if they had not been visited. These bin-specific firing rates were plotted in a heat map, showing where the preferred firing location of a cell was in a given environment. The rate maps were generated using an algorithm described by the following equations.

The Gaussian kernel used is given by:

$$g\left( x \right) = \exp \left( {\frac{{ - x^{2} }}{2}} \right)$$

The summary algorithm for calculating firing rate for each spatial bin is then given by:

$$\lambda \left( x \right) = \mathop \sum \limits_{i = 1}^{n} g\left( {\frac{{S_{i - x} }}{h}} \right){/}\mathop \smallint \limits_{0}^{T} g\left( {\frac{y\left( t \right) - x}{h}} \right){\text{d}}t$$

where *S*_{i} represents the positions of every recorded spike, *x* is the centre of the current bin, the period [0, *T*] is the recording session time period, *y(t)* is the position of the rat at time *t*, and *h* is a smoothing factor, which was set to 2.5 cm.

The percentage of active bins for each session was calculated by dividing the number of bins in the firing rate map which contained spikes by the number of bins visited. Place fields were defined as areas in the firing rate maps of at least 9 contiguous bins with firing rate > 20% of maximum bin firing rate [46]. In cases where secondary place fields were detected, only the main place field was included in the analysis of place field size.

To assess the stability of spatial firing, we calculated the Pearson correlation between firing rate maps of successive recording sessions. This analysis was only conducted on identified cells which exhibited spatial firing, defined as SI > 0.5 bits per spike, in both sessions.

### Spectral analysis

Position data from each session were binned into 500-ms epochs, and the velocity for each epoch was calculated. Raw LFP traces (4.8 kHz) were z-scored (mean was subtracted and divided by standard deviation). LFP data analysis was done on all the 4 s periods of activity (> 3 cm/s) following periods of immobility. Time–frequency spectrograms were calculated using Chronux Toolbox [http://chronux.org; [47]], function *mtspecgramc()* using a window size and time step of 20 s and 10 s, respectively [48]. Power estimates for the frequency bands of interest [Theta (6–12 Hz), Slow Gamma (30–45 Hz), Medium Gamma (55–100 Hz)] were excised from the spectrogram and averaged. The average spectrograms for each genotype group in each session are represented in Additional file 1: Fig. S9. For the relationships between running speed and oscillation power, the recording was divided into 500-ms bins and EEG signals from all 500-ms bins were stratified based on the velocity (3 cm/s wide bins). Power spectra estimation during each bin was done by means of the Welch periodogram method (50% overlapping Hamming windows), which was obtained by using the *pwelch()* function from MATLAB Signal Processing Toolbox. Specific band powers were computed by integrating the power spectral density (PSD) estimate for each frequency range of interest [MATLAB function *bandpower()*].

### Phase-locking analysis

To investigate spike timing with respect to oscillations, a band-pass filter was applied to the LFP signals. The low cut-off stop band was the low passband minus 2 Hz; the high cut-off stop band was the high passband plus 2 Hz [Theta (4–14 Hz), Slow Gamma (28–47 Hz), Medium Gamma (58–102 Hz)]. Both the instantaneous amplitude and the phase time series of a filtered signal were computed from the Hilbert transform, which was obtained by using the *hilbert()* function from the MATLAB Signal Processing Toolbox. Only spikes during bins (500 ms) of strong oscillations (> 2 standard deviations of mean power) were included in this analysis [49, 50]. Every recorded spike from these periods was assigned a spike phase *θ*_{j}, where *j* denotes the *j-th* spike. The mean resultant vector r was calculated as:

$$r = \mathop \sum \limits_{j} \exp \left( {i\theta_{j} } \right){/}N$$

where *N* is the total number of spikes. The strength of phase locking (resultant length) was defined as \(\left| r \right|\). Theoretically, this value ranges from 0 to 1. The value is zero if the phases are uniformly distributed along the phases of gamma oscillations, while it is one if all spikes fire at exactly the same phase. In practice, the values for individual neurons are distributed mostly in the range of 0–0.2 as shown in Fig. 7 and Additional file 1: Fig S11. The trough of gamma oscillation was defined as 0/360°.

### Histology

At the end of the in vivo recording experiments, animals were given an overdose of pentobarbital intraperitoneally (Euthatal, Merial Animal Health Ltd., Essex, UK) and perfused with 0.9% saline solution followed by a 4% formalin solution. The brain was extracted and stored in 4% formalin for at least seven days prior to any histological analyses. The brains were sliced in 32-µm sections on a freezing microtome at − 20°. These sections were stained with a 0.1% Cresyl violet solution and the tissue section that best revealed the electrode track was imaged using ImageJ software (ImageJ, NIH, Bethesda).

### Ex vivo electrophysiology

Ex vivo brain slices were prepared as previously described [12]. Briefly, rats were sedated with isoflurane, anaesthetized with sodium pentobarbital (100 mg/kg) and then transcardially perfused with ice-cold, carbogenated (95% O2/5% CO2), and filtered, sucrose-modified artificial cerebrospinal fluid (sucrose-ACSF; in mM: 87 NaCl, 2.5 KCl, 25 NaHCO_{3}, 1.25 NaH_{2}PO_{4}, 25 glucose, 75 sucrose, 7 MgCl_{2}, 0.5 CaCl_{2}). Once perfused, the brain was rapidly removed and 400 μm slices containing the dorsal pole of the hippocampus were cut on an oscillating blade vibratome (VT1200S, Leica, Germany) in the coronal plane. Slices were then transferred to a submerged chamber containing sucrose-ACSF at 35 °C for 30 min, then at room temperature until needed.

For recording, slices were transferred to a submerged chamber perfused with pre-warmed carbogenated ACSF (in mM: 125 NaCl, 2.5 KCl, 25 NaHCO_{3}, 1.25 NaH_{2}PO_{4}, 25 glucose, 1 MgCl_{2}, 2 CaCl_{2}) at a flow rate of 4–6 mL.min^{-1} at 31 ± 1 °C) which contained 50 µM picrotoxin to block GABA_{A} receptor-mediated currents. Neurons were visualized under infrared differential interference contrast (IR-DIC) microscopy with a digital camera (SciCamPro, Scientifica, UK) mounted on an upright microscope (SliceScope, Scientifica, UK) with a 40 × water-immersion objective lens (1.0 N.A., Olympus, Japan). Whole-cell patch-clamp recordings were performed with a Multiclamp 700B (Molecular Devices, CA, USA) amplifier, using recording pipettes pulled from borosilicate glass capillaries (1.5 mm outer/0.86 mm inner diameter, Harvard Apparatus, UK) on a horizontal electrode puller (P-97, Sutter Instruments, CA, USA). Pipettes were filled with a K-gluconate based internal solution (in mM 142 K-gluconate, 4 KCl, 0.5 EGTA, 10 HEPES, 2 MgCl_{2}, 2 Na_{2}ATP, 0.3 Na_{2}GTP, 1 Na_{2}Phosphocreatine, 2.7 Biocytin, pH = 7.4, 290–310 mOsm) which gave a 3–5 MΩ tip resistance. Neurons were rejected if: they were more depolarized than − 50 mV, had an access resistance > 30 MΩ, or the access resistance changed by more than 20% during the recording. Cell-attached recordings were performed as above, but without breaking through into the whole-cell configuration.

Intrinsic membrane properties were measured in current clamp. Passive membrane properties, including resting membrane potential, membrane time constant, input resistance, and capacitance were measured from small hyperpolarizing current steps (10 pA, 500 ms duration), from a zero-current level. Active properties were determined from a series of depolarizing current steps (0 to + 400 pA, 500 ms) from − 70 mV, maintained by addition of bias current. AP properties were determined from the first, second or fifth AP elicited at rheobase. Stimulation of the Schaffer collateral (SC) and temporoammonic (TA) pathways were made with a bipolar twisted Ni:Chrome wire electrode placed in either *str. radiatum* or *str. lacunosum-moleculare* in distal CA1. In all stimulation slices, CA3 was severed to prevent recurrent activation from antidromic activation of CA3. To assess synaptic strength of afferent inputs, 2 × stimuli of 200 µs duration (50 ms interval) were delivered at 10-s intervals at 30 V, 60 V, and 90 V levels from a constant-voltage stimulation box (Digitimer, Cambridge, UK). Recordings were first performed in cell-attached mode to identify cell spike output. Following breakthrough into whole-cell mode, EPSPs were recorded in current-clamp configuration with membrane potential biased to − 70 mV. All recordings were filtered online at 10 kHz with the built-in 4-pole Bessel filter and digitized at 20 kHz (Digidata1440, Molecular Devices, CA, USA). Traces were recorded in pCLAMP 9 (Molecular Devices, CA, USA) and stored on a personal computer. Analysis of electrophysiological data was performed offline using the open-source software package Stimfit [51], blind to both genotype and treatment conditions.

### Axon initial segment labelling and neuron visualization

Additional ex vivo brain slices were collected during preparation of tissue for ex vivo recordings (see above) and fixed for 1 h at room temperature in 4% paraformaldehyde in 0.1 M phosphate buffer (PB). Following fixation, slices were transferred to 0.1 M PB + 0.9% saline (PBS) and stored for up to 1 week. Immunohistochemistry was performed as previously described [52]. Briefly, slices were rinsed 3–4 times in PBS, then blocked in a solution containing 10% normal goat serum, 0.3% Triton X-100 and 0.05% NaN_{3} diluted in PBS for 1 h. Primary antibodies raised against AnkyrinG (1:1000; 75–146, NeuroMab, USA) and NeuN (1:1000, Millipore EMD, UK) were applied in a solution containing 5% normal goat serum, 0.3% Triton X-100 and 0.05% NaN_{3} diluted in PBS, for 24–72 h at 4 °C. Slices were then washed in PBS and secondary antibodies (AlexaFluor 488 and AlexaFluor 633, Invitrogen, UK, both 1:500) were applied in a solution containing 3% normal goat serum, 0.1% Triton X-100 and 0.05% NaN_{3} overnight at 4 °C. Slices were rinsed in PBS, desalted in PB and mounted on glass slides with Vectashield Hard-Set mounting medium (Vector Labs, UK). Stacks of images of the lower *str. pyramidale* upper *str. oriens* were acquired on a Zeiss LSM800 laser scanning confocal microscope, under a 60x (1.2 NA) objective lens at 2048 × 2048 resolution, with a step size of 0.25 µm. Axon Initial Segment (AIS) lengths were measured offline using ImageJ as segmented lines covering the full extent of AnkyrinG labelling observed. A minimum of 25 AISs were measured for each rat.

For CA1 pyramidal neuron reconstructions, fixed slices containing recorded neurons were fixed overnight in 4% paraformaldehyde + 0.1 M PB at 4 °C. Slices were then transferred to 0.1 M PB and stored until processing. For visualization, slices were washed 2–3 times in 0.1 M PB and then transferred to a solution containing Streptavidin conjugated to AlexaFluor568 (1:500, Invitrogen, UK) and 0.3% Triton X-100 and 0.05% NaN_{3}. Slices were then incubated for 48–72 h at 4 °C. Slices were then washed in 0.1 M PB and mounted on glass slides with an aqueous mounting medium (VectaShield, Vector Labs, UK) and cover slipped. Neurons were imaged on an upright confocal (as above) with image stacks collected with a 20 × objective lens (2048 × 2048, 1 µm steps). Neurons were reconstructed with the SNT toolbox for FIJI/ImageJ [53], Sholl analysis performed, and branch lengths measured for the different dendritic compartments.

Dendritic protrusion analysis was performed on short dendritic segments (secondary dendrites) that were imaged with a 63 × objective lens (2.4 × digital zoom, 2048 × 2048 resolution giving 40 nm pixels, 0.13 µm z-step). These images were deconvolved (Huygens Software Package, Scientific Volume Imaging, The Netherlands), then dendritic protrusions counted as a function of length in FIJI. To estimate the total number of dendritic protrusions per dendritic compartment, the density was multiplied by the total length of dendrites in that compartment.

### Statistical analyses

#### In vivo* electrophysiology*

We compared the firing properties of the identified pyramidal neurons across days and sessions in WT and *Fmr1*^{−/y} rats in two ways. First, we modelled our data using a generalized linear mixed model (GLMM) approach in order to take into account the hierarchy of dependency in our data sets (genotypes-rats-neurons) and account for random effects. Second, we analysed the neuronal properties at the rat level by calculating the average value for each property across the neurons recorded in each rat [for additional discussion of the choice of statistical approach, see [53, 54]]. The results for GLMM analyses are presented in the main manuscript, while the results from the rat level analysis are presented in supplementary figure legends.

Statistical modelling routines for the linear mixed effects (LME) models were written and run using RStudio 1.0.153 (RStudio Team, 2016). Depending on the data distribution, linear mixed models (LMMs) or generalized linear mixed models (GLMMs) were fitted to single unit data metrics using the R package lme4 v1.1–17 [55]. Animal and cell identity (cluster number) were included in models as random effects, and the variables (terms) of interest (genotype, day, session-in-day) along with all interactions between them were included as fixed effects. Interactions and terms are progressively eliminated when a simpler model (i.e. a model not containing that term or interaction) fits the data equally well (based on likelihood ratio test). Consequently, the *p*-values reported in the context of LMEs are given by likelihood ratio tests between a model containing the variable or interaction in question and a model without that variable or interaction (a reduced/null model). When significant interactions were indicated by the LME, *post hoc* tests for between- and within-subjects effects were conducted by comparing estimated marginal means with t-tests with a Tukey correction for multiple comparisons.

Pearson’s correlation coefficients (*r*) are bounded between [− 1, 1], and the sampling distribution for highly correlated variables is highly skewed. Therefore, in order to convert the distribution to normal, r values were transformed to (*z*) values using the *Fisher's z transformation*:

$$r = \left( {0.5} \right)\ln \frac{1 + r}{{1 - r}}$$

For analysis of the cellular data at the rat level, the mean value for all cells from a given rat was calculated for each measure and analysed using a three-way ANOVA (genotype (between subjects) x day x session (within-subjects, session nested within day)). This same three-way ANOVA model was also used to analyse oscillatory power in each band. The effects of velocity on power of each oscillatory band of interest (Additional file 1: Fig S10) were analysed using a three-way ANOVA (genotype (between subjects) x day x velocity (within-subjects, velocity nested within day)).

The normality of all rat means’ distributions (i.e. group/sessions/metric) was tested using Kolmogorov–Smirnov (KS) tests. Nearly all rat means’ distributions passed the normality test (Distributions that did not pass the KS normality test: Firing rate: WT-session 3, *Fmr1*^{−/y} -session 1; Burst Prob: *Fmr1*^{−/y} -session 4,6; Sparsity: *Fmr1*^{−/y} -session 6; Place field size: *Fmr1*^{−/y} -session 2,3,5; MVL sgamma: WT-session 1, *Fmr1*^{−/y} -session 3; Theta PWR: *Fmr1*^{−/y} -session 1). However, given the small size of the distributions (*n* = 7 for rats for both genotypes), any estimations of distribution type cannot be accurate. Given that fitting an LME model that does not contain random effects would be the same as an ANOVA, we proceeded to use ANOVA for these rat-level analyses, despite the isolated distributions that did not satisfy the assumption of normality. The alternative would involve using nonparametric tests; however, these do not allow for hierarchical structure of repeated factors (session-in-day).

Power spectrograms were tested across all frequencies for significance at a *p* < 0.05 level, using a nonparametric randomization test, corrected for multiple comparisons across frequencies [22, 56].

The effects of genotype and session on the percentage of phase locked cells by each oscillatory band (Fig. 8) were analysed by fitting a series of multiple logistic regression models. The process is equivalent to that of hypothesis testing using LME. For each dataset, a full multiple logistic regression model was fit to the data with genotype, session and genotype x session interaction, and parameters: Phaselock (yes/no) ~ Intercept + Genotype + Session + Genotype x Session (Model 1). The fit of Model 1 was compared using log-likelihood ratio (*G*^{2} test) to the fit of a reduced model that did not contain the interaction term: Phaselock ~ Intercept + Genotype + Session (Model 2). To explore main effects of genotype and session, two separate models were used: Phaselock ~ Intercept + Genotype (Model 3) and Phaselock ~ Intercept + Session (Model 4). Their fit was compared to the null hypothesis that the simplest (intercept-only) model is correct again using log-likelihood ratio (*G*^{2} test). For individual comparisons between sessions and genotypes, we used two-proportion *z-test* [50] with correction for false discovery rate (alpha = 0.05) with Benjamini–Hochberg procedure.

As the LME framework for analysis of circular data is still under development, for analysis of oscillatory phase preference (Fig. 9), we first used Harrison-Kanji test [57] to analyse effects of genotype and day, as well as the interaction between them, with neuron as the unit of measurement. For comparisons between genotypes and days, we used the Watson-Williams test [58].

Statistical evaluation of data is presented in figure legends, main manuscript and supplementary tables. Average ± SEM values are reported throughout the manuscript unless stated otherwise. Significance was set at *p* < 0.05. Statistical analysis was carried out in SPSS 16.0 (IBM), R v.3.4.4 (R Core Team, 2018) or MATLAB (CircStat MATLAB toolbox [59]), and graphs created in GraphPad (Prism 8).

#### Down-sampling analysis

We report below that CA1 pyramidal cells in WT (but not *Fmr1*^{−/y}) rats showed experience-dependent changes in firing rate, as well as in spatial firing properties. To examine whether the experience-dependent changes in spatial coding were secondary to the experience-dependent changes in firing rate also observed in WT but not *Fmr1*^{−/y} rats, we performed a bootstrapping-like down-sampling analysis. We sampled uniformly at random, 30 cells from each day and each genotype, 1000 times, with replacement. The size of subsamples was chosen to approximate the average cell number per rat at each session. Each of the subsamples was constrained to have an average firing rate that is equal to the overall mean firing rate of the WT cell population on day 2 (+ / − 5%). For each subpopulation of each genotype and day, we tested whether other metrics taken at the cell level (burst probability, spatial information, sparsity, place field size, % active bins, mean vector lengths relative to theta and gamma oscillations, and preferred theta phase) were statistically different from their overall population (two-sample t-test except for preferred theta phase). The portion of subpopulations that were statistically different from their overall population in each measure was used as the probability of the measure in question to be driven by changes in mean firing rate for the population tested (*p* < 0.05 indicating no modulation from mean firing rate; Additional file 2: Table S8).

For each subpopulation, we calculated the mean for each measure. These means (*n* = 1000) formed the distributions plotted in Additional file 1: Fig. S12.

Similarly, to control for the effect of mean firing rate change on firing rate map stability between the last session of day 1 (session 3) and the first session of day 2 (session 4), we performed two down-sampling analyses. For the first, the subsamples from both WT and *Fmr1*^{−/y} cells had to have an average firing rate decrease that is equal to the average firing rate decrease of WT cell population between session 3 and session 4 (+ / − 5%). For the second down-sampling, the subsamples from both WT and *Fmr1*^{−/y} cells had to have no change in firing rate (+ / − 5% of WT). As described above, the portion of 1000 subpopulations of each genotype that were statistically different from the overall population distribution was used as the probability of firing rate correlations to be driven by changes in mean firing rate for the population tested (*p* < 0.05 indicating no modulation from mean firing rate; Additional file 2: Table S8).

#### Ex vivo electrophysiology and anatomical analysis

Data generated from ex vivo brain slices were analysed as described previously [12]. Group sizes were chosen based on a presumed effect size of 15% and an overall statistical power of 80% (*N* = 7–8/group). For assessment of genotype effect, data were analysed using an LME based approach (see above), with animal and slice identity included as random effects. The *p*-value was then approximated using the Wald test, with effect size and variation estimated from the LMEs fitted to the data. For synaptic stimulation experiments, either the amplitude of the EPSP or the spike-probability were plotted per slice and compared using a 2-way ANOVA. If a genotype/stimulus interaction was observed, then Sidak *post hoc* tests were performed (corrected for multiple comparisons). For AIS lengths and morphology analysis, an LME analysis was performed, again using animal and slice identity as random effects with *p*-value approximated using the Wald test. For dendritic protrusion analysis, the animal average was analysed with Student’s t-test.