Ysabel Milton

J Frances Kamhi

Vincent Fourcassié

Mathieu Moreau

Simon K A Robson

Adina Rusakov

Lindsey Wimberly

Alexandria Diloreto

Adrianna Kordek

James F A Traniello

Lifespan behavioral and neural resilience in a social insect

Keywords: Senescence, neurodegeneration, biogenic amines, task performance, ants

Analyses of senescence in social species are important to understanding how group living influences the evolution of aging in society members. Social insects exhibit remarkable lifespan polyphenisms and division of labor, presenting excellent opportunities to test hypotheses concerning aging and behavior. Senescence patterns in other taxa suggest that behavioral performance in aging workers would decrease in association with declining brain functions.

Using the ant Pheidole dentata as a model, we found that 120 day-old minor workers, having completed 86% of their laboratory lifespan, showed no decrease in sensorimotor functions underscoring complex tasks such as alloparenting and foraging. Collaterally, we found no ageassociated increases in apoptosis in functionally specialized brain compartments or decreases in synaptic densities in the mushroom bodies, regions associated with integrative processing. Furthermore, brain titers of serotonin and dopamine -neuromodulators that could negatively impact behavior through age-related declines -increased in old workers. Unimpaired task performance appears to be based on the maintenance of brain functions supporting olfaction and motor coordination independent of age. Our study is the first to comprehensively assess lifespan task performance and its neurobiological correlates and identify constancy in behavioral performance and the absence of significant age-related neural declines over the worker lifespan.

Introduction

Evolutionary theories of senescence predict behavioral declines in old age [START_REF] Williams | Pleiotropy, natural selection, and the evolution of senescence[END_REF][START_REF] Medawar | An unsolved problem of biology[END_REF][START_REF] Kirkwood | Evolution of ageing[END_REF] in association with physiological and genetic processes that deteriorate over the lifespan [START_REF] Guarente | Genetic pathways that regulate ageing in model organisms[END_REF][START_REF] Martin | The biology of aging: 1985-2010 and beyond[END_REF].

Aging nervous systems may functionally decline, leading to sensory and motor deficits [START_REF] Yeoman | Ageing and the nervous system: insights from studies on invertebrates[END_REF][START_REF] Erickson | The neurobiology of memory changes in normal aging[END_REF] due to neurodegeneration, manifest as apoptosis (programmed cell death), which may increase with age [START_REF] Haddadi | Brain aging, memory impairment and oxidative stress: a study in Drosophila melanogaster[END_REF], disease [START_REF] Friedlander | Apoptosis and caspases in neurodegenerative diseases[END_REF], or development [START_REF] Degterev | A decade of caspases[END_REF]. Few studies have examined the influence of sociality on aging and life history [START_REF] Rueppell | Regulation of life history determines lifespan of worker honey bees (Apis mellifera L.)[END_REF][START_REF] Rueppell | Aging without functional senescence in honey bee workers[END_REF][START_REF] Bourke | Kin selection and the evolutionary theory of aging[END_REF], and little is understood about cognitive decline and neurobiological changes accompanying senescence in social animals, apart from humans [START_REF] Rueppell | Aging without functional senescence in honey bee workers[END_REF][START_REF] Seehuus | Cellular senescence in honey bee brain is largely independent of chronological age[END_REF][START_REF] Behrends | Cognitive aging is linked to social role in honey bees (Apis mellifera)[END_REF][START_REF] Remolina | Senescence in the worker honey bee Apis mellifera[END_REF]. Social insects have striking lifespan polyphenisms [START_REF] Keller | Social insects as a model to study the molecular basis of ageing[END_REF][START_REF] Rueppell | Aging of social insects[END_REF][START_REF] Amdam | Social context, stress, and plasticity of aging[END_REF][START_REF] Giraldo | Worker senescence and the sociobiology of aging in ants[END_REF]: queens often live more than a decade, whereas workers may live only several months [START_REF] Carey | Insect biodemography[END_REF], indicating that the differentiation of reproductive and sterile castes has had profound effects on senescence, which may be influenced by the social organization of colony labor. The relationship of task performance to age-related changes in the worker brain, however, is not well understood.

The ant Pheidole dentata has served as a model to explore the evolution and ecology of social structure, as well as the neurobiological underpinnings of age-related worker behavior [START_REF] Wilson | Behavioral discretization and the number of castes in an ant species[END_REF][START_REF] Seid | Age-related repertoire expansion and division of labor in Pheidole dentata (Hymenoptera: Formicidae): a new perspective on temporal polyethism and behavioral plasticity in ants[END_REF][START_REF] Muscedere | Age and task efficiency in the ant Pheidole dentata: young minor workers are not specialist nurses[END_REF][START_REF] Muscedere | Serotonin modulates worker responsiveness to trail pheromone in the ant Pheidole dentata[END_REF][START_REF] Muscedere | Brood-care experience, nursing performance, and neural development in the ant Pheidole dentata[END_REF][START_REF] Ilieş | Neuroanatomical and morphological trait clusters in the ant genus Pheidole: evidence for modularity and integration in brain structure[END_REF]. Minor workers expand their task repertoires from eclosion to approximately three weeks of age [START_REF] Seid | Age-related repertoire expansion and division of labor in Pheidole dentata (Hymenoptera: Formicidae): a new perspective on temporal polyethism and behavioral plasticity in ants[END_REF] while their brains undergo synaptic remodeling [START_REF] Seid | Age-related changes in the number and structure of synapses in the lip region of the mushroom bodies in the ant Pheidole dentata[END_REF] and serotonergic systems that influence behavioral development and task performance mature [START_REF] Muscedere | Serotonin modulates worker responsiveness to trail pheromone in the ant Pheidole dentata[END_REF][START_REF] Seid | Age-related changes in biogenic amines in individual brains of the ant Pheidole dentata[END_REF][START_REF] Seid | Age-and subcaste-related patterns of serotonergic immunoreactivity in the optic lobes of the ant Pheidole dentata[END_REF][START_REF] Muscedere | Division of labor in the hyperdiverse ant genus Pheidole is associated with distinct subcaste-and age-related patterns of worker brain organization[END_REF]. How do workers age behaviorally, and do age-related and brain-based neuroanatomical and neurochemical changes occur that could negatively impact lifespan task performance? Using individuals of known age and robust and comprehensive assays to quantify effectiveness of task performance in minor workers, we tested the hypothesis that behavioral performance declines across the P. dentata minor worker lifespan in association with age-related patterns of apoptosis and cellular modifications in synaptic complexes considered significant to sensory processing, integration, and motor control, and thus behavioral efficacy [START_REF] Stieb | Visual experience affects both behavioral and neuronal aspects in the individual life history of the desert ant Cataglyphis fortis[END_REF][START_REF] Groh | Density of mushroom body synaptic complexes limits intraspecies brain miniaturization in highly polymorphic leaf-cutting ant workers[END_REF]. In addition, we quantified levels of neuromodulators known to influence neural structure and signaling [START_REF] Neckameyer | Neurotrophic actions of dopamine on the development of a serotonergic feeding circuit in Drosophila melanogaster[END_REF] that could alter circuit function in an age-dependent manner to regulate task performance or alter other physiological processes associated with aging. We predicted that if workers functionally senesce, nursing and foraging performance should decrease, and sensory and motor processes regulating worker responsiveness to social signals and cues that guide these tasks should covary with age-related neurobiological declines. We localized cell death in functionally specialized brain compartments -the optic lobes (OL; vision), antennal lobes (AL; olfaction), mushroom bodies (MB; integration, learning and memory), central complex (CC; motor response and integration), subesophageal zone (SEZ; control of mouthparts), and the remainder of the central brain (RCB) [START_REF] Strausfeld | Arthropod Brains: Evolution, Functional Elegance, and Historical Significance[END_REF] -to quantify neural changes that could underscore senescence and impact task performance. We hypothesized that apoptosis in the brain would increase with age, and the density of synaptic complexes of microglomeruli (MG) associated with cognitive function [START_REF] Groh | Density of mushroom body synaptic complexes limits intraspecies brain miniaturization in highly polymorphic leaf-cutting ant workers[END_REF][START_REF] Groh | Comparison of microglomerular structures in the mushroom body calyx of neopteran insects[END_REF] would decrease prior to or concurrent with age-related declines in task performance.

Finally, we predicted that brain biogenic amine titers, notably serotonin (5HT) and dopamine (DA), would decrease as workers aged and compromise the functionality of systems under neuromodulatory control, as well as neuroplasticity [START_REF] Rodríguez | The serotonergic system in ageing and Alzheimer's disease[END_REF][START_REF] Kamhi | Biogenic amines and collective organization in a superorganism: neuromodulation of social behavior in ants[END_REF].

Materials and Methods

Ant husbandry

Colonies of Pheidole dentata were collected in and around Alachua County, Florida and reared in Harris environmental chambers maintained at 25°C and 40-55% relative humidity and cultured as described in Seid et al. [START_REF] Seid | Age-related changes in the number and structure of synapses in the lip region of the mushroom bodies in the ant Pheidole dentata[END_REF]. Subcolonies with minors of known age were established with 40-70 pupae within 72 hours of eclosion, the queen, brood, and approximately 150 marked workers. Workers were sampled from subcolonies derived from 5-15 parent colonies and assigned haphazardly to assays; numbers of subcolonies are provided for each assay below. Details of subcolony establishment and marking are provided in supplemental material. Minor workers of known ages (20-22, 45-47, 95-97 and 120-122 days) were selected for behavioral analyses that encompass the breadth of the minor worker repertoire [START_REF] Wilson | Behavioral discretization and the number of castes in an ant species[END_REF][START_REF] Seid | Age-related repertoire expansion and division of labor in Pheidole dentata (Hymenoptera: Formicidae): a new perspective on temporal polyethism and behavioral plasticity in ants[END_REF]. Workers reared in our queenright subcolonies live up to 140 days; because few workers survived to 120 days, sample sizes were smaller at this age than for other worker ages due to the diminishing return on attempting to acquire samples of very old workers.

Behavioral assays

Nursing effort

Nursing ability was assayed in a cylindrical chamber (34 mm inner diameter) with a humidified plaster-like bottom (dental stone) to prevent larvae from desiccating. Sides were coated with Fluon to prevent escape. Eight 2 nd to 4 th instar larvae with dark guts were added to the chamber and evenly distributed along the circumference of a 20 mm circle. A cover bisected by a 10 mm diameter tube was placed over the chamber, and a single minor worker was introduced to the central tube using featherweight forceps. After the worker acclimated for 5 minutes, the lid was gently removed, allowing access to larvae. Responses were recorded for 20 minutes using a Canon FS400 digital camcorder placed above the assay chamber. The number and duration of approaches and acts to larvae were scored manually using JWatcher Video (www.jwatcher.ucla.edu) by an observer blind to the age of the ant (N=13, 16, 17, 6 for 20, 45, 95, and 120 day old ants respectively from 10 subcolonies). We quantified the number of times a worker approached, carried, fed, piled or otherwise provided care to larvae and recorded the duration of feeding, carrying, and unspecified brood-directed behavior, which could include licking or other manipulation of brood items. Details are provided in supplemental material. Two-way Chi-square was used for brood-care act frequencies and two-way ANOVA was used for durations to test for effects of age, differences in frequencies and durations of behaviors and interaction effects. Statistical analyses were performed in JMP.

Pheromone trail-following ability

To determine if workers experienced age-related declines in sensorimotor functions associated with the perception of trail pheromone and trail-following ability, individual ants were presented with artificial pheromone trails at concentrations of 1, 0.1, or 0.01 poison glands per trail [START_REF] Muscedere | Serotonin modulates worker responsiveness to trail pheromone in the ant Pheidole dentata[END_REF]. Minor workers did not follow trails at 0.001 glands per trail. Details are provided in supplemental material. We video recorded each assay of worker responsiveness to an artificial trail and subsequent orientation using a Canon FS400 digital camcorder for 5 minutes and used Ctrax [START_REF] Branson | Highthroughput ethomics in large groups of Drosophila[END_REF] to quantify worker movement. Worker age was masked with a random number so that analyses were conducted blind. Trail-following was assessed by tracking activity within and outside a 1 cm diameter annulus digitally drawn along the chemical trail to estimate the active space of the pheromone. Annulus size was determined conservatively after observing numerous occurrences of trail-following behavior. Using larger annuli did not significantly affect results (data not shown). Of the 23 95 day-old minors sampled, 6 were raised in a subcolony lacking a queen. These ants were not significantly different in any trail-following metrics than age-matched workers from queenright colonies tested at the same pheromone concentrations, and data were therefore pooled.

Trail-following metrics (mean deviation from the trail axis [accuracy], duration and distance of following activity within the annulus, and mean and maximum duration and distance of individual following bouts were used to quantify the integration of sensory and motor activity. Details are provided in supplemental material. We tested 20 and 95 day old minors using pheromone concentrations of 1.0, 0.1, and 0.01 gland per trail (20-day: N=7, 10, 7; 95-day: N=7, 9, 7 for 1.0, 0.1, and 0.01 gland/trail TPC respectively, sampled from 7 subcolonies). Accuracy, duration, distance, mean and maximum distance and duration of individual following bouts were analyzed using a two-way ANOVA for age and pheromone concentration in JMP; to correct for multiple tests a FDR correction was applied [START_REF] Pike | Using false discovery rates for multiple comparisons in ecology and evolution[END_REF].

Worker predatory behavior

Ants were isolated for two minutes in a small Fluon-lined Petri dish. A live fruit fly, tethered by its wings or abdomen end with fine watchmakers forceps affixed to a small platform, was then introduced into the arena. Only flies that responded to touch with movement were used. Each ant was assigned a random number, and worker response was video recorded for 2 minutes. Predatory response by the worker was scored on a four-point scale: 1: no aggression; 2: mandible flaring; 3: latent attack (delayed or not sustained for the duration of the assay); 4: attack. Because this assay was scored preliminarily in real time, it was not always possible to record responses blind to the age of the ant, for instance, if only one age was being tested on a day. However, videos that did not involve immediate and consistent attack, which was unambiguous, were reviewed at a later date by a blinded observer. Chi-squared tests were performed in JMP to examine the effect of age (N= 59, 41, 34, 17 for each age group from 20 to 120 days from 15 subcolonies) on predatory response.

Age-related changes in neuroanatomy

Measurement of apoptosis in the brain

Brains of minor workers aged 20-22 or 95-97 days were selected for analysis by Tdtmediated dUTP-biotin nick end labeling (TUNEL). TUNEL identifies fragmented DNA characteristic of apoptotic cell death [START_REF] Gavrieli | Identification of programmed cell death in situ via specific labeling of nuclear DNA fragmentation[END_REF] and serves as a primary method for identification of apoptosis in a variety of tissues [START_REF] Mccall | Detection of apoptosis in Drosophila[END_REF][START_REF] Galluzzi | Guidelines for the use and interpretation of assays for monitoring cell death in higher eukaryotes[END_REF]. Negative controls, brain tissue not treated with the active TUNEL enzyme, terminal transferase, were generated according to manufacturer instructions (Roche In Situ Cell Death Detection Kit, Fluorescein, Cat. no. 11 684 795 910). For positive controls, we adapted procedures developed for Drosophila to confirm assay function in Pheidole brains. Workers of unknown age were selected for positive controls and were briefly cold immobilized and then impaled in the head with a metal pin, (0.1mm diameter, Fine Science Tools) between the mandibles and into the brain. Injured ants were maintained in groups with food and water for 16-20 hours prior to dissection. TUNEL reactions were performed according to manufacturer instructions, vibratome sectioned at 100 µm, incubated with DAPI and mounted in 80% glycerol. Details are provided in supplemental material. All control brain sections were imaged on an Olympus FluoView 10i confocal microscope using a 10x objective. TUNELpositive cells were confirmed using a 60x objective and examination of nuclear morphology. A set of controls and experimental brains was processed at one time; all brains were discarded from any set in which positive or negative controls failed for a total of 22 usable brains (N=12, 10 for 20 and 95 days from 6 subcolonies). Known-age ant brain sections were scanned in entirety with a 60x objective using 2 µm optical sections.

Brains were assigned a random number and images were analyzed manually using FluoView software (FV10-ASW 3.0 Viewer) by an observer blind to worker age. TUNELpositive cells were identified visually by their brightly fluorescent cell bodies. In some instances, only a portion of the nucleus appeared TUNEL-positive. Apoptosis was confirmed by observing nuclear morphology: apoptotic nuclei often show enhanced DNA condensation [START_REF] Robertson | Review: nuclear events in apoptosis[END_REF]. Cells identified as apoptotic were TUNEL-positive, co-localized with a nucleus, and exhibited atypical nuclear morphology. Cells were counted and categorized according to the nearest neuropil.

Although we could not always be certain that cell bodies projected to an adjacent neuropil region, our method reasonably estimated brain compartment variation in cell death.

To compare the frequency of apoptosis between functional brain regions that differ in volume and cell number, we employed an unbiased stereological approach to estimate total cell number. Volumes were measured directly on a subset of brains by an experimenter blind to brain age, and means for each age group calculated. Apoptosis was then scaled to total cell number in each brain region. Cell number per region was estimated using an optical disector [START_REF] Gundersen | The new stereological tools: disector, fractionator, nucleator and point sampled intercepts and their use in pathological research and diagnosis[END_REF] on one brain of each age group and extrapolated for other brains. We were thus able to calculate the proportion of apoptotic cells across age groups and brain regions. Proportions of apoptotic cells (number of apoptotic cells/estimated cell number) were calculated for each brain region. Because the total number of cells per region is large relative to the total number of apoptotic cells, small errors in total cell estimation have negligible effects on results. A mixed-effects ANOVA was run in SPSS to test for effects of age, brain region, and age x brain region interaction effects on the log-transformed proportion of apoptotic cells with age as a between-subjects factor and brain region as a within-subject factor. Differences between brain regions were identified using pairwise comparisons and Bonferroni corrections. Details are provided in supplemental material.

Quantification of microglomeruli (MG) in the mushroom body lip

MG, synaptic complexes characterized by a synapsin-immunoreactive presynaptic bouton surrounded by a halo of phalloidin-labeled postsynaptic terminals, were immunohistochemically labeled in 20 and 95-day old minors (N=28, 18 from 14 subcolonies) following the protocols of Groh et al. [START_REF] Groh | Synaptic organization in the adult honey bee brain is influenced by brood-temperature control during pupal development[END_REF]. Details are provided in supplemental material. To quantify age-related changes in MG densities, the imaging plane where the peduncle completely bisects the calyx and the collar is maximally visible was selected because it could be easily identified across samples. We thus minimized potential spatial effects by selecting approximately the same location. All images were taken using an Olympus FluoView 10i confocal microscope with a 60x objective and analyzed blind to brain age in ImageJ [START_REF] Schneider | NIH Image to ImageJ: 25 years of image analysis[END_REF]. Global adjustments were made to brightness and contrast in single-channel images, which were then merged and pseudocolored to count MG in two circles (400 µm diameter each) drawn over the lip region. Details of placement and counting criteria are provided in supplemental material. Mean counts per calyx (lateral or medial) and means of both calyces were analyzed with a one-way ANOVA. Counts were converted to MG per µm 3 using calyx neuropil measurements from Muscedere and Traniello [START_REF] Muscedere | Division of labor in the hyperdiverse ant genus Pheidole is associated with distinct subcaste-and age-related patterns of worker brain organization[END_REF].

Quantification of biogenic amines

Biogenic amine titers of individual brains were measured using high performance liquid chromatography with electrochemical detection as described in Muscedere et al. [START_REF] Muscedere | Serotonin modulates worker responsiveness to trail pheromone in the ant Pheidole dentata[END_REF] by an experimenter blind to worker age. Details are provided in supplemental material. Volume measurements of the rind, the outer region of the brain where cell bodies are located, in 20 and 95 day-old minors show no significant differences with age; neuropil volumes would be expected to show similar patterns. Therefore, it was not necessary to correct for brain size.

Eleven of 98 minor workers sampled for our assessment of amine titers across age and social role were from a colony lacking a queen. Neither 5HT nor DA titers in these workers differed significantly from titers of age-matched minors from queenright colonies; data were therefore pooled. Amine titers are reported in pg/brain for workers from 13 subcolonies (5HT: N=23, 31, 18, 14, DA: N=23, 29, 17, 13 for each age group from 20 to 120 days). Octopamine (OA) titers were not measured because levels of this monoamine are very low and do not change with age from eclosion to 20 days in P. dentata, a period during which 5HT and DA titers both significantly increase [START_REF] Seid | Age-related changes in biogenic amines in individual brains of the ant Pheidole dentata[END_REF]. Effects of age on amine titers were tested with an ANOVA in JMP and significant differences between groups determined with Tukey's post-hoc test.

Power analysis

To be confident that negative results biologically reflected lack-of-age effects, we performed retrospective power analyses using suggested effect sizes from Cohen 1988 [START_REF] Cohen | Statistical Power Analysis for the Behavioral Sciences[END_REF]; see also [START_REF] Thomas | Retrospective power analysis[END_REF][START_REF] Nakagawa | The case against retrospective statistical power analyses with an introduction to power analysis[END_REF][START_REF] Smith | Power rangers: No improvement in the statistical power of analyses published in Animal Behaviour[END_REF]). Power, expressed as a proportion ranging from 0 to 1, reflects the probability of correctly rejecting the null hypothesis [START_REF] Thomas | Retrospective power analysis[END_REF] and therefore the ability to detect a statistically significant result. Power greater than 0.8 is generally considered sufficient to detect a specified effect size [START_REF] Cohen | Statistical Power Analysis for the Behavioral Sciences[END_REF]). We used standardized effect sizes to estimate the power of our analyses and hence our ability to detect significance. For TUNEL analysis, we calculated power using a simulation method for an effect size of 0.5 as well as 2.5, which we found between brain regions. A 2.5 fold difference between ages was used as benchmark for detecting apoptotic cells in association with negligible senescence [START_REF] Traniello | Age-related changes in stem cell dynamics, neurogenesis, apoptosis, and gliosis in the adult brain: A novel teleost fish model of negligible senescence[END_REF] and an effect size of ~2.5 was found for age-related changes in MG density [START_REF] Groh | Environment-and age-dependent plasticity of synaptic complexes in the mushroom bodies of honeybee queens[END_REF]. Our effect sizes of 0.3 and 0.5 are thus conservative. All other tests had power of minimally 0.77 for an effect size of 0.5. We are thus confident that we could detect effects of relevant size in all assays. All power analyses were conducted in PASS 14 (NCSS Statistical Software, Kaysville, Utah).

Results

Task performance

We measured the efficacy of tasks performed within and outside the nest that comprise the breadth of the P. dentata minor worker repertoire at four ages: 20-22, 45-47, 95-97 and 120-122 days. Laboratory mortality of minors is 50% at 77 days and 25% at 117 days (Kaplan-Meier survival estimate), with a maximum lifespan of 140 days.

Nursing effort

Behavioral components of nursing involving sensory and motor functions did not significantly vary with worker age and the frequencies of behaviors were not significantly different from each other (two-way Wald test, age: χ 150 2 =7.53 x 10 -6 , p=1.00, behavior: 1B; power = 0.942 and 0.366, respectively, for 0.5 and 0.3 effect sizes).

χ 200 2 =0

Responsiveness to social signals regulating foraging and other collective actions

We examined the impact of worker age on fundamental sensorimotor functions (olfactory responsiveness, motor activity and motion coordination) and thus the ability of workers to participate in cooperative foraging by quantifying osmotropotactic pheromone-trail following.

Neither worker age nor trail-pheromone concentration (TPC) significantly affected trailfollowing accuracy, without an interaction effect (two-way ANOVA, F 1F; power = 0.768 and 0.366, respectively, for effect sizes of 0.5 and 0.3 for all trail-following metrics). 1C; power = 0.977 and 0.728, respectively, for effects sizes of 0.5 and 0.3).

Age-related changes in predatory behavior

Age-related neurobiological changes

Minor worker age and distribution of apoptosis in brain compartments

Across all ages, minor workers had very few apoptotic cells in all brain regions (Fig. 2A).

The proportion of apoptotic cells was highly variable and did not differ between 20 and 95 day- RCB, and SEZ respectively, Fig. 2B). The CC and OLs had a significantly lower proportion of apoptotic cells than the RCB. For an effect size of 0.5, power was 0.16 for age, 0.33 for brain region and 0.20 for interaction effect. Assuming an effect size of 2.5, as we found between the CC and RCB and was the smaller of our two significant differences, power was 0.79, 1.0, and old workers retain the range of sensory abilities necessary to be behaviorally pluripotent and switch tasks having different spatial distributions. Neither the efficacy nor plasticity of task performance appeared to be compromised in aging workers. Our results suggest age-related losses in cell numbers in the brain were extremely low and thus insignificant, and appear to have no impact on behavioral functions. Therefore, processing power underscoring social signal and cue perception and response appears to be maintained in old workers. The CC and OLs had lower levels of apoptosis than the RCB, suggesting that brain regions critically important to information processing and responsiveness to task stimuli may be particularly buffered from decline. The CC is being increasingly implicated in integrative functions as well as motor output [START_REF] Pfeiffer | Organization and functional roles of the central complex in the insect brain[END_REF], and maintenance of the OL neuropil with increasing age could be particularly important to extranidal task performance. P. dentata have relatively small eyes and OLs [START_REF] Muscedere | Division of labor in the hyperdiverse ant genus Pheidole is associated with distinct subcaste-and age-related patterns of worker brain organization[END_REF] which could contribute to lower levels of redundancy in these circuits and hence greater importance for their protection. High variability in the proportion of apoptotic cells in the CC likely stems from the small number of cells that comprise this region, causing a small absolute change in the number of dying cells to more strongly influence this proportion. Nevertheless, the CC showed significantly lower levels of apoptosis than the RCB. Titers of 5HT -a neuromodulator significant for olfactory social functions in P. dentata [START_REF] Muscedere | Serotonin modulates worker responsiveness to trail pheromone in the ant Pheidole dentata[END_REF] -and DA increased with age, rather than showing senescence-associated declines [START_REF] Rodríguez | The serotonergic system in ageing and Alzheimer's disease[END_REF][START_REF] Luijtelaar | Similarities between aberrant serotonergic fibers in the aged and 5,7-DHT denervated young adult rat brain[END_REF]. DA can have neurotrophic functions, and 5HT and DA may interact to promote circuit development and neuroplasticity [START_REF] Neckameyer | Neurotrophic actions of dopamine on the development of a serotonergic feeding circuit in Drosophila melanogaster[END_REF] as well as modulate sensory [START_REF] Dacks | Modulation of olfactory information processing in the antennal lobe of Manduca sexta by serotonin[END_REF][START_REF] Lazarini | Adult neurogenesis restores dopaminergic neuronal loss in the olfactory bulb[END_REF] and motor function [START_REF] Mustard | Modulation of motor behavior by dopamine and the D1-like dopamine receptor AmDOP2 in the honey bee[END_REF][START_REF] Pearlstein | Contribution of 5-HT to locomotion -the paradox of Pet-1(-/-) mice[END_REF], perhaps contributing to the preservation of task performance in aging workers. In sum, we did not identify age-related deficits in behavioral abilities or aminergic or cell deterioration, suggesting that P. dentata minor workers do not exhibit senescence throughout much of their lifespan and are able to continue to effectively contribute to colony labor well into their final weeks of life.

old
Older P. dentata minors are more efficient at nursing [START_REF] Muscedere | Age and task efficiency in the ant Pheidole dentata: young minor workers are not specialist nurses[END_REF] and show a significantly increased response than young minors (< ~10-15 days of age) to colony conditions that reflect greater brood-care needs [START_REF] Seid | Age-related repertoire expansion and division of labor in Pheidole dentata (Hymenoptera: Formicidae): a new perspective on temporal polyethism and behavioral plasticity in ants[END_REF]. Our results demonstrate that minor workers retain the olfactory sensitivity required to assess brood welfare and nurture growth and development, as well as provide motor control to mouthparts to manipulate delicate eggs and immatures, thus allowing them to remain effective alloparents late in life.

As in many ant species, olfaction is the predominant sensory modality in P. dentata.

Responsiveness to chemical cues and pheromones can develop with maturity [START_REF] Gadenne | Hormonal control of pheromone responsiveness in the male black cutworm Agrotis ipsilon[END_REF] and decline with senescence [START_REF] Cook-Wiens | Dissociation between functional senescence and oxidative stress resistance in Drosophila[END_REF]. However, results suggest that old P. dentata minors do not decline in performing foraging or nursing tasks that differ qualitatively in olfactory social cue and signal arrays. Odorant inputs are transduced to trigger motor output through the SEZ to control the mouthparts [START_REF] Jørgensen | Two closely located areas in the suboesophageal ganglion and the tritocerebrum receive projections of gustatory receptor neurons located on the antennae and the proboscis in the moth Heliothis virescens[END_REF] and thoracic ganglia to direct leg movements [START_REF] Niven | Diversity and evolution of the insect ventral nerve cord[END_REF]. Our assessment of predation showed no effect of worker age on sensory responsiveness to prey or the motor execution of attack. Minors of all ages did not appear impaired in attack mechanics, including biting behavior, suggesting that mandibular muscle functions and SEZ neuropil appear well-maintained with age.

Again, contrary to senescence theory, we found improvements in trail following and activity level (supplemental material, Fig. S1) in aging minors, suggesting continued development and/or experience-dependent enhancements of behavior into old age. Workers did not decrease in trailfollowing accuracy; surprisingly, 95-day minors followed trails for longer distances than younger individuals, perhaps due to their higher activity level (Fig. S1), enhanced olfactory responsiveness to trail pheromone, or both. Therefore, older minors not only did not exhibit senescence, but in fact improved in certain functions, suggesting selection for effective task performance throughout the lifespan. This does not imply behavioral specialization by older workers on outside-nest tasks; indeed P. dentata do not appear to exhibit strong age-related variation in worksites (Giraldo et al. in review). Specialized workers may in fact not be more efficient in task performance in at least some taxa (Temnothorax albipennis; [START_REF] Dornhaus | Specialization does not predict individual efficiency in an ant[END_REF]).

Pharmacological depletion of 5HT in P. dentata decreases responsiveness to trail-pheromone, likely through modulation of olfactory sensitivity [START_REF] Muscedere | Serotonin modulates worker responsiveness to trail pheromone in the ant Pheidole dentata[END_REF]. Although declining monoamine titers could cause olfactory and hence behavioral deficits, 5HT and DA titers increased with age, potentially enabling olfaction to remain intact.

Social insect workers have been hypothesized to experience programmed death at an age marginally greater than their life expectancy in nature [START_REF] Oster | Caste and Ecology in the Social Insects[END_REF], implying that task performance abilities either gradually diminish or abruptly decline with age. Although worker longevity in the field is not known in P. dentata, it is reasonably anticipated to be shorter than the 140-day lifespan we recorded in the laboratory, given increased worker mortality associated with the transition to extranidal tasks performed in more unpredictable environments [START_REF] Giraldo | Worker senescence and the sociobiology of aging in ants[END_REF][START_REF] Schmid-Hempel | Life duration and turnover of foragers in the ant Cataglyphis bicolor (Hymenoptera, Formicidae)[END_REF][START_REF] Kwapich | Demography, demand, death, and the seasonal allocation of labor in the Florida harvester ant (Pogonomyrmex badius)[END_REF].

Although we cannot exclude the possibility that P. dentata minor workers decline rapidly just before death, this appears to be unlikely because precipitous senescence [START_REF] Morbey | Rapid senescence in pacific salmon[END_REF] is rare and associated with unusually high investment in reproduction [START_REF] Finch | Longevity, Senescence, and the Genome[END_REF], which is absent in sterile workers. The lack of functional senescence in P. dentata minors contrasts with the rapid aging exhibited by most genetic gerontological models [START_REF] Austad | Comparative biology of aging[END_REF]. Studies on aging honey bees are equivocal regarding functional senescence in workers [START_REF] Rueppell | Aging without functional senescence in honey bee workers[END_REF][START_REF] Seehuus | Cellular senescence in honey bee brain is largely independent of chronological age[END_REF][START_REF] Behrends | Cognitive aging is linked to social role in honey bees (Apis mellifera)[END_REF][START_REF] Remolina | Senescence in the worker honey bee Apis mellifera[END_REF], which do not decline in responsiveness to light and sucrose, olfactory associative learning, or locomotion as they age [START_REF] Rueppell | Aging without functional senescence in honey bee workers[END_REF]. However, chronological age is only one factor influencing senescence in honey bees:

overwintering bees, which can be more than six months old, maintain tactile and olfactory learning but show deficits in olfactory long-term memory in comparison to chronologically younger foragers [START_REF] Behrends | Learning at old age: a study on winter bees[END_REF]. Our behavioral metrics encompassed measures of sensorimotor function similar to those used in studies of honey bees, as well as efficacy assessments of task performance inside and outside the nest required to fully evaluate worker capability in a species that retains a broad task repertoire throughout the worker lifespan. Such differences in hymenopteran aging phenotypes may be related to the lack of temporal caste discretization in P.

dentata [START_REF] Seid | Age-related repertoire expansion and division of labor in Pheidole dentata (Hymenoptera: Formicidae): a new perspective on temporal polyethism and behavioral plasticity in ants[END_REF][START_REF] Johnson | Within-nest temporal polyethism in the honey bee[END_REF] and contrasting nesting and foraging ecology.

Eusociality has had profound consequences for the evolution of behavioral development, immune function, and genetic regulation of aging [START_REF] Keller | Social insects as a model to study the molecular basis of ageing[END_REF][START_REF] Rueppell | Aging of social insects[END_REF][START_REF] Amdam | Social context, stress, and plasticity of aging[END_REF]. Social interactions appear to mediate metabolic homeostasis and affect mortality rates [START_REF] Koto | Social isolation causes mortality by disrupting energy homeostasis in ants[END_REF]. Division of labor could in part lead to selection for the maintenance of individual functionality throughout the sterile worker lifespan [START_REF] Giraldo | Worker senescence and the sociobiology of aging in ants[END_REF]. In ants, specialized morphologies and task performance are key to social complexity; worker polymorphism, task repertoire development, and behavioral specialization are underscored by brain neuropil growth and investment patterns [START_REF] Muscedere | Division of labor in the hyperdiverse ant genus Pheidole is associated with distinct subcaste-and age-related patterns of worker brain organization[END_REF]. Complex task repertoires are generated by a miniature brain that even at an extremely small size does not appear to compromise cognitive ability [START_REF] Muscedere | Investment in higher order central processing regions is not constrained by brain size in social insects[END_REF], suggesting that ant brains may operate with a level of metabolic efficiency that could enable conserved energy to be distributed to provide molecular protection against neural and behavioral senescence. The lack of functional senescence in P.

dentata minor workers, underscored by the maintenance of neuroanatomical and neurochemical substrates that activate and support task performance, suggests that the ant nervous system has evolved robust functionality throughout the relatively short sterile worker lifespan. This resilience may be associated with energy savings resulting from the absence of reproductive costs of workers, reduced neuron and neural circuit size, and lower requirements for redundancy and information storage that could minimize neurometabolic costs in individual worker brains [START_REF] Chittka | Are bigger brains better?[END_REF][START_REF] Eberhard | Grade changes in brain-body allometry. morphological and behavioural correlates of brain size in miniature spiders, insects and other invertebrates[END_REF][START_REF] Seid | The allometry of brain miniaturization in Page 27 of 31[END_REF][78]. Additionally, the benefits of living in a highly integrated homeostatic social system capable of collective information processing and emergent cognition may allocate cost reductions in brain metabolism to neural systems operational maintenance and thus effective lifetime behavioral performance.

ants. Brain. Behav. Evol.

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 31 ://mc.manuscriptcentral.com/prsb Submitted to Proceedings of the Royal Society B: For Review Only

Fig. 1 .

 1 Fig. 1. Number (A) and duration (B) of nursing behaviors (boxes show quartiles and whiskers

Fig. 2 .

 2 Fig. 2. Neuroanatomical and neurochemical metrics. A. Representative apoptotic cell in the MB

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prsb Submitted to Proceedings of the Royal Society B: For Review Only Aging

  minors showed no decline in responsiveness to prey or predatory attack (χ 9 2 =7.25, p=0.61; 20, 45, 95, and 120 days: N= 59, 41, 34, 17, Fig.

  workers. Apoptotic cell counts differed by brain region (mixed effects ANOVA, age F 1,78 =2.570, p=0.120, brain region F 5,27.8 =5.403, p<0.001, age x brain region F 5 =1.974,

p=0.1863, 20 days: N= 11, 7, 9, 8, 9, 11; 95 days: 10, 10, 10, 9, 9, 7 for the MB, AL, OL, CC,

  In aggregate, our behavioral and neurobiological results capture the pattern of minor worker aging through comprehensive assays of task performance and suggest negligible senescence throughout at least 85% of the minor worker lifespan. Results of behavioral assays were consistent with records of low levels of apoptosis throughout the brain and particularly in the MBs, and ALs, and OLs of aging workers. The age-invariance of MG density suggests olfactory processing abilities remain intact in old age. Extranidal work involves individual and collective actions requiring orientation and navigation, and the sampling of diverse sensory environments. Responsiveness to light, which cues the performance of outside-nest work, did not decline with age, and old minors showed positive phototaxis, providing evidence that light level discrimination does not senesce (supplemental material, Fig S1). Our results indicate that

	Brain titers of dopamine and serotonin
	Brain 5HT and DA levels significantly increased with age (ANOVA, 5HT: F 3, 82 =10.443,
	p<0.0001, N=23, 31, 18, 14; power = 0.973 and 0.597 for 0.5 and 0.3 effect sizes; DA:
	F 3,78 =20.921, p<0.0001, N=23, 29, 17, 13; Fig. 2D; power = 0.970 and 0.585 for effect sizes of
	0.5 and 0.3). 5HT was significantly higher in brains of 95 and 120-day old minors than 20 and
	45-day old minors. DA titer increased beyond 45 days of age.
	Density of synaptic complexes
	MG density did not significantly change with worker age (mean ± standard error, 20
	days: 0.0891 ± 0.00179, 95 days: 0.0859 ± 0.00224 MG/µm 3 of calyx, N= 28, 18, ANOVA,
	F 1,44 =1.211, p= 0.28, Fig. 2C; power= 0.9125 and 0.512 for effect sizes of 0.5 and 0.3
	respectively).

1.0 for age, brain region, and age x brain region.

Discussion

With advancing age, P. dentata minor workers showed no apparent deficits in the suite of behaviors we assayed, no increase in apoptosis in brain compartments that regulate task performance, and no decline in densities of synaptic structures considered significant to cognitive ability.

  77, 5-13. 78. Wehner, R., Fukushi, T. & Isler, K. 2007 On being small: Brain allometry in ants. Brain. Behav. Evol. 69, 220-228.

http://mc.manuscriptcentral.com/prsb Submitted to Proceedings of the Royal Society B: For Review Only

Acknowledgements

Prof. Rhondda Jones and Dr. Iulian Ilieş provided valuable statistical advice. We thank Drs.

Wulfila

Gronenberg, Karen Warkentin and Kimberly McCall for their critical reading of earlier drafts of the manuscript and technical insights. Two anonymous reviewers provided constructive comments. Positive controls for TUNEL were adapted from procedures developed by Dr. J. I. Etchegaray. YMG was supported by the National Institute on Aging of the National Institutes of Health (grant F31AG041589) and the National Science Foundation (grants IOB 0725013 and IOS 1354291; JFT sponsor). Support was also provided by Boston University Undergraduate Research Opportunity Program to AR, AK, and AD. The work presented here is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Data Accessibility

Datasets for this article have been uploaded to Dryad.

Competing Interests

We have no competing interests.

Authors' Contributions

YMG conceived the study, designed and performed experiments, analyzed data, performed statistics, and drafted and edited the manuscript. JFK was involved in experimental design, data analysis, and manuscript editing for the apoptosis study. VF and MM analyzed trail-following assays. SJKR assisted with statistical analyses. AR, LW, AD and AK performed experiments, assisted in data analysis, and contributed to drafting the manuscript. JFAT co-conceived the studies, designed experiments, and drafted and edited the manuscript. All authors gave final approval of the manuscript.


Selene Leya
email: selene.cerna@gmail.com

Cerna Ñahuis

Christophe Guyeux
email: christophe.guyeux@univ-fcomte.fr

Héber Hwang Arcolezi

Anna Diva

Plasencia Lotufo

Raphaël Couturier
email: raphael.couturier@univ-fcomte.fr

Guillaume Royer
email: guillaume.royer@sdis25.fr

S L C Ñahuis

A D P Lotufo
email: anna.lotufo@unesp.br

Long Short-Term Memory for Predicting Firemen Interventions

Many environmental, economic and societal factors are leading fire brigades to be increasingly solicited, and they therefore face an ever-increasing number of interventions, most of the time on constant resource. On the other hand, these interventions are directly related to human activity, which itself is predictable: swimming pool drownings occur in summer while road accidents due to ice storms occur in winter. One solution to improve the response of firefighters in constant resource is therefore to predict their workload, i.e. their number of interventions per hour, based on explanatory variables conditioning human activity. The purpose of this article is to show that these interventions can indeed be predicted, in a nonabsurd way, from state-of-the-art tools such as recurrent long short-term memory neural networks (LSTM). From the list of interventions in the Doubs (France), we show that it is possible to build, from scratch, a neural network capable of reasonably predicting the interventions of 2017 from those of 2012-2016. While the results could be improved, they are already promising and would allow the actions of firefighters with a constant resource to be optimized.

I. INTRODUCTION

Fire departments in the world constantly seek strategies to decrease their response time to interventions since it is one of the most important factors to consider; their ability to save more lives and rescue people depends on it. The data collected through the years about their interventions during fires, road accidents, and other types of incidents could be used to develop a data-driven decision making approach in order to understand the trends of certain events such as knowing the hours following a particular event the number of likely interventions ensuing as well as their type or place. In this way, the efficiency of their response could increase and their operational costs would be decreased.

Moreover, nature has inspired most of the inventions that humans have developed and brain's architecture is an example of inspiration on how to build an intelligent machine. We learn considering our memories, we comprehend contexts based on our understanding of previous situations and we can complete phrases using first words as a basis. These characteristics are well represented in recurrent neural networks with Long Short-Term Memory (LSTM), which have emerged as effective and scalable model for several learning problems related to sequential data (e.g., handwriting recognition, speech recognition, human activity recognition and traffic prediction), and it does not suffer from the effect of the vanishing or exploding gradient problem as simple recurrent networks do [START_REF] Graves | Supervised Sequence Labelling with Recurrent Neural Networks[END_REF]. One of the central keys behind LSTM success is its memory cell, which can maintain its state over time by learning what to store in the long-term state, what to throw away and what to read from it by passing on nonlinear gating units regulating the information flow into and out of the cell. Fig. 1 shows in more details how the longterm state c t-1 initially goes through a forget gate, dropping out some memories, and then it adds some new memories that were properly selected by an input gate. The result c t is sent straight out without any further transformation, i.e., at each time step, some memories are dropped and others are added. Furthermore, after passing by the input gate, the long-term state is copied and passed through an activation function tanh, and finally the result is filtered by an output gate. This procedure generates the short-term state h(t) that is equal to the cell's output for this time step y(t).

Mathematically, it is expressed as:

i t = σ(W T xi • x t + W T hi • h t-1 + b i ) (1)
f t = σ(W T xf • x t + W T hf • h t-1 + b f ) (2)
o t = σ(W T xo • x t + W T ho • h t-1 + b o ) (3)
g t = tanh(W T xg • x t + W T hg • h t-1 + b g ) (4)
c t = f t ⊗ c t-1 + i t ⊗ g t ( 5
)
y t = h t = o t ⊗ tanh(c t ) (6)
where W xi , W xf , W xo and W xg are the weight matrices of each four layers for their connection to the input vector x t ; W hi , W hf , W ho and W hg are the weight matrices of each four layers for their connection to the previous shortterm state h t-1 ; and b f , b g , b i and b o are the bias terms of each of the four layers. For more details about LSTM architecture, interested readers are strongly advised to read and consult [START_REF] Graves | Supervised Sequence Labelling with Recurrent Neural Networks[END_REF]- [START_REF] Greff | LSTM: A search space odyssey[END_REF].

To the best of the authors' knowledge, researches based on the forecast of the number of interventions, response speed, materials and engine used by fire departments are scarce in the literature. In particular, the use of LSTM neural networks to predict the number of firefighters interventions is provided for the first time throughout this paper. The data collected from firefighters interventions is considered as a sequential data set that will feed our LSTM model to afterwards predict the number of future incidents. To complete our data set, several factors are included such as weather, traffic, holidays, height of the rivers, disease statistics, etc. Therefore, this will help firefighters to define better strategies to respond immediately in case of incidents and thus to save more lives with less effort. In order to make a fair comparison, we establish as baseline the average number of interventions per hour to compare the LSTM model results.

The following sections of this paper are structured as follows: in Section II the state of the art is briefly presented; in Section III the way that data were acquired and encoded is explained; in Section IV feature and model selection is exhibited; in Section V prediction results are given and a discussion highlighting results is provided; in Section VI concluding remarks and future works are given.

II. STATE OF ART

Researches to forecast the number of interventions, response speed, materials and engine used by fire departments are scarce in the literature. However, there are machine learning techniques applied to forecast crime, traffic incidents, traffic flow and speed, occupational accidents, and others. In [START_REF] Sarkar | Application of optimized machine learning techniques for prediction of occupational accidents[END_REF] authors presented a proposal to forecast occupational accidents using Support Vector Machine (SVM) and Multi-Layer Perceptron (MLP) optimized by Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), where the aim was to predict the accident outcomes such as injury and property damage using occupational accident data.

As another example, [START_REF] Ren | A Deep Learning Approach to the Citywide Traffic Accident Risk Prediction[END_REF] worked with a deep learning approach, using LSTM neural networks to predict the risk of the traffic accident, taking into account weather variables, periodical patterns and the spatial distribution patterns of traffic accidents; the traffic accident data were discretized in space and time to train the deep model; then, the model was provided with recent historical data to eventually obtain the real-time traffic accident risk prediction.

Gerber [START_REF] Gerber | Predicting crime using twitter and kernel density estimation[END_REF] presented a study on the use of spatiotemporally tagged tweets for crime prediction using Kernel Fig. 1: LSTM Cell [START_REF] Géron | Hands-On Machine Learning with Scikit-Learn and Ten-sorFlow[END_REF] Density Estimation (KDE) differing from the standard hotspot models. The author collected crime data for a specified period from the Chicago Police Department and tweets tagged with geographical positioning system coordinates in the limits of Chicago and Illinois cities. Subsequently, author quantified the crime prediction gains using Twitterderived information to compare to a standard KDE approach achieving improvements for 19 of the 25 crime types.

In [START_REF] Ma | Long short-term memory neural network for traffic speed prediction using remote microwave sensor data[END_REF] authors developed a LSTM NN to capture the nonlinear traffic dynamic to catch the long-term temporal dependency for predicting short-term travel speed. The data were collected for a month from two different locations in Beijing and were divided in twenty five days for training and five days for testing. The performance of the proposed LSTM model was compared with others RNN and Artificial Intelligence (AI) methods. Results for LSTM NN were superior to other methods in most of the tests proving to be an effective approach for short-term travel speed prediction.

[9] proposed a LSTM Regression model to predict 24hours traffic counts data by collecting and labelling 24hours traffic data of some districts in Texas, constructing the LSTM and a Logistic Regression model to compare results, and finally analyzing the potential resource allocation patterns according to the obtained results. Results proved that the LSTM regression model is more powerful than logistic regression and that the mean square error of logistic regression is about 5 times higher than LSTM. Conclusion remarks for resource allocation strategy, were that using LSTM would provide more accurate results to decide the distribution of traffic resources.

Further, [START_REF] Pettet | Incident analysis and prediction using clustering and bayesian network[END_REF] developed a data-driven toolchain to forecast the likelihood of vehicular incidents in given time and location using incident data from the Nashville Fire Department in USA, considering weather and road type information as added variables; authors combined a Similarity Based Agglomerative Clustering to categorize incidents with similar characteristics, a survival analysis to learn the probability of incidents per cluster and a Bayesian Network inference technique to map the clusters to the spatial locations.

III. DATA ACQUISITION AND ENCODING

The fire and rescue department, SDIS 25, in the region Doubs-France has provided us with a list of interventions collected from 2012 to 2017 containing information on a total number of 195,628 interventions. This data file contains: the identifier code of an intervention, date and time of the beginning and end of an intervention, date and time in which the first engine arrives, the community in which the intervention take place, the classification of the incident, response time and duration of the intervention.

In this section, we will explain how the data were collected and prepared before being selected and used as input in the prediction phase.

A. Data Acquisition

From the list of interventions collected, we extracted from each individual intervention the date and time of when it happened, in order to detect tendencies correlated with these parameters. For instance, the number of car accidents increases on Saturday nights because young people tend to drink and drive during this period of time.

Other factors considered in the occurrence of incidents are the weather conditions, that affect significantly the number of road accidents, fires and casualties; traffic hours, height of the main rivers in the Doubs, epidemiological data, academic vacations, holidays, moonrise, moonset and moon phases. All of this in order to predict the number of interventions that will occur in the following hour or in the following three hours. Therefore, at the beginning, a dictionary was created in which extracted data from the fire department were save and the supplementary data were imported from other sources together. The process is explained as follows:

• The dictionary is initialized containing keys ranging from "01/01/2012 00:00:00" until "31/12/2017 23:00:00" of the form "YYYYMMJJhhmmss". The keys are generated by blocks of 1 hour. • The following weather-related data reported by "Meteo France" [11] was imported from three stations located in Dijon-Longvic, Bale-Mulhouse, and Nancy-Ochey: temperature, pressure, pressure variation each 1h, barometric trend types, total cloudiness, humidity, dew point, last hour precipitation, last three hours precipitation, average wind speed for every 10 minutes, average wind direction for every 10 minutes, bursts over a period, horizontal visibility, and finally the current time. However, the data were not complete, for this reason, it was necessary to apply a linear interpolation to fill the blanks. Finally, the meteorological data were added to the dictionary. • It was also introduced various temporal information as: hour, day, day in the week, day in the year, month and year. • The height of twelve rivers, which are the most representative of the Doubs department were also considered. The data were collected from "Hydro" [12], then the dictionary was filled with the average of the readings closest to the time of the block considered, the standard deviation of variation of the water height on this block, the number of readings during this block, the maximum height occurred during this block of time with the alert 1 (true) if the height of the river exceeds a limit established as a flood alert or 0 (false) if not. • From the list of interventions given by the fire brigade department, the interventions were classified according to the date of occurrence, grouping them by a period of one hour to add them to the dictionary. • Holidays were considered as a binary variable initialized with 0 (false), that would be 1 (true) for any 1h block within an academic holiday period. Also, the starting and ending days of vacations were considered as a binary variable where it is 1 (true) for the days corresponding to the beginning and end of holiday periods and 0 (false) if not.

• Public holidays were added (1 or 0, for true or false), as well as a second key that is set to 1 the days before public holidays, for the hours ranging from 3:00 pm to 11:00 pm (otherwise 0).

• Information related to the "Bison Futé" [13] were included, which is a system put in place in France to communicate to motorists all the recommendations of public authorities regarding traffic, traffic jams, bad weather, accidents, advice, etc. It classifies the days at risk according to several colors: green = fluid traffic, orange = dense traffic, red = difficult traffic, black = to avoid because of traffic jams and slow traffic. These information were integrated through two additional keys related to the departure and the return. They are 0, 1, 2 or 3, depending on whether the traffic forecasts correspond to Green, Orange, Red or Black. • Weekly epidemiological information organized by each given hour and related to the incidence of chickenpox, influenza and acute diarrhea, were incorporated to the dictionary. The data were collected from the "Sentinelles" network [14]. • Finally, a boolean variable to know if it is a day (0) or night (1) for each given hour was added. Moreover, another boolean variable was included to recognize if the moon had already risen. This procedure considered the given hour plus 30 minutes, and what the moon phase was.

B. Data Encoding

Often, the initial data do not have the format feature/value. For this reason, it is necessary to extract what could be potentially useful features to convert them in the format that the model needs as input. This process is called feature extraction [START_REF] Garreta | Learning scikit-learn: Machine Learning in Python[END_REF].

To complete this task, "StandardScaler" from Scikit-learn library [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF], which is a method that standardizes features by rescaling the distribution of values to zero mean and unit variance, was used; the variables standardized were: year, hour, wind direction, humidity, nebulosity, moon phase, dew point, precipitations, rafales, temperature, visibility, wind speed, chickenpox statistics, influenza statistics, acute diarrhea statistics, rivers height variables except by the alert variable, etc. Also, from Pandas library [START_REF] Mckinney | Data structures for statistical computing in python[END_REF], the "Get Dummies" (OneHotEncoder) method, that converts categorical variables into dummy/indicator features was used; for instance: bison futé variables, time variables such as day, day of the week, day of the year and month, holiday indicator, night indicator, barometric trend, river height alert variable, etc. Finally, the target feature "nbInterventions" was not standardized, after several tests, it was decided to keep the original values.

IV. FEATURE AND MODEL SELECTION A. Feature Selection

Usually, using every available feature in the learning data set seems preferable, since it is believed that using as much information would build a better model. However, there are two main reasons why the number of considered features should be restricted. First, it is possible that unimportant features could establish correlations between features and the target that arise just by chance and would not correctly model the problem, leading to poor generalization or adding redundant information. And second, a large number of features could greatly increase the computation time without any improvement [START_REF] Garreta | Learning scikit-learn: Machine Learning in Python[END_REF].

As a result, working with a smaller set of features may conduct to better results. So, for this work, the "Mutual Info Regression" method from the open source library Scikitlearn [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF] was used to select features. Mutual Info Regression is a nonparametric method to evaluate the mutual correspondence for a continuous target variable based on entropy estimation from k-nearest neighbors distances. Two random features are chosen to calculate their mutual information, the result is a nonnegative value which measures the dependency between the features. When two random variables are independent the output is zero, but higher outputs mean higher dependency.

To get mutual information regression scores, 800 neighbors were used; then, scores were scaled between 0 and 1. Finally, the threshold was established as 0.01, all features with scores higher than 0.01 are considered as input to our model. Hence, from a total of 830 features extracted, 56 were taken to train our model.

B. Model Selection

Another important step is the selection of the model parameters, known as hyperparameters. In this investigation, the hyperparameters considered were the number of layers, the number of neurons, epochs, batch size and learning rate to build our LSTM model. The models were developed with Keras library [START_REF] Chollet | Keras[END_REF].

First, after encoding and selecting the features, data were split into three data sets, the training set (2011-2015), the validation set (2016) and the testing set (2017). The first and second set are used to build a model that will predict the number of interventions for 1h and 3h blocks and the latter is used to verify the accuracy of these predictions.

After several tests, the results improved by establishing a constant number of neurons in the first and second layer of our LSTM architecture, the other hyperparameters were chosen within a range as described in Table I. Then, a random search is performed with 50 iterations searching for the best hyperparameters. The number of neurons for the third layer, batch size and learning rate change in each iteration randomly to discover which combination of values gives a better result. The maximum number of epochs is 5000, but an early stopping method from [START_REF] Chollet | Keras[END_REF] was used ,i.e., if after 15 epochs the loss function of validation set did not improve, the LSTM NN stopped.

Fig. 2: Genetic algorithm design

The best 10 results were saved to be the starting population for our genetic algorithm, which is different from the original one better detailed in [START_REF] Sastry | Genetic algorithms[END_REF]. The GA was also executed 50 more times; this process is implemented in order to tune the hyperparameters obtained before. The steps for the developed GA (Fig. 2) are described bellow:

1) A population of size ten is defined, each individual has the following parameters: number of neurons in the first, second and third layer, batch size and learning rate. 2) Two tournaments are made and in each one two individuals are selected randomly and their Mean Absolute Error (MAE) is compared, the individual with the best MAE wins the tournament.

3) The two winners are combined to generate two offspring. 4) The offspring with the best MAE is mutated. An individual position is selected randomly, if the position belongs to the number of neurons or batch size, the value will be mutated by adding or subtracting 1; if the position belongs to the learning rate, the value will be multiplied by a number randomly generated between 0 and 1.5. 5) If the new mutated individual is better than the worst individual in the population, then the worst will be replaced by the former and a new iteration is executed from step 2.

V. PREDICTION RESULTS AND DISCUSSION

A. Prediction Results

In this section our results are presented and analyzed. The metrics used to evaluate the results are the Root Mean Square Error (RMSE), the MAE as principal and the Number of

B. Discussion

The aim of this work was to predict the number of interventions using data from 2012-2015 for testing, 2016 for validation and 2017 for testing, and different time step configurations for the next one and three hours in the future. As presented in Table II, for the first case, the model with 12 time steps outperforms the others regarding to MAE metric. As can be seen in Fig. 3 the LSTM model is trying to find a fairly acceptable sequence pattern for future interventions, i.e., when the number of interventions increases the model tends to increase smoothly and in the same way when there is a valley. Additionally, the analysis of NBINT shows that this model is able to predict more accurately from a total of 8748 interventions, 1835 interventions are exactly predicted, but if it is considered a margin of error ±1 the number of exact predictions increases to 4818 (55%), which means that considering such tolerance, the model continues being feasible in real applications. For the second case, the result using 24 time steps is better than 3 and 12 respecting to MAE metric, from a total of 2912 interventions, 328 interventions are exactly predicted and with a margin error ±1 NBINT increases to 925 (32%). Contrary to the previous case, this model remains more or less continuous even in spite of peaks and valleys it does not try to increase or decrease the sequence pattern value. This behavior could produce higher RMSE and MAE in contrast to the first case. Another interesting fact to mention is that the number of intervention per year is increasing, which is the expected due to population growth. However, this increment is not linear and the year 2017 was exceptionally larger than previous ones as informed by the SDIS 25 fire Department, making predictions more difficult even for our LSTM model.

Finally, the best 60 models generated for the next one hour prediction and other 60 for the next three hours prediction were taken in order to analyze and understand the tendency of our hyperparameters. The fANOVA framework developed by Hutter et al. [START_REF] Hutter | An efficient approach for assessing hyperparameter importance[END_REF] was used, which is a tool that uses different hyperparameter settings to fit a random forest that captures the relationship between hyperparameters and performance and then evaluates their influence. For this analysis, the number of trees used was 200 and results in Fig. 7 showed that the best batch size was around 140 (it is verified for both prediction horizons). We could observe that for one hour prediction the learning rate was smaller and more concentrated between 0.00001 and 0.0001 values, while the learning rate for three hours prediction tended to 0.0002. Furthermore, the model with three hours prediction needed more epochs during the training and neurons in third layer increased from being around 70, for one hour horizon, to 100 for three hours horizon.

VI. CONCLUSION

The ability to predict the number of interventions at a given time in the future could help fire departments around the world to deal more efficiently with forthcoming incidents and to improve the management of human and mobile resources. This paper presents a Long Short-Term Memory Neural Network to predict the number of interventions of firefighters in the region of Doubs-France to the next one and three hours. To validate the performance of the developed LSTM model, 6 years of interventions data from the departmental fire and rescue SDIS 25 in the region Doubs-France were collected. Results demonstrated that the LSTM model is trying to find a sequence pattern to predict the number of interventions, which is suitable for practical purposes to anticipate the management of resources to improve response time. We do recognize that these results have to be improved in a more accurate way to be used as first decision making approach by fire departments.

For future work, we will test different Machine Learning methods, better explore LSTM architectures and combinations with other neural networks models (e.g., Convolutional Neural Networks) and search for different optimization methods to improve results using intelligent techniques. Other attractive directions are to analyze the features with other methods for feature selection (e.g., F-test, Principal Component Analysis -PCA), find a way to model the data that allows to learn the increment of the number of interventions over the years, and increase the number of time steps. Moreover, we will develop techniques capable of predicting the type of intervention and the location to complement and work as toolchain with this research.

Fig. 3

 3 exhibits results for 200 samples to the best 12 hours as time steps trying to predict one hour in the future and Fig.4the exact number of predictions with 0 to max 16 errors. The LSTM architecture for this case is composed of 3 LSTM layers with 4, 57 and 72 neurons respectively and 1 Dense layer with one neuron as output. Similarly, Fig.5exhibits the prediction results for 200 samples to the best 24 hours of time steps for the next three hours in the future and Fig.6the exactly number of predictions with 0 to max 25 errors. For this case the LSTM architecture consists of 3 LSTM layers with 4, 57 and 66 neurons respectively and 1 Dense layer with one neuron as output. Note that in Figs.5 and 6, 200 samples represent 600 ones from the previous case due to the fact that samples are grouped by 3 hours instead of just 1. Also, results were rounded to integer values, i.e., considering that the LSTM model predicts real values (e.g., 2.31 interventions) results were transformed to integer ones (e.g., 2 interventions) to be consistent with real applications. Lastly, the same sequential NN architecture developed with Keras[START_REF] Chollet | Keras[END_REF] was kept, i.e., the first LSTM layer has 4 neurons, the second LSTM layer has 57 neurons, the third LSTM could change the number of neurons and the last Dense layer has one neuron.

Fig. 3 :Fig. 5 :Fig. 6 :

 356 Fig. 3: Predictions for 1h future

Fig. 7 :

 7 Fig. 7: Hyperparameters for 1 hour prediction

TABLE I :

 I Hyperparameters Settings

	Hyperparameter	Values
	Neurons first layer	4
	Neurons second layer	57
	Neurons third layer	[50, 100]
	Epochs	[60, 5000]
	Batch size	[55, 160]
	Learning rate	[0.000001, 0.001]

TABLE II :

 II Prediction results on test data 2017Exact Predictions (NBINT). In order to compare with some reference values, this paper considers as baseline the average value calculated for each block of hour, which achieved scores as RMSE 2.4724, MAE 1.8013 and NBINT 1726. TableIIpresents results of the LSTM model trying to predict the number of interventions for the next one and three hours using different values 3, 12 and 24 hours of time steps with the best performance marked in bold.

		Predicting next 1h	Predicting next 3h
	Time steps (hrs)	RMSE	MAE	NBINT	RMSE	MAE	NBINT
	3h	2.2864	1.6996	1820	4.4295	3.3394	314
	12h	2.2901	1.6934	1835	4.2834	3.2496	302
	24h	2.2828	1.7006	1813	4.2706	3.2142

ACKNOWLEDGMENT

This study was financed in part by the Coordenac ¸ão de Aperfeic ¸oamento de Pessoal de Nível Superior -Brasil (CAPES) -Finance Code 001, by the EIPHI Graduate School (contract "ANR-17-EURE-0002"), by the Interreg RESponSE project, and by the SDIS25 firemen brigade.

*This work was supported by the Coordenac ¸ão de Aperfeic ¸oamento de Pessoal de Nível Superior -Brasil (CAPES), by the EIPHI Graduate School (contract "ANR-17-EURE-0002"), by the Interreg RESponSE project, and by the SDIS25 firemen brigade.