Carolina Imianosky

Douglas A Santos
email: douglas.santos@umontpellier.fr

Douglas R Melo

Felipe Viel
email: viel@univali.br

Luigi Dilillo
email: luigi.dilillo@umontpellier.fr

Implementation and Reliability Evaluation of a RISC-V Vector Extension Unit

The space environment challenges the reliable functioning of electronic systems due to radiation exposure and extreme temperatures. To mitigate potential failures, fault tolerance techniques are crucial in these systems. With the implementation of fault tolerance techniques, the performance of the system is affected, often impairing data processing. One way to accelerate data processing is to use vector instructions, which allow operating on a data vector with only one instruction. Therefore, we developed a Vector Extension Unit that supports a subset of the RISC-V Vector Extension for HARV, a RISC-V-based processor. We evaluated the impact of using the Vector Extension instructions over the scalar instructions. We assessed the reliability of the core by simulation based on fault injection campaigns with both baseline and hardened HARV. The vector unit offers substantial performance acceleration of up to 8.1 times when compared to scalar operations, and, despite the hardware overhead, it enhanced the reliability of the executions from 93.9% to 97.9% for the baseline HARV and from 97.9% to 99.3% for the hardened HARV.

Index Terms

RISC-V, System-on-Chip, Vector Instructions, Fault Tolerance, Space Systems

I. INTRODUCTION

With radiation exposure and extreme temperatures, the space environment affects the functioning of systems during a mission. The potential occurrence of critical failures requires spacecraft to be designed using fault tolerance techniques to improve their reliability [START_REF] Yang | Fault-tolerance techniques for spacecraft control computers[END_REF].

The RISC-V is an Instruction Set Architecture (ISA) that has gained popularity due to its simplicity, openness, and modularity, i.e., it consists of a basic ISA and optional extensions [START_REF] Mascio | Leveraging the openness and modularity of RISC-V in space[END_REF]. Among the ISA extensions defined in the standard, the RISC-V Vector Extension (RVVE) [START_REF] Organization | RISC-V "V" Vector Extension[END_REF] enables systems to execute a single instruction on multiple data elements simultaneously. This extension provides higher data parallelism levels, improving critical factors for space systems, such as processing latency and power consumption. Thus, it is possible to speed up onboard applications such as AI, which are effective in remote sensing, as for image classification and target detection [START_REF] Furano | Ai in space: applications examples and challenges[END_REF].

The HARV (HArdened RISC-V) [START_REF] Santos | A low-cost fault-tolerant RISC-V processor for space systems[END_REF] is a low-cost fault-tolerant RISC-V processor, hardened against SEUs (Singleevent Upsets) and SETs (Single-event Transients) using Triple Modular Redundancy (TMR) and Error-Correcting Code (ECC). Furthermore, this processor has been characterized in different irradiation facilities [START_REF] Santos | Enhancing fault awareness and reliability of a fault-tolerant RISC-V system-on-chip[END_REF], proving suitable for reliable applications.

The use of AI in nano-and pico-satellite is an alternative for compensating for its lack of resources (power, volume, computing) due to the ability to process the data onboard instead of sending them to the ground station [START_REF] Furano | Ai in space: applications examples and challenges[END_REF]. Meanwhile, the faults caused by the space environment can lead to prediction errors. Besides that, combining AI with fault-tolerance techniques increases hardware costs and reduces processor performance [START_REF] Duddu | Towards enhancing fault tolerance in neural networks[END_REF]. The vector extension can speed up AI processing but is intrinsically prone to radiation-induced failures since it essentially comprises sequential logic elements such as registers. Thus, evaluating the reliability of AI applications that use vector extension is crucial.

In this context, this work presents an extension of the HARV processor to include a Vector Extension Unit (VEU) that supports a subset of the RVVE, reducing the processing latency of the processor, which is affected by the implemented fault tolerance techniques. To validate our implementation, we execute and compare benchmarks using scalar and vector instructions in HARV with baseline and hardened configurations.

The main contribution of this work is the description of the proposed vector unit and its reliability characterization in the HARV-SoC (HARV System-on-Chip). This characterization enables the improvement's assessment of the core regarding its performance and fault tolerance. The reliability assessment of the RVVE in the processor was performed by fault injection simulations. This assessment provides an insightful analysis of the impact of using vector extension for reliable applications.

The remainder of this paper is organized as follows. Section II discusses the related work. Next, Section III presents additional concepts on the RISC-V ISA and its vector extension, and Section IV describes our VEU design. Section V presents the materials and methods employed in this study, while Section VI discusses the experimental results. Finally, the final remarks are shown in Section VII.

II. RELATED WORK

Some commercial and academic cores currently implement or rely on the RVVE. For example, [START_REF] Di Mascio | Extending the noel-v platform with a risc-v vector processor for space applications[END_REF] describe the implementation of an RVVE on the HPP64 NOEL-V platform for space applications. This platform aims to improve the performance and capabilities of space processors while considering the specific constraints and requirements of satellite data systems. Their study compares the performance and resource utilization of the vector processor with different levels of data-level parallelism (DLP) to the baseline scalar processor.

Another example is [START_REF] Kuo | Integration of a real-time ccsds 410.0-b-32 error-correction decoder on fpga-based risc-v socs using risc-v vector extension[END_REF], which integrates two non-binary low-density parity-check decoding algorithms for deepspace communication standards on RISC-V SoCs using vector extensions. The authors discuss the migration of critical computing tasks in communication systems from dedicated devices to general-purpose processors, such as GPUs and Field-Programmable Gate Arrays (FPGAs). The work aimed to increase flexibility, reduce costs, and improve efficiency through constant upgrades in hardware and software designs.

The authors in [START_REF] Ali | Vector processing unit: A risc-v based simd co-processor for embedded processing[END_REF] implemented a vector processing unit based on the RISC-V architecture but focused on incorporating SIMD capabilities. Their goal was to enhance the performance of embedded processing tasks. This unit was integrated into the CV32E40P [START_REF] Gautschi | Near-threshold risc-v core with dsp extensions for scalable iot endpoint devices[END_REF] RISC-V-based processor and was evaluated based on resource utilization, power consumption, and performance for different design configurations. The authors compared the metrics when using only the CV32E40P processor and when using it with the unit.

Both [START_REF] Di Mascio | Extending the noel-v platform with a risc-v vector processor for space applications[END_REF] and [START_REF] Kuo | Integration of a real-time ccsds 410.0-b-32 error-correction decoder on fpga-based risc-v socs using risc-v vector extension[END_REF] present RVVE implementations designed for space applications and use hardened processor cores. However, none of them presented evaluations of the reliability of the core with the RVVE.

Given this context, we implemented the VEU for the HARV core to assess the performance gain and the hardware overhead of the implementation. Also, we performed fault injection simulations for reliability analysis.

III. RISC-V VECTOR EXTENSION

The RISC-V ISA is a Reduced Instruction Set Computer (RISC) architecture designed to be modular. It consists of a basic instruction set and various optional extensions that can be added to form a more robust instruction set [START_REF] Waterman | The RISC-V instruction set manual[END_REF]. The RVVE is an optional extension that supports vector architectures, which explore Data-Level Parallelism (DLP) concepts. With this, it is possible to operate simultaneously on multiple vector data elements, speeding up computational processing [START_REF] Hennessy | Computer Architecture: A Quantitative Approach[END_REF].

Vector architectures originated from SIMD processing, which emerged in the 1970s for partitioning large registers (e.g., 128-bit registers) into multiple elements and operating them in parallel. However, in SIMD instructions, the operation code (Opcode) defines the operation and the data width, meaning that increasing the width of the vectors also implies an increase in the instruction set [START_REF] Patterson | The RISC-V Reader: an open architecture Atlas[END_REF]. Implementation of vector architectures, on the other hand, defines the size of the vector rather than the Opcode. Thus, it reduces the size of the instruction set and makes the hardware design more flexible for data parallelization without affecting algorithm development.

The RVVE adds 32 vector registers to the base RISC-V and enables partitioning them to perform multiple operations simultaneously. The size of the elements is configured via seven additional registers called Control and Status Registers (CSRs) [START_REF] Waterman | The RISC-V instruction set manual[END_REF], and the Configuration-Setting instructions change the values of the CSRs. Vector arithmetic instructions operate on values stored in vector registers, and memory read and write operations transfer data elements between memory and registers. All instructions in this set fit into two existing instruction formats: LOAD-FP/STORE-FP from the floating-point extension and OP-V, an exclusive RVV format [START_REF] Organization | RISC-V "V" Vector Extension[END_REF].

IV. HARV VECTOR EXTENSION UNIT

In this work, we developed a VEU (Fig. 1) for the HARV processor. We implemented the VEU so that the maximum size of the vector can be configurable by the implementation. The VEU comprises the interface units, the Vector Register File (VRF), a vector elements counter, and the vector execution unit. To enable the HARV's support to the VEU, we modified two components of the core: the instruction decode and the execution.

Fig. 1. Vector Extension Unit

The HARV control unit integrates the instruction decoder. The instruction bits 6 to 0 are the input to a combinational logic component that determines the instruction format, according to the RISC-V ISA specification [START_REF] Patterson | The RISC-V Reader: an open architecture Atlas[END_REF]. Afterward, the outputs of the control component are either enabled [START_REF] Yang | Fault-tolerance techniques for spacecraft control computers[END_REF] or disabled (0) according to the instruction's operation. To support the RVVE subset, we added the three instruction formats defined in the RVVE v1.0 specification: Load-FP, Store-FP, and OP-V [START_REF] Organization | RISC-V "V" Vector Extension[END_REF].

In the HARV microarchitecture [START_REF] Santos | A low-cost fault-tolerant RISC-V processor for space systems[END_REF], the main and ALU control units were merged as a single component to simplify the implementation. So we extended it also to control the Vector Execution Unit. Also, the HARV processor reads the source register during the decoding stage and does the same for the VRF.

The HARV's execution unit performs the arithmetic and logic operations. These operations include: add, subtraction, logical shift (left or right), arithmetic shift (right only), set to 1 (on less than), AND, OR, and XOR. To support the vector instructions, this unit was extended to operate on 64-bit operands and is used to complement the Vector Execution Unit, eventually operating in some vector elements.

The Interface Units are responsible for directing the inputs and outputs of the VEU. The inputs are signals from the controller, the addresses to read and write from the VRF, the result from the external ALU, and the values from the vector CSRs. The outputs are one signal indicating if all the necessary elements were processed; and two arrays of data that serve either for memory writing or as input for the external ALU if required.

The VRF contains 32 registers similar to the scalar register file but exclusive to the VEU. Thus, it can perform two readings and one writing simultaneously. The data outputs are defined to have the size of maximum vector size specified by the implementation in a way that all the elements of the vector are read at once. The data input is defined as 64-bit since it is the maximum element size, so for writing, a 64-bit element is handled as two 32-bit elements. The element counter holds the number of vector elements that were already processed. Thus, it defines the following array of data within the whole data vector to be processed.

The vector execution unit comprises four 8-bit simplified ALUs operating on the vector elements and exclusive to arithmetic vector instructions. The simplified ALUs have carry-in and carry-out signals, which are multiplexed to enable simultaneous operations for two 16-bit or one 32-bit element. A diagram of this unit is shown in Fig. 2. In the case of 32-and 64-bit vector elements, the external HARV ALU is also used to operate on one element. With this architecture, it is possible to operate on one 64-bit, two 32-bit, two 16-bit, or four 8-bit elements simultaneously.

The primary goal of this work was to support simple vector instructions to optimize application processing, such as Neural Networks, and assess the behavior of the HARV with the Vector unit in fault injection simulations. Therefore, the subset of instructions was limited to sequential instructions for memory access (word, half-word, and byte) and integer arithmetic operations such as addition and subtraction.

V. MATERIALS AND METHODS

We implemented the vector instruction support using VHDL (VHSIC Hardware Description Language) since HARV-SoC was also implemented using this HDL. In this work, we propose an improvement of the architecture introduced in [START_REF] Imianosky | A Performance Evaluation of a Fault-tolerant RISC-V with Vector Instruction Support to Space Application[END_REF] that enables 64-bit width elements and has a different VEU organization. Furthermore, this enhanced architecture is used to assess HARV-SoC's reliability with the VEU through fault injection simulations.

We used the Xilinx Vivado 2020.2 Design Suite tool and the Zynq ZC7020 FPGA SoC device to collect the synthesis data. Thus, we analyzed the number of Look-up Tables (LUTs) and Flip-Flops (FFs), the maximum operating frequency (F max ), and the dynamic power dissipation (P dyn ) for the HARV-SoC. The implemented applications for all algorithms were compiled using GNU Compiler Collection (GCC) for RISC-V [START_REF]Gnu toolchain for risc-v, including gcc[END_REF], and its vector operations were implemented in Assembly vector instructions. The following subsections detail the setups used for the performance and reliability evaluation.

VECTOR EXECUTION UNIT

8-bit ALU

A. Performance evaluation

To estimate the performance gain, we implemented an Assembly algorithm that reads two vectors of the memory, adds each of their elements, and stores the result in the memory. The maximum vector length was set to 256 bits. With this algorithm, we varied the vector length from 32-to 256-bit and the data width of the vector elements from 8to 64-bit. The algorithm was executed using the baseline HARV and the HARV with VEU.

We measured the processing latency in both executions by reading the cycle counter register (mcycle) at the start and the end of the algorithm execution. The difference between these two values is the number of cycles the processor spends to execute the program. The acceleration metric was obtained by dividing the number of cycles for execution in the baseline HARV by the number of processor cycles used for the executions with the VEU.

B. Reliability evaluation

We evaluated reliability through fault injection simulations using TCL (Tool Command Language) and Python scripts with the ModelSim SE-64 2019.01 software. At first, a golden run is executed, which runs the application without fault injections. Then, we extract baseline indicators to run the simulations with fault injection, such as system FFs, execution time, and UART (Universal Asynchronous Receiver/Transmitter) output. After the golden run, we run the fault injection simulations.

First, all register signals are fetched, and the simulation time is set to zero. Then, for each simulation, it selects random locations and simulation times to inject bit flips, based on neutron-characterized flip-flop FIT NYC (Failure In Time for a billion hours in the New York City's neutron flux at sea level) of 248 and a neutron flux of 2.5 × 10 10 n/cm 2 /s. We calculate the neutron fluence since the last incremented time for every randomly generated simulation time and use the cross-section to calculate the FF error rate from a given fluence. We iterate through them to decide if we should inject an error on a given FF and randomly choose if the injection should occur. All the FFs of the SoC and the processor are susceptible to bit-flip.

Regarding the benchmark algorithm for the fault injection simulations, we implemented an algorithm in C language and the Assembly for the vector instructions. This algorithm adds two vectors with 8192 16-bit elements each. We executed the algorithms with the baseline processor (RV32I) and with the vector extension (RV32IV). Without the VEU, each vector element is read and operated sequentially in a loop. For the execution with the VEU, the vectors are subdivided into 256-bit vectors of 16-bit elements and operated using OP-V instructions. Thus, the VEU reads the two 256-bit vectors from the data memory, adds the elements, and writes the result to the memory.

We ran 1024 experiments for each of the four scenarios: baseline HARV-SoC, baseline HARV-SoC with the VEU, hardened HARV-SoC, and hardened HARV-SoC with the VEU. This way, we could assess the impact of the VEU in terms of fault tolerance for each SoC version.

We used the internal registers of the processor and the UART output to evaluate the reliability of the SoC. Thus, we classified the executions into four categories: (i) correct, when the application was executed correctly; (ii) benchmark error, when the application is executed but has incorrect results; (iii) hang, when the application does not end the execution nor produces any result; and (iv ) exception, when an unscheduled event disrupts the program execution [START_REF] Hennessy | Computer organization and design RISC-V edition: The hardware software interface[END_REF]. The exceptions available were: instruction address misaligned, instruction access fault, illegal instructions, load access fault, and store access fault.

The classification of the executions was performed using a Python script that analyses the files that contain the UART outputs of each execution. Thus, we could determine the number of executions for each category. This script also reports the average number of injected faults and the average execution time.

VI. RESULTS

The following subsections present the results of the VEU implementation. First, we describe the synthesis results, such as the number of FFs and LUTs, maximum operating frequency, and dynamic power dissipation. After, we show the acceleration obtained in comparison to the baseline processor. Finally, we show the results of the fault injection simulations.

A. Synthesis

The plot in Fig. 3 reports the number of LUTs and FFs for each implementation. The plot shows the resource usage by the baseline HARV-SoC and the HARV-SoC with 32-, 64-, 128-, and 256-bit VEU. The number of the LUTs and FFs increases according to the vector length. The baseline processor needs 3759 LUTs, whereas the version with the 32-, 64-, 128-, and 256-bit VEU requires 1.23, 1.77, 2.07, and 2.31 times the amount of LUTs, respectively. For FFs, it requires 2816, and the versions with the 32-, 64-, 128-, and 256-bit VEU requires 1.39 times more LUTs than baseline HARV-SoC.

For the hardened versions of the implementations, the number of LUTs and FFs is represented in Fig. 4. In the hardened versions, the baseline processor needs 6172 LUTs, whereas the version with the 32-, 64-, 128-, and 256-bit VEU requires 1.16, 1.67, 1.85, and 2.01 times more LUTs, respectively. The number of necessary FFs is 3864 and increases 1.28 times for all the versions with different sizes of VEU.

Table I provides an overview of the values for the (F max ) and (P dyn ). The HARV-SoC achieves a F max of 57.9 MHz and consumes 129 mW of dynamic power for the baseline scenario. The addition of the 32-bit VEU exhibits a slightly lower F max of 56.8 MHz while consuming 131 mW of power. The 64-bit VEU reduces the F max to 49.2 MHz and increases the power consumption to 146 mW. Similarly, the 128-bit VEU shows a decrease in F max to 47.8 MHz while maintaining the same power consumption of 146 mW. Lastly, the 256-bit VEU causes a slight improvement in F max to 50.3 MHz with a power consumption of 140 mW. Considering the hardened scenarios, the HARV-SoC achieves a F max of 38.8 MHz and dissipates 158 mW. With 32-bit VEU, the F max decreases to 34.1 MHz while dissipating 188 mW. The 64-bit VEU reduces the F max to 34.3 MHz and increases the P dyn to 188 mW. Similarly, the 128-bit VEU decreases the F max to 33.7 MHz with a P dyn of 183 mW. Lastly, the 256-bit VEU has a F max of 34.8 MHz with a P dyn of 187 mW.

B. Performance

The plot in Fig. 5 presents the acceleration values achieved through the execution of vector operations compared to scalar operations. It shows the performance improvements obtained through different vector configurations, varying between 32-, 64-, 128-, and 256-bit vectors, along with 8-, 16-, 32-, and 64-bit elements. For the scalar execution, the 64-bit vectors are treated as two 32-bit, due to the core architecture (RV32I) and its register width, making the execution time in this case similar to the two 32-bit elements. With the VEU, it is possible to operate in just one 64-bit element per instruction, and for 32-bit elements, it is possible to operate in two elements simultaneously. Thus, due to the architecture of the implementation, the acceleration values from scalar to vector executions for 32-bit and 64-bit elements are similar.

The acceleration for all the vector lengths is more significant for 8-bit elements and decreases as the element width increases. For 32-bit vectors, an element width of 8 bits results in a speedup of 3.3 times and increases 1.5 times for 64-bit vectors. The 128-bit vector shows an increase of 1.8 times compared to the 64-bit. For the 256-bit, it has an acceleration increase of 1.5 times compared to the 128-bit vector.

The 16-bit elements show an increase of approximately 1.7 times as the size of the vector increases. For 32-and 64-bit elements, the acceleration is similar in all cases. It is worth noting that 32-bit vectors have no executions with 64-bit elements. The acceleration increase is 0.3 times from the 64-to the 32-bit vectors and the 128-to 64-bit. From the 256-to the 128-bit, the difference in acceleration is 0.4 times.

C. Fault Injection Simulation

We evaluated the output of the UART of each execution using the Python script and the four categories of results mentioned in Section V-B. The experimental results are presented in Table II, which compares the results of the baseline scalar and baseline vector approaches and the hardened scalar and hardened vector approaches. Thus, it presents the number of correct executions, benchmark errors, hangs, and exception executions achieved by each approach for the 1024 executions.

In the baseline processor, the vector approach showed an increase of 40 correct executions. Within the hardened category, the vector approach improved with 15 more correct executions. The scalar approach had one less execution with benchmark errors than the vector in the baseline processor. Meanwhile, the hardened scenario presented one more benchmark error than the vector. For the hang executions, the vector approach showed an improvement of 25 executions in the baseline scenario. In the hardened design, the vector approach has a difference of 14 executions, where it did not show any case of hang executions. Regarding the exceptions, the baseline processor with the vector approach had 16 instances less than the scalar. The hardened scalar scenario had two more exceptions than the vector scenario. Table III compares the average number of fault injections and execution times of the baseline and hardened scenarios for both scalar and vector operations to assess the impact of the execution time on the number of injected faults. In both baseline and hardened systems, the average execution time of the vector approach was approximately half of the scalar one. The difference in the execution time directly impacts the number of injections since the longer it takes to execute, the more faults are likely to be injected. In the baseline scenarios, the scalar execution had an average of 2.1 fault injections, while the vector had just one. In the hardened scenarios, the scalar operation had an average of 4.44 injected faults, and the vector operation had 2.05.

D. Discussion

On the synthesis side, the comparison between the baseline processor and the processor with the VEU reveals that the VEU implementation incurs additional LUTs and FFs compared to the baseline processor, with the number increasing as the VEU width expands. Specifically, the wider VEUs require more resources due to the multiplexing logic to access the VRF. Adding a VEU slightly reduces the F max and increases power consumption. The impact on F max and power consumption varies with VEU sizes. In conclusion, incorporating a VEU introduces hardware overhead regarding LUTs and FFs. However, it is crucial to consider the trade-off between the hardware overhead and the acceleration improvement.

Regarding performance, the VEU has significantly improved processing latency compared to scalar operations. We observed substantial speedups in all tested scenarios by analyzing different vector lengths (32-, 64-, 128-, and 256bit) and element widths (8-, 16-, 32-, and 64-bit). As the vector length increased, we noticed that the accelerations improved. Additionally, we observed a correlation between the element width and the achieved acceleration, with narrower element widths, such as 8 bits, exhibiting higher accelerations than wider ones. This suggests that narrower element widths benefit more from vectorization, allowing them to exploit the increased parallelism vector operations offer.

Regarding reliability, the fault injection simulation results have shown that using the VEU significantly reduces error propagation. One of the primary benefits of the VEU is its ability to execute operations more quickly than a baseline processor. The results demonstrate that the vector approach enhances system responsiveness, contributing to better fault tolerance. By performing operations at a higher speed, the window of vulnerability to potential faults is minimized, reducing the average number of injected faults.

The VEU showed better results than the scalar approach in both baseline and hardened scenarios, exhibiting higher rates of correct executions and enhanced resilience against benchmark errors, hangs, and exceptions. This increase makes the VEU a promising solution for applications where system dependability is critical, such as AI applications for space systems.

VII. CONCLUSION

This work describes the implementation of a VEU that supports a subset of the RVVE for the HARV processor. The main goals were to accelerate data processing applications by exploring data-level parallelism and to assess its reliability.

We evaluated the impact of vector instructions over scalar processing to measure speedup. The results showed that the VEU proved to be a valuable addition to the processor, delivering significant performance acceleration of up to 8.1 times over scalar operations due to exploiting parallelism. Although it introduces hardware overhead, its ability to enhance reliability makes it an attractive choice for demanding applications that require high performance and system dependability.

In future work, we intend to extend the fault tolerance techniques to the VEU and expand it to support multiplication operations, allowing us to test AI applications and assess their performance and reliability improvement. We also intend to submit this architecture to a fault injection campaign in particle accelerator facilities, enabling comparing and validating the obtained results with actual irradiation tests.

  The results presented in this paper have been obtained in the framework of the EU project RADNEXT, receiving funding from the European Union's Horizon 2020 research and innovation programme, Grant Agreement no. 101008126, the Region d'Occitanie and the École Doctorale I2S from the University of Montpellier (contract nos. 20007368/ALDOCT-000932 and 22009671), the Foundation for Support of Research and Innovation, Santa Catarina (FAPESC-2021TR001907), and the Brazilian National Council for Scientific and Technological Development (CNPq -processes 138179/2021-2, 140368/2021-3 and 350794/2023-5).

Fig. 2 .

 2 Fig. 2. Vector Execution Unit

Fig. 3 .

 3 Fig. 3. Resources utilization for the baseline HARV-SoC and the HARV-SoC with different widths VEUs.

Fig. 4 .

 4 Fig. 4. Resource usage for the hardened HARV-SoC and the HARV-SoC with different VEU widths.

Fig. 5 .

 5 Fig. 5. Execution acceleration for different VEU widths.

TABLE I MAXIMUM

 I OPERATING FREQUENCY AND DYNAMIC POWER DISSIPATION RESULTS.

HARV-

SoC VEU Width Fmax (MHz) P dyn (mW)

		-	57.9	129
		32 bits	56.8	131
	Baseline	64 bits	49.2	146
		128 bits	47.8	146
		256 bits	50.3	140
		-	35.8	158
		32 bits	34.1	165
	Hardened	64 bits	34.3	188
		128 bits	33.7	183
		256 bits	34.8	187


F Stephen Dobson

Claire Saraux

Vincent A Viblanc

PHENOTYPIC PLASTICITY IN REPRODUCTIVE AND SOMATIC EFFORTS OF FEMALE COLUMBIAN GROUND SQUIRRELS

Keywords: Columbian ground squirrel, phenotypic plasticity, repeatability, reproductive effort, somatic effort, Urocitellus columbianus

Phenotypic plasticity of life-history traits is well known among vertebrate species. We estimated reproductive and somatic efforts of female Columbian ground squirrels (Urocitellus columbianus (Ord, 1815)) to test for plasticity of these important resource allocations. We examined a 27-year dataset of life-history traits on these long-living (8-10 years), hibernating, montane-living mammals. Environmental variation was estimated from two important traits of mothers, their relative timing of breeding and spring maternal body mass (initial "capital" for use in subsequent reproduction). Results from 183 known-aged mothers and 508 litters revealed considerable variation in the relative timing of breeding, initial maternal mass, and reproductive and somatic efforts, as well as significant variation among age and years. Results from 125 mothers that reproduced more than once (and 450 litters) revealed significant plasticity of reproductive and somatic efforts with respect to relative timing of breeding and spring maternal mass. A within-subject centering statistical approach showed that phenotypically plastic reproductive and somatic efforts were due to variation within individuals, but were not always reflected by the pattern of responses among individuals in the population. The plastic responses of different mothers appeared to be similar in strength.

INTRODUCTION

How maternal resources are allocated to reproduction in iteroparous species (where individuals reproduce more than once in their lifetime) is a fundamental question in evolutionary biology. At the simplest, the options are allocation to current reproduction versus allocation in oneself, viz. somatic allocation, the latter supporting reproduction at a later time. This basic division for iteroparous organisms led [START_REF] Hirshfield | Natural selection and the evolution of reproductive effort[END_REF] to point out that for a given energy budget, resources should be allocated in a way that maximizes reproductive value [START_REF] Fisher | The genetical theory of natural selection[END_REF]. Reproductive value, in turn, has two components [START_REF] Williams | Natural selection, the costs of reproduction, and a refinement of Lack's principle[END_REF]): current and future reproduction (termed "residual reproductive value"). Thus, for organisms that reproduce more than once, we should expect natural selection to favor a "trade-off" between resource allocations to current and future reproductive efforts [START_REF] Stearns | Life-history tactics: a review of the ideas[END_REF]. Future reproduction, of course, is supported by additional underlying factors, including somatic growth, stored resources, and enough personal maintenance to provide the best chance of survival to reproduce again. For the trade-off to evolve via natural selection, it must have a genetic basis, something that has proved difficult to demonstrate in nature [START_REF] Reznick | Costs of reproduction: an evaluation of the empirical evidence[END_REF][START_REF] Houle | Genetic covariance of fitness correlates: what genetic correlations are made of and why it matters[END_REF][START_REF] Reznick | Big houses, big cars, superfleas, and the costs of reproduction[END_REF]. Even documenting a phenotypic basis for the trade-off of current reproductive effort and residual reproductive value faces substantial challenges, such as bias from variation in resource availability among individuals (e.g., [START_REF] Van Noordwijk | Acquisition and allocation of resources: their influence on variation in life history tactics[END_REF].

Over an iteroparous lifespan, individuals with traits that respond to changing environmental conditions, that is, traits that are phenotypically plastic, should be favored by natural selection (reviewed by [START_REF] De Villemereuil | Fluctuating optimum and temporally variable selection on breeding date in birds and mammals[END_REF]. For instance, traits such as reproductive effort should be greater when more environmental resources are available, and less when environmental resources are scarce [START_REF] Van Noordwijk | Acquisition and allocation of resources: their influence on variation in life history tactics[END_REF]. Plastic responses of traits, such as individual reproductive effort, to alternative environmental conditions are termed "reaction norms" [START_REF] Stearns | The evolutionary significance of phenotypic plasticity[END_REF]). The occurrence of several reaction norms for a given trait in a population indicates the presence of several trait forms and genetic variation in plasticity, and thus a genotype by environment interaction (Via and Lande 1980;[START_REF] Scheiner | Genetics and evolution of phenotypic plasticity[END_REF][START_REF] Via | Adaptive phenotypic plasticity: consensus and controversy[END_REF].

In the presence of genetic variation in phenotypic plasticity, we might expect to see considerable variation in fitness, and a genotype by environment interaction in fitness traits such as reproductive effort. Alternatively, a "general-purpose genotype" that produces the best phenotype for each environment circumstance might be shared among individuals, i.e., a genotype for which trait responses are variable, but in an optimal manner given alternative environments. In this case, considerable phenotypic variation might be produced by organismal or environmental variation, rather than by genetic variation. A review of plastic responses to temperature found no significant evidence of selection on phenotypic plasticity [START_REF] Arnold | Sparse evidence for selection on phenotypic plasticity in response to temperature[END_REF]), suggesting at least the possibility that variation within populations due to climatic change might be underlain by one or a very few reaction norms.

Columbian ground squirrels (Urocitellus columbianus (Ord, 1815)) are ideal for a study of phenotypic plasticity in reproductive and somatic efforts. These hibernating rodents show considerable variation in reproduction, growth, and investments in survival, both within and among individuals [START_REF] Murie | The costs of reproduction in columbian ground squirrels[END_REF][START_REF] Risch | Is mean litter size the most productive? A test in Columbian ground squirrels[END_REF][START_REF] Dobson | Increasing returns in the life history of Columbian ground squirrels[END_REF][START_REF] Broussard | Senescence and age-related reproduction of female Columbian ground squirrels[END_REF][START_REF] Broussard | Age-specific resource investment strategies: evidence from female Richardson's ground squirrels[END_REF][START_REF] Rubach | Testing the reproductive and somatic trade-off in female Columbian ground squirrels[END_REF]. They inhabit montane environments where there is considerable yearly variation in reproductive traits with variation in environmental conditions, such as daily resource abundance and growing season length [START_REF] Murie | Annual variation of spring emergence and breeding in Columbian ground squirrels (Spermophilus columbianus)[END_REF]Dobson andKjelgaard 1985a, 1985b;Zammuto andMillar 1985a, 1985b;[START_REF] Dobson | A comparison of methods for studying life history in Columbian ground squirrels[END_REF][START_REF] Dobson | Interpretation of intraspecific life history patterns: evidence from Columbian ground squirrels[END_REF][START_REF] Dobson | The limits of phenotypic plasticity in life histories of Columbian ground squirrels[END_REF][START_REF] Dobson | Regulation of population size: evidence from Columbian ground squirrels[END_REF]. The montane environment appears to constrain female reproductive effort, since mothers have relatively lower litter size for their body size when faced with shorter growing seasons [START_REF] Murie | Annual variation of spring emergence and breeding in Columbian ground squirrels (Spermophilus columbianus)[END_REF]Zammuto andMillar 1985a, 1985b;[START_REF] Dobson | Interpretation of intraspecific life history patterns: evidence from Columbian ground squirrels[END_REF][START_REF] Dobson | The limits of phenotypic plasticity in life histories of Columbian ground squirrels[END_REF][START_REF] Dobson | Seasonal activity and body mass of Columbian ground squirrels[END_REF].

Reproductive effort might be influenced by the initial condition of a mother when breeding starts [START_REF] Broussard | The effects of capital on an income breeder: evidence from female Columbian ground squirrels[END_REF][START_REF] Rubach | Testing the reproductive and somatic trade-off in female Columbian ground squirrels[END_REF]. Ground squirrel females that begin the breeding season in top body condition have greater reproductive success, a condition termed capital breeding [START_REF] Jönsson | Capital and income breeding as alternative tactics of resource use in reproduction[END_REF][START_REF] Broussard | The effects of capital on an income breeder: evidence from female Columbian ground squirrels[END_REF]. However, most of their annual reproductive effort is supported by daily foraging, and the great majority of mothers gain personal body mass during the reproductive period, while they both gestate and lactate [START_REF] Broussard | Senescence and age-related reproduction of female Columbian ground squirrels[END_REF]. As such, reproductive effort may trade off with personal allocations that mothers make in themselves as they are breeding, part of their somatic effort [START_REF] Dobson | Increasing returns in the life history of Columbian ground squirrels[END_REF][START_REF] Broussard | Senescence and age-related reproduction of female Columbian ground squirrels[END_REF][START_REF] Broussard | The effects of capital on an income breeder: evidence from female Columbian ground squirrels[END_REF][START_REF] Broussard | Previous experience and reproductive investment of female Columbian ground squirrels[END_REF][START_REF] Skibiel | Maternal influences on reproduction in two populations of Columbian ground squirrels[END_REF][START_REF] Rubach | Testing the reproductive and somatic trade-off in female Columbian ground squirrels[END_REF]Viblanc et al. 2016a). Indeed, mothers that begin the breeding season in poor condition gain considerable personal mass while reproducing, compared to mothers that are initially better endowed with capital in the form of body mass [START_REF] Rubach | Testing the reproductive and somatic trade-off in female Columbian ground squirrels[END_REF]. The allocations that mothers make to reproductive and somatic efforts might exhibit a negative association between reproductive and personal mass allocations, as expected under the trade-off model of van Noordwijk and de Jong (1986). Alternatively, the same model could produce a positive association of reproductive and somatic efforts if individuals differed greatly in their total resource acquisition. Thus, we tested whether a negative or positive association of reproductive and somatic allocations occurred.

Next, we examined the repeatability of reproductive and somatic efforts for individual breeding females in different years. High repeatability would indicate low scope for plasticity within individuals, and low repeatability would indicate greater scope for plasticity with respect to reproductive effort. Given sufficient variation in reproductive and somatic efforts of maternal ground squirrels, we made an initial evaluation of the plasticity of these efforts. For this, we used traits of the females themselves as integrative reflections of the environmental conditions that they faced. The first trait was the timing of breeding within years, relative to other mothers that were breeding in the same year, statistically controlled for the age of the mother. This trait is closely associated with emergence from hibernation, the latter trait under significant selection favoring earlier timing [START_REF] Viblanc | Measuring fitness and inferring natural selection from long-term field studies: different measures lead to nuanced conclusions[END_REF]. The second trait was the initial body mass of mothers at the beginning of the breeding season, statistically controlled for both age of the mother and the specific year in which she bred. Maternal body mass at the initiation of breeding has strong and significant influences on the number and size of subsequent production of offspring [START_REF] Dobson | Increasing returns in the life history of Columbian ground squirrels[END_REF][START_REF] Skibiel | Maternal influences on reproduction in two populations of Columbian ground squirrels[END_REF]). We used these initial conditions for breeding as reflections of previous environmental conditions that might influence preparations for breeding, and examined whether subsequent reproductive and somatic efforts were sensitive to these initial conditions.

If individuals exhibited similar reaction norms, it might indicate a general-purpose genotype for reproductive effort or for somatic effort. We tested whether the mean associations of reproductive and somatic efforts with initial breeding conditions of mothers within the population could be accounted for by the plasticity of individual females. For this, we tested whether the patterns for individual females were significant, and whether they differed from the patterns among the females in the population at large (after van de Pol and Wright 2009).

Additionally, large deviations of slopes among mothers might indicate individual differences in reproductive or somatic tactics favored by either natural selection or perhaps genetic migration of alternative tactics into the population. Thus, we tested for significant differences among mothers in the slopes of their plastic responses of reproductive and somatic efforts to their initial breeding conditions (relative timing of the breeding season and initial body mass), using only those mothers that successfully bred more than once.

METHODS

Study population and monitoring

From 1992 to 2020, we studied Columbian ground squirrels in a 1.8 ha subalpine meadow along the Sheep River drainage in southwestern Alberta, Canada, within Sheep River Provincial Park (1550m elevation; 50°38010″N, 114°39056″W). Over the years, the spring population at emergence from hibernation varied in size between 32 and 120, and averaged about 62.7 female ground squirrels (does not include young-of-the-year). A total of 195 females produced 559 litters (a mean of 19.2 litters/year) of an average of 2.82 weaned young per single annual litter during this time.

Breeding ground squirrels emerged from hibernation in the spring in mid-to late-April, through mid-May. At spring emergence, we trapped all ground squirrels on the study site, usually within a couple of days of their first sighting. We captured ground squirrels in live traps (13x13x40 cm, Tomahawk Live Trap Co., Hazelhurst, WI, USA) baited with a small amount of peanut butter, placed near a burrow opening that was used by the active ground squirrel. Each captured individual was weighed to the nearest 5g in a cloth handling bag using a spring-slide balance (Pesola AG, Schindellegi, Switzerland) and examined for reproductive condition, wounds, and ectoparasites. If not already permanently ear-tagged, a pair of uniquely numbered fingerling tags (Monel #1; National Band & Tag Co., Newport, KY, USA) were attached, one to each ear. Finally, each ground squirrel received an individually unique dye-mark symbol on the dorsal pelage via application of hair dye (Clairol ® Hydrience, 052 Black Pearl, Proctor and Gamble, Stamford, CT, USA). These dye-marks were used for later identification from a distance, using binoculars, from ground locations on the meadow and five elevated wooden benches (2-4m high) that were spread about the study site.

Most females began to breed at 2 years of age, producing a single litter each year [START_REF] Rubach | Comparing fitness measures and the influence of age of first reproduction in Columbian ground squirrels[END_REF]. The annual mating period for a female was 5-7 hours long, usually 3-5 days after emerging from hibernation [START_REF] Murie | Annual variation of spring emergence and breeding in Columbian ground squirrels (Spermophilus columbianus)[END_REF][START_REF] Murie | Mating behavior of Columbian ground squirrels. I. Multiple mating by females and multiple paternity[END_REF]. We monitored the mating day of females with observations of unique behaviors associated with the estrous period (such as female behavioral solicitation of matings), examination of vaginal swelling, and from copulatory plug material deposited in the fur or vulva of the female (for details, see [START_REF] Murie | Mating behavior of Columbian ground squirrels. I. Multiple mating by females and multiple paternity[END_REF][START_REF] Manno | Why are male Columbian ground squirrels territorial?[END_REF]Manno et al. 2008;[START_REF] Raveh | Mating order and reproductive success in male Columbian ground squirrels (Urocitellus columbianus)[END_REF][START_REF] Raveh | Male reproductive tactics to increase paternity in the polygynandrous Columbian ground squirrel (Urocitellus columbianus)[END_REF]. After mating, males make little or no subsequent investment in raising offspring (Festa-Bianchet and Boag 1982; [START_REF] Murie | Social interactions and dominance relationships between female and male Columbian ground squirrels[END_REF][START_REF] Nesterova | Premating behavioral tactics of Columbian ground squirrels[END_REF]. For females, mating is followed by about 24 days of gestation, birth, and about 27 days of lactation [START_REF] Murie | Mating behavior of Columbian ground squirrels. I. Multiple mating by females and multiple paternity[END_REF]Harris 1982, 1988). During lactation, mothers nurse their young in a specially constructed, single-entrance nest burrow.

Observations of mothers entering and leaving their nest burrow allowed us to anticipate the emergence of litters at about the time of weaning.

As young ground squirrels emerged above ground for the first time from nest burrows (near the time of weaning), we trapped complete litters and their mothers, usually within a day of their first sighting and rarely up to 2 days later; at these times young were still dependent on the mother's milk. Newly emerged young were weighed to the nearest 1g with a spring-slide balance. The young were fitted with a pair of numbered fingerling ear tags and given a unique black dye marking on the dorsal pelage. Since the young had begun their lives in utero at a body mass close to zero, we used the summed mass of the young in a litter at initial capture as an index of the mass that the mother had allocated to reproduction, and termed this her reproductive effort [START_REF] Broussard | Age-specific resource investment strategies: evidence from female Richardson's ground squirrels[END_REF]. The difference between the mass of the mother when the young first emerged from nest burrows and her mass when she emerged from hibernation (near the time of mating) was used to estimate her personal mass allocation during the breeding period. This latter estimate was used as an index of the somatic effort of the mother, during the period when she was also investing in reproduction [START_REF] Michener | Reproductive effort during gestation and lactation by Richardson's ground squirrels[END_REF][START_REF] Broussard | Senescence and age-related reproduction of female Columbian ground squirrels[END_REF][START_REF] Broussard | The effects of capital on an income breeder: evidence from female Columbian ground squirrels[END_REF]. These two indices represent the total allocation of energy to mass by the mother while breeding (gestating and lactating for young that were subsequently weaned) (Viblanc et al. 2016a). Subsequent to weaning the young, all ground squirrels fattened for the 8-9-month hibernation period that began in mid-to-late summer [START_REF] Dobson | Seasonal activity and body mass of Columbian ground squirrels[END_REF].

All field procedures, including trapping, handling and marking, and field observations were approved by animal care and use committees of Auburn University, the University of Calgary, and Alberta Fish & Wildlife.

Initial conditions, reproductive effort and somatic effort

We selected cases of mothers and their litters from those with complete annual data during the 28-year study period (n = 508 records and 183 females, a mean of 2.8 litters/mother).

We also examined initial conditions that appear important to successful breeding and fitness: relative date of mating and body mass at the start of the season [START_REF] Dobson | Increasing returns in the life history of Columbian ground squirrels[END_REF][START_REF] Broussard | The effects of capital on an income breeder: evidence from female Columbian ground squirrels[END_REF][START_REF] Rubach | Testing the reproductive and somatic trade-off in female Columbian ground squirrels[END_REF]). To estimate the initial "capital" ("IM") that mothers could allocate while breeding, we used their mass at emergence from hibernation, 3-5 days before mating [START_REF] Murie | Annual variation of spring emergence and breeding in Columbian ground squirrels (Spermophilus columbianus)[END_REF]. On average, mothers began their breeding season by mating around 1 May ( 6.3 days standard deviation) at an initial spring mass of 421.2 grams ( 53.3g). Our measure of reproductive timing was the estimated relative mating date ("RMD"). For this, we subtracted the mean date of mating from the individual mating dates of mothers within each year (after [START_REF] Viblanc | Measuring fitness and inferring natural selection from long-term field studies: different measures lead to nuanced conclusions[END_REF]. For individual mothers, RMD ranged from -12.8 days to 16.1 days (mean = 0.0 4.3 days). Initial mass of mothers was not adjusted to be relative within years, since in an especially good or poor year all females might be in relatively good or poor condition with respect to their initial body mass and thus have more or less resources, on average, to allocate to reproductive and somatic efforts.

The mass of litter (viz., reproductive effort) that these mothers produced, measured near the time of weaning, was 300.2g ( 90.1g). Over the same period these mothers gained (concurrent somatic effort) an average of 101.8g ( 48.5g). The association of reproductive and somatic efforts was trivial and not significantly different from zero (r = 0.043, t [506] = 0.98, p = 0.33).

Basic patterns of age and year

Female ground squirrels begin breeding at different ages, usually as 2-or 3-year-olds and very rarely during their 1 st year of post-hibernation activity [START_REF] Rubach | Comparing fitness measures and the influence of age of first reproduction in Columbian ground squirrels[END_REF]. Reproductive and somatic efforts vary with age of the mothers and from year to year, with the oldest females showing signs of reproductive senescence [START_REF] Broussard | Senescence and age-related reproduction of female Columbian ground squirrels[END_REF][START_REF] Broussard | Previous experience and reproductive investment of female Columbian ground squirrels[END_REF]. Yearling mothers are also significantly lighter than older females [START_REF] Dobson | Body mass, structural size, and life history patterns of the Columbian ground squirrel[END_REF][START_REF] Broussard | Senescence and age-related reproduction of female Columbian ground squirrels[END_REF]. Reproductive effort varies considerably from year to year, and the timing of the reproductive season also changes from year to year [START_REF] Murie | Annual variation of spring emergence and breeding in Columbian ground squirrels (Spermophilus columbianus)[END_REF][START_REF] Dobson | Increasing returns in the life history of Columbian ground squirrels[END_REF][START_REF] Skibiel | Maternal influences on reproduction in two populations of Columbian ground squirrels[END_REF]. A measure related to reproductive effort, annual fitness (based in part on litter size) varied strongly over a 20 to 30-year period [START_REF] Lane | Delayed phenology and reduced fitness associated with climate change in a wild hibernator[END_REF]Dobson 2016;[START_REF] Viblanc | Measuring fitness and inferring natural selection from long-term field studies: different measures lead to nuanced conclusions[END_REF]. Therefore, we examined the effects of age and year and their interaction, using regression models. Mothers aged 9 to 13 years were pooled to obtain a suitable sample of the oldest age classes. Statistically controlling for age, year, and maternal identity confirmed the lack of relationship between reproductive and somatic efforts (mixed model of RE ~ SE; marginal R 2 = 0.004, conditional R 2 = 0.354; F [1,372.0] = 2.17, p = 0.14). Thus, we examined these two allocations separately in further analyses of phenotypic plasticity.

We examined possible influences on initial maternal body mass, using an intercept mixed regression model in which maternal age, year, and identity were random variables. Maternal identity could potentially explain 25.5% ( 0.8 standard deviations) of the variation in IM, year explained 6.2% ( 0.4), and age explained 51.3% ( 1.1) (total variance = 4376.7, n = 508 mother-years, combined 82.9% of the variance in IM explained) In a similar analysis of relative mating date (but without year because data were year-mean standardized), maternal identity explained 21.7% ( 10.6) of the variance in RMD, and age explained 8.1% ( 6.5) (total variance = 19.1, n = 508 mother-years, combined 29.8% of the variance in RMD explained). In further analyses, maternal identity, year, and age were entered, where possible, as fixed factors in repeatability analyses and random variables in mixed models.

Population patterns

We examined whether the initial breeding traits of relative reproductive timing and maternal body mass (independent variables) were associated with energy allocations, measured in grams of mass, to the mother's reproductive effort and concurrent somatic effort. For this, relative date of mating and initial maternal body mass were standardized, since they were measured on different scales (days and grams). Maternal age and identity, as well as year, were included as random variables. Analyses were run on the complete dataset of 183 mothers and 508 successful reproductive events and on smaller dataset of 125 mothers that reproduced more than once during their lifetimes (450 weaned litters, mean 3.60 litters/mother, range 2-9 litters/mother). Results were very similar, and we present results only for the 125 mothers that reproduced more than once. The sample of 125 mothers should have produced suitable power to detect patterns of plasticity [START_REF] Martin | Measuring individual differences in reaction norms in field and experimental studies: a power analysis of random regression models[END_REF][START_REF] Van De Pol | Quantifying individual variation in reaction norms: how study design affects the accuracy, precision and power of random regression models[END_REF]. We examined the interaction between relative mating date and initial maternal body mass in both models, but excluded them because they were low and not significant (reproductive effort, t [441.2] = 1.0, p = 0.32; somatic effort, t [420.2] = 1.7, p = 0.08).

Repeatability

For the 125 females that produced more than a single litter in their lifetime, we examined repeatability (the intraclass correlation coefficient, or ICC), where maternal identity was used as the class variable. ICC was calculated as = s 2^/ (s 2 + s 2^) . s 2^ is the among-individual variance component and s 2 is the within-individual variance component (Lessels and Boag 1987;Nakagawa andSchielzeth 2010, 2013;[START_REF] Nakagawa | The coefficient of determination R 2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded[END_REF]. Repeatability varies between 0.0 and 1.0, and is usually calculated using a single partitioning of the variance in a trait into that accounted for by individual identity and an error term. Low repeatability indicates considerable flexibility in a trait, due perhaps to phenotypic plasticity but also reflecting sampling variation.

High repeatability reflects trait inflexibility, as would occur if a trait were highly heritable, though repeatability is not a direct measure of heritability. We examined the repeatability of relative timing of breeding, initial spring body mass of mothers, reproductive effort, and somatic effort. To adjust for influences of age and year, we included these as fixed factors. We used a Monte Carlo method of estimation of repeatability [START_REF] Nakagawa | The coefficient of determination R 2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded[END_REF], using 1000 bootstrap values.

Within versus among mothers

Phenotypic plasticity was examined using the mixed-model procedures described by van de [START_REF] Van De Pol | A simple method for distinguishing within-versus between-subject effects using mixed models[END_REF], that evaluate variations in characteristics within versus among mothers. For these analyses, we used the 125 females that produced more than one litter. We partitioned variation in reproductive and somatic efforts into within-subject and among subject effects, regressed onto the initial conditions of relative breeding date and maternal body mass.

When within-individual effects were significant (Table 1b), we moved on to examine whether the two types of effects differed in their slopes, by running a further model that compared individual and population-wide patterns (Table 1c).

These models assumed that the slopes for individual females were similar. Finally, we tested whether females differed in their slopes of responses, by asking whether a "random slope" model was a significant improvement over the model that assumed similar slopes. For this last test, the models were compared statistically and the preferred model was the one with the lowest Akaike Information Criterion (AIC). For the influence of initial maternal mass on somatic effort, the model fit was singular and did not converge when we examined mothers that produced at least 2 litters. So, we used a smaller dataset of mothers that produced at least 3 litters (370 litters for 85 mothers) and dropped the variables age and year from the model.

RESULTS

Population patterns

Reproductive effort was significantly and positively influenced by both relative timing of breeding and initial maternal body mass, with the former influence about half that of the latter (Table 1a, column RE~RMD and RE~IM; relative mating date, t [418.4] = 2.7, p = 0.007; initial maternal mass, t [277.0] = 4.7, p < 0.001). The influence of the two initial variables, however, was moderate at best (marginal R 2 = 0.069, conditional R 2 = 0.348). Somatic effort was also significantly influenced by both relative timing of breeding (a positive association) and initial maternal body mass (a negative association), with the former influence about a third that of the latter (Table 1a, column SE~RMD and SE~IM; relative mating date, t [415.4] = 5.6, p < 0.001; initial maternal mass, t [318.6] = -12.5, p < 0.001), and the influence of these variables was fairly strong (marginal R 2 = 0.308, conditional R 2 = 0.729). In summary, later breeding led to higher reproductive and somatic efforts, while a higher initial mass resulted in higher reproductive, but lower somatic, effort. Because we had identified these significant influences, we further examined variation within individual mothers, reflecting phenotypic plasticity, and variation among the mothers in our population.

Repeatability

ICC (and standard error) of relative mating date (RMD) was 0.252 ( 0.055, P < 0.001), initial spring body mass (IM) was 0.581 ( 0.044, P < 0.001), litter mass near weaning (RE) was 0.218 ( 0.053, P < 0.001), and change in maternal mass during the breeding season (SE) was 0.137 ( 0.054, P < 0.001). Despite significant repeatabilities for all four traits, unexplained variation (about 42% to 86%) still showed quite a bit of "scope" for change over time in the "initial" breeding variables (RMD and IM) and subsequent allocation variables (RE and SE). Of course, the unexplained variation also contained an unknown amount of sampling variation.

Within versus among mothers

Reproductive effort varied significantly and positively with the relative timing of breeding (Table 1b, column RE~RMD; within individual effect, F [1,317.1] = 6.7, p < 0.01; among individual effect, F [1,137.6] = 0.1, p = 0.78). Individual mothers exhibited a change in the mass of their litters of about 2.99 grams per day; thus, compared to other females and over a 3-week mating period, this could result in about a 63g increase in RE). However, the pattern among females (at about 0.52 grams/day) was not significant. The individual and population-wide patterns did not differ significantly in slope (Table 1c; F [1,243.1] = 1.3, p = 0.26). Nor did the inclusion of random slopes, which we used to test for differences in plasticity among individuals, improve the model (Figure 1a; AIC without random slopes = 5296, with random slopes = 5299, = 1.0, p = 0.60). In summary, within-individual pattern indicated significant phenotypic plasticity in reproductive effort in response to relative breeding date, and the plasticity appeared fairly similar among mothers.

Reproductive effort was much more responsive to maternal body mass at about the time that females mated. Reproductive effort increased significantly with spring body mass (at 0.37 grams of weaned litter/gram of initial maternal body mass) and a similar significant pattern occurred among mothers (at 0.46 grams of weaned litter/gram of maternal mass) (Table 1b, column RE~IM; within individual effect, F [1,266.7] = 7.6, p < 0.01; among individual effect, F [1,136.4] = 13.4, p < 0.001). Comparison of the slopes of the within versus among mother patterns was not significant (Table 1c; F [1,346.4] = 0.3, p = 0.58). We included random slopes in our comparison of litter mass at weaning to initial spring maternal mass, and allowing slopes to vary did not significantly improve the model (Figure 1b; AIC without random slopes = 5284, with random slopes = 5287, = 0.7, df = 2, p = 0.70). The significant within-individual effects indicated that reproductive effort was phenotypically plastic in response to the initial spring maternal body mass, and again, individual mothers did not appear to greatly differ in the strengths of their plastic responses.

Somatic effort during breeding varied significantly with the timing of breeding (Table 1b, column SE~RMD). Individual mothers gaining about 2.67 grams during breeding for every additional 1-day delay in the relative timing of breeding, compared to other females (over a 3week mating period, this could result in about a 56g increase in SE), and among mothers this average was very similar at 2.66 grams gained for each day of delay (respectively; F [1,316.2] = 24.3, p < 0.001, F [1,137.0] = 12.7, p < 0.001). The slopes of the within individual and among individual effects of timing on maternal change in body mass were not significantly different (Table 1c; F [1,273.3] = 0.0, p = 1.00). Random-slope models for both datasets of females with 2 or more and 3 or more litters were singular, likely due to the similarity of the individual and population responses (Table 1b,1c). While the singularity precluded statistical testing, visual examination suggested a roughly similar pattern of slopes among mothers (Figure 1c).

Phenotypic plasticity was indicated by the significant within-individual change in somatic effort with relative mating date. This pattern was also reflected by the significant among-individual result and the virtual lack of difference between the within-and among-individual patterns.

Somatic effort during the breeding season was significantly influenced by the mother's initial body mass when breeding was initiated ( 1c; F 1,326.6] = 33.7, p < 0.001). We included random slopes in our comparison of litter mass at weaning to initial spring maternal mass, and allowing slopes to vary did not significantly improve the model (Figure 1d; analysis of the 125 mother dataset was singular, likely due to similarity of slopes; statistical comparison of models with the reduced dataset of 85 mothers with  2 litters, AIC without random slopes = 3828, with random slopes = 3830, = 2.3, df = 2, P = 0.33). Somatic effort was phenotypically plastic with respect to spring maternal mass (initial capital), such that females with greater initial body mass put on much less personal body mass during breeding. The within-individual plasticity was much stronger than the among-individual population wide effect, and slopes of individual mothers did not greatly differ.

DISCUSSION

Phenotypic plasticity is commonly examined over variable environmental conditions (e.g., review by [START_REF] Forsman | Rethinking phenotypic plasticity and its consequences for individuals, populations and species[END_REF]. We examined how allocations of energy (as expressed by accumulated mass) to concurrent reproductive and somatic efforts were influenced by two important initial traits of the mothers themselves. One was the timing of breeding with respect to other females, a trait with a strong genetic association with the timing of emergence from hibernation [START_REF] Lane | A quantitative genetic analysis of hibernation emergence date in a wild population of Columbian ground squirrels[END_REF], itself under significant selection for earlier activity and thus perhaps earlier breeding [START_REF] Viblanc | Measuring fitness and inferring natural selection from long-term field studies: different measures lead to nuanced conclusions[END_REF]. The other initial trait was female body mass at emergence from hibernation, closely associated with body condition and with strong influences on subsequent reproductive and somatic allocations [START_REF] Dobson | Increasing returns in the life history of Columbian ground squirrels[END_REF][START_REF] Broussard | Senescence and age-related reproduction of female Columbian ground squirrels[END_REF][START_REF] Broussard | The effects of capital on an income breeder: evidence from female Columbian ground squirrels[END_REF][START_REF] Skibiel | Maternal influences on reproduction in two populations of Columbian ground squirrels[END_REF][START_REF] Rubach | Testing the reproductive and somatic trade-off in female Columbian ground squirrels[END_REF]. Body mass may be considered "capital" that mothers can later use to augment their reproductive and active season somatic efforts [START_REF] Jönsson | Capital and income breeding as alternative tactics of resource use in reproduction[END_REF][START_REF] Broussard | The effects of capital on an income breeder: evidence from female Columbian ground squirrels[END_REF]). These two traits not only influence subsequent reproductive and somatic allocations, but likely reflect to at least some degree the environmental conditions that influenced past energy acquisition and expenditure by individual mothers [START_REF] Neuhaus | Effects of a late snowstorm and rain on survival and reproductive success in Columbian ground squirrels (Spermophilus columbianus)[END_REF][START_REF] Lane | Delayed phenology and reduced fitness associated with climate change in a wild hibernator[END_REF][START_REF] Dobson | Fitness implications of seasonal climate variation in Columbian ground squirrels[END_REF].

We examined the allocation of mass by mother Columbian ground squirrels to their offspring while breeding, an estimate of reproductive effort (after [START_REF] Hirshfield | Natural selection and the evolution of reproductive effort[END_REF].

At the same time, most mothers also allocated resources to themselves by putting on body mass, an aspect of somatic effort. We specifically wanted to know if and to what extent reproductive and somatic efforts during breeding were phenotypically plastic traits, given that ground squirrels are highly iteroparous, maturing at 1-3 years of age [START_REF] Rubach | Comparing fitness measures and the influence of age of first reproduction in Columbian ground squirrels[END_REF]) and some living to ages of 8-10 years (rarely to 14 years of age, Viblanc et al. 2016b;[START_REF] Sosa | Social stress in female Columbian ground squirrels: densityindependent effects of kin contribute to variation in fecal glucocorticoid metabolites[END_REF]).

Thus, mothers allocate resources to both their current reproduction and to their own maintenance and survival, and the latter involves gaining personal mass. Because they have a long hibernation season of about 70% of their year [START_REF] Young | Hibernating patterns of free-ranging Columbian ground squirrels[END_REF][START_REF] Dobson | Seasonal activity and body mass of Columbian ground squirrels[END_REF][START_REF] Lane | Phenotypic plasticity and local adaptation in a wild hibernator evaluated through reciprocal translocation[END_REF], mothers must accumulate sufficient energy reserves in the form of body mass (primarily fats, [START_REF] Buck | Annual cycle of body composition and hibernation in freeliving arctic ground squirrels[END_REF][START_REF] Humphries | The role of energy availability in mammalian hibernation: a cost-benefit approach[END_REF] to survive winter conditions and reproduce again. This is likely an issue for many hibernating mammals that are also annual breeders [START_REF] Constant | Integrating mortality risks and the adaptiveness of hibernation[END_REF]).

An initial problem was the possible influences of age and year on reproductive and somatic efforts. For Columbian ground squirrels, a few one-year-old mothers were not fully grown in body size (though only 12 of 183 mothers first bred as yearlings), as reflected by structural skeletal measures [START_REF] Dobson | Body mass, structural size, and life history patterns of the Columbian ground squirrel[END_REF]) and by body mass [START_REF] Dobson | Interpretation of intraspecific life history patterns: evidence from Columbian ground squirrels[END_REF][START_REF] Dobson | Increasing returns in the life history of Columbian ground squirrels[END_REF][START_REF] Broussard | Senescence and age-related reproduction of female Columbian ground squirrels[END_REF]. Furthermore, considerable among-year variation has been found in several life-history variables, including maternal body mass [START_REF] Dobson | The limits of phenotypic plasticity in life histories of Columbian ground squirrels[END_REF][START_REF] Neuhaus | Effects of a late snowstorm and rain on survival and reproductive success in Columbian ground squirrels (Spermophilus columbianus)[END_REF][START_REF] Dobson | Fitness implications of seasonal climate variation in Columbian ground squirrels[END_REF]. Maternal age and year of breeding accounted for between about 7% and 22% of the variation in relative mating date and initial maternal mass. Thus, we accounted for the influences of age and year statistically.

Our best index of reproductive and somatic allocations was the mass of the litters that mothers were producing and the concurrent personal changes in body mass that females exhibited. For the latter variable, it was noteworthy that in 98% of cases (496 of 508 breeding events), mothers increased in body mass while breeding, augmenting their body mass by an average of about a quarter of their initial spring body mass [START_REF] Broussard | The effects of capital on an income breeder: evidence from female Columbian ground squirrels[END_REF]. Examination of individual females showed that these allocations of energy to mass were highly variable, even when known variation associated with age and year-to-year variations were accounted for statistically. Reproductive and somatic efforts of mothers, however, were not closely linked with respect to their magnitudes; despite our large samples, they exhibited an insignificant and trivial correlation. As pointed out by van Noordwijk and de Jong (1986), variation among mothers in resource availability or acquisition can cause reproductive and somatic efforts to exhibit a variety of associations, even positive. Thus, we conservatively conducted separate analyses of plastic responses of reproductive and somatic efforts to initial conditions of the timing of breeding (relative mating date) and personal resources (initial maternal body mass after emergence from hibernation).

Previous evidence suggested that many life-history traits of these ground squirrels are plastic and highly variable under geographic and temporal variations, as well as with both natural and experimental changes in food resources (e.g., [START_REF] Dobson | Interpretation of intraspecific life history patterns: evidence from Columbian ground squirrels[END_REF][START_REF] Dobson | The limits of phenotypic plasticity in life histories of Columbian ground squirrels[END_REF][START_REF] Dobson | Regulation of population size: evidence from Columbian ground squirrels[END_REF][START_REF] Neuhaus | Effects of a late snowstorm and rain on survival and reproductive success in Columbian ground squirrels (Spermophilus columbianus)[END_REF][START_REF] Risch | Is mean litter size the most productive? A test in Columbian ground squirrels[END_REF][START_REF] Dobson | Increasing returns in the life history of Columbian ground squirrels[END_REF][START_REF] Dobson | The demographic basis of population regulation in Columbian ground squirrels[END_REF]. Reproductive and somatic efforts, however, were not previously tested for phenotypic plasticity. A few species have been examined for plasticity in reproductive traits, and these traits were associated Such studies suggest that life histories are highly phenotypically plastic in response to changes in environmental conditions. Among mammalian species, plasticity of allocations of resources to both reproduction and soma have been little studied. In Columbian ground squirrels, we found an ideal situation for testing plasticity in energy allocations. In this species, at least some sources of environmental variation, specifically age and year, could be included in the analyses to statistically control their significant influences.

Repeatability of reproductive and somatic efforts provided an initial test of phenotypic plasticity. When repeatability is high, mothers are similar among years in their allocations of mass to their litters and themselves. If reproductive and somatic allocations were highly phenotypically plastic and changeable from year-to-year, however, we would expect their repeatability to be low. We found that repeatability of reproductive effort was about 22%, and somatic effort was about 14% for individual mothers that successfully bred more than once.

While these values were highly significant, statistical tests are for deviations from 0%, given the expected variation due to sampling. However, our interest was in "scope" for plasticity; that is, variation that was not explained by age of the mother or year of sampling. For both reproductive and somatic efforts, there was substantive unexplained variation, 78% and 86% respectively.

This indicates the presence of variation that may have been due to plastic responses.

We began a more direct analysis of plasticity with a comparative examination of the influences of relative timing of breeding and initial personal resources on subsequent reproductive and somatic efforts (Table 1a). A mother's initial personal body mass appeared to be at least twice as important as the timing of breeding to reproductive effort, though both had significant influences. Despite these variables accounting for only about 7% of the variation in reproductive effort, allocations to reproduction were greater for later breeding females and those that were heavier when emerging from hibernation and mating. This was surprising, since annual fitness is greatest for early emerging females [START_REF] Viblanc | Measuring fitness and inferring natural selection from long-term field studies: different measures lead to nuanced conclusions[END_REF]. Perhaps mothers compensated for later emergence with greater allocations of energy to reproduction, perhaps facilitated by the ongoing "green-up" of the growing season. During the breeding season (from conception through weaning), mothers that emerged later compared to their peers put on a bit more personal body mass (viz., had greater concurrent somatic effort). However, much more evident and significant was a pattern of females emerging from hibernation at low body mass putting on more personal mass [START_REF] Rubach | Testing the reproductive and somatic trade-off in female Columbian ground squirrels[END_REF]). Together, timing of breeding and initial maternal mass accounted for a substantial ~30% of the variation in somatic effort during breeding.

One caveat with this first analysis (i.e., Table 1a) was that it did not examine the plasticity of individual mothers (van de Pol and Wright 2009). Within-subject effects of timing of breeding and initial maternal capital on reproductive and somatic efforts were significant and fairly substantial, indicating plastic responses of individual mothers (Table 1b). In addition, slopes that likely reflected the strength of the plastic responses were not significantly different among mothers. Thus, mothers were not only plastic in their allocations to reproduction and themselves, but their plasticity exhibited similar characteristic changes. Some mothers undoubtedly had higher quality home ranges to extract resources from, and this is consistent with differences in intercepts of females in their plastic responses (Figure 1). Similar plastic responses of reproductive effort (number or mass of offspring) but lack of significant differences in the degree of plasticity among mothers have been found in other species (e.g., red deer, Froy et al. 2017;blue tits, Chik et al. 2022;review by Arnold et al. 2019).

Population responses mainly mirrored these patterns, but for two cases: the influence of relative timing of the breeding season on reproductive effort and the influence of initial maternal capital on somatic effort (Table 1c). In the first case, the population pattern was much weaker than the within-mother pattern (Table 1b); mean responses of individuals (reflected by the dots in Figure 1a) were scattered widely among the relative mating dates and showed little pattern.

Thus, mothers were plastic in reproductive effort with respect to mating date, but widely variable in their mean responses, perhaps reflecting variation in resource availability on their foraging ranges (a mismatch between processes that produce individual and population levels; [START_REF] Westneat | Collision between biological process and statistical analysis revealed by mean centring[END_REF]). In the latter case, mothers were highly plastic in somatic effort with respect to their initial body mass, but again the population pattern was more mild than the plastic response of individual mothers (Figure 1d), perhaps reflecting differences in the quality or quantity of resources on different foraging ranges. It appeared that in both cases, the population patterns were diluted, and further examination of this phenomenon seems warranted, since one might conclude a lack of plasticity (or less so) from population-level analyses, where stronger individual-based plasticity actually exists.

The plasticity of reproductive and somatic efforts to the initial spring maternal body mass indicated a partial tradeoff. Mothers that began breeding with greater mass-capital allocated more energy to reproductive effort and less to somatic effort. For example, compared to a mother that mated weighing 380g, a mother weighing 480 grams allocated, on average, about 36 grams more to reproductive effort and 76 grams less to herself over the course of the breeding season. On average, the heavier female at the start of breeding would also allocate 40 grams less overall. Again, our evidence on plasticity suggests that these differences could be present in an individual mother in different years. Clearly, energy dynamics are complicated in Columbian ground squirrels, and the low marginal coefficients of determination in our analyses suggest that other influences on reproductive and somatic efforts are likely. These might include such things as the number of offspring produced [START_REF] Dobson | Increasing returns in the life history of Columbian ground squirrels[END_REF], and the resource quality and quantity of the territories that females maintain during breeding (e.g., [START_REF] Murie | Social interactions and dominance relationships between female and male Columbian ground squirrels[END_REF].

Female Columbian ground squirrels live in mountain environments at a variety of elevations [START_REF] Murie | Annual variation of spring emergence and breeding in Columbian ground squirrels (Spermophilus columbianus)[END_REF]Dobson and Kjelgaard 1985a;Zammuto andMillar 1985a, 1985b;[START_REF] Dobson | Interpretation of intraspecific life history patterns: evidence from Columbian ground squirrels[END_REF][START_REF] Dobson | Regulation of population size: evidence from Columbian ground squirrels[END_REF][START_REF] Dobson | The demographic basis of population regulation in Columbian ground squirrels[END_REF][START_REF] Oli | The relative importance of life-history variables to population growth rate in mammals: Cole's prediction revisited[END_REF].

Likely due to these environments, individuals exhibit high degrees of phenotypic plasticity in many life-history traits, including date of emergence from hibernation, age at maturity, body mass, litter size, and both juvenile and adult differences in rates of survival (Dobson and Kjelgaard 1985b;[START_REF] Dobson | Interpretation of intraspecific life history patterns: evidence from Columbian ground squirrels[END_REF][START_REF] Murie | The costs of reproduction in columbian ground squirrels[END_REF][START_REF] Dobson | The limits of phenotypic plasticity in life histories of Columbian ground squirrels[END_REF]. In this study, we showed that reproductive and somatic efforts were also phenotypically plastic. Given the fairly high rates of gene flow among Columbian ground squirrel populations at different elevations and habitats [START_REF] Dobson | Measures of gene flow in the Columbian ground squirrel[END_REF], the hypothesis that mothers in different populations have similar genetic propensities for phenotypic plasticity of life-history traits seems to be supported.

The long lives of the ground squirrels and year-to-year variations in ecological conditions might also favor plastic responses (e.g., [START_REF] Lane | Delayed phenology and reduced fitness associated with climate change in a wild hibernator[END_REF]). Here we tested and found support for similar phenotypic plasticity among mothers in their concurrent reproductive and somatic efforts, providing preliminary support for the hypothesis of similar genotypes underlying the plasticity in these traits. However, phenotypic variation in individual plasticity was always present (Figure 1), and thus underlying genetic variation may have been present, though perhaps unlikely [START_REF] Nussey | The evolutionary ecology of individual phenotypic plasticity in wild populations[END_REF].

Figure 1 .

 1 Figure 1. Changes in traits of reproductive female Columbian ground squirrels (Urocitellus

Table 1b

 1b

	, column SE~IM). Individual mothers
	gained 0.76 grams less in personal body mass during breeding for each additional gram of mass
	when they initiated breeding (F [1,329.4] = 184.4, p < 0.001), and a weaker negative pattern was
	evident among individuals that lost on average 0.32 grams of initial gram of mass for every
	additional gram of initial capital (F

[1,,140

.7] = 33.2, p < 0.001). In this case, the slopes of the within-individual and among-individual declines in mass gain during breeding with increases in maternal body mass at the beginning of the breeding season were significantly different, with individuals showing a significantly stronger pattern (Table

Table 1 .

 1 Mixed regression models that test variation in reproductive (RE) and somatic efforts (SE) with relative to within-year reproductive timing (relative mating date, RMD) and spring capital (initial body mass near the time of mating, IM). a) regressions that test for variation of RE and SE separately on both RMD and IM. b) regressions that test for variation of, separately, RE and SE within individual mothers and among those mothers, evaluated for RMD and IM separately (4 tests). c) tests for significant differences in the slopes of the regressions of, separately, RE on RMD and on IM, and then the same comparisons for SE. In all models, age, year, and maternal identity are included as random effects. Both marginal and conditional R 2 values are given for models a) and b). Sample sizes are 125 mothers and 450 litters.

	RE ~ RMD	RE ~ IM	SE ~ RMD	SE ~ IM

*p 0.01, **p < 0.001

ACKNOWLEDGMENTS

Our greatest thanks are to J.O. Murie, who initiated the long-term study (in 1992) and recorded many years of data (through 2000). Any long-term study has many assistants, students, and volunteer helpers, and ours is no exception. Literally scores of field workers contributed to our dataset and we offer the warmest thanks to them all. Alberta Parks, and Alberta Environment, Fish & Wildlife, granted access to the study sites and assigned our permits for the research. Field methods were approved by Auburn University Institutional Animal Care and Use Committee (IACUC), by the University of Calgary, and by Alberta Fish & Wildlife.

DATA ACCESSABILITY STATEMENT

Data available upon request.

COMPETING INTERESTS

The authors declare no competing interests.