Jana Partners, the investor, encouraged the organic grocery chain to do a top-to-bottom reevaluation of its strategies and practices. Jana said it hoped to have discussions with Whole Foods management about everything from its real estate portfolio to customer analytics to inventory management and labor scheduling.

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It remains to be seen which of those steps Whole Foods will take, and whether any of them will make a difference.

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In a statement,the grocer said: “Whole Foods Market welcomes investment in the Company and is open to the views and opinions of all of our shareholders. We value constructive dialogue toward our shared goals of creating shareholder value, successfully executing on our strategic priorities and taking actions that will position the Company for continued success.”

One thing, though, seems hard to ignore: Jana has a point. The retailer saw a 2.5 percent decline in comparable sales last year, a measure of sales at stores open at least a year. Its forecast for 2017 isn’t too cheery, either; the company predicts it will deliver comparable sales of “-2.5 percent or better.”

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That’s a concerning pattern for a chain that has every reason to be successful in this moment, in which shoppers are gravitating toward healthy food, and when an increasing share of the grocery industry’s sales are coming from the fresh items such as produce and meat that Whole Foods built its reputation on.

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Whole Foods’ challenges are wide-ranging, but one of its biggest hurdles is attracting more customers. According to data from Kantar Retail’s ShopperScape survey, the organic grocer had a 7 percent penetration rate back in 2009 when it had some 273 stores. In other words, 7 percent of respondents in Kantar’s customer survey said they shopped at Whole Foods on a monthly basis. Since then, the chain has been on a breakneck march to open more stores, its fleet now numbering more than 430 locations. So what is its market penetration now, with all those added stores? Just 8 percent, according to Kantar. It’s practically unchanged.

That means its major capital investments in building those stores — and the ongoing expense of staffing and maintaining them — have not done much to grow its share of devoted shoppers.

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Diane Sheehan, a grocery industry analyst with Kantar, said this might in part reflect the fact that Whole Foods stores are sometimes clustered close together. For example, she pointed to the suburbs of Chicago, where the chain has three stores in a four-mile range. That means those stores probably are not expanding the base of Whole Foods shoppers; they’re just fighting among themselves for the same crowd.

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Across the wider retail business, talk abounds of being “overstored,” the industry’s term for having too many stores. Whole Foods doesn’t have that problem, exactly, but it has its own version of it. It is overstored in certain neighborhoods.

Meanwhile, as Whole Foods aggressively courts millennials with in-store wine bars and date-night cooking classes, Kantar’s research finds that it has lost some Generation X and baby-boomer shoppers over the past five years.

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“They are leaking tons of shoppers in those non-core demographic groups,” Sheehan said.

Leaning so hard on millennials may have long-term benefits, but for now, Whole Foods is missing out on sales due to its weakened resonance with older consumers.

Where are those shoppers going? Likely to one of the competitors that has elbowed into the organics business. Simple Truth, the private-label organics line from Kroger, delivered an eye-popping $1.7 billion in sales last year, surely snatching some spending away from Whole Foods. Target, Walmart and others are also ramping up their offerings in the category. And many shoppers prefer that these outlets allow them to get organic and conventional groceries in one place. They can get their grass-fed beef and Coca-Cola in one trip, for example, or they can get their cage-free eggs without having to shell out for natural, unbleached paper towels.

All of these problems suggest it’s going to be tough for Whole Foods to find avenues for growth in the immediate future. Indeed, check out Kantar’s forecast for its growth rate in edible grocery sales over the next five years, compared with the prospects of its competitors:

Whole Foods’ stock was up 1 percent in Wednesday morning trading, after a report that e-commerce behemoth Amazon.com had earlier considered bidding for the organic grocer.

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Jana Partners has had a couple of recent successes urging change at major companies: In February, it pushed drugmaker Bristol-Myers Squibb and luxury retailer Tiffany & Co. to shake up their boards of directors.