When Apple (AAPL -1.18%) reports its first quarter earnings in January, just remember this: For every million iPad Mini sales, there might have been between 500,000 and 700,000 iPad 4 sales if the iPad Mini had never existed. That's right! Between 50% to 70% of all Apple iPad Mini sales are cannibalized iPad 4 sales.

The iPad 2 turns cannibal
Tech-Thought's Sameer Singh recently reviewed data made available to the public through the Apple-Samsung patent debacle. When Apple released the New iPad with Retina display, unofficially dubbed the iPad 3, it simultaneously slashed the price of the iPad 2 by $100 in order to clear shelf space.

Singh calculated the range of likely product mixes under cannibalization due to the lower-priced iPad 2. By comparing the drop in the average iPad selling price in Apple's second quarter earnings release with the surge in the number of total units sold, Singh was able to extract a limited range of product mixes that fit the data.

The result? The discounted iPad 2 cannibalized between 54%-62% of all iPad 3 sales, simply due to its $100-off price tag.

This discount-cannibalization effect is amplified during the holiday season. Most holiday shoppers have a limited budget and a fixed number of friends, relatives and co-workers to purchase gifts for. That means trade-offs.

Since the iPad Mini is priced $70 lower than the iPad 2, it is likely to draw more first-time, price-sensitive consumers, as it allows for that $70 in savings to be transferred to the next recipient on the shopping list.

If gift differentiation is major factor -- between brothers and/or sisters, for example -- one recipient could receive a 32 GB Wi-Fi-only model for approximately the same price as a 16 GB Wi-Fi plus cellular model. For families, this would mean that there's no need to exit the ecosystem in order to avoid gift duplication.

The hidden switching costs of ecosystems
This last point is important because one of the consequences of vertical integration are hidden switching costs between proprietary ecosystems. Many families have hundreds if not thousands of dollars invested in Apple's proprietary ecosystem. That makes implicit switching costs much higher than analysts typically allow for.

With the introduction of the iPad Mini, Apple now has a lower-margin product that's cannibalizing not only the iPad 2, which the base-model iPad Mini undercuts by $70, but the iPad 4, which the Mini undercuts by $170. Taken together with the current segmentation of the tablet market, Singh calculates that iPad Mini sales will cannibalize 50%-70% of iPad sales.

Not everyone's results tally with Singh's conclusions. Cohen & Co. conducted a survey asking adults what device they would have purchased if the iPad Mini didn't exist. Out of 1,225 consumers surveyed, just 16.6% said they intended it as a replacement for another device, and of those, 29% said the gadget to be replaced was an iPad (13% said that device to be replaced was a Kindle Fire, and 42% a Windows PC).

In other words, for many consumers for whom the only option was iPad Mini or Bust, then Apple did itself a real favor.

When replacement means something else
However, Cohen's results fall into doubt when we consider the way in which the words "replacement device" can be understood.

Imagine I took a survey two years from now of 42-inch HDTV owners and asked them if they were purchasing the new Apple TV as a replacement for their old HDTV and I received identical results: 83.4% of respondents replied in the negative. Would that mean that Apple TV sales weren't impacting HDTV sales? Of course not. It would only mean that 83.4% of those surveyed had no intention of throwing away a perfectly good HDTV.

Most analysts have adopted the significantly lower cannibalization estimates ranging from 15%-20%.Analyst Kate Huberty of Morgan Stanley recently commented that while the iPad Mini was clearly cannibalizing some full-size iPad sales, concerns over the trend are "overblown," citing recent in-house survey results that suggested that roughly half of all iPad purchases were made by consumers who were new to the platform.

However, anecdotal evidence and retail-side surveys certainly appear to favor Singh's figures. Citigroup (C 1.38%) recently conducted a telephone poll of 50 Apple retail stores and found limited quantities only of the iPad Mini, while the iPad 4 was widely available. Of stores called, 80% indicated that only a few versions of the iPad Mini were still in stock, usually the higher-end models.

How many stores had the iPad 4 languishing on the shelves? 100%.

Foolish bottom line
What does all this mean for Apple investors? It seems to me that profits will be pushed forward as Cupertino's iPad business model switches from net profit-per-unit to net profit-per-user. Apple's profit margin on tablets will decrease, as Tim Cook has already admitted that Apple makes "significantly less" money on the iPad Mini than it does on the iPad.However, Apple likely have more users for its ecosystem where it makes about $150 per iOS user, regardless of device. Any initial disappointment following January's earnings would therefore present an attractive buy-in point for investors willing to wait for iOS gains to seize the narrative over the medium term.

Apple still rules the roost in consumer electronics. The fact that the product with the biggest holiday breakout isn't running an Android or Windows operating system despite the continuing success of Samsung's rival products, Amazon's sell-at-cost model, and the potentially disruptive innovation by Microsoft is a demonstration of the resiliency of Apple's vertically integrated model.

Analysts fears are overblown (again). Supply chains, Apple Maps, increased competitor activity, management shakeups, and even Cupertino's misguided "evolutionary, not revolutionary" design ethic: When push came to shove, nothing could stop Apple from killing it in 2012. For the patient investor, Apple could have some more magic in store for 2013.