The graphs immediately above show the changes in size (here expressed as weight) for males (left) and females (right) of the Yellowstone grizzly bear population. Weight is on the y-axis and age on the x-axis. Each dot represents the weight of a bear at the corresponding age. The solid black line is fit to these data assuming that weight increases to some sort of maximum (an asymptote) which is characteristic of the population (the number at the termination of the black line). The formula used to estimate this trend is one that is typically used by researchers to describe the growth of animals (the von Bertalanffy equation). This equation includes a parameter called the "growth constant." This constant is an estimate of the characteristic rate of growth for whichever group of animals is being characterized. A high value indicates rapid growth to maximum weight, a low value, slow growth. This growth constant is given for males and females in the small insets immediately above, along with a depiction of how growth rate varies with age, from rapid to slow. The light gray line labeled with "5.8" denotes the average age at which females first give birth to cubs in the Yellowstone ecosystem. Finally, the blue line surrounded by blue shading was fit to the data employing no assumptions about the nature of growth (a method called LOESS). The blue shading encompasses the region within which one can be 99% sure that the estimated line will fall using repeat samples of the same population.

 

The graph inset in the upper right shows characteristic growth parameters (in bar form) for the Yellowstone population contrasted with the same values estimated for three grizzly bear populations in the arctic regions of Alaska (Western Brooks) and Canada (Tuktoyaktuk and Northern Yukon). Two additional values featured in this graph are, first, the age at which an animal attains roughly 90% of maximum average weight and, second, the average age at which females first reproduce. The contrast between age of first reproduction and attainment of 90% of maximum weight is particularly instructive given that it is difficult for a female to devote energy to producing cubs at the same time that she is accumulating lean body mass. Information on the arctic populations comes from the pioneering work on the topic of bear growth published by Brian Kingsley.

 

Some conclusions

As is the case with virtually all bear populations, the female segment grows to its maximum size much more rapidly than does the male segment, and the maximum is substantially higher for males (230 kg, in Yellowstone) compared to females (125kg, see Differences in bear size). This sex-related difference in growth rate is represented explicitly in the inset graphs. It makes sense that females would grow fast and then stop because of the urgent need to divert resources from growth to reproduction, which is much more demanding on females than on males. On the other hand, males benefit from continued growth because large physical size is an advantage in the violent head-to-head competition that occurs for limited mating opportunities with females (see Life strategy). The other main conclusion derives from comparing growth of Yellowstone's females bears (at a latitude of roughly 44o N) with growth of females bears in the arctic (at latitudes greater than 60oN). Not surprisingly, Yellowstone's females grow to a larger maximum size at a faster rate, which means they attain 90% of maximum weight sooner (at a little over 4 years of age)...which means, in turn, that they can start reproducing sooner. The exception is posed by the Tuktoyaktuk population, which is, indeed, an anomaly among the high-latitude bear populations studied so far. I'm not sure why females were estimated to reproduce at such a young age here; my suspicion is that the answer has to do partly with the methods used for studying and analyzing reproduction in this population.