I  think that you try to build  Bertalanffy curve of length growth. Parameter "to"  is only formal paramener for 3-parametric equation  and very often  it is negative.  It shoud not scare you.

Asymptotic length is too high -that may mean  1) the growth is linear for the age interval which you have   or  2) the sample is too small

Best wishes,   Tatiana

Thank you Tatiana!

Any von Bertalanffy curve fit to a dataset that does not include some data on large/old individuals is apt to produce wildly wrong estimated of asymptotic length. The fitting procedure will do what it can with the data you give it but, if there are no data from near the asymptote, then the curve will be fit to such data as are available, with asymptotic length varying as necessary. Another way to think of that is that the curve-fitting procedure will be good at estimating the L[inf]/K ratio but poor at putting a number on either of those parameters.

Trevor

The negative birth length (or positive t[0]) problem could arise from more than one cause. Most likely, the true growth pattern of the species is not perfectly matched by the abstraction of the von Bert function. In teleosts, we usually see a negative t[0], meaning that very young fish grow faster than von Bert expects, catching up to the fitted curve at a few months of age. Perhaps, in your sharks, new-born pups grow more slowly. The extent of the problem is likely to depend on the ages for which you have data: If you included the lengths of new-born pups as the length-at-age-zero, you could likely force the curve through that point, at the cost of a worse fit to data from older individuals -- when the point of a von Bert curve usually involves accuracy at those higher ages.

Another common problem arises from ageing protocols. Correctly assigning individuals to their year-classes requires setting an arbitrary "birthday", usually around the time of year when a recognizable annulus is laid down. If that "birthday" is different to the pupping season, "Age 0" could be up to 6 months off the actual date of birth. If your length-at-age data are relative to a zero age some months before birth, the von Bert curve could well indicate negative length at that zero age.

Trevor

There is quite a bit of literature about the short comings of the von Bertalanffy function, especially where samples are not available across all ages/lengths of the population (in other words, in many circumstances..). My recollection is that the function originated with modelling growth of individual pigs, whereas it has been adapted to age-at-length data for populations, so it is perhaps not surprising it meets  with varying levels of success. Trying to draw conclusions from the parameters values is tempting, but must be done with caution for all of the reasons noted above. For example you can estimate l-infinity for some species that seems to be unfeasibly large, if your expectation is that some individuals should be observed to reach that size, however they may never realise such sizes because although they have rapid growth they don't live very long. As a result, you may want to consider using some of the various reparameterised versions of the function that are around (e.g. see Francis 1988, link included below), that have the benefit of allowing a direct comparison of expected size at age where your samples overlap, and such comparisons are statistically more robust than trying to compare the conventional VB parameters, which are highly correlated (see Welsford and Lyle, 2005, link included below). 

If you intend to use the von Bertalanffy parameters to then try and estimate and compare other parameters such as relationships between k and natural mortality, I would advise against it, as these relationships are not going to be reliable for parameters estimated on partial datasets. 

http://www.nrcresearchpress.com/doi/abs/10.1139/f88-115#.Vj_1l03otaQ

http://fishbull.noaa.gov/1034/wels.pdf

T0 is the time at length=0, not the length at time=0.  This is a common misconception.  As such, it should always be negative, as fish have length at hatch (i.e. length at time=0 is positive).  If you truly mean that the length at time=0 is negative, then yes, you have a problem.  One solution is to add data for size at birth ( length at time = 0) using values from the literature and "fix" the size at time=0 to that size at birth.  This can be done in many modeling platforms by fixing the y intercept.

If you are only trying to use your growth curve for estimating age from size of small animals, I wouldn't worry about the poor fit to L infinity, as you will never extrapolate beyond the range of your data.  If this is a curve you intend to publish, then you will need more representative samples.