Unit testing, model validation, and biological simulation

A simple introduction to unit testing

The basic concept behind software testing is quite simple. Suppose we have a piece of code which takes some number of inputs and produces corresponding outputs. A unit test, verification test, or simply test is a function that compares an input-output pair and returns a boolean value True or False. A result of True indicates that the code is behaving as intended, and a result of False indicates that it is not, and consequently, that any program relying on that code cannot be trusted to behave as intended.

Let us take a simple example. Suppose we have a function that takes a list of numbers and then returns them in sorted order, from lowest to highest. Sorting is a classic algorithmic task, and there are many different sorting algorithms with different performance characteristics; while the specific strategies they employ differ wildly, ultimately the result should be the same for any implementation. A unit test for one’s sorting algorithm should take as input a list of numbers, feed it to the sorting algorithm, and then check that each element in the output list is less than or equal to the one that comes after it. The unit test would return True if the output list had that property, and False if not.

If one has multiple implementations of a sorting algorithm, then one can use a reliable reference implementation as a testing mechanism for the others. In other words, a test might return True if a novel sorting algorithm gives the same result as one widely known to be valid. There are other strategies along these lines. For example, suppose we have an implementation of an algorithm for multiplication called multiply. If we have a trusted implementation of an algorithm for addition, we can test that our multiplication algorithm works as expected by checking its behavior against the appropriate number of addition operations, e.g., multiply(3,5) = 3 + 3 + 3 + 3 + 3. See Listing 1 for an implementation of this test in Python code.

Listing 1. Simple test for the multiplication operation.

 1 def test_multiply():
 2     """
 3     Test our multiplication function against the
 4     standard addition operator
 5     """
 6     assert multiply(3, 5) == 3 + 3 + 3 + 3 + 3

In the previous example, the hypothetical unit test verified the core functionality of the algorithm. We had an algorithm that claimed to sort things, and we wanted to check that it worked as advertised. But there are many other kinds of tests that we might be compelled to write in order to know that our software is working correctly. For instance, what happens if we feed an empty list to our sorting algorithm (this is an example of an edge case)? Should it simply return the list, generate an error message, or both? What if a user accidentally gives the algorithm something that is not a list, say for example, an image? What should the error message be in this case? Should there be a single error message to cover all cases, or should the error message be tailored to the specific case at hand? One can easily write unit tests to verify that the correct behavior has been implemented in all of these cases.

The sum total of all of the desired behaviors of an algorithm is called a specification, or spec for short. For instance, the specification for a sorting algorithm might look like the following:

In Listing 2, we have given a suite of unit tests for a sorting algorithm called mySort based on this specification. The basic notion demonstrated in the context of the sorting algorithm extends to any piece of software. In OpenWorm, we make extensive use of unit testing to verify both the functional properties of the system, as well as the validity of the data and models that comprise the simulation. For instance, the two tests given below in Listing 3 check that any worm model has 302 neurons, and that the number of synapses for a given type of neuron is in accordance with its known value from the scientific literature. We will examine the different types of tests in more detail in the next section.

Listing 2. Sample tests for the sorting specification given in the text. The class SortingTest is a container for all of the individual tests that define the specification and can be extended if more tests are added.

 1 import random
 2 import unittest
 3 from my_code import my_sort
 4
 5 """
 6 Specification:
 7 1) When given a list of numbers,
 8 return the list sorted from smallest to largest.
 9
10 2) When given a list of strings,
11 return the list sorted in lexicographic order.
12
13 3) If the input is an empty list,
14 return the empty list and do not generate an error message.
15
16 4) If the input is not a list, generate the error message:
17 "Input should be a list of real numbers or strings".
18 """
19
20 class SortingTest(unittest.TestCase):
21     """A class implementing tests for a sorting function"""
22     def setUp(self):
23         self.f = my_sort # The function we will test is mySort
24
25     def test_number_sort(self):
26         """Test that numbers sort correctly"""
27         sorted_list = range(100000)
28         shuffled_list = random.shuffle(range(100000))
29         self.assertEqual(self.f(shuffled_list), sorted_list)
30
31     def test_string_sort(self):
32         """Test that strings sort correctly"""
33         word_file = ’/usr/share/dict/words’
34         words = open(word_file).read().splitlines()
35         sorted_words = words
36         shuffled_words = random.shuffle(words)
37         self.assertEqual(self.f(shuffled_words), sorted_words)
38
39     def test_empty_list(self):
40         """Test that empty list returns empty list"""
41         self.assertEqual(self.f([]), [])
42
43     def test_not_list(self):
44         """Test that invalid inputs generate correct error message"""
45         message = ’Input should be a list of real numbers or strings.’
46         self.assertRaisesRegexp(TypeError, message, self.f, ’a’)
47
48     def test_mixed_list(self):
49         """Test that mixed lists generate appropriate error message"""
50         mixed_list = [1, 2, ’a’, ’b’, 3]
51         message = ’Input should be a list of real numbers or strings.’
52         self.assertRaisesRegexp(TypeError, message, self.f, mixed_list)

Listing 3. Excerpts from basic biological integrity tests for worm models. Given the size of the data repositories that OpenWorm relies upon, there are many simple tests such as these for ensuring the correctness of the associated data.

 1 import PyOpenWorm
 2 import unittest
 3
 4 class BiologicalIntegrityTest(unittest.TestCase):
 5     """
 6     Tests that read from the database and ensure that basic
 7     queries have expected results, as a way to ensure data quality.
 8     """
 9     def test_correct_neuron_number(self):
10         """
11         This test verifies that the worm model
12         has exactly 302 neurons.
13         """
14         net = PyOpenWorm.Worm().get_neuron_network()
15         self.assertEqual(302, len(set(net.neurons())))
16
17     def test_neuron_syn_degree(self):
18         """
19         This test verifies that the number of chemical synapses
20         associated with a given neuron AVAL is equal to 90.
21         """
22         aval = PyOpenWorm.Neuron(name=’AVAL’)
23         self.assertEqual(aval.Syn_degree(), 90)

In test-driven development, the specification for a piece of software, as well as the corresponding unit tests are written before coding the software itself^4,7. The argument for test-driven development is that having a well-developed testing framework before beginning the actual process of software development increases the likelihood that bugs will be caught as quickly as possible, and furthermore, that it helps the programmer to clarify their thought processes. In practice, while some tests are written before-hand, others are written in parallel with the rest of code development, or shortly after a piece of code is written but before it is integrated.

We mention here that, in the software community, a distinction is often made between unit tests and integration tests⁷. Strictly speaking, a unit test is a test which is applicable to the smallest, functional unit of code, and which has no external dependencies. On the other hand, tests which verify that different components work together are classified as integration tests; they verify that multiple components are integrated correctly. Some of the tests discussed below would strictly be considered integration tests. For the sake of simplicity, we will not distinguish between unit tests and integration tests in this article, and will refer to both as simply tests or unit tests. The primary distinction that we make here is instead between ordinary verification tests (to verify that code works as intended) and model validation tests (to validate a model against experimental data), which we discuss in more depth below.

Unit testing in OpenWorm

The software that makes up OpenWorm shares common ground with all other pieces of software, whether the sorting algorithm described above, a word processor, or an operating system. As a result, there are a range of unit tests that need to be written to ensure that basic pieces of the software infrastructure function correctly. Many of these tests will not be of any scientific significance; they are simply sanity checks to ensure correct behavior for predictable cases. For instance, there are tests for checking that certain internal functions return the appropriate error messages when given incorrect inputs; there are tests for verifying that databases are loaded correctly; there are tests which check that functions adhere to a specific naming convention which will help automated tools process the code-base.

As a data-driven, scientific research project, however, OpenWorm also makes use of several other categories of tests that do not typically appear in software development. For instance, the PyOpenWorm subproject of OpenWorm is a simple API that provides a repository of information about C. elegans anatomy (https://github.com/openworm/PyOpenWorm). Given that the aim of OpenWorm is to produce a realistic simulation of the nematode, a carefully curated repository of empirical information is a cornerstone of the project.

In the context of unit testing, there needs to be a category of tests that ensure that a curated datum has been appropriately verified and, furthermore, that its internal representation in the PyOpenWorm database is consistent. For example, for each “fact” in PyOpenWorm, there needs to be an associated piece of evidence, which serves as a reference. Practically, this evidence consists of a Digital Object Identifier⁹, or DOI, which corresponds to a research paper from which the fact was originally retrieved. For this class of tests, we traverse the database of facts and verify that for each fact there is an associated source of evidence, i.e., a DOI. Furthermore, these tests verify that each DOI is valid, and that the URL corresponding to the DOI is accessible. There are also tests to check the internal consistency of the PyOpenWorm database, for instance, that neurons with the same name have the same identifier. Listing 4 gives several excerpts from the PyOpenWorm testing framework. It consists of tests to verify the references in the database, i.e., the DOIs which correspond to research papers.

Listing 4. Verifying data integrity is an integral component of testing in OpenWorm. Below, we give several sample tests to verify the existence of valid DOIs, one technique used to ensure that facts in the PyOpenWorm repository are appropriately linked to the research literature.

 1 import _DataTest # our in-house setup/teardown code
 2 from PyOpenWorm import Evidence
 3
 4 class EvidenceQualityTests(_DataTest):
 5 	    """A class implementing tests for evidence quality."""
 6 	def test_has_valid_resource(self):
 7 	    """Checks if the object has either a valid DOI or URL"""
 8 	    ev = Evidence()
 9 	    allEvidence = list(ev.load())
10 	    evcheck = []
11
12 	    """Loop over all evidence fields in the database"""
13 	    for evobj in allEvidence:
14 	        if evobj.doi():
15 	      	    doi = evobj.doi()
16 	      	    val = requests.get(’http://dx.doi.org/’ + doi)
17 	      	    evcheck.append(val.status_code == 200)
18
19 	       elif evobj.url():
20 	      	    url = evobj.url()
21 	      	    val = requests.get(url)
22 	      	    evcheck.append(val.status_code == 200)
23
24 	       else:
25 	      	    evcheck.append(False)
26
27 	  self.assertTrue(False not in evcheck)

In Listing 5, we give several tests for verifying the contents of the PyOpenWorm repository. Since each of the functions below is designed to test properties of Neuron objects, they are part of a single class called NeuronTest. These tests fall into the category of verification tests, and several of the tests, such as test_name and test_type simply check that the database is working correctly.

Listing 5. An assortment of verification tests from PyOpenWorm. These verify that the database behaves as we would expect it to, that properties of certain objects (Neuron objects, in this case) are correctly specified, and that the database is not populated with duplicate entries.

 1 import _DataTest # our in-house setup/teardown code
 2 from PyOpenWorm import Neuron
 3
 4 class NeuronTest(_DataTest):
 5 	"""
 6 	AVAL, ADAL, AVAR, and PCVL are individual neurons in C. Elegans.
 7 	AB plapaaaap is the lineage name of the ADAL neuron.
 8 	A class implementing tests for Neuron objects.
 9 	"""
10 	def test_same_name_same_id(self):
11 	     """
12 	     Test that two Neuron objects with the same name
13 	     have the same identifier().
14 	     """
15 	     c = Neuron(name=’AVAL’)
16 	     c1 = Neuron(name=’AVAL’)
17 	     self.assertEqual(c.identifier(query=True),c1.identifier(query=True))
18
19 	def test_type(self):
20 	     """
21 	     Test that a Neuron’s retrieved type is identical to
22 	     its type as inserted into the database.
23 	     """
24 	     n = self.neur(’AVAL’)
25 	     n.type(’interneuron’)
26 	     n.save()
27 	     self.assertEqual(’interneuron’, self.neur(’AVAL’).type.one())
28
29 	def test_name(self):
30 	     """
31 	     Test that the name property is set when the neuron
32 	     is initialized with it.
33 	     """
34 	     self.assertEqual(’AVAL’, self.neur(’AVAL’).name())
35 	     self.assertEqual(’AVAR’, self.neur(’AVAR’).name())
36
37 	def test_init_from_lineage_name(self):
38 	     """
39 	     Test that we can retrieve a Neuron from the database
40 	     by its lineage name only.
41 	     """
42 	     c = Neuron(lineageName=’AB plapaaaap’, name=’ADAL’)
43 	     c.save()
44 	     c = Neuron(lineageName=’AB plapaaaap’)
45 	     self.assertEqual(c.name(), ’ADAL’)
46
47 	def test_neighbor(self):
48 	     """
49 	     Test that a Neuron has a ’neighbors’ property, and that the
50 	     correct Neuron is returned when calling the ’neighbor’ function.
51 	     """
52 	     n = self.neur(’AVAL’)
53 	     n.neighbor(self.neur(’PVCL’))
54 	     neighbors = list(n.neighbor())
55 	     self.assertIn(self.neur(’PVCL’), neighbors)
56 	     n.save()
57 	     self.assertIn(self.neur(’PVCL’), list(self.neur(’AVAL’).neighbor()))

Model validation with SciUnit

Many computational models in biology are compared only informally with the experimental data they aim to explain. In contrast, we formalize data-driven model validation in OpenWorm by incorporating tests to validate each dynamical model in the project against experimental data from the literature. As an example, consider a scenario where a developer creates a new model and provides parameter values for a simulation. In addition to running all of the verification tests described above, the model and parameter values must be validated with respect to established experimental results. In general, each summary output of the model is validated against a corresponding piece of data. One example of a summary model output is the “IV Curve” (i.e. current evoked in response to each of a series of voltage steps) of a given neuronal ion channel. We expect that our model will possess only ion channels which behave similarly to those observed experimentally, i.e. that the model IV Curve matches the experimentally-determined IV curve. If our model’s IV curve deviates too greatly from that observed experimentally, the model developers should be alerted and provided with information that will allow them to investigate the source of the discrepancy¹⁰. This may mean that parameter values must be modified, or in some cases the model itself must be substantially revised. In the case of OpenWorm, the necessary data for validating models is part of the PyOpenWorm and ChannelWorm subprojects (https://github.com/openworm/ChannelWorm), which are repositories of curated information about C. elegans anatomy and ion channels.

Ordinary unit testing frameworks do not readily lend themselves to this kind of model validation. Rather than simply comparing an input-output pair, model validation tests should perform the same procedure that a scientist would perform before submitting a newly hypothesized model for publication. That is, they should generate some kind of summary statistic encoding the deviation between experimental data and model output. For example, in the case of an IV Curve, one might use the area between the model and data curves as a summary statistic. In the case of OpenWorm, because these models are part of a continuously updated and re-executed simulation, and not simply static equations in a research paper, the model validation process must happen automatically and continuously, alongside other unit tests.

To incorporate model validation tests, we use the Python package SciUnit¹¹ (http://sciunit.scidash.org). While there are some practical differences between writing SciUnit tests and ordinary unit tests, the concepts are quite similar. For example, a SciUnit test can be configured to return True if the test passes, i.e. model output and data are in sufficient agreement, and False otherwise. Ultimately, a scientific model is just another piece of software—thus it can be validated with respect to a specification. In the case of dynamical models, these specifications come from the scientific literature, and are validated with the same types of tests used before submitting a model for publication. SciUnit simply formalizes this testing procedure in the context of a software development work-flow. In Listing 6, we give an example of SciUnit tests using the neuron-specific helper library NeuronUnit (http://neuronunit.scidash.org) for neuron-specific models.

Listing 6. Excerpt from a SciUnit test in ChannelWorm, a repository of information about ion channels. The test listed here verifies that a given ion channel has the correct current / voltage behavior. In terms of the informal classification of tests given above, this test falls under the category of model validation tests.

 1 import os, sys
 2 import numpy as np
 3 import quantities as pq
 4 from neuronunit.tests.channel import IVCurvePeakTest
 5 from neuronunit.models.channel import ChannelModel
 6 from channelworm.ion_channel.models import GraphData
 7
 8 # Instantiate the model; CW_HOME is the location of the ChannelWorm repo
 9 ch_model_name = ’EGL-19.channel’
10 channel_id = ’ca_boyle’
11 ch_file_path = os.path.join(CW_HOME, ’models’, ’%s.nml’ % ch_model_name)
12 model = ChannelModel(ch_file_path, channel_index=0, name=ch_model_name)
13
14 # Get the experiment data and instantiate the test
15 doi = ’10.1083/jcb.200203055’
16 fig = ’2B’
17 sample_data = GraphData.objects.get(
18 	    graph__experiment__reference__doi=doi,
19 	    graph__figure_ref_address=fig
20 	)
21
22 # Current density in A/F and membrane potential in mV.
23 obs = zip(*sample_data.asarray())
24 observation = {’i/C’:obs[1]*pq.A/pq.F, ’v’:obs[0]*pq.mV}
25
26 # Use these observations to instantiate a quantitative test of the peak
27 # current (I) in response to a series of voltage pulses (V) delivered
28 # to the channel.
29 test = IVCurvePeakTest(observation)
30
31 # Judge the model output against the experimental data.
32 # Score will reflect a measure of agreement between I/V curves.
33 score = test.judge(model)
34 score.plot()

In the preceding example, the statistic is computed within the SciUnit method judge, which is analogous to the self.assert statements used in the ordinary unit tests above. While the ordinary unit test compares the output of a function pair to an accepted reference output, judge compares the output of a model (i.e. simulation data) to accepted reference experimental data. Internally, the judge method invokes other code (not shown) which encodes the test’s specification, i.e. what a model must do to pass the test. The output of the test is a numeric score. In order to include SciUnit tests alongside other unit tests in a testing suite, they can be configured to map that numeric score to a boolean value reflecting whether the model/data agreement returned by judge is within an acceptable range.

The output of these model validation tests can also be inspected visually; Figure 2 shows the graphical output of the test workflow in Listing 6, and illustrates for the developers why the test failed (mismatch between current-voltage relationship produced by the model and the one found in the experimental literature). Further details about the output of this test – including the algorithm for computing model/data agreement, and the magnitude of disagreement required to produce a failing score – can also be accessed via attributes and methods of the score object (not shown, but see SciUnit documentation). Consequently, full provenance information about the test is retained.

Figure 2. Graphical output from Listing 6, showing a failed test which alerts developers to an inconsistency between model and data.

Some computational science projects use ad-hoc scripts that directly run models and compare their outputs to reference data. This can be adequate in simple cases, but for larger projects, particularly distributed open-source projects with many contributors, the mixing of implementation and interface carries significant drawbacks¹². For example, in order to record and store the membrane potential of a model cell–to then compare to reference data–one could determine which functions are needed to run the simulation in a given simulation engine, extract the membrane potential from the resulting files, and then call those functions in a test script. However, this approach has three major flaws. First, it may be difficult for a new contributor or collaborator to understand what is being tested, as the test code is polluted with implementation details of the model that are not universally understood. Second, such a test will not work on any model that does not have the same implementation details, and thus has limited re-usability. Third, any changes to the model implementation will require parallel changes to the corresponding tests. In contrast, by separating tests from implementation details, tests can work on any model that implements a well-defined set of capabilities exposed via an interface. SciUnit does this by design, and SciUnit tests interact with models only through an interface of standard methods, for example, those provided by NeuronUnit. It is the responsibility of the model developer to match this interface by referencing standard methods, e.g. run, get_membrane_potential, etc. Ultimately, the separation of implementation from interface leads to greater code clarity, more rapid development, and greater test re-usability.

Test coverage

The coverage of a testing suite is defined as the percentage of functions in a code-base which are being tested. Since there is no rigorous measure of what constitutes an adequate test, precise figures of test coverage should be interpreted with caution. Nonetheless, automated tools which analyze a code-base to determine test coverage can be a valuable resource in suggesting areas of a code-base in need of additional attention. Ideally, test coverage should be as high as possible, indicating that a large fraction of or even the entire code-base has been tested according to the intended specifications.

In PyOpenWorm, we make use several of pre-existing tools in the Python ecosystem for calculating test coverage of the Python code-base, specifically, the aptly-named Coverage package¹³, as well as a GitHub extension dedicated to tracking the coverage of such projects known as Coveralls¹⁴. We adopted these tools in an effort to track which parts of the code-base need additional tests, and to give further backing to the test-driven culture of the project. PyOpenWorm currently has a test coverage of roughly 73%. If a contributor to PyOpenWorm introduces some new code to the project but does not add tests for it, the contributor will see that test coverage has been reduced. By making changes in test coverage explicit, for example with a badge on the project’s homepage, it is easier to track the impact of a growing code-base.

Continuous integration

Modern software is often written using a process of continuous integration or CI^15,16, whereby the contributions of developers are integrated into a shared repository multiple times a day by an automated system. Typically, the output of a testing suite will determine whether or not the new contributions of a developer can be immediately integrated, or whether changes are required to avoid regression, i.e. failing unit tests that passed before the new contribution.

The benefits of continuous integration include early detection of bugs, eliminating development bottle-necks close to the release date (in the case of commercial software), and the regular availability of usable versions of the software. The process of continuous integration also encourages shifts in how developers think about structuring their code, and encourages regular, modular contributions, rather than massive, monolithic changes that can be difficult to debug.

The entire OpenWorm project, including the PyOpenWorm and ChannelWorm modules make use of continuous integration (see Figure 3), taking advantage of a free service called Travis-CI (https://travis-ci.org) that tests changes to the code-base as they are pushed to the collaborative software development portal GitHub¹⁷. With each change, the entire project is built from scratch on a machine in the cloud, and the entire test suite is run. A build that passes all tests is a “passing build”, and the changes introduced will not break any functionality that is being tested. Because the entire project is built from scratch with each change to the code-base, the dependencies required to achieve this build must be made explicit. This ensures that there is a clear roadmap to the installation of dependencies required to run the project successfully – no hidden assumptions about pre-existing libraries can be made.

Figure 3. Sample output from the OpenWorm continuous integration dashboard.

Each row corresponds to a single set of contributions, known as a commit, submitted by a given developer. A commit is assigned a build number, which is given in the second column, and the result of the build process is indicated by the color of the corresponding row. If any of the unit tests fail, the build will be marked as failed (errored, in red), and the code contributions will be rejected. The developer is then responsible for identifying and fixing the corresponding bugs, and resubmitting their contributions to the code repository.

Skipped tests and expected failures

Suppose we have rigorously employed a process of test-driven development. Starting with a carefully designed specification, we have written a test suite for a broad range of functionality, and are using a continuous integration system to incorporate the ongoing contributions of developers on a regular basis.

In this scenario, given that we have written a test suite prior to the development of the software, our CI system will reject all of our initial contributions because most tests fail, simply because the code that would pass the tests has not been written yet! To address precisely this scenario, many testing frameworks allow tests to be annotated as expected failures or simply to skip a given test entirely. The ability to mark tests as expected failures allows developers to incrementally enable tests, and furthermore draws attention to missing functionality. Consequently, the fraction of tests passed becomes a benchmark for progress towards an explicit development goal, that goal being encoded by the set of all tests that have been written.

The OpenWorm code-base makes extensive use of skipped tests and expected failures as a core part of the culture of test-driven development. In PyOpenWorm, for example, data integrity tests are often added in advance of the data itself being incorporated to the database. These tests provide a critical safety net as new information is curated from the scientific literature. Prior to the curation of this information, the tests are simply skipped. Once the information is curated, the tests are run, and indicate whether the information is usable by the project.

Frivolous tests and overly specific tests

Tests are typically sufficiently straightforward to write that it is easy to proliferate a testing suite with a large number of unnecessary tests. Often, these tests will be completely frivolous and cause no harm, beyond causing a testing suite to take much longer than necessary to run. However, tests which are overly specific can actually hinder the process of development. If there are tests which are too specific and constrain internal behavior that is not meant to be static, a developer’s contributions may be unnecessarily rejected during the process of continuous integration.